In this paper, we describe the completeness of a calculation procedure of logic programs. The procedure is the combination of two procedures, a replacement procedure of atoms in the goal by the bodies or the negation of the bodies of rules in the program, and a transformation procedure of equations to disjunctive normal forms equivalent under Clark's Equational Theory. To combine replacement of atoms in the goal to logical formulae determined from the program and transformation (...) of equations to DNF equivalent under CET is a method by which procedures with the capability of expressing answers in DNF can be build, so it is a leading method for expressing answers in a form including negation. Some procedures based on the method are devised, and their calculation capabilities are shown by applying the theory of completed programs. However, the procedure that uses the bodies or the negation of the bodies of rules for replacement has higher calculation capability, and is intuitively more natural than they. Therefore, to clarify the calculation capability of the procedure is considered an important subject for research into calculation procedures of logic programs with the capability for expressing answers in a form including negation. Moreover, since the completeness is realized by standing on the viewpoint of treating the implication symbol as a different implication symbol from usual, and interpreting logic programs in three-valued logic, examples which support the viewpoint are also described. (shrink)

In this paper, we describe an improvement of a calculation procedure of logic programs. The procedure proposed before is the combination of a replacement procedure of logical formulae and a transformation procedure of equations to disjunctive normal form, and it can calculate logical consequences of the completion of any given first-order logic program, which is equivalent to the FLP in two-valued logic, soundly and completely in three-valued logic. The new procedure is also the combination (...) of them, but the transformation procedure is improved to be able to calculate two-valued logical consequences of the FLP more than the old one. We prove that it can calculate logical consequences of a completed program, which is not equivalent to the completion of the FLP, soundly and completely in three-valued logic. (shrink)

While philosophers feel relatively comfortable about talking of the present and the past, some of them feel uncomfortable about talking in just the same way of future events. They feel that, in general, discourse about the future differs significantly from discourse about the past and present, and that these differences reflect a logical asymmetry between the past and future beyond the merely defining fact that the future succeeds, and the past precedes, the present time. The problem is: how can we (...) talk about events which have not yet happened, or at any rate are not yet bound to happen, or whose participants do not yet exist? The effect of these worries has led them to claim to recognise restrictions on our talk about the future which do not govern talk about the past and present. The most famous of these views is Aristotle's. According to one familiar interpretation, he holds that a statement about a future event which is not yet settled, a contingent event in the future, is neither true nor false, even though the statement that the event either will or will not happen is necessarily true. Proponents of this view felt that if a future-tensed statement were already true then the fact that it stated would already be settled. I do not propose to discuss this well-known and muchdiscussed doctrine of Aristotle's, but I do want to consider some allied views which have been aired recently, and to look at their philosophical significance. Before I look at these, however, it will be convenient to recall three of the main reasons why the Aristotelian doctrine is unpopular. In the first place it is paradoxical to accept that a statement of the form p v ∼ p is true while claiming that neither of its disjuncts is true. Then there are misgivings about the notion of truth involved: many feel that truth is essentially an attribute of timeless propositions and that it is nonsense to talk of a statement's becoming true as you would of Aristotle's views if the event described became inevitable. There is also the difficulty of accounting for the meaning of a future-tensed sentence which may express a statement that is neither true nor false simply because what it states is not yet settled. It could not be said of the sentence expressing such a statement that you know what it means if you know what it is for the sentence to express a true statement. I know the meaning of the present-tensed sentence ‘A sea-battle is now being waged’ if I know that it can normally be used to make a true statement precisely in the event of there being a sea-battle being waged at present. But I do not know the meaning of the future-tensed sentence ‘A sea-battle will be waged tomorrow’ simply by knowing that the sentence expresses a true statement if it is already settled that there is going to be a battle: the statement doesn't mean that the battle is already settled, otherwise it would not lack a truth-value when the matter was still open – it would be false. (shrink)

We consider equational theories based on axioms for recursively defining functions, with rules for equality and substitution, but no form of induction—we denote such equational theories as PETS for pure equational theories with substitution. An example is Cook’s system PV without its rule for induction. We show that the Bounded Arithmetic theory $\mathrm {S}^{1}_2$ proves the consistency of PETS. Our approach employs model-theoretic constructions for PETS based on approximate values resembling notions from domain theory (...) in Bounded Arithmetic, which may be of independent interest. (shrink)

Several attempts have been done to distinguish “positive” information in an arbitrary first order theory, i.e., to find a well behaved class of closed sets among the definable sets. In many cases, a definable set is said to be closed if its conjugates are sufficiently distinct from each other. Each such definition yields a class of theories, namely those where all definable sets are constructible, i.e., boolean combinations of closed sets. Here are some examples, ordered by strength:Weak normality describes (...) a rather small class of theories which are well understood by now (see, for example, [P]). On the other hand, normalization is so weak that all theories, in a suitable context, are normalizable (see [HH]). Thus equational theories form an interesting intermediate class of theories. Little work has been done so far. The original work of Srour [S1, S2, S3] adopts a point of view that is closer to universal algebra than to stability theory. The fundamental definitions and model theoretic properties can be found in [PS], though some easy observations are missing there. Hrushovski's example of a stable non-equational theory, the first and only one so far, is described in the unfortunately unpublished manuscript [HS]. In fact, it is an expansion of the free pseudospace constructed independently by Baudisch and Pillay in [BP] as an example of a strictly 2-ample theory. Strong equationality, defined in [Hr], is also investigated in [HS]. (shrink)

In contrast to Hintikka’s enormously complex distributive normal forms of first- order logic, this paper shows how to generate minimized disjunctive normal forms of first-order logic. An effective algorithm for this purpose is outlined, and the benefits of using minimized disjunctive normal forms to explain the truth conditions of propo- sitions expressible within pure first-order logic are presented.

Coalgebras of polynomial functors constructed from sets of observable elements have been found useful in modelling various kinds of data types and state-transition systems. This paper continues the study of equational logic and model theory for polynomial coalgebras begun in Goldblatt , where it was shown that Boolean combinations of equations between terms of observable type form a natural language of observable formulas for specifying properties of polynomial coalgebras, and for giving a Hennessy–Milner style logical characterisation of (...) observational indistinguishability of states.Here we give a structural characterisation of classes of coalgebras definable by observable formulas. This is an analogue for polynomial coalgebras of Birkhoff's celebrated characterisation of equationally definable classes of abstract algebras as being those closed under homomorphic images, subalgebras, and direct products. The coalgebraic characterisation involves new notions of observational ultraproduct and ultrapower of coalgebras, obtained from the classical construction of ultraproducts by deleting states that assign “nonstandard” values to terms of observable type. A class of polynomial coalgebras is shown to be the class of all models of a set of observable formulas if, and only if, it is closed under images of bisimulation relations, disjoint unions and observational ultrapowers.Observational ultraproducts are also used to discuss compactness—which holds only under limited conditions; to characterise finitely, axiomatisable classes of polynomial coalgebras; and to show that there are axiomatisable classes that are not finitely axiomatisable. (shrink)

Chapter 1: An Introduction: The ‘Semantic Sting’ Argument Describes Dworkin’s theory as concerning the conditions of legal validity. “A legal system is a system of norms. Validity is a logical property of norms in a way akin to that in which truth is a logical property of propositions. A statement about the law is true if and only if the norm it purports to describe is a valid legal norm…It follows that there must be certain conditions which render certain (...) norms, but not others, legally valid. Hence it also follows that there can be two types of disagreement over the truth or falsehood of propositions about the law. People can disagree over the question ‘What are the conditions of legal validity?’, in which case their disagreement is a theoretical one. Or they can agree on the conditions of validity, and disagree as to whether or not those conditions actually obtain in a given case or not.” Argues that the best way to interpret Dworkin’s ‘semantic-sting argument’ is as a general argument against conventionalism in legal positivism. Summarizes the outcome of Dworkin’s argument as follows: “[I]f Dworkin is right about the legal reasoning of lawyers and judges, conventionalism would be self-defeating: if lawyers and judges recognize as legally binding not only those norms which are uncontroversially identifiable under the Rule of Recognition, that is, if what they recognize as binding is not only source-based law, then conventionalism turns out to be false on its own terms. In other words, either law is not what lawyers and judges think that it is, in which case law is not a matter of conventions, or – if it is what lawyers and judges think – conventionalism is false, as they do not see the law as purely a matter of conventions.” Dworkin’s theory, then, is a new conception of jurisprudence aiming to present itself as a rival to conventionalism. The book will be concerned with re-examining positivism in light of the interpretative challenge. Chapter 2: Meaning and Interpretation “[R]oughly, interpretation can be defined as an understanding or explanation of the meaning of an object.” Interpretation in this narrow sense is distinct from a less formal and broader use of interpretation that makes it equivalent to explanation. “Hence also, only those objects which are capable of bearing some meaning qualify as objects of interpretation.” [Why shouldn’t we think of interpretation as object-identification? This seems to be closer to what Dworkin has in mind.] Thus, a consideration of the philosophical work on meaning is appropriate. First, a consideration of Davidson on interpretation. The thesis is that Davidson’s “radical interpretation” can only account for sentence meaning and not for linguistic interpretation in general. Davidson cannot account for the non-rule-governed aspects of communication. “Semantics, as opposed to interpretation, concerns those aspects of communication which are rule or convention governed…but such rules are normally unavailable as reasons or justifications for an interpretation. On the contrary, interpretation is usually required because the issue is not determined by rules or conventions.” Interpretation, rather, is parasitic with understanding the meaning of an expression and not equivalent with it. As Dummett notes, any reflection on the meanings of words assumes prior knowledge of ordinary meanings. “This leads to the conclusion that understanding or explaining the meaning of an expression and interpreting it, are two conceptually separate things. It also indicates that seman ics can only be employed, if at all, to elucidate the concept of interpretation by way of contrast: interpretation concerns those aspects of communication which are under-determined by semantic rules or conventions.” Pragmatics, the study of problems posed by discrepancies between utterer’s meaning and sentence meaning, would seem to be closer to inquiry into interpretation. Both are concerned with understanding how meaning is possible where conventional rules leave off. Contemporary pragmatics, moreover, recognizes the logically indeterminate character of communicative inferences beyond conventional meaning and that the contextual conditions that account for the possibility cannot be realized in the semantic structure of the sentence. However, different criteria of success may be at work in pragmatics than interpretation. Pragmatics is concerned with how communication is achieved and thus the criteria of success would be grasping a speaker’s intentions. Many think, however, that communication is unimportant in certain spheres of communication, e.g. artistic interpretation, and that in these cases the aim of interpretation is not to uncover the actual artist’s intentions. What kind of meaning is interpretation aimed at then? It cannot be the meaning the object has for the interpreter. “Interpretation purports to be a statement about the object interpreted, not about the subject who offers the interpretation…it is crucial to remember that not everything we say about a work of art, or any other text, amounts to an interpretation of it. Only those aspects of a text which can shed light on its meaning form part of the text’s interpretation. What the text means for someone rarely entails anything about what the text means.” [This is puzzling to some extent for it remains somewhat ambiguous what it means to talk of subject-independent meaning.] Interpretive meaning attribution is, rather, counterfactual. “In general, I will suggest that the answer to this question consists in the fact that meaning is assigned by a counterfactual statement. Given that x is the meaning attributed to, for instance a text T, and x is not the literal meaning of T, nor is it the meaning of T intended by its author, then the attribution of meaning x to T can only be understood as the contention that on the basis of certain assumptions a certain fictitious or stipulated speaker would have meant x by expressing T.” Thus, on this account, interpretation, when it does not concern an actual speaker, turns out to be a kind of counterfactual intention attribution. Twofold point: “First, that interpretation is essentially a matter of attributing intentions, that is, in the pragmatics sense of ‘meaning’, namely, meaning that such-and-such by an act or expression. At the same time, interpretations need not be based on the intentions of actual authors; the meaning of an act or expression is understandable in terms of counterfactual intentions.” [Are we really restricted to understanding the coherence and integrity of meaning in such a way? Presumably the author is a kind of device for organizing meaning, much like Dworkin’s integrity, but need it take that format?] The logic of interpretation is typically reducible to intention attribution. [What role does the counterfactual author play in structuring meaning?] The criteria of interpretive success will depend upon the object, whether it is the real author or the counterfactual author. If the former, success will depend upon the retrieval of the author’s actual intentions. “Likewise, if the author is characterized in terms of some ideal representative of a certain genre, for instance, the presumptions which are taken to determine this c aracterization would provide the criteria of success for the particular interpretation offered.” [The criteria of success would seem, then, to be the principles, ideals, etc. that we attribute to the counterfactual author. These attributed qualities would be doing all the work – is the attribution of intention to the hypothetical author, then, really necessary at all?] [Does this account presuppose a weird dichotomy between what an object is and what it means? This dichotomy is different, if present at all, in Dworkin.] Chapter 3: Dworkin’s Theory of Interpretation and the Nature of Jurisprudence Three main insights of Dworkin’s theory of interpretation: “First, that interpretation strives to present its object in its best possible light. Second, that interpretation is essentially genre-dependent. And third, that there are certain constraints that determine the limits of possible interpretations of a given object.” Why the best light? Dworkin doesn’t really address this question in depth but claims that otherwise we are left with no way of justifying and choosing an interpretation or we are left with the author’s intention model, which we should reject. [Marmor doesn’t seem clear on what precisely it means to present something in its best light – seems to conflate it with most appealing light which, I take it, is different than what Dworkin has in mind.] “Dworkin is quite right to maintain that without having some views about the values inherent in the genre to which the text is taken to belong, no interpretation can take off the ground. The values we associate with the genre partly, but crucially, determine what would make sense to say about the text, what are the kinds of meaning we could ascribe to it.” There is no necessity for an interpretation to present an object in its best light with regards to the genre it is taken to be part of. Interpretations “could simply strive to present it in a certain light, perhaps better than some, worse than others, but in a way which highlights an aspect of the meaning of the text which may be worth paying attention to for some reason or another.” [What kind of reasons would count in choosing to present it in one light rather than another?] There is simply zero grounds for Dworkin’s assertion that we have no reason to pay attention to an interpretation that does not present it in its best light. Take a psychoanalytic interpretation of Hamlet, for example – not the best light, but a legitimate one. [This seems related to the next criticism – clearly Dworkin would have to loosen his insistence on the best, though not to detriment.] Moreover, especially with regards to art, it doesn’t appear possible to make an all things considered judgment about the best interpretation given the incommensurability of different values that are taken to inhere in a given genre. [Dworkin can respond here that we may have different available interpretations that could be justified with respect to the relevant value. Moreover, a lack of common denominator does not prevent any comparison whatsoever.] Constructive interpretation concerns social practices constituted by norms – it imposes a purpose or value rendering intelligible the normative character of the practice. There is a separate aspect of constructive interpretation that maintains that elements of the practice are sensitive to the point of the practice. It is important to note that different social practices will institutionalize themselves in different ways – thus, different practices will establish varying conditions on how the practice can be altered. The position of the positivists is that evaluative judgments concerning what the law should be are insufficient for determining what the law is given the nature of law’s institutionalization.&nb p; [This would seem to reside on a certain conception of law, i.e. an interpretation about where the value of law lies.] “[T]his being one of the main points of dispute between Dworkin and his positivist opponents, Dworkin cannot at this initial state presume law to be sensitive to its value in the manner that other, non-institutional practices might be, without incurring the charge of having assumed the very point at issue.” The upshot for Dworkin is that any explanation of a social practice such as law requires the same kind of reasoning as participation in that practice. This will be called the hermeneutic thesis. We can try to reconstruct a justification for this view based on the necessity of shared background assumptions – but this will not do since Dworkin’s claim is stronger: it contends that participants’ and theorists’ must “adopt one and the same normative point of view.” [The sense of normative here is unclear. It is true, though, that shared background assumptions do not imply viewing the law as valuable in any particular way, or at least it does not imply this in any strong sense.] Dworkin makes two distinct points with the hermeneutic thesis: “First, that the explanation of a social practice, like law or the arts, is essentially interpretative, and as such, necessarily value laden. Second, that the interpretation of such social practices, which Dworkin calls ‘argumentative’, is unique in the sense that the practice itself is an evaluative enterprise, and that therefore the interpreter of such a practice must form an evaluative judgment of her own about those values which are inherent in the practice that she purports to interpret.” [As stated, the first thesis is terribly ambiguous – for Dworkin, it clear implies a commitment to constructive interpretation. For Marmor, who accepts it, it is totally unclear what commitment he intends to make. He seems to mean simply that we have criteria for success concerning what counts as a successful explanation.] Mamor denies the second thesis. “What Dworkin seems to ignore here is that there is a crucial difference between forming a view about the values which are manifest in a social practice, like law, and actually having evaluative judgments about them.” [The problem, however, it that it is a contentious matter what values are part of the law – a theorist’s account of what values are constitutive of a particular legal system must rely on the kind of arguments which participants rely on. Of course, a theorist might simply note a debate about values and attempt to remain agnostic, but this will fail to be a full theoretical account of what law is!] Dworkin’s thesis seems to depend exclusively on his account of constructive interpretation. [This seems exactly right.] Chapter 4: Coherence, Holism, and Interpretation: The Epistemic Foundation of Dworkin’s Legal Theory Begins with discussion of Rawls’ reflective equilibrium. Sums up dual criticism as follows: “[T]he assumption that intuitions are independently true and the converse one, that their truth depends on fitting a coherent scheme, both seem to yield paradoxical results.” Dworkin, in his article “The Original Position”, claims that Rawls cannot commit himself to ethical realism. “[T]he natural model presupposes some form of ethical realism, while the constructive model does not. One important difficulty arising from an attempt to apply the natural model to Rawls is, that under the natural model, any theory which dopes not account for an intuition, at least for one which is held firmly, cannot be wholly satisfactory, just as scientific theory which does not account for certain observational data it is supposed to cover, would not be satisfactory in a familiar way.” Rawls, rather, is committed to a constructivist view of morality. Moreover, the reason we value coherence epistemically in moral theory is that it itself is a value of political morality – fairness requires consistency and publicity in the application of moral standards. Marmor notes the following problem with such a view: “[I]f coherence is justified, as it is here, with reference to certain moral values, that is, a specific conception of fairness, then we face the following problem: the presupposed values of fairness must themselves be based upon intuitive convictions, in which case the question of their truth cannot be ignored. If they are taken to be true…we are driven back to the perplexities of the natural model.” Discusses, helpfully, the Fish/Dworkin debate. The upshot is that Dworkin’s interpretive model is best off if it commits itself to a Quineian holism. However, this undermines his distinction between internal and external skepticism since holism must deny that moral judgments constitute a closed system. [This analysis seems exactly right.] Endorses Simmonds view that Dworkin’s theory does not meet the requirements of complexity he identifies as necessary to avoid vicious circularity in interpretive judgments of fit and identity. Coherence is doing the work through and through and therefore the interpretive theory of law is circular. [Will require further investigation, though it is unclear how coherence is doing any work in the pre-interpretive stage. At this stage, the judgments, if interpretive, seem to be derived from different sources. In any case, using coherence as a value seems to be highly suspect.] Why doesn’t Dworkin just reject Fish’s assumptions: because of his jurisprudence. “If legal texts can have a meaning that is not entirely dependent on a process of interpretation, then it is at least sometimes the case that the law can simply be understood, and applied, without the mediation of interpretation. And if that is the case, then the argument from interpretation against legal positivism collapses. It is no longer the case that every conclusion about what the law is, depends on evaluative considerations about what it ought to be.” Chapter 5: Semantics, Realism, and Natural Law Assessment of Michael Moore’s legal realism and its implications. [The final criticisms of Moore are not decisive.] Chapter 6: Constructive Identification and Razian Authority A consideration of Dworkin’s denial that the communication model of interpretation is appropriate for legal interpretation. Marmor argues that intentions do play a crucial role in the identification of legal norms in a way that is incompatible with Dworkin’s “coherence thesis”. Marmor takes Dworkin to be committed to the constructive identification thesis: that the identification of something as part of the legal, artistic, etc. genre can be done sufficiently by evaluative considerations. “Here, one must maintain that evaluative considerations are sufficient to determine whether something is a legal norm or a work of art”. [Fit, however, constrains possible evaluative considerations – thus evaluative considerations are not sufficient in themselves.] “Now the crucial point here is this: if you maintain the possibility of constructive identification in art, you must assume that works of art can be identified as such on the basis of certain features they happen to possess, features which contain no reference to any particular intention to create a work of art…unless we take intentions into account, how can we discriminate between the concept of an aesthetic artifact and the con ept of a work of art?” [It is unclear, and I think false, that constructive interpretation of anything requires identifying something irrespective of an artificers intentions. Those intentions may be relevant, dependent upon the genre under which we are trying to classify the object. Nothing, seemingly, about constructive interpretation in general excludes this possibility.] Marmor’s point is that it turns out to be impossible to identify art as art without reference to an artist’s intentions – especially given the state of contemporary art. [It is notable that Marmor’s response to counterexample implicitly depends upon a fully developed theory of aesthetics. His cursory comments on the matter of identifying art seem insufficient to say the least.] The rest of the chapter considers the incompatibility of Raz’s account of authority with constructive interpretation. The incompatibilities mentioned do not move beyond what Raz identifies in his article “Authority, Law and Morality”, but a defense of this notion of authority is defended in several [inconclusive] respects. [Raz and Marmor want to separate identification from content. This is not clearly a defensible separation.] Chapter 7: No Easy Cases? Chapter defends notion that there is a distinction between easy and hard cases in the positivist sense. Takes a Hartian approach and ultimately defends the distinction by associating it Wittgenstein’s conception of rule following. The point is that one need to look the purpose of rule in order to understand what the rule requires. Chapter 8: Legislative Intent and the Authority of Law Examines the following doctrine concerning the role of legislative intent in adjudication: “[F]irst, it would hold that laws, at least in certain cases, are enacted with relatively specific intentions, and that this is a matter of fact which is discernible through an ordinary fact-finding procedure. Second, that in certain cases the presence of such a fact, namely, that the law was enacted with a certain intention, provides judges with a reason to decide the legal dispute in accordance with the relevant legislative intent.” [It is important that for Marmor, interpretive strategies are only appropriate in hard cases. However, we should wonder what grounds positivism can offer for deciding a hard case in any manner which is not the morally best manner according to the judgment of the judge. There are no legal grounds, by definition, in hard cases and so what justificatory strategy would endorse any judicial decision except for the morally best one?] We can ascribe intentions to a legislative body, when this is possible at all, by taking the shared intentions of the majority, rather than some group intention, to be the significant intentions. Moreover, we should expect a good deal of consensus about intentions for otherwise it is hard to explain how legislative bodies are able to produce so much legislation. Discussion of kinds of intentions concludes as follows: “I have distinguished between three main types of intention that are potentially relevant from the legal point of view. Apart from the intentions that are manifest in the language of the law itself, legislators typically have further intentions in enacting a given law, and sometimes they would have certain intentions bearing on its proper application. I have also suggested that some of these further intentions may be essentially non-avowable, in which case they are rendered initially irrelevant. Finally, I have pointed out that considerations of consistency require that the legislator’s application intentions be taken into account only if, and to the extent that, they are in accord with his further intentions.” The manner in which intentionalism is to be justif ed relies on the distinction, Marmor maintains, between expert and mere collective action authority. “The point I wanted to make is strictly conditional: if, and only if, a certain law is justified on the basis of the expertise branch of the normal justification thesis, would it make sense to defer to the legislature’s intentions in the interpretation of the law, that is, to the extent that there is, in fact,; such an intention and it can clarify something that needs clarification.” Insofar as a legislature can be considered an expert on the matter requiring adjudication and interpretation should the body’s intention be taken into account. Chapter 9: Constitutional Interpretation Begins by laying out general necessary features of a constitution. Then Marmor moves on to consider general questions of constitutional legitimacy. First, he considers what grounds might be offered for the legitimacy of a constitution at all. He notes that the central question is what permits a single generation to bind future generations. He then examines four arguments to avoid this problem. The first is based on the moral legitimacy of the constitution; Marmor rejects this solution for the [truly dubious] reason that the constitution would make no practical difference because it would not supply reasons in addition to those provided by morality [but, presumably, the point is that these legally valid rules would be institutionally enshrined]. The second is based on the moral authority of the framers and Marmor rightly rejects this on the basis of the idealization of the framers it requires and less rightly on the basis that there cannot be moral authorities. Third is the “argument from interpretation” which claims that “as long as the particular content of the constitution is determined by its interpretation, and the authoritative interpretation at any time correctly instantiates the values which ought to be upheld in the community, the constitution would be morally legitimate”. The fourth is Raz’s which argues that a constitution is valid so long as its constraints are morally permissible because conventions of this type might aid the continuity of the legal system, i.e. it is important to have a convention of this type and the constitution is a kind of this type. Marmor appears to endorse these two approaches and concludes: “The conditions for the legitimacy of a constitution must comprise the following conditions. First, the values and principles enshrined in it must be morally permissible…Second, when certain choices are made in particular cases, they would be legitimate if they are either morally underdetermined, or else, morally correct…It follows from this that both arguments must assume that at least in those areas in which the constitution would make a moral difference, it can be interpreted to make the difference that it should, that is, according to the true moral principles that should apply to the particular case...the moral legitimacy of constitutions very much dependent on the practices of their interpretation. In other words, a great deal of the burden of moral legitimacy is shifted by these arguments to the application of the constitution, thus assuming that the constitution is legitimate only if the courts are likely to apply the constitution in a morally desirable way.” [This implies that the only significant value constitutions have is in providing a conventional practice where some such practice is required.] Moves on to argue that courts typically rely, and rightly so, on moral considerations when deciding constitutional issues because typically, in cases of the kind that reach the supreme or constitutional court, there is no law on the case. Much of this relies on his earlier discussion about the nature of interpretation in the law – that legal interpretation is always a matter of cha ging the law. (shrink)

Demonstrating the different roles that logic plays in the disciplines of computer science, mathematics, and philosophy, this concise undergraduate textbook covers select topics from three different areas of logic: proof theory, computability theory, and nonclassical logic. The book balances accessibility, breadth, and rigor, and is designed so that its materials will fit into a single semester. Its distinctive presentation of traditional logic material will enhance readers' capabilities and mathematical maturity. The proof theory portion presents classical propositional (...) logic and first-order logic using a computer-oriented (resolution) formal system. Linear resolution and its connection to the programming language Prolog are also treated. The computability component offers a machine model and mathematical model for computation, proves the equivalence of the two approaches, and includes famous decision problems unsolvable by an algorithm. The section on nonclassical logic discusses the shortcomings of classical logic in its treatment of implication and an alternate approach that improves upon it: Anderson and Belnap's relevance logic. Applications are included in each section. The material on a four-valued semantics for relevance logic is presented in textbook form for the first time. Aimed at upper-level undergraduates of moderate analytical background, Three Views of Logic will be useful in a variety of classroom settings. Gives an exceptionally broad view of logic. Treats traditional logic in a modern format. Presents relevance logic with applications. Provides an ideal text for a variety of one-semester upper-level undergraduate courses. (shrink)

The thesis deals with the concept of truth and the paradoxes of truth. Philosophical theories usually consider the concept of truth from a wider perspective. They are concerned with questions such as - Is there any connection between the truth and the world? And, if there is - What is the nature of the connection? Contrary to these theories, this analysis is of a logical nature. It deals with the internal semantic structure of language, the mutual semantic connection of sentences, (...) above all the connection of sentences that speak about the truth of other sentences and sentences whose truth they speak about. Truth paradoxes show that there is a problem in our basic understanding of the language meaning and they are a test for any proposed solution. It is important to make a distinction between the normative and analytical aspect of the solution. The former tries to ensure that paradoxes will not emerge. The latter tries to explain paradoxes. Of course, the practical aspect of the solution is also important. It tries to ensure a good framework for logical foundations of knowledge, for related problems in Artificial Intelligence and for the analysis of the natural language. Tarski’s analysis emphasized the T-scheme as the basic intuitive principle for the concept of truth, but it also showed its inconsistency with the classical logic. Tarski’s solution is to preserve the classical logic and to restrict the scheme: we can talk about the truth of sentences of a language only inside another essentially richer metalanguage. This solution is in harmony with the idea of reflexivity of thinking and it has become very fertile for mathematics and science in general. But it has normative nature | truth paradoxes are avoided in a way that in such frame we cannot even express paradoxical sentences. It is also too restrictive because, for the same reason we cannot express a situation in which there is a circular reference of some sentences to other sentences, no matter how common and harmless such a situation may be. Kripke showed that there is no natural restriction to the T-scheme and we have to accept it. But then we must also accept the riskiness of sentences | the possibility that under some circumstances a sentence does not have the classical truth value but it is undetermined. This leads to languages with three-valued semantics. Kripke did not give any definite model, but he gave a theoretical frame for investigations of various models | each fixed point in each three-valued semantics can be a model for the concept of truth. The solutions also have normative nature | we can express the paradoxical sentences, but we escape a contradiction by declaring them undetermined. Such a solution could become an analytical solution only if we provide the analysis that would show in a substantial way that it is the solution that models the concept of truth. Kripke took some steps in the direction of finding an analytical solution. He preferred the strong Kleene three-valued semantics for which he wrote it was "appropriate" but did not explain why it was appropriate. One reason for such a choice is probably that Kripke finds paradoxical sentences meaningful. This eliminates the weak Kleene three valued semantics which corresponds to the idea that paradoxical sentences are meaningless, and thus indeterminate. Another reason could be that the strong Kleene three valued semantics has the so-called investigative interpretation. According to this interpretation, this semantics corresponds to the classical determination of truth, whereby all sentences that do not have an already determined value are temporarily considered indeterminate. When we determine the truth value of these sentences, then we can also determine the truth value of the sentences that are composed of them. Kripke supplemented this investigative interpretation with an intuition about learning the concept of truth. That intuition deals with how we can teach someone who is a competent user of an initial language (without the predicate of truth T) to use sentences that contain the predicate T. That person knows which sentences of the initial language are true and which are not. We give her the rule to assign the T attribute to the former and deny that attribute to the latter. In that way, some new sentences that contain the predicate of truth, and which were indeterminate until then, become determinate. So the person gets a new set of true and false sentences with which he continues the procedure. This intuition leads directly to the smallest fixed point of strong Kleene semantics as an analytically acceptable model for the logical notion of truth. However, since this process is usually saturated only on some transfinite ordinal, this intuition, by climbing on ordinals, increasingly becomes a metaphor. This thesis is an attempt to give an analytical solution to truth paradoxes. It gives an analysis of why and how some sentences lack the classical truth value. The starting point is basic intuition according to which paradoxical sentences are meaningful (because we understand what they are talking about well, moreover we use it for determining their truth values), but they witness the failure of the classical procedure of determining their truth value in some "extreme" circumstances. Paradoxes emerge because the classical procedure of the truth value determination does not always give a classically supposed (and expected) answer. The analysis shows that such an assumption is an unjustified generalization from common situations to all situations. We can accept the classical procedure of the truth value determination and consequently the internal semantic structure of the language, but we must reject the universality of the exterior assumption of a successful ending of the procedure. The consciousness of this transforms paradoxes to normal situations inherent to the classical procedure. Some sentences, although meaningful, when we evaluate them according to the classical truth conditions, the classical conditions do not assign them a unique value. We can assign to them the third value, \undetermined", as a sign of definitive failure of the classical procedure. An analysis of the propagation of the failure in the structure of sentences gives exactly the strong Kleene three-valued semantics, not as an investigative procedure, as it occurs in Kripke, but as the classical truth determination procedure accompanied by the propagation of its own failure. An analysis of the circularities in the determination of the classical truth value gives the criterion of when the classical procedure succeeds and when it fails, when the sentences will have the classical truth value and when they will not. It turns out that the truth values of sentences thus obtained give exactly the largest intrinsic fixed point of the strong Kleene three-valued semantics. In that way, the argumentation is given for that choice among all fixed points of all monotone three-valued semantics for the model of the logical concept of truth. An immediate mathematical description of the fixed point is given, too. It has also been shown how this language can be semantically completed to the classical language which in many respects appears a natural completion of the process of thinking about the truth values of the sentences of a given language. Thus the final model is a language that has one interpretation and two systems of sentence truth evaluation, primary and final evaluation. The language through the symbol T speaks of its primary truth valuation, which is precisely the largest intrinsic fixed point of the strong Kleene three valued semantics. Its final truth valuation is the semantic completion of the first in such a way that all sentences that are not true in the primary valuation are false in the final valuation. (shrink)

Herbrand disjunctions are a means for reducing the problem ofwhether a first-oder formula is valid in an open theory T or not to theproblem whether an open formula, one of the so called Herbrand disjunctions,is T -valid or not. Nevertheless, the set of Herbrand disjunctions, which hasto be examined, is undecidable in general. Fore this reason the practicalvalue of Herbrand disjunctions has been estimated negatively .Relying on completeness proofs which are based on the algebraizationtechnique presented in [30], but taking (...) a more optimistic view, we show howHerbrand disjunctions become the base of a method for building in theoriesinto automatic theorem provers [26]. Surveying newer results we discusshow to treat heterogeneous theories [29] as well as practical implications ofdifferent normal form transformations. (shrink)

Nondeterministic programs occurring in recently developed programming languages define nondeterminate partial functions. Formulas (Boolean expressions) of such nondeterministic languages are interpreted by a nonempty subset of {T (true), F (false), U (undefined)}. As a semantic basis for the propositional part of a corresponding nondeterministic three-valued logic we study the notion of a truth-function over {T, F, U} which is computable by a nondeterministic evaluation procedure. The main result is that these truth-functions are precisely the functions satisfying four basic (...) properties, called -isotonic, –-isotonic, hereditarily guarded, and hereditarily guard-using, and that a function satisfies these properties iff it is explicitly definable (in a certain normal form) from if..then..else..fi, binary choice, and constants. (shrink)

ABSTRACT: In its strongest unqualified form, the principle of wholistic reference is that in any given discourse, each proposition refers to the whole universe of that discourse, regardless of how limited the referents of its non-logical or content terms. According to this principle every proposition of number theory, even an equation such as "5 + 7 = 12", refers not only to the individual numbers that it happens to mention but to the whole universe of numbers. This principle, (...) its history, and its relevance to some of Oswaldo Chateaubriand's work are discussed in my 2004 paper "The Principle of Wholistic Reference" in Essays on Chateaubriand's "Logical Forms". In Chateaubriand's réplica (reply), which is printed with my paper, he raised several important additional issues including the three I focus on in this tréplica (reply to his reply): truth-values, universes of discourse, and formal ontology. This paper is self-contained: it is not necessary to have read the above-mentioned works. The principle of wholistic reference (PWR) was first put forth by George Boole in 1847 when he espoused a monistic fixed-universe viewpoint similar to the one Frege and Russell espoused throughout their careers. Later, Boole elaborated PWR in 1854 from the pluralistic multiple-universes perspective. (shrink)

As it was proved in [4, Sect. 3], the poset of extensions of the propositional logic defined by a class of logical matrices with equationally-definable set of distinguished values is a retract, under a Galois connection, of the poset of subprevarieties of the prevariety generated by the class of the underlying algebras of the defining matrices. In the present paper we apply this general result to the three-valued paraconsistent logic proposed by Hałkowska–Zajac [2]. Studying corresponding prevarieties, we prove (...) that extensions of the logic involved form a four-element chain, the only proper consistent extensions being the least non-paraconsistent extension of it and the classical logic. RID=""ID="" Mathematics Subject Classification (2000): 03B50, 03B53, 03G10 RID=""ID="" Key words or phrases: Many-valued logic – Paraconsistent logic – Extension – Prevariety – Distributive lattice. (shrink)

Statman and Orevkov independently proved that cut-elimination is of nonelementary complexity. Although their worst-case sequences are mathematically different the syntax of the corresponding cut formulas is of striking similarity. This leads to the main question of this paper: to what extent is it possible to restrict the syntax of formulas and — at the same time—keep their power as cut formulas in a proof? We give a detailed analysis of this problem for negation normal form , prenex (...) class='Hi'>normal form and monotone formulas. We show that proof reduction to NNF is quadratic, while PNF behaves differently: although there exists a quadratic transformation into a proof in PNF too, additional cuts are needed; the elimination of these cuts requires nonelementary expense in general. By restricting the logical operators to {,,,}, we obtain the type of monotone formulas. We prove that the elimination of monotone cuts can be of nonelementary complexity . On the other hand, we define a large class of problems where cut-elimination of monotone cuts is only exponential and show that this bound is tight. This implies that the elimination of monotone cuts in equational theories is at most exponential. Particularly, there are no short proofs of Statman's sequence with monotone cuts. (shrink)

Translated by Drew S. Burk and Anthony Paul Smith. Excerpted from Struggle and Utopia at the End Times of Philosophy , (Minneapolis: Univocal Publishing, 2012). THE END TIMES OF PHILOSOPHY The phrase “end times of philosophy” is not a new version of the “end of philosophy” or the “end of history,” themes which have become quite vulgar and nourish all hopes of revenge and powerlessness. Moreover, philosophy itself does not stop proclaiming its own death, admitting itself to be half dead (...) and doing nothing but providing ammunition for its adversaries. With our sights set on clearing up this nuance, we differentiate philosophy as an institutional entity, and the philosophizability of the World and History, of “thought-world,” which universalizes the narrow concept of philosophy and that of “capital.” We also give an eschatological and apocalyptical cause to this end, of “times” or “ages” rather than those of philosophical practice. Last but not least, it is the Future itself in the performativity of its ultimatum that determines this end times, reversing these times from the Identity the Future accorded to it, withdrawing the thought-world from the lie of its death. Why this style of axioms and oracles, these more or less subtle distinctions, old and debased, with an appeal to the ultimata , to end times and last words? We fight to give, parallel to the concept of Hell, its new theoretical position, for its philosophical return and its non-philosophical transformation. No more so than any other word, Hell is not a metaphor here, just the Principle of Sufficient World. Every man, no doubt, has his “hell” readily available, connivance, control, conformism, domestication, schooling, alienation, extermination, exploitation, oppression, anxiety, etc. We have our little list that the Contemporaries established in the previous century in the same way one used to construct lists of virtues and vices or honors and wealth. They invented it for us without knowing it, for us-the-Futures who have as our responsibility to invent its use. In the Christian and Gnostic tradition, the struggle of the End Times takes place “on earth.” The most sophisticated of believers have it taking place in Heaven as well, above all in Heaven. The various kinds of gnosis imagine infinite falls and vertiginous highs, the vertigo of salvation. On Earth as in Heaven, a hell is available. The Marxists have the law of profit and the control of production, the class struggle Capital imposes on man. The Nietzscheans, the dull grumble of the struggle in the foundations of World and History, the domestication of man, the society of control. The phenomenologists, the capture of being, the most superficial amongst them, the age of suspicion. But all of these “hells” are taken from World, History, Society, and Religion. What we call Hell is no longer of the order of these specific and total intra-worldly generalities, it is both more singular and more universal, no longer being at all of the same order, it is the determinant Identity of these small hells strung out through history but unified here in the name of the last Humaneity. It is even found within the French idiom for hell [ enfer ], en-fer literally means “in-irons.” We are as much “in-irons” as we are “alive” [ en-Vie ]. We believe in Hell but as non-philosophers and it is even because we are non-philosophers that we can believe in it outside of any sort of religion. Hell is less mythological than ideological, it combines philosophizability with universal capital. Under what form? A single term could work for them without being a metaphor or something they would participate in by analogy, a more innovative and conjectural term than control, more universal than profit. It would denote the growing and permanent extortion of a surplus-value of communication, of speed and of urgency in change, in productivity and in work, in the pressure of images and slogans. It would be worse than solicitation, more tenacious than capture, more active and persecutory than control, softer and more insidious than a frontal attack, just as perverse as questioning and accusation, less brutal and offensive than extermination, less ritualized than inquisition, it would be soft and dispersed, instantaneous and vicious, it would be a crime without declared violence. Collusion and conformism, it would be afraid to show itself. Related to rumor, from which it borrows its infinite and tortuous ways. It is harassment. As a modernized form of Hell, perhaps harassment has a long future in front of it, of innocent torture, slow assassination, in short the fall, but radical with no way of recovering and which tolerates only salvation. THE PHILOSOPHICAL PAST OF NON-PHILOSOPHY Non-philosophy is thus Man as the utopian identity of the philosophical form of the World, a utopia destined to transform it. We still have to understand these equations, in particular that of the being-uni-versed from Man, and this book adheres to this by re-exposing non-philosophy in a different way via one of its new possibilities. It uses this opportunity to once again take up formulations that lead to objections answering certain external critics, as well as revisiting diverging interpretations specific to non-philosophers. A portion of this book is devoted to going through these theories via a strict or “lengthy” presentation of non-philosophy, and its defense against more expeditious solutions. This work of rectification is the occasion, merely the occasion, for refocusing non-philosophy on Man (the “Man-in-person,” “Humaneity”), and in a more innovative manner, on its utopian vocation established since the book Future Christ . As for this “occasion,” it is quite obvious. A school of posture, not to say a school of thought, supposes a minimum of closure from the most liberating of knowledge, a heritage, its utilization, and its no less certain dispersal. Within its development, a variety of interpretations will no doubt appear, deviations that are as much normalizations, and a struggle against this multiplication of divergent tendencies. These are perhaps not inevitable evils, especially here, merely a normal development according to the twisting paths of history. But the problem is made worse by the fact that this school of non-philosophers is that of utopia. Not the former attempts devoted to commenting on the worst authoritarian and criminal forms of the past and the present, but utopia as the determinant principle for human life, or to put it another way, of the Future as an irreducible presupposition of (for) thinking the World and History. Non-philosophers are engaged in an aleatory navigation between the respect for the most rigorous utopia, whose rules are not that of the reproductive imagination but those from the Future determining imagination itself, as well as the temptations, diversions, and remorse of history. Little by little, we will begin to understand that the Future as we understand it no longer has any temporal consistency or positive content, without being an empty form or a nothingness, but that it is foreclosed to past and present History, just as it is foreclosed to the place of places, the World, and that it is the only method for establishing the practice of thinking in a non-imaginary instance. Because it is the World and History that are imaginary and have a terrible materiality, it is not necessarily utopia. We will overlap two objectives here: the defense of non-philosophy against the (non-) philosophers that we are, only occasionally, and the introduction of philosophy to a rigorous future. Together they set out to definitively render, without any possible return to philosophical conformism or towards the facilities of the past and present, the non-philosophical enterprise understood as utopia or uchronia. Imagination and speculation, left to themselves and thus undistinguished, are quite good for participating in the grand game of History but have little value or worse for the Future which is unimaginable and unintelligible and must be maintained as such. MAN-IN-PERSON AS SUSPENSION OF THE PHILOSOPHICAL CHORA The point where philosophical resistance is concentrated is without a doubt the invention of the Name-of-Man, first name, oracular as much as axiomatic, of the determining cause for the non-philosophical posture. And that which concentrates the differends is the style of non-philosophy as identity that possesses the dual aspect, of discipline and of the oeuvre, of the theorem and of the oracle. But the real difficulty in understanding the simplicity of non-philosophy is profoundly hidden in the depths of philosophy itself. Because philosophy, from Parmenides to Derrida, even Levinas, continues to be a divided gesture, without a veritable immanence, transforming its thematic contents of transcendence in also forgetting to transform the operative transcendence in the element from which the ontology of surface is established which we will call, in memory of Plato, the chorismos. The general effect of the chora literally gives place to philosophy, demanding binding and sutures to which we will once and for all “oppose” the Man-in-person, his power of cloning, and his future being. All philosophy contains a hinter-philosophy in which it deploys its operations and weaves its tradition like an understudy of a topographical nature and in the best of cases being itself topological. Philosophy as well consists of two levels, its pre-ontological operative conditions on the one hand, and its superficial theme on the other, it too has its presupposed, but is not aware of it or erases it within the unity of appearance named Logos. Rightly, the Logos, and its flash or lightning nature, possesses a “dark precursor,” the chora, which is as much a virtual image, and philosophy, dazzled by its own lightning flash, seems to completely forget about it at the same time it sets itself up within it. Non-philosophy risks taking this same path, of confusing what it believes to be the real with its phantom double, contenting itself to working on the thematic level of philosophy, not its surface objects and its idle chatter (we stopped talking about this a long time ago and in any case they are merely simple materials for inducing a work of transformation), but the transcendence-form of its objects. In the end it risks, through precipitation, taking back up the heritage of philosophy, a heritage of a misunderstood presupposed, even more profound than the play of transcendences. This is what the imperative of the radicality of immanence meant, to treat immanence in an immanent manner, not to make a new object out of it. And from here we get non- (philosophy) and its refusal of the Platonic chorismos , symbol of all abstraction, and thus all transcendental appearance. There are no illusions. The message will leave a heritage in tattered pieces and interpretations. But it was difficult not to dispute the differend to its core. There will be complete confusion of the multiple, possible, and necessary effectuations of non-philosophy with its interpretations. The non-philosophical or human freedom of philosophical effectuation and the philosophical freedom of interpretation. Effectuations demand non-philosophy to return to zero from the point of view of its philosophical material and thus also but within these limits the formulation of its axioms , but in no way providing from the outset divergent interpretations of the aforementioned axioms. They are divergent because they do not take into account the material from which these axioms are derived within non-philosophy, and because they do not see themselves as symptoms of another vision of the World. The utterances of non-philosophy are not mathematical theorems and pure axioms, they merely have a mathematical aspect . They are, by their extraction or origin, mathematical and transcendental. And by their determined function in-Real, within non-philosophy, they are identically in-the-last-Humaneity entities which have an aspect of an axiom and an aspect of interpretation (or an oracular aspect as we say) that attempts (sometimes it is ourselves who provide the occasion) to isolate and transform, in complete freedom of interpretation. There will be an opportunity to complain about the complex character of the language of non-philosophy, an idiom saturated with classical references, sophisticated in a contemporary way. Its freedom of decision up against the whole of philosophy demands these effects of “complication” and “privatization,” as the saying goes. But it also demands fighting against the drift [ dérive ] of the pedagogical-all and the mediatic-all that leads philosophy into the shallow depths of opinion, which is the site of its impossible death. The noble idealism of “pop-philosophy” has been consumed into a “philo-reality;” against this we propose philo-fiction. Parricide, which is at the bottom of these interpretations and which we can judge as being quite fertile, although it has informed tradition, only takes place once or within one lone meaning. In regards to Parmenides, it was possible; Plato introduced the Other as non-being and language, bringing into existence the philosophical system of the World, but is it possible to repeat it again with the same fecundity in regards to non-philosophy, this time in introducing (non) religion or (non) art, still mixing them without taking into account this mixture, alternatively as a philosophical or religious resentment? If philosophy begins via a crime, it is no doubt obliged to continue down similar pathways, to the effect that the crimes of philosophy, once the founding crime has been committed, are a reaction of self-defense. It is undoubtedly from this that we get Marx’s declaration that history begins by tragedy and repeats itself or ends in farce. The preservation of rigor and fecundity is, in every respect, a psychologically difficult task within a theory such as non-philosophy. Having posited an essential objective of liberation in regards to philosophy and its services, one has often understood this objective as an authorization of providing particular interpretations of its axioms and ends up obliterating their scope. This ends up confusing, on one hand, two kinds of freedoms in regards to non-philosophy, the freedom of its interpretations and the freedom of its effectuations. On the other hand, any defense of “principles” against precipitated interpretations is immediately taxed with a will to orthodoxy, a prohibitive objection when we are dealing with, as is the case here, a heretical theory of thought. Nevertheless, it is time to stop confusing heresy as the cause of thought with an ideology of heresies, which is certainly not at all our object, but rather a form of normalization. As for the “disciplinary” aspect, which is not the only aspect, it demands something other than philosophical “answers to objections,” a precision in the definition and use of its procedures in the formation of utterances, since non-philosophy is neither a supplementary doctrine interior to philosophy nor a vision of the world but one whose priority is a “vision of Man,” or rather Man as “vision” that implies a theory and a practice of philosophy. In the end, struggle is only one aspect of non-philosophy, not its whole or telos, struggle coming only from its materiality. In particular, if the discipline of non-philosophy is inseparable from struggle, it is not a question of reducing the monomaniacal obsession of its “marching orders.” This would reduce its complexity and kill its indivisibility, deploying it in a “long march” and a form of Maoization whose philosophical presuppositions no longer have any pertinence here, a case of the One and the Two, which are now cloned and no longer tied together. More generally, non-philosophy is a complex thought composed of a multitude of aspects, which is to say, unilateral interpretations, of a philosophical origin but reduced by their determination in-the-last-instance . The “liberalism” of non-philosophy is merely one of the aspects of which it is capable, not an essence. Similarly, it is only capable of having a “Maoist” aspect. Let us generalize. The weakness of non-philosophy is due to a specific cause, the determination-in-the-last-Humaneity of a subject for the World. Everything that has a right to the philosophical city can be said about it in turn and in a retaliatory mode since Man contributes nothing of himself that Man takes from the World. We can consider non-philosophy as being pretentious, absurd, idealistic, empty, materialistic, formalistic, contradictory, modern, post-modern, Zen, Buddhist, Marxist; it endures or tolerates, perhaps “appeals” to, or at least renders possible, sarcasms, ironies, and insults without even talking about the misunderstandings, partly for the same reason as psychoanalysis. All of this goes beyond simple “deviations.” They are its aspects, which is to say, its “unilateral” philosophical interpretations in both senses of the word, being either sufficient coming from the mouth of philosophers, or reduced to their absolute dimension of sufficiency and totality in the mouths of non-philosophers, and both times due to the weakness and strength of Man-in-person as their determination only in-the-last-instance. The non-philosopher is certainly not a Saint Paul fantasizing about a new Church. The non-philosopher is either a (Saint) Sebastian whose flesh is pierced with as many arrows as there are Churches, or a Christ persecuted by a Saint Paul. What is engaged in here is the practice of retaliation. A negative rule of the non-philosophical ethics of outlawed discussion by way of argumentation (the sufficient is you, the orthodox one is always you, you are the fashionable one, and when a master you are someone else) that is founded on the confusion of effectuations of non-philosophy and of its overall interpretations. Retaliation is the law but as with any too-human law, it must acquire a dimension that displaces it, or rather emplaces it and takes away its authority but not all of its effectiveness. If the non-philosopher is only authorized by himself, which is to say by philosophy but limited by the Real-of-the-last-instance, its critique of other non-philosophers can merely be retaliatory under the same conditions, only by the Real limited in-the last-instance. THE TREE OF PHILOSOPHICAL SAINTLINESS The thematic horizon or material of these debates is in the relationships between philosophy, religion as gnosis, and non-philosophy. It is inevitable, regarding non-philosophers in general (whether they are non-philosophers by name or simply its neighbors) that we often end up evoking Marx’s Holy Family and imagining, arranged on the neighboring branches of the tree of philosophy and annexed, sometimes abusively, to non-philosophy, authors who would quite evidently and quite rightly refuse this label. So it is that we find, for example, a Saint Michel, a Saint Alain, a Saint Gilles 1 without even mentioning the youngest who aspire as well to the freedom of “saintliness” and who make their muted voices heard here. If there is a Holy Family of non-philosophers, it extends completely beyond these three, provided that the sectarian spirit can save us. This book is organized in the following manner: To begin, in order to recall the essential part of the problematic, we have organized a Summary of Non-Philosophy , a vade-mecum of notions and basic problems, in a classical style. Secondly, there is Clarifications On the Three Axioms of Non-Philosophy , designed to posit their proper use as much as to elucidate their meaning. Thirdly, an analysis of Philosophizability and Practicity , both being extreme constituents of philosophical material or the contents of the third axiom. Fourthly, the heart of this work: Let us Make a Tabula Rasa of the Future or of Utopia as Method . Fifthly, we have a theoretical outline of a non-institutional utopia, The International Organization of Non-Philosophy, L’Organisation Non-Philosophique Internationale, (ONPHI) already created in practice but under the conditions of possibility and functioning from which here we put into question “de jure,” thus not without a perplexity concerning “facts,” in any case, without the capability of “getting to the bottom of things.” Sixthly, an essay characterizing The Right and the Left of Non-Philosophy , a brief topology of several philosophizing and normalizing positions of proponents or tenants of this problematic. Seventhly, Rebel in the Soul: A Theory of Future Struggle , a systematic discussion starting from a confrontation of non-philosophical gnosis and non-religious gnosis to the extent that they pose, posed or perhaps still will pose themselves as rivals to non-philosophy in a mixture of fidelity and infidelity. Despite the fact that it can also be read as putting non-philosophy into perspective: it pits against a standard Platonism two contemporary appropriations of Gnosticism. On the basis of the paradigm of Man who never ceases to come as the Future-in-person, each one of these moments strives to reestablish not the “true” non-philosophy and its orthodoxy, but the minimal conditions to respect in order to allow for its maximum fecundity. And in order to bring about one of the last possibilities of its development, making explicit Humaneity as a utopia-for-the-World. In introducing these considerations in the form of a “testament” and “ultimatum,” we want to indicate two things: First, that this is the last time we will intervene in order to caution non-philosophers against the temptation of returning and looking backwards towards philosophy. Only a disillusioned nostalgia for the former World and its traditions barely remain permissible to us.… Secondly, that non-philosophy is also a sort of ultimatum for considering one’s life and transforming one’s thought from the perspective of a uni-version rather than a conversion. Man as future is this ultimatum in action, not an impatient self-proclaimed genius, and philosophy is his testament. It is obviously the ultimatum that determines this testament as “old” with a view towards a life that is, itself, non-testamentary. In and of itself, the “old” can never bear a veritable eschaton. Thus, this book intersects according to the logic of this paradigm, under the sign of the ultimate or “last” as future, philosophy as testament and cautionary note for maintaining the non-philosophical oeuvre as “future” or “utopian.” We will see that between these two dimensions it cradles a theory of struggle. In the end, this book envisions non-philosophers in multiple ways. It inevitably sees them as subjects of knowledge, most often academics insofar as life in the world demands, but above all as close relatives of three great human types. The analyst and political militant are quite obvious, for non-philosophy is close to psychoanalysis and Marxism insofar as it transforms the subject in transforming philosophy. Here again, one must have a sense not of certain nuances but of aspects (of the interpretations, albeit unilateralized) and not in order to construct a simple proletarization or militarization of thought as theory. To be rigorous, rather than authoritarian or spiteful, is its task. And lastly, non-philosophy is a close relative of the spiritual but definitely not the spiritualist. Those who are spiritual are not at all spiritualists, for the spiritual oscillate between fury and tranquil rage, they are great destroyers of the forces of Philosophy and the State, which are united under the name of Conformism. They haunt the margins of philosophy, gnosis, mysticism, science fiction and even religions. Spiritual types are not only abstract mystics and quietists; they are heretics for the World. The task is to bring their heresy to the capacity of utopia, and their utopia to the capacity of the paradigm. NOTES We will recognize allusions, and sometimes references, to closely related or distant themes, but which are related, in the work of Michel Henry, Alain Badiou and via the representative of “non-religious” gnosis of a Platonic origin, in Gilles Grelet. It goes without saying that these discussions are current and local, neither concerning the ensemble of doctrines nor prejudging the eventual evolution of certain amongst them. This concerns defining certain proximities with non-philosophy (rather than adversaries which in some sense they are) and typological and emblematic differends (rather than conflicts with a certain author). (shrink)

The paper explicates the stages of the author’s philosophical evolution in the light of Kopnin’s ideas and heritage. Starting from Kopnin’s understanding of dialectical materialism, the author has stated that category transformations of physics has opened from conceptualization of immutability to mutability and then to interaction, evolvement and emergence. He has connected the problem of physical cognition universals with an elaboration of the specific system of tools and methods of identifying, individuating and distinguishing objects from a scientific theory domain. (...) The role of vacuum conception and the idea of existence (actual and potential, observable and nonobservable, virtual and hidden) types were analyzed. In collaboration with S.Crymski heuristic and regulative functions of categories of substance, world as a whole as well as postulates of relativity and absoluteness, and anthropic and self-development principles were singled out. Elaborating Kopnin’s view of scientific theories as a practically effective and relatively true mapping of their domains, the author in collaboration with M. Burgin have originated the unified structure-nominative reconstruction (model) of scientific theory as a knowledge system. According to it, every scientific knowledge system includes hierarchically organized and complex subsystems that partially and separately have been studied by standard, structuralist, operationalist, problem-solving, axiological and other directions of the current philosophy of science. 1) The logico-linguistic subsystem represents and normalizes by means of different, including mathematical, languages and normalizes and logical calculi the knowledge available on objects under study. 2) The model-representing subsystem comprises peculiar to the knowledge system ways of their modeling and understanding. 3) The pragmatic-procedural subsystem contains general and unique to the knowledge system operations, methods, procedures, algorithms and programs. 4) From the viewpoint of the problem-heuristic subsystem, the knowledge system is a unique way of setting and resolving questions, problems, puzzles and tasks of cognition of objects into question. It also includes various heuristics and estimations (truth, consistency, beauty, efficacy, adequacy, heuristicity etc) of components and structures of the knowledge system. 5) The subsystem of links fixes interrelations between above-mentioned components, structures and subsystems of the knowledge system. The structure-nominative reconstruction has been used in the philosophical and comparative case-studies of mathematical, physical, economic, legal, political, pedagogical, social, and sociological theories. It has enlarged the collection of knowledge structures, connected, for instance, with a multitude of theoreticity levels and with an application of numerous mathematical languages. It has deepened the comprehension of relations between the main directions of current philosophy of science. They are interpreted as dealing mainly with isolated subsystems of scientific theory. This reconstruction has disclosed a variety of undetected knowledge structures, associated also, for instance, with principles of symmetry and supersymmetry and with laws of various levels and degrees. In cooperation with the physicist Olexander Gabovich the modified structure-nominative reconstruction is in the processes of development and justification. Ideas and concepts were also in the center of Kopnin’s cognitive activity. The author has suggested and elaborated the triplet model of concepts. According to it, any scientific concept is a dependent on cognitive situation, dynamical, multifunctional state of scientist’s thinking, and available knowledge system. A concept is modeled as being consisted from three interrelated structures. 1) The concept base characterizes objects falling under a concept as well as their properties and relations. In terms of volume and content the logical modeling reveals partially only the concept base. 2) The concept representing part includes structures and means (names, statements, abstract properties, quantitative values of object properties and relations, mathematical equations and their systems, theoretical models etc.) of object representation in the appropriate knowledge system. 3) The linkage unites a structures and procedures that connect components from the abovementioned structures. The partial cases of the triplet model are logical, information, two-tired, standard, exemplar, prototype, knowledge-dependent and other concept models. It has introduced the triplet classification that comprises several hundreds of concept types. Different kinds of fuzziness are distinguished. Even the most precise and exact concepts are fuzzy in some triplet aspect. The notions of relations between real scientific concepts are essentially extended. For example, the definition and strict analysis of such relations between concepts as formalization, quantification, mathematization, generalization, fuzzification, and various kinds of identity are proposed. The concepts «PLANET» and «ELEMENTARY PARTICLE» and some of their metamorphoses were analyzed in triplet terms. The Kopnin’s methodology and epistemology of cognition was being used for creating conception of the philosophy of law as elaborating of understanding, justification, estimating and criticizing legal system. The basic information on the major directions in current Western philosophy of law (legal realism, feminism, criticism, postmodernism, economical analysis of law etc.) is firstly introduced to the Ukrainian audience. The classification of more than fifty directions in modern legal philosophy is suggested. Some results of historical, linguistic, scientometric and philosophic-legal studies of the present state of Ukrainian academic science are given. (shrink)

Given a three-valued definition of validity, which choice of three-valued truth tables for the connectives can ensure that the resulting logic coincides exactly with classical logic? We give an answer to this question for the five monotonic consequence relations $st$, $ss$, $tt$, $ss\cap tt$, and $ts$, when the connectives are negation, conjunction, and disjunction. For $ts$ and $ss\cap tt$ the answer is trivial (no scheme works), and for $ss$ and $tt$ it is straightforward (they are the (...) collapsible schemes, in which the middle value acts like one of the classical values). For $st$, the schemes in question are the Boolean normal schemes that are either monotonic or collapsible. (shrink)

In classical game theory the idea that players randomize between their actions according to a particular optimal probability distribution has always been viewed as puzzling. In this paper, we establish a fundamental connection between n-person normal form games and quantum mechanics, which eliminates the conceptual problems of these random strategies. While the two theories have been regarded as distinct, our main theorem proves that if we do not give any other piece of information to a player in (...) a game, than the payoff matrix—the axiom of “no-supplementary data” holds—then the state of mind of a rational player is algebraically isomorphic to a pure quantum state. The “no supplementary data” axiom is captured in a Lukasiewicz’s three-valued Kripke semantics wherein statements about whether a strategy or a belief of a player is rational are initially indeterminate i.e. neither true, nor false. As a corollary, we show that in a mixed Nash equilibrium, the knowledge structure of a player implies that probabilities must verify the standard “Born rule” postulate of QM. The puzzling “indifference condition” wherein each player must be rationally indifferent between all the pure actions of the support of his equilibrium strategy is resolved by his state of mind being described by a “quantum superposition” prior a player is asked to make a definite choice in a “measurement”. Finally, these results demonstrate that there is an intrinsic limitation to the predictions of game theory, on a par with the “irreducible randomness” of quantum physics. (shrink)

The paper consists of two parts. The first part begins with the problem of whether the original three-valued calculus, invented by J. Łukasiewicz, really conforms to his philosophical and semantic intuitions. I claim that one of the basic semantic assumptions underlying Łukasiewicz's three-valued logic should be that if under any possible circumstances a sentence of the form "X will be the case at time t" is true (resp. false) at time t, then this sentence must (...) be already true (resp. false) at present. However, it is easy to see that this principle is violated in Lukasiewicz's original calculus (as the cases of the law of excluded middle and the law of contradiction show). Nevertheless it is possible to construct (either with the help of the notion of "supervaluation", or purely algebraically) a different three-valued, semi-classical sentential calculus, which would properly incorporate Łukasiewicz's initial intuitions. Algebraically, this calculus has the ordinary Boolean structure, and therefore it retains all classically valid formulas. Yet because possible valuations are no longer represented by ultrafilters, but by filters (not necessarily maximal), the new calculus displays certain non-classical metalogical features (like, for example, nonextensionality and the lack of the metalogical rule enabling one to derive "p is true or q is true" from" 'p ∨ q' is true"). The second part analyses whether the proposed calculus could be useful in formalizing inferences in situations, when for some reason (epistemological or ontological) our knowledge of certain facts is subject to limitation. Special attention should be paid to the possibility of employing this calculus to the case of quantum mechanics. I am going to compare it with standard non-Boolean quantum logic (in the Jauch-Piron approach), and to show that certain shortcomings of the latter can be avoided in the former. For example, I will argue that in order to properly account for quantum features of microphysics, we do not need to drop the law of distributivity. Also the idea of "reading off" the logical structure of propositions from the structure of Hilbert space leads to some conceptual troubles, which I am going to point out. The thesis of the paper is that all we need to speak about quantum reality can be acquired by dropping the principle of bivalence and extensionality, while accepting all classically valid formulas. (shrink)

Correspondence analysis is Kooi and Tamminga’s universal approach which generates in one go sound and complete natural deduction systems with independent inference rules for tabular extensions of many-valued functionally incomplete logics. Originally, this method was applied to Asenjo–Priest’s paraconsistent logic of paradox LP. As a result, one has natural deduction systems for all the logics obtainable from the basic three-valued connectives of LP -language) by the addition of unary and binary connectives. Tamminga has also applied this technique (...) to the paracomplete analogue of LP, strong Kleene logic \. In this paper, we generalize these results for the negative fragments of LP and \, respectively. Thus, the method of correspondence analysis works for the logics which have the same negations as LP or \, but either have different conjunctions or disjunctions or even don’t have them as well at all. Besides, we show that correspondence analyses for the negative fragments of \ and LP, respectively, are also suitable without any changes for the negative fragments of Heyting’s logic \ and its dual \ and LP). (shrink)

We introduce a notion of semantical closure for theories by formalizing Nepeivoda notion of truth. [10]. Tarski theorem on truth definitions is discussed in the light of Kleene's three valued logic (here treated with a formal reinterpretation of logical constants). Connections with Definability Theory are also established.

In his celebrated paper of 1931 [7], Kurt Gödel proved the existence of sentences undecidable in the axiomatized theory of numbers. Gödel's proof is constructive and such a sentence may actually be written out. Of course, if we follow Gödel's original procedure the formula will be of enormous length.Forty-five years have passed since the appearance of Gödel's pioneering work. During this time enormous progress has been made in mathematical logic and recursive function theory. Many different mathematical problems have (...) been proved recursively unsolvable. Theoretically each such result is capable of producing an explicit undecidable number theoretic predicate. We have only to carry out a suitable arithmetization. Until recently, however, techniques were not available for carrying out these arithmetizations with sufficient efficiency.In this article we construct an explicit undecidable arithmetical formula,F(x, n), in prenex normal form. The formula is explicit in the sense that it is written out in its entirety with no abbreviations. The formula is undecidable in the recursive sense that there exists no algorithm to decide, for given values ofn, whether or notF(n, n)is true or false. MoreoverF(n, n)is undecidable in the formal (axiomatic) sense of Gödel [7]. Given any of the usual axiomatic theories to which Gödel's Incompleteness Theorem applies, there exists a value ofnsuch thatF(n, n)is unprovable and irrefutable. Thus Gödel's Incompleteness Theorem can be “focused” into the formulaF(n, n). Thus some substitution instance ofF(n, n)is undecidable in Peano arithmetic, ZF set theory, etc. (shrink)

J. Michael Dunn’s Theorem in 3-Valued Model Theory and Graham Priest’s Collapsing Lemma provide the means of constructing first-order, three-valued structures from classical models while preserving some control over the theories of the ensuing models. The present article introduces a general construction that we call a Dunn–Priest quotient, providing a more general means of constructing models for arbitrary many-valued, first-order logical systems from models of any second system. This technique not only counts Dunn’s and Priest’s (...) techniques as special cases, but also provides a generalized Collapsing Lemma for Priest’s more recent plurivalent semantics in general. We examine when and how much control may be exerted over the resulting theories in particular cases. Finally, we expand the utility of the construction by showing that taking Dunn–Priest quotients of a family of structures commutes with taking an ultraproduct of that family, increasing the versatility of the tool. (shrink)

We give inequational and equational axioms for semirings with a fixed-point operator and formally develop a fragment of the theory of context-free languages. In particular, we show that Greibach’s normal form theorem depends only on a few equational properties of least pre-fixed points in semirings, and eliminations of chain and deletion rules depend on their inequational properties . It follows that these normal form theorems also hold in non-continuous semirings having enough fixed points.

The central concern in this tightly reasoned, technically written book is the logic of scientific explanation and its relation to the logic of ordinary language. Empirical differentiation, through the conceptual systems that shape ordinary discourse, can take various forms, but all utilize the related basic concepts of individuals, classes, and continua. In ordinary discourse these notions are essentially inexact, a feature which Körner handles through an adaption of Kleene's three valued logic. Any explanatory system, e.g., scientific theories, based (...) on two valued logic automatically represents an idealization introduced to provide a deductive unification of experience. In treating scientific theories Körner concentrates on mathematical systems and on explicating the various meanings of "necessary" which may characterize scientific laws. The final third of the book, on the relation between experience and scientific explanation, emphasizes the role of man as an active decision maker. Though Körner's conceptualistic approach raises difficulties and leaves many questions unanswered—and even unasked—his carefully ordered and precisely elaborated development presents a new and significant interpretation of the relation between an ordinary and theoretical language and their respective roles in man's understanding of reality.—E. M. M. (shrink)

There are several three-valued logical systems that form a scattered landscape, even if all reasonable connectives in three-valued logics can be derived from a few of them. Most papers on this subject neglect the issue of the relevance of such logics in relation with the intended meaning of the third truth-value. Here, we focus on the case where the third truth-value means unknown, as suggested by Kleene. Under such an understanding, we show that any truth-qualified (...) formula in a large range of three-valued logics can be translated into KD as a modal formula of depth 1, with modalities in front of literals only, while preserving all tautologies and inference rules of the original three-valued logic. This simple information logic is a two-tiered classical propositional logic with simple semantics in terms of epistemic states understood as subsets of classical interpretations. We study in particular the translations of Kleene, Gödel, ᴌukasiewicz and Nelson logics. We show that Priest’s logic of paradox, closely connected to Kleene’s, can also be translated into our modal setting, simply by exchanging the modalities possible and necessary. Our work enables the precise expressive power of three-valued logics to be laid bare for the purpose of uncertainty management. (shrink)

In this paper we present a general theory of normal forms, based on a categorial result for the free monoid construction. We shall use the theory mainly for proposictional modal logic, although it seems to have a wider range of applications. We shall formally represent normal forms as combinatorial objects, basically labelled trees and forests. This geometric conceptualization is implicit in and our approach will extend it to other cases and make it more direct: operations of (...) a purely geometric and combinatorial nature will be introduced in order to give a mathematical description of the basic logical/algebraic constructions .We begin by recalling the above-mentioned categorial construction: we need a careful inspection of it because in the various examples considered later we plan to deduce from it in a uniform way the normal forms and the description of finitely generated free algebras. This method always works whenever we can describe the category of algebras corresponding to the logic under consideration as a T-objects category. When this simple description seems not to be available, still the general theory might be of some interest, because a description of the category of algebras as a T-objects category plus equation is possible .The central part of the paper is more advanced and specific: we show how the general approach presented here can provide some insights even in the basic case of the modal system K. Section 4 contains a contribution to the theory of normal forms, namely the description of the uniform substitution. This result will enable us to give a duality theorem for the category of finitely generated free modal algebras and in Section 5 to provide a characterization of the collections of normal forms which happen to be normal forms for a logic, thus giving a description of the lattice of modal logics.Section 6 deals with some applications: we shall show how to use normal forms in order to prove for the modal system K the definability of higher-order propositional quantifiers and of the tense operator F .As to the prerequisites, the paper is almost self-contained. The reader is only assumed to have familiarity with standard techniques in algebraic logic ). Knowledge of the basic facts about adjoint functors is required too, see e.g. McLane or the appendix. (shrink)

We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, (...) Priest's Collapsing Lemma and Dunn's Theorem in 3-Valued Logic. (shrink)

Contemporary realist theories of value claim to be compatible with natural science. In this paper, I call this claim into question by arguing that Darwinian considerations pose a dilemma for these theories. The main thrust of my argument is this. Evolutionary forces have played a tremendous role in shaping the content of human evaluative attitudes. The challenge for realist theories of value is to explain the relation between these evolutionary influences on our evaluative attitudes, on the one hand, and the (...) independent evaluative truths that realism posits, on the other. Realism, I argue, can give no satisfactory account of this relation. On the one hand, the realist may claim that there is no relation between evolutionary influences on our evaluative attitudes and independent evaluative truths. But this claim leads to the implausible skeptical result that most of our evaluative judgements are off track due to the distorting pressure of Darwinian forces. The realist’s other option is to claim that there is a relation between evolutionary influences and independent evaluative truths, namely that natural selection favored ancestors who were able to grasp those truths. But this account, I argue, is unacceptable on scientific grounds. Either way, then, realist theories of value prove unable to accommodate the fact that Darwinian forces have deeply influenced the content of human values. After responding to three objections, the third of which leads me to argue against a realist understanding of the disvalue of pain, I conclude by sketching how antirealism is able to sidestep the dilemma I have presented. Antirealist theories of value are able to offer an alternative account of the relation between evolutionary forces and evaluative facts —
an account that allows us to reconcile our understanding of evaluative truth with our understanding of the many non-rational causes that have played a role in shaping our evaluative judgements. (shrink)

Today philosophical discussion on indicative conditionals is dominated by the so called Lewis Triviality Results, according to which, tehere is no binary connective '-->' (let alone truth-functional) such that the probability of p --> q equals the probability of q conditionally on p, so that P(p --> q)= P(q|p). This tenet, that suggests that conditonals lack truth-values, has been challenged in 1991 by Goodman et al. who show that using a suitable three-valued logic the above equation may be (...) restored. In this paper it is first analysed a long neglected paper by Bruno de Finetti, written in 1935, where the essentials of Goodman's theory was clearly outlined. It is also stressed that de Finetti anticipated Kleene's as well as Bochvar and Blamey ideas. In the second part of the paper it is argued that the de Finetti-Goodman's original theory is defective and leads to absurd results. However, a new semantics, called semantics of hypervaluations, is here defined, that avoids the defects of the original theory. This appears to be a powerful challenge to Lewis Triviality results and to the thesis by which conditionals lack truth-values as well. (shrink)

Easy to understand philosophy papers in all areas. Table of contents: Three Short Philosophy Papers on Human Freedom The Paradox of Religions Institutions Different Perspectives on Religious Belief: O’Reilly v. Dawkins. v. James v. Clifford Schopenhauer on Suicide Schopenhauer’s Fractal Conception of Reality Theodore Roszak’s Views on Bicameral Consciousness Philosophy Exam Questions and Answers Locke, Aristotle and Kant on Virtue Logic Lecture for Erika Kant’s Ethics Van Cleve on Epistemic Circularity Plato’s Theory of Forms Can we trust our (...) senses? Yes we can Descartes on What He Believes Himself to Be The Role of Values in Science Modern Science Kant’s Moral Philosophy Plato’s Republic as Pol Potist Bureaucracy Schopenhauer on Human Suffering Bertrand Russell on the Value of Philosophy The Philosophical Value of Uncertainty Logic Homework: Theorems and Models Searle vs. Turing on the Imitation Game Hume, Frankfurt, and Holbach on Personal Freedom Manifesto of the University of Wisconsin, Madison Secular Society Michael’s Analysis of the Limits of Civil Protections Bentham and Mill on Different Types of Pleasure Set Theory Homework Aristotle on Virtue Nagel On the Hard Problem Wittgenstein on Language and Thought Camus and Schopenhauer on the Meaning of Life Camus’ Hero as Rebel without a Cause My Little Finger: Camus’ Absurdism Illustrated Are Late-term Abortions Ethical? Does Mathematics Assume the Truth of Platonism? The Self-defeating Nature of Utilitarianism and Consequentialism Generally What is The Good Life? Bentham and Mill regarding types of pleasures Kant’s Moral Philosophy Five Short Papers on Mind-body Dualism Tracy Latimer’s Father had the Right to Kill Her: Towards a doctrine of generalized self-defense Arguments Concerning God and Morality Goldman, Rousseau and von Hayek on the Ideal State J.S Mill on Liberty and Personal Freedom A Kantian Analysis of a Borderline Date-rape Situation Living Well as Flourishing: Aristotle’s Conception of the Good Life Three Essays on Medical Ethics: Answers to Exam Questions on Elective Amputation, Vaccination, and Informed Consent Hobbes, Marx, Rousseau, Nietzsche: Their Central Themes De Tocqueville on Egoism Mill vs. Hobbes on Liberty Exam-Essays on the Moral Systems of Mill, Bentham, and Kant Kant’s Moral System Aristotle on Virtue Plato’s Cave Allegory An Ethical Quandary Superorganisms The Tuskegee Experiment A Rawlsian Analysis Why Moore’s Proof of an External World Fails A Defense of Nagel’s Argument Against Materialism A Utilitarian Analysis of a Case of Theft The Paradox of the Self-aware Wretch: An Analysis of Pascal’s Moral Philosophy Jean-Paul Sartre: Decline and Fall of a Marxist Sell-out A One Page Proof of Plato’s Theory of Forms Plato’s Republic as Pol Potist Bureaucracy The problem of the one and the many Four Short Essays on Truth and Knowledge What is ‘the Good Life?’ The Ontological Argument Different Political Philosophies: Plato, Locke, Madison, Rousseau, Hayek, and Mill on the State What do I know with certainty? Skepticism about skepticism Neuroscience and Freewill Operant Conditioning What makes us special? Are Late-term Abortions Ethical? No Two Papers on Epistemology: Gettier and Bostrom Examination Nietzsche on Punishment God’s Foreknowledge and Moral Responsibility . (shrink)

In this article, I develop three conceptual innovations within the area of formal metatheory, and present a computer program, called Reconstructor, that implements those developments. The first development consists in a methodology for testing formal reconstructions of scientific theories, which involves checking both whether translations of paradigmatically successful applications into models satisfy the formalisation of the laws, and also whether unsuccessful applications do not. I show how Reconstructor can help carry this out, since it allows the end-user to specify (...) a formal language, input axioms and models formulated in that language, and then ask if the models satisfy the axioms. The second innovation is the introduction of incomplete models (for which the denotation of some terms is missing) into scientific metatheory, in order to represent cases of missing information. I specify the paracomplete semantics built into Reconstructor to deal with sentences where denotation failures occur. The third development consists in a new way of explicating the structuralist notion of a determination method, by equating them with algorithms. This allows determination methods to be loaded into Reconstructor and then executed within a model to find out the value of a previously non-denoting term (i.e. it allows the formal reconstruction to make predictions). This, in turn, can help test the reconstruction in a different way. Finally, I conclude with some suggestions about additional uses the program may have. (shrink)

Psychological research on people’s understanding of natural language connectives has traditionally used truth table tasks, in which participants evaluate the truth or falsity of a compound sentence given the truth or falsity of its components in the framework of propositional logic. One perplexing result concerned the indicative conditional if A then C which was often evaluated as true when A and C are true, false when A is true and C is false but irrelevant“ (devoid of value) when A is (...) false (whatever the value of C). This was called the “psychological defective table of the conditional.” Here we show that far from being anomalous the “defective” table pattern reveals a coherent semantics for the basic connectives of natural language in a trivalent framework. This was done by establishing participants’ truth tables for negation, conjunction, disjunction, conditional, and biconditional, when they were presented with statements that could be certainly true, certainly false, or neither. We review systems of three-valued tables from logic, linguistics, foundations of quantum mechanics, philosophical logic, and artificial intelligence, to see whether one of these systems adequately describes people’s interpretations of natural language connectives. We find that de Finetti’s (1936/1995) three-valued system is the best approximation to participants’ truth tables. (shrink)

With each projective geometry we can associate a Lyndon algebra. Such an algebra always satisfies Tarski's axioms for relation algebras and Lyndon algebras thus form an interesting connection between the fields of projective geometry and algebraic logic. In this paper we prove that if G is a class of projective geometries which contains an infinite projective geometry of dimension at least three, then the class L(G) of Lyndon algebras associated with projective geometries in G has an undecidable (...) class='Hi'>equational theory. In our proof we develop and use a connection between projective geometries and diagonal-free cylindric algebras. (shrink)

A quantization procedure without Hamiltonian is reported which starts from a statistical ensemble of particles of mass m and an associated continuity equation. The basic variables of this theory are a probability density ρ, and a scalar field S which defines a probability current j=ρ ∇ S/m. A first equation for ρ and S is given by the continuity equation. We further assume that this system may be described by a linear differential equation for a complex-valued state variable (...) χ. Using these assumptions and the simplest possible Ansatz χ(ρ,S), for the relation between χ and ρ,S, Schrödinger’s equation for a particle of mass m in a mechanical potential V(q,t) is deduced. For simplicity the calculations are performed for a single spatial dimension (variable q). Using a second Ansatz χ(ρ,S,q,t), which allows for an explicit q,t-dependence of χ, one obtains a generalized Schrödinger equation with an unusual external influence described by a time-dependent Planck constant. All other modifications of Schrödinger’ equation obtained within this Ansatz may be eliminated by means of a gauge transformation. Thus, this second Ansatz may be considered as a generalized gauging procedure. Finally, making a third Ansatz, which allows for a non-unique external q,t-dependence of χ, one obtains Schrödinger’s equation with electrodynamic potentials A,φ in the familiar gauge coupling form. This derivation shows a deep connection between non-uniqueness, quantum mechanics and the form of the gauge coupling. A possible source of the non-uniqueness is pointed out. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Free Will’s Value: Criminal Justice, Pride, and Love by John LemosJohn DavenportLEMOS, John. Free Will’s Value: Criminal Justice, Pride, and Love. New York: Routledge, 2023. 284 pp. Cloth, $160.00It is a pleasure to read John Lemos’s latest work on moral free will, understood as the control needed for us to be morally responsible in “the just deserts sense.” Lemos is a clear writer who carefully lays out the (...) positions that he reviews and critiques. This book would be wonderful as a main text in a graduate seminar: The first six chapters critically address most of the main theories and moves in this wide field during the last twenty to twenty-five years, providing a very helpful overview while setting up Lemos’s own position. He advances an “indeterministic weightings” version of leeway-libertarianism about moral freedom that builds on both Robert Kane’s event-causal account and Robert Nozick’s older account of fixing the weight of practical considerations in the moment of choice. Lemos’s new account significantly refines the position that he defended against hard incompatiblism in his 2018 book. [End Page 721]Free Will’s Value also discusses responsibility in applied contexts, such as criminal justice and loving relationships. There are two chapters arguing that hard incompatibilists cannot save the “just deserts” aspect of criminal punishment or explain all the wrongness of taking the liberty of innocent persons mistakenly convicted. Their “public health quarantine” account of criminal justice will be utilitarian, and thus have a hard time justifying the beyond-reasonable-doubt standard for conviction. And, building on the critiques of compatibilism that he develops partly from Derk Pereboom and Bruce Waller, Lemos includes three chapters arguing that “axiological/pragmatist reasons” provide more evidence for libertarian free will than psychological evidence alone can.The final chapter in particular offers a novel argument that valuable sorts of interhuman loves need to involve self- or character-forming initiatives that are not primarily determined by factors beyond our control. The intrinsic value of some types of love, such as deep friendships—including romantic friendships—involve their being autonomous (my term), which in turn requires a kind of leeway-control. This involves arguing that “our will, effort, or a decision to love” is important to values achieved in sustaining loving relationships.Lemos’s own theory contends that Kane’s account of “self-forming actions” (SFAs) and “willings” (SFWs) in terms of dual “tryings” (or decisions) to do A or B in a fraught situation suffers from the “phenomenological problem” stated by Laura Ekstrom and Marc Balaguer, namely, that we do not normally experience fraught choices as involving such opposed tryings. This is even more evident, I believe, if we consider choices involving three or more salient options. Lemos is not convinced by Kane’s reply that the dual or multiple simultaneous efforts are usually unconscious, because he thinks responsibility for unconscious mental processes will (normally) trace to patterns of conscious choices made earlier in life. In fact, unconscious efforts, Lemos says, cannot meet even “plausible minimal compatibilist standards of responsibility” for elements of agency.I’m not convinced by this last claim, because it seems that an unconscious choice, C, could be responsive to (or counterfactually guided by) reasons relevant to C that the agent has considered in the past. Perhaps the problem is that “trying” is normally associated with attempting to act on an intention, but Kane uses it to describe the more elusive processes of agency involved in forming an intention via decision in the face of competing relevant options, which thereby incorporates motives into the intention. This sheds light on the further problem that it appears irrational to try to do multiple incompatible things at once. Pace Lemos, I think that Kane is right that “will-settling” is a special context in which it is not irrational for a single person’s agency to be engaged along dual pathways. Even if we do not call this “trying,” the agent’s interactions with the salient options are not like those of a detached spectator; they are volitional as well as evaluative. [End Page 722]Lemos’s account recognizes three loci... (shrink)

The first chapter explores the theory developed in Kripke's "Outline of a Theory of Truth." A tension in Kripke's account of the concept of truth is revealed--a conflict between two intuitions. The first intuition, called the "fixed point conception of truth," is that the whole meaning of the truth predicate is given by the formula "we may assert of a sentence that it is true iff we may assert that sentence." The second intuition, called the "thesis of the (...) supervenience of semantics," is that the interpretation of the truth predicate is determined by the interpretations of all the other non-logical constants of the language. I show that these two intuitions cannot be reconciled within the context of Kripke's theory, and I argue for the choice of the fixed point conception of truth over the principle of the supervenience of semantics. Chief among the considerations that I advance is the fact that the fixed point conception of truth yields a natural logic of truth. In the second chapter I present that logic of truth in the form of a cut-free sequent calculus. I then turn, in chapter three, to a discussion of the significance of such cut-free sequent calculi. I argue that we may view the sequent calculus introduction rules for a logical constant as giving the meaning of that constant, under certain conditions. In particular, we can see our logic of truth as providing an explication of our intuitive concept of truth which complements Kripke's original model-theoretic explication. The fourth chapter takes up some criticisms of Kripke's theory which center on the logic of truth. In addition, the general ideas developed in the first three chapters are applied in a discussion of the various schemes of three-valued logic which can be used in the development of Kripke's approach. Finally, in the last chapter, it is shown that Kripke's technical concepts, and the logical ideas developed in the second and third chapters, can be used to provide a unified account of many contexts in which paradox arises. (shrink)

In this paper we study 12 four-valued logics arisen from Belnap's truth and/or knowledge four-valued lattices, with or without constants, by adding one or both or none of two new non-regular operations—classical negation and natural implication. We prove that the secondary connectives of the bilattice four-valued logic with bilattice constants are exactly the regular four-valued operations. Moreover, we prove that its expansion by any non-regular connective (such as, e.g., classical negation or natural implication) is strictly functionally (...) complete. Further, finding axiomatizations of the quasi varieties generated by the 12 logics involved (that prove to be varieties), we find naturell equational axiomatizations of these logics. Finally, applying Pynko's general theory of algebraizable sequential consequence operations, we also find equivalent natural sequentiell axiomatizations of the logics under consideration that expand either of two Pynko's sequential calculi for the constant-free truth-lattice four-valued logic. (shrink)

continent. 1.2 (2011): 78-91. This article consists of three parts. First, I will review the major themes of Quentin Meillassoux’s After Finitude . Since some of my readers will have read this book and others not, I will try to strike a balance between clear summary and fresh critique. Second, I discuss an unpublished book by Meillassoux unfamiliar to all readers of this article, except those scant few that may have gone digging in the microfilm archives of the École (...) normale supérieure. The book in question is Meillassoux’s revised doctoral dissertation L’Inexistence divine (or The Divine Inexistence ), with its seemingly bizarre vision of a God who does not yet exist but might exist in the future. Without literally accepting this view, I will claim that it is philosophically interesting in ways that even a hardened sceptic might be able to appreciate. Third and finally, I will speculate on the possible future of Meillassoux’s speculative materialism itself. And here I mean its future development not by Meillassoux, but by those readers who might be inspired by his book. Plato could never have predicted the emergence of Aristotle’s philosophy, despite the obvious debt of the latter to the former. Nor could Descartes have predicted Spinoza and Leibniz, nor Kant the German Idealists, and neither could Husserl in 1901 have foreseen the later emergence of Heidegger. How are the works of interesting philosophers transformed by later thinkers of comparable importance? While it may seem that there are countless ways to do this, I think there are only two basic ways in which this happens: you can radicalize your predecessors, or you can reverse them. I will close this article with a few words about these two methods, and try to imagine how Meillassoux might be radicalized or reversed by some future admirer. My view is that the more important thinkers are, the easier they are to radicalize or reverse. This helps explain why the great philosophers of the West have so often appeared in clusters, succeeding one another at relatively brief intervals during periods of especial ferment. 1. After Finitude After Finitude is unusually short for such an influential book of philosophy: running to just 178 pages in the original French, and an even more compact 128 pages in the English version, despite the introduction of roughly eight pages of new material for the English edition. Rather than summarizing Meillassoux’s book in the order he intended, I will focus on six points that strike me as the pillars of his debut book. Along the way, I will offer a few criticisms as well. The first pillar of the book is Meillassoux’s own term “correlationism.”1 Although he introduces this term as the name for an enemy, it is striking that Meillassoux remains impressed by correlationism much more than his fellow speculative realists are. This continued appreciation for his great enemy influences the shape of his own ontology. Is there a world outside our thinking of it, or does the world consist entirely in being thought? Traditionally, this dispute between realism and idealism has been dismissed in continental philosophy as a “pseudo-problem,” in a strategy pioneered by Husserl and extended by Heidegger. We cannot be realists, since following Kant we have no direct access to things-in-themselves. But neither are we idealists, since the human being is always already outside itself, aiming at objects in intentional experience, deeply engaged with practical implements, or stationed in some particular world-disclosing mood. The centuries-old dispute between realism and idealism is dissolved by saying that we cannot think either real or ideal in isolation from the other. There is neither human without world nor world without human, but only a primordial correlation or rapport between the two. This is what “correlationism” means: philosophy trapped in a permanent meditation on the human-world correlate, trying to find the best model of the correlate: is it language, intentionality, embodiment, or some other form of correlation between human and world? Among other problems, this generates some friction between philosophy and the literal meaning of science. When cosmologists say that the universe originated 13.5 billion years ago, they do not mean “13.5 billion years ago for us ,” but literally 13.5 billion years ago, well before conscious life existed, and thus at a time when there was no such thing as a correlate. Meillassoux also coins the term “ancestrality” (10) for the reality that predated the correlate, and later expands this term to “dia-chronicity,” (112) to refer to events occurring after the extinction of human beings no less than to those occurring before we existed. Up to this point, Meillassoux’s focus on ancestral entities existing prior to consciousness might seem like a straightforward realist who wants to unmask correlationism as just another form of idealism. Yet Meillassoux also admires the correlationist maneuver, which can obviously be traced back to Kant. Unlike a thinker such as Whitehead, Meillassoux feels no nostalgia for the pre-critical realism that came before Kant: “we cannot but be heirs of Kantianism,” he says (29). What impresses Meillassoux about correlationism is something both simple and familiar. If we attempt to think a tree outside thought, this is itself a thought . Any form of realism which thinks it can simply and directly address the world the way it is fails to escape the correlational circle, since the attempt to think something outside of thought is itself nothing other than a thought, and thereby collapses back into the very human-world correlate that it pretends to escape. For Meillassoux this step, suggested by Kant but first refined by the ensuing figures of German Idealism, marks decisive forward progress in the history of philosophy that must not be abolished. Any attempt to break free from the correlate must first acknowledge its mighty intellectual power. Realist though he may seem, Meillassoux’s works are filled with praise of such figures as Fichte and Hegel, not of so-called “naïve realists.” It is also the case that for Meillassoux, not all correlationisms are the same. The second pillar of his book is a distinction between various positions that I have termed “Meillassoux’s Spectrum,” though of course he is never so immodest as to name it after himself. He distinguishes between at least six different possible positions, and perhaps we could add even subtler variations if we wished. But in its simplest form, Meillassoux’s Spectrum allows for just four basic outlooks on the question of realism vs. anti-realism. Three of these are easy to understand, since we have already been discussing them. At one extreme is so-called “naïve realism,” which holds that a world exists outside the mind, and that we can know this world. Meillassoux rejects this naïve realism as having been overthrown by Kant’s critical philosophy. At the other extreme is subjective idealism, in which nothing exists outside the mind. For to think a dog outside thought immediately turns it into a thought, and therefore there cannot be anything outside; the very notion is meaningless. In between these two is what we have called correlationism. And here comes a crucial moment for Meillassoux, since he distinguishes between the two forms of “weak” and “strong” correlationism, and chooses the strong form as the launching pad for his own philosophy. Weak correlationism is easy to explain, since we all know it from the philosophy of Kant. The things-in-themselves can be thought but not known. They certainly must exist, since there cannot be appearances without something that appears. And we can think about them, which idealism holds to be impossible. They are simply unknowable due to the finitude of human thought. Strong correlationism is the new position introduced by Meillassoux (though he sees it at work in numerous twentieth century thinkers), midway between weak correlationism and subjective idealism. The major difference between the three positions is as follows. Weak correlationism says: “The things-in-themselves exist, but we cannot know them.” The subjective idealist says: “This is a contradiction in terms, since when we think the things-in-themselves, we already turn them into thoughts.” But the strong correlationist says: “Just because ‘things-in-themselves’ is a meaningless notion does not mean that they cannot exist. No one has ever traveled to the world-in-itself and come back to make a report on it. Thus, the fact that we cannot think things-in-themselves without contradiction does not prove that they do not exist anyway. There may be things-in-themselves, we simply are not capable of thinking them without contradiction form within the correlational circle.” This step is crucial for Meillassoux, since strong correlationism is the position he attempts to radicalize into his own new standpoint: speculative materialism. As I see it, this step of the argument fails. Strong correlationism cannot avoid collapsing into subjective idealism, since the statements of the strong correlationist are rendered meaningless from within. All three of the other positions in the Spectrum make perfectly good sense even for those who disagree with them. The naïve realist says that things-in-themselves exist and we can know them; the meaning of this statement is clear. The weak correlationist can say that things-in-themselves exist but lie forever beyond our grasp; this too makes perfect sense, even though the German Idealists try to show a contradiction at work here. We can also understand the claim of the subjective idealist that to think anything outside thought turns it into a thought, and that for this reason we cannot think the unthought. The strong correlationist, alone among the four, speaks nonsense . This person says “I cannot think the unthought without turning it into a thought, and yet the unthought might exist anyway.” But notice that the final phrase “the unthought might exist anyway” is fruitless for this purpose. For we have already heard that to think any unthought turns it into a thought. But now the strong correlationist wants to do two incompatible things simultaneously with this unthought. On the one hand, he neutralizes the unthought by showing that it instantly changes into just another thought. But on the other hand, he wants to appeal to the unthought as a haunting residue that might exist outside thought, thereby undercutting the absolute status of the human-world correlate found in idealism. But this is impossible. If you accept the argument that thinking the unthought turns it into a thought, you cannot also add “but maybe there is something outside that prevents this conversion from being absolutely true,” because this “something outside” is immediately converted into nothing but a thought for us. In short, Meillassoux here seems to be offering a kind of Zen koan: his “strong correlationism” is reminiscent of the gateless gate, or the sound of one hand clapping, or the command to punch Hegel in the jaw when meeting him on the road. We cannot at the same time both destroy the realist challenge of the things-in-themselves in order to undercut realism and reintroduce that very realist sense in order to undercut idealism. In a world where everything is instantly converted into thought, we cannot claim that there might be something extra-mental anyway, because this “might be something” is itself converted into a thought by the same rules that condemned dogs, trees, and houses to the idealist prison. This brings us to the third pillar of Meillassoux’s argument, which is the key to all the rest: the necessity of contingency. His strategy is to transform our supposed ignorance of things-in-themselves into an absolute knowledge that they exist without reason, and that the laws of nature can change at any time for no reason at all. In this way the cautious agnosticism of Kantian philosophies is avoided, but so is the collapse of reality into thought as found in German Idealism. Meillassoux does try to prove the existence of things-in-themselves existing outside thought; he simply holds that they must be proven after passing through the rigors of the correlationist challenge, not just arbitrarily decreed to exist in the manner of naïve realism. As he puts it, “Everything could actually collapse: from trees to stars, from stars to laws, from physical laws to logical laws; and this not by virtue of some superior law whereby everything is destined to perish, but by virtue of the absence of any superior law capable of preserving anything, no matter what, from perishing” (53). If idealism thinks that the human-world correlate is absolute, for Meillassoux it is the facticity of the correlate that is absolute. He tries to show this with a nice brief dialogue between five separate characters (55-59) which is covered in detail in my forthcoming book,2 but which I will simplify here for reasons of time. In this simplified version, we first imagine a dogmatic realist arguing with a dogmatic idealist. The realist says that we can know the truth about the things-in-themselves; the idealist counters that we can only the truth about thought, since all statements about reality must be turned into statements concerning our thoughts about reality. Here the correlationist enters and proclaims that both of these positions are equally dogmatic. For although we have access to nothing but thoughts, we cannot be sure that these thoughts are all that exist; there could be a reality outside thought, there is simply no way to know for sure. And this latter position is the one that Meillassoux attempts to transform from an agnostic, skeptical point into an ontological claim about the contingency of everything. Consider it this way. How does the correlationist defeat the idealist? The idealist holds that the existence of anything outside thought is impossible. The correlationist, by contrast, holds that something might exist outside the human-world correlate. But this “something might” has to be an absolute possibility. It cannot mean that “something outside thought might exist for thought ,” because that is what the idealist already says. No, the correlationist must mean that something might exist outside thought quite independently of thought. In other words, the correlationist says that idealism might be wrong, and this means it is absolutely true that idealism might be wrong. Thus, correlationism is no longer just a skeptical position. It holds that all the possibilities of the world are absolute possibilities. We have absolute knowledge that any of the possibilities about the existence or non-existence of things-in-themselves might be true, and this means that correlationism flips into Meillassoux’s own position: speculative materialism. As Meillassoux sees it, there are only two options here. Option A is to absolutize the human-world correlate, which is what the idealist does: there absolutely cannot be anything outside thought. Option B, by contrast, is to absolutize the facticity of the correlate: its character of simply being given to us, without any inherent necessity. The correlationist cannot have it both ways by saying: “there absolutely might be something outside thought, yet maybe this is absolutely impossible.” In other words, once we escape dogmatism we can only be idealists or speculative materialists, not correlationists. The human-world correlate is merely a fact, not an absolute necessity. But this facticity itself cannot be merely factical: it must be absolute. Here Meillassoux coins the French neologism factualité , which has been suitably translated into the English neologism “factiality.” (7, 122-3) Factialty means that for everything that exists, it is absolutely possible that it might be otherwise, not just that we cannot know whether or not it might be otherwise. Just as Kant transformed philosophy into a meditation on the categories governing human finitude, Meillassoux wishes to turn philosophy into a meditation on the necessary conditions of factiality, which he calls “figures”—a new technical term for him. (80) One such figure is that the law of non-contradiction must be true, and for an unusual reason. Since everything is proven to be contingent, nothing that exists can be contradictory, for whatever is contradictory has no opposite into which it might be transformed, and thus contingency would be impossible.3 Another such figure is that there must be something rather than nothing: for since contingency exists, something must exist in order to be contingent. It is a daring high-wire act, one that sacrifices realism to the correlational circle in order to rebuild it from out of its own ashes. Some might conclude that the lack of reason in things is a byproduct of the ignorance of finite humans, Meillassoux is making precisely the opposite point. For in fact, the doctrine of finitude usually leads directly to belief in a hidden reason. The fact that it lies beyond human comprehension merely increases our belief in this arbitrarily chosen concealed ground. By defending anew the concept of absolute knowledge Meillassoux evacuates the world of everything hidden. The reason for things having no reason is not that the reason is hidden, but that no reason exists. Thus, even while insisting on the necessity of non-contradiction, he rejects the other Leibnizian principle: sufficient reason. Everything simply is what it is, in purely immanent form, without deeply hidden causes. Or as Meillassoux puts it: “There is nothing beneath or beyond the manifest gratuitousness of the given—nothing but the limitless and lawless power of its destruction, emergence, or persistence” (63).The world is a “hyper-chaos”(64). But this is not the same thing as flux. For the chaos of the world is such that stability might occur just as easily as constant, turbulent change. Let’s now digress a bit, and return to the question of ancestrality, which Meillassoux transforms later in the book into “dia-chronicity.” Correlationism holds that all talk of a world outside the correlate is immediately recuperated by the correlate. The phrase “13.5 billion years ago” becomes “13.5 billion years ago for us ,” and the phrase “the universe following the extinction of humans” becomes “the universe following the extinction of humans for humans .” But notice that whether we talk about the world before or after humans, in both cases it is time that is used to challenge the correlate. Meillassoux has no interest in challenges that might be posed by space. For example, what about a vase in a lonely country house that topples to the floor and smashes when no one is there to watch it? Isn’t this also a challenge to correlationism, no less than the Big Bang or the heat death of the universe long after humans have vanished? In an eight-page supplement to the English translation of After Finitude ,4 possibly in response to my own 2007 review of the French original,5 Meillassoux bluntly denies that space is of any relevance to the question. Spatial distance is a merely harmless challenge to the human-world correlate. After all, even though no one is there in the lonely country house to witness the shattering of the vase, we can say that had there been an observer , that observer would have witnessed the toppling and destruction of the vase. For this event still occurs in a world in which the human-world correlate already exists, whereas the diachronicity of events both before and after the existence of humans makes it impossible to say that had there been an observer they would have witnessed the Big Bang occurring in such and such a fashion. However, it seems to me that Meillassoux merely asserts that the temporal simultaneity of our existence with that of the vase in the lonely country house is enough to render it harmless. It is true that the house does not exist prior to the correlate, but nonetheless it exists outside the correlate, and that is enough to make the same challenge. It is difficult to see why the “had there been an observer” maneuver succeeds in the case of a vase in the countryside in April 2011 but fails in the case of the Big Bang. This is not just a matter of nitpicking Meillassoux’s argumentative style: the fact that he bases his argument on time has at least two important consequences for his position. For in the first place, even though Meillassoux insists that the laws of nature are absolutely contingent, this turns out to be true only in a temporal sense. That is to say, it is a paradoxical feature of Meillassoux’s philosophy that he does allow for the existence of laws of nature, and simply believes that they can change at any moment without reason. Within any given moment, laws of nature do exist. He never suggests that different parts of the universe can have different laws at the same time, nor does he have any interest in the laws of part/whole composition that take place within any given instant. Could it be the case that rather than being made of gold atoms, a small chunk of gold could be made of silver atoms, cotton, horses, or that this same small piece of gold could be made of gigantic vaults filled with even more gold? These are not topics that draw Meillassoux’s attention, since he is focused solely on how the laws of nature might change or endure from one moment to the next . Another implication for Meillassoux’s system is that his concept of things-in-themselves turns out to be to be inadequate. For when he proves that things-in-themselves can exist without humans, this turns out to be true only in a temporal sense as well. Namely, things-in-themselves existed ten billion years ago, and they will continue to exist after all humans have succeeded in exterminating themselves. However, being able to exist before our births and after our deaths is just one small part of what it means to be a thing-in-itself. The more important part is that even if a thing is sitting on a table right now, in front of me, even if I stroke it lovingly or press my face up against it directly, I am still dealing only with a phenomenal version of the thing; the thing-in-itself continues to withdraw from all access. Yet no such thing is acknowledged by Meillassoux. For him finitude is a disaster, and absolute knowledge is in fact possible. Meillassoux’s thing-in-itself exists in independence only of the human lifespan , not of human knowledge. The fifth pillar of Meillassoux’s argument is his use of Cantor’s transfinite mathematics to show that even if the laws of nature are contingent, they need not be unstable, and thus we cannot use the apparent stability of nature to disprove his metaphysics of absolute contingency. What Cantor showed is that there are different sizes of infinity, and that all these infinities cannot be totalized in a single infinite number of infinities. Meillassoux sees this as crucial, since it allows him to discredit any “probabilistic” argument against his theory. The probabilistic argument (as defended quite clearly by Jean-René Vernes)6 would say this: given that the laws of nature seem so stable, it it is extremely improbable that there is no hidden reason for their remaining so stable. As Meillassoux sees it, probability is of value only when we can index an accessible total of cases. These can even be infinite: for example, there are an infinite number of points where a rope can break when stretched tight, but this does not stop us from calculating probabilities for various sections of the rope to break. By contrast, there is no way to sum up the number of possible laws of nature. For here there is no way to totalize; we cannot stand outside of nature and calculate the possible number of laws so as to determine the probabilities that any one of them might change. Therefore, although we can speak of probability when dealing with intraworldly events such as elections, horse races, and coin-flips, we cannot use the words “probable” or “improbable” when describing alterations at the level of nature as a whole. Rather than commenting on the validity of this argument and its use of Cantor, let me simply note that it once again creates a dualistic ontology. We already saw that Meillassoux treats time differently from space. In analogous fashion, he now treats the level of world differently from that of intraworldly events. The emergence of worlds is purely contingent and virtual and governed by no probability at all, while events within the world necessarily follow laws (even if these laws can change at any moment without reason), and thus their probabilities can be calculated. It is a strategy deeply reminiscent of Badiou’s (2005) own dualism between the normal “state of the situation” and the rare and intermittent “event.” The sixth and final pillar of Meillassoux’s book can be dealt with briefly, since we have already touched on it elsewhere. It comes at the very beginning of the book, when Meillassoux says that we must revive the distinction between primary and secondary qualities, and that the primary qualities are the ones that can be mathematized. He admits that he has not yet published a proof of this idea, though in fact it is already known as one of his primary doctrines. And here we encounter the familiar problem with Meillassoux’s inadequate conception of things-in-themselves. “Primary qualities” refers to those qualities that a thing has independently of its relations with us or anything else. But if the primary qualities can be mathematized, this means that they are not entirely independent of us, since our knowledge can get right to the bottom of them. The mathematized qualities of things are independent of us only in Meillassoux’s sense that they will still have those qualities even when all humans are dead. But to repeat, autonomy from the human lifespan is not the same as autonomy from human access. Here once more Meillassoux is concerned only with independence from the human-world correlate across time, not in any given instant. 2. L’Inexistence divine In 1997, the same year in which he turned thirty years old, Meillassoux earned his doctorate at the École normale supériuere with a brazen dissertation entitled L’Inexistence divine ( The Divine Inexistence ). The work was substantially revised in 2003. But even then, with typical fastidiousness, Meillassoux decided that the work was not yet ready for press. It has now been scrapped in favor of some future, multi-volume work bearing the same title. While writing my book on Meillassoux for Edinburgh University Press, I was permitted to translate excerpts from this unpublished work for use as an appendix in my own book; in total, the appendix contains approximately twenty percent of Meillassoux’s 2003 manuscript, the first time any of it will be published in any language. Nonetheless, a portion of the argument was already tested in the article “Spectral Dilemma,” published in English in the journal Collapse (2008: 261-75). There the philosophical motives for the virtual God are already made clear. What troubles us most are early deaths, brutal deaths, deaths of especial injustice– the sorts of deaths in which the brutal twentieth century was so abundant. And here, neither the atheist nor the believer can help us. The atheist can offer nothing but a sad and cynical resignation when reflecting on the victims of these terrible crimes. The believer does little better, being unable to explain how God could have allowed such things to happen, due to the famous intractability of the problem of evil. The solution offered to this dilemma by Meillassoux is bold, and all the more so given that he emerges from such a deeply Leftist, materialist, and unreligious background. His solution is that God does not yet exist, and therefore is not blameworthy for these catastrophes. Given that everything is contingent in Meillassoux’s philosophy, this God and divine justice might never exist, but they can at least exist as an object of hope. Let’s begin by jumping to the end of L’Inexistence divine , where the alternatives are laid out so nicely. There are four basic attitudes that humans can have towards God, Meillassoux says. First, we can believe in God because he exists. This is the classical theist attitude, rejected for the simple reason that it would be amoral and blasphemous to believe in a God who allows children to be eaten by dogs, to use Dostoevsky’s example. Second, we can disbelieve in God because he does not exist: the classical atheist attitude. But this leads to sadness, cynicism, and a sneering contempt for the greatness of human capacity. The third option, rather more complex, is to disbelieve in God because he does exist: in other words, to exist in rebellion against God as the one who must be blamed for the evils of the earth. The examples here might range from Lucifer himself, to the more human figure of Captain Ahab in Melville’s Moby-Dick , to Werner Herzog’s even more recent catchphrase, “Every man for himself, and God against all.” That leaves only the fourth option: believing in God because he does not exist. Meillassoux closes his book by saying that the fourth option has now been tried (namely, in the course of his own book), and that now that all four have been specified, we must choose. The first reaction to this theory of the inexistent God will be laughter. Few readers will ever be literally convinced by it, and probably none will immediately be convinced by it. But if we ask ourselves why we laugh, the answer is because it sounds so improbable that an inexistent God might suddenly emerge and resurrect the dead. It obviously sounds more like a gullible theology than a rigorous piece of philosophical work. Yet two things need to be kept in mind. First, Meillassoux’s theories are hardly more unlikely than those of great philosophers of the past such as Plato, Plotinus, Avicenna, Malebranche, Spinoza, Leibniz, Nietzsche, or Whitehead. We read the great philosophers not because their systems are plausible in commonsense terms that can be measured by the laws of probability. Instead, we read them precisely because they shatter the existing framework of common sense and open up new window on the universe. Second, and even more importantly, Meillassoux has already rejected probability as a valid measuring stick in philosophy. Or rather, he accepts probability in the intra-worldly realm (where it is linked with potentiality), and rejects it at the level of the world itself (where potentiality is replaced with what he calls virtuality). The virtual God can appear at any moment for no reason at all, just as any other new configuration of laws of nature can appear: in a manner that the laws of probability cannot calculate. Responding to those who might ridicule the idea of a sudden emergence of God and a resurrection of the dead, Meillassoux cites Pascal, who asserts that the resurrection of the dead would be far less incredible than the fact that we were born in the first place. This shifts philosophy onto new ground. Rather than concerning ourselves with what is likely to happen in the world as we know it, we focus instead on the most important things that could happen. For this reason, the expected objection that a virtual God is no more likely to appear than a virtual unicorn or a virtual flying spaghetti monster misses the point. Unicorns and spaghetti monsters could also appear, just like any other non-contradictory thing. But these would just be novel bizarre entities among others, not the heralds of completely new worlds. For Meillassoux, the emergence of matter, life, and thought have been the three truly amazing advents of the world so far, each of them dependent on the advent(s) preceding them. As he sees it, there can be no greater intraworldly entity than the human beings who already exist, since nothing in the world is better than the absolute knowledge of which humans alone are capable. This means that the next great advent must be something that perfects human beings rather than superseding them. And this can only be the world of justice, in which the dead are resurrected and their horrible deaths partially cancelled (Meillassoux never considers the possibility of a God who would literally erase the pre-divine past so that it never happened at all). The only immortality worth having is an immortality of this life, not an existence in some ill-defined afterworld. Human existence, he holds, must always be governed by a “symbol” that gives us the “immanent and comprehensible inscription of values in a world.” And just as cosmic history made the three great contingent leaps of matter, life, and thought, with a leap to justice as the only one still to come, a similar structure occurs within human culture and its symbols, which consist so far of the cosmological, naturalistic, and historical symbols, with a “factial” symbol still to come. We can review each of these symbols briefly. The cosmological symbol refers to the ancient dualism between the terrestrial and celestial spheres. Here below everything is conflict, corruption, and decay; but in the heavens nothing is perishable, all movement is circular, and everything is arranged in mutual harmony. This symbol is ended by modern physics when Galileo discovers such blemishes as sunspots and craters on the moon, and when Newton integrates both celestial and terrestrial movement into a single gravitational law. Next comes the naturalistic or romantic symbol, in which perfection comes not from the sky but from nature itself. The world is filled with pretty flowers (Meillassoux claims that the ancients never discussed the beauty of flowers until Plotinus in the third century) and with living creatures naturally moved by pity, at least until society corrupts them. This symbol collapses in the face of reality as we know it, since pity is no more common than war, corruption, and violence. This brings us to the historical symbol, which only now is passing away. Bad things may happen, but history has an inner logic of its own, such that everything works out in the end. The ultimate form of the historical symbol is the economic symbol, whether in a Marxist or neo-liberal form. Just as the Marxist holds that the inner economic logic of the capitalists will inexorably lead them to self-destruction, the neo-liberal assumes that the sum total of individual selfish actions will lead, in the long run, to the greatest possible good. We worship the economy and let it guide history for us, just as the ancients worshipped celestial bodies and held them to be free from blemish. The final remaining symbol is the factial symbol, which Meillassoux hopes will now emerge. Factiality, we recall, is his term for the absolute contingency of everything that exists. Once we have grasped this absolute contingency, we are free to expect the dramatic advent of the coming fourth World: the world of justice, inaugurated by a virtual God and even mediated by a messianic human figure. There is the added feature, however, that this messiah must abandon all claims to special status once the messianic realm of justice is achieved. The messianic figure will then be no more special than any person on the street, since a reign of human equality will have arisen. Although this focus on human being might seem like a return to standard humanism, Meillassoux holds that human pre-eminence has never truly been maintained. Previously, humans have been treated as special only because they contemplate the Good, because they resemble their omnipotent creator, or because they happen to be the temporary victors in a cruel Darwinian death-match between millions of living species. For Meillassoux, by contrast, humans have value because they know the eternal. But it is not the eternal that is important, since this merely represents the blind, anonymous contingency of each thing. What is important is not knowledge of the eternal , but knowledge of the eternal. We should not admire Prometheus for stealing fire from the gods; Prometheus is simply as bad as all the gods, no matter how much he increased our power. Feuerbach and Marx were wrong to say that God is a projection of the human essence, since for Meillassoux the usual concept of God represents the degradation of the human essence. If the traditional God was allowed to inflict plagues and tsunamis on the human race, the Promethean human of the twentieth century simply assumes the right to inflict death camps and atomic fireballs instead. In this respect, we have simply begun to imitate the degradation of humanity that was formerly invested in an omnipotent and arbitrary God. In response to charges that absolute contingency might lead to political quietism, Meillassoux counters that the World of justice would mean nothing unless we had already hoped for it beforehand. A World of justice that came along at random would merely be an improved third World of thought: indeed, a perfect one. But it would have satisfied no craving, and would therefore have no redemptive power. For this reason, we must actively hope for the fourth World of justice for such a fourth World ever to arise. Not only justice, but beauty is dependent on such hope: for Meillassoux, who is here somewhat dependent on Kant, beauty means an accord between our human symbolization and the actual world, which could never be present in a World of the blessed any more than justice could. And just as a messianic figure is needed to incarnate our hope and then abandon power once the World of justice is realized, it is the figure of the child whose fragile contingency shows us a dignity and a demand for justice beyond all power. 3. Meillassoux Radicalized or Reversed Given the promising reception of Meillassoux’s first book, it would not be groundless to engage in early speculation about what it might take to earn him a place in the history of philosophy. Maybe this will never happen—who knows?—but quite possibly it will: his lucid argumentative methods and sheer philosophical imagination at least make him a good candidate to be read well into the future, especially following further elaboration in print of his mature system. Philosophy is often practiced as thought it were nothing more than the amassing of “knockdown arguments.” But this is no more insightful than saying that good architecture is the amassing of steal beams. It is true that poorly constructed building cannot stand for long, but sound construction is merely the first, indispensable step in building. In fact, I am inclined to say that what really makes a philosopher important is not being right, but being wrong . I mean this in a very specific sense. I once heard the interesting remark about twentieth century culture that “you have to remember that the sixties really happened in the seventies.” That is to say, it was in the 1970’s rather than the more honored 1960’s that civil rights, free love, long hair, and the rock and roll drug culture really took root. With respect to the history of philosophy, we might just as easily say: “you have to remember that Plato really happened in Aristotle,” that “Kant really happened in Hegel” or “Hume really happened in Kant,” or that “Husserl’s phenomenology first achieved its truth in Heidegger.” One becomes an important philosopher not by being right, but by attracting rebellious admirers who tell you that you are wrong , even as their own careers silently orbit around your own. To recruit faithful disciples may be comforting and flattering, but the greatest thinkers have generally had to experience refutation at the hands of their most talented heirs. For this reason, I would propose that we size up the magnitude of living thinkers not by deciding how many times they are right and wrong, but by asking instead: who would take the trouble to refute this author? For this reason I do not ask: “Is Meillassoux right?”, since I do not believe in the virtual God myself, nor am I convinced by any important aspect of Meillassoux’s philosophy. Instead, I ask if there are interesting ways to overturn him. Only by being overturned, by no longer remaining a contemporary, does one become a classic. Let’s begin with a simple model of refutation, which can be refined further at a later date once the basic point is established. One kind of refutation simply consists in saying: “This author is a complete idiot.” The refuter now walks away in celebration, and no link between the present and the future is built; all is reduced to rubble. But this sort of mediocre triumphalism is generally practiced by those who achieve little of their own, and is not especially interesting. Much more interesting is the sort of refutation that does not take its target to be a complete idiot. I would like to suggest that there are just two basic ways in which this can be done: radicalization and reversal . It has not escaped my notice that this is a fairly good match for the Deleuzian distinction between irony and humor. Whereas irony critiques and adopts the opposite principle of what it attacks, humor accepts what it confronts but pushes it into highly exaggerated form. The ironist is like the worker who sows chaos by rebeling and contradicting the boss, while the humorist is like the worker who follows orders to an absurdly literal degree, with equally chaotic results. Let’s start with a few examples. In Aristotle’s treatment of Plato, and Heidegger’s of Husserl, we find reversal. Plato’s eidei are transformed by Aristotle into mere secondary substances, and the individual worldly things despised by Plato become what is primary. For Husserl what is primary is whatever is present to consciousness, while for Heidegger this is precisely what is secondary, since the primary stuff of the world withdraws from any form of presence at all. As for radicalization, it is most easily found in the transformation of Kant by German Idealism: “Kant was right to wall off the things-in-themselves from human access, and simply should have realized that the thought of the Ding an sich is also a thought, and thereby the noumena are just special cases of the phenomena,” with much following from this discovery. It would also be easy to read Spinoza as a radicalizer of Descartes, and Berkeley and Hume as radicalized versions of Locke. Perhaps the distinction is now sufficiently clear. Admiring refutations are not those that say “Professor X is an idiot,” which is merely the flip side of the eager disciple’s fruitless “Professor X got everything right.” Instead, it will be some variant of one of the following two options: “Professor X is important, but got it backwards,” or “Professor X is important, but didn’t push things far enough.” In the history of philosophy these two latter cases have often been painful in purely human terms: Aristotle expresses sadness at refuting Plato, Kant is openly annoyed at Fichte, and Husserl feels betrayed and used by Heidegger. Rude handling from later figures almost seems to be the sine qua non of being a great philosopher. Now, it has already been claimed that Meillassoux is an emerging philosopher of the first importance, and by no less a figure than Alain Badiou: “It would be no exaggeration to say that Quentin Meillassoux has opened up a new path in the history of philosophy…” (Preface, vii). But rather than taking Badiou’s word for it, or rejecting his word, we might experiment by asking how Meillassoux could be radicalized or reversed. Are there interesting ways of doing this that might launch whole new schools of philosophy, unexpected or even condemned by Meillassoux himself? While no one can see the future, the present is poor when it is not riddled with virtual futures. The relation between philosophers and their predecessors and successors is always somewhat complicated, of course. But generally there is one central divergence at stake, which might be taken as the key to all the others. On this basis we could say that new thinkers primarily radicalize or primarily reverse the main ideas of their chief philosophical forerunner. There may be specific historical conditions and perhaps even personality traits connected with these two types, but this question can be left aside for now. More important for us is that radicalizers will generally be followed by reversers, and vice versa. Consider the textbook example of a reversal in the history of philosophy: Kant’s Copernican Revolution, which inverts the so-called dogmatic tradition that addresses the world itself, and makes the world revolve instead around the conditions by which it is known. While it is not completely impossible that Kant’s successors might have re-reversed this principle back into a new and stronger dogmatic realism, conditions were premature for such a move. Anyone doing this too early would likely have been an angry anti-Kantian reactionary rather than an original thinker in command of a genuinely new realist principle. The far more likely outcome is the one that actually happened: Kant’s reversal of his predecessors was viewed as incomplete, or as retaining lamentable bits of the traditional view, which despite his admirable breakthrough he was unable to shake off. This was the view of German Idealism, anyway. In similar fashion, Spinoza could also be viewed as a radicalizer of Descartes, who is equally accused of preserving various Scholastic dogmas in an otherwise radical project of philosophical reversal. The point is this: reversals in the history of thought tend to be followed soon thereafter by radicalizations of those reversals. The same may hold true in reverse: radicalizations might generally be followed by reversals, given that it is not always possible to be more radical than the radicals have already been. Consider the case of Husserl, who radicalizes Brentano’s early vagueness about what lies beyond immanent objectivity, and Twardowski’s assertion that there must be an external object lying outside the intentional content, by collapsing everything into the intentional sphere: there is no difference between the Berlin in my consciousness and the actual Berlin that is home to millions of people. It is difficult to see how one could be even more radical than Husserl’s idealist turn here. And thus the road is paved to Heidegger’s reversal of classical phenomenology, in which the key point is what lies deeper than any presence to consciousness: the Sein whose power and obscurity cannot be made exhaustively present, but only sends itself in historical epochs. In similar fashion we might also read Leibniz as a reverser of Spinoza’s radicalization, retrieving a strong sense of individual substance and a certain validity of what the Scholastics had said. Returning to Meillassoux, we might ask which kind of philosopher he is: a radicalizer or a reverser? At present, Meillassoux looks to me like a radicalizer (though for now his future remains shrouded in mist). He takes the correlationist tradition, which allows us to speak only of the relation between human and world, and tries to raise it into an even more extreme claim about the absolute contingency of everything. But whereas German Idealism did this by trying to collapse the distinction between thought and world entirely into the “thought” side, Meillassoux does it by trying to shift the non-absolute contingency of the thought-world correlate from epistemology to ontology. It is no longer a question of the inability of human knowledge to know what lies outside the correlate, but the inability of reality itself to be rooted in any definite laws. Furthermore, if we look at the various features of Meillassoux’s philosophy identified earlier tonight, all but one are already so radical that there is no obvious way to push them further. The one exception would be his claim that the world as a whole can change for no reason at any moment, coupled with the inconsistent claim that within a given world there are laws of nature that everything must follow. If gravitational attraction between all masses is a current law in our world, then for Meillassoux there can be no exceptions to this law for as long as it remains in force. A toppled vase will fall to the floor every time for sure,unless there is a cosmic change by which the laws of nature as a whole have altered. (This is reminiscent of the late medieval distinction between the absolute and ordained power of God, according to which God has the power to set or change the laws of nature, but not to contravene those laws locally once they are set.) On this point, to radicalize Meillassoux would simply be to say: there are no laws of nature even in the local sense. Everything that happens, even in the world here and now, is purely contingent and not governed by even a trace of law. And while this would be a more consistent development of Meillassoux’s thoughts on contingency, it is difficult to see how it could lead to a new philosophy. Instead, the admiring successors of Meillassoux are more likely to reverse one of his already sufficiently radical points. At least four candidates come to mind: *First, we have seen that Meillassoux thinks correlationism is challenged by a time before or after consciousness, but not by a space lying outside it. Perhaps this could be reversed into saying that spatial exteriority is the really crucial point. The arguments on this point are perhaps the least convincing in After Finitude (and do not even occur in the original French edition), and therefore it might be a candidate for the “blind spot” of which no philosopher is ever free. *Second, Meillassoux uses Cantor to claim that the contingency of laws of nature would not entail that they are unstable. A successor of Meillassoux might claim that it does make them unstable, and celebrate this fact. This person would then have to explain why common sense seems to encounter a relatively stable world despite its truly rampant instability. Whereas Meillassoux’s problem is to show how stability might exist despite contingency, this successor’s problem would be slightly different: to show why actual, full-blown instability might have the appearance of stability. *Third, Meillassoux claims that the primary qualities of things are those that can be mathematized. He might be reversed by a successor who says the opposite: the mathematizable qualities are the secondary ones, and the primary ones are those that elude symbolic formulation. While this is a perfectly valid possible objection to Meillassoux, it is one that is made in advance by some of his predecessors and is still made by some of his peers, making it less interesting for futurology than some of his other points. *Fourth and finally, whereas Meillassoux claims that God does not exist but might exist in the future, a successor might argue even more bizarrely that God has always existed but might vanish in the future. Let’s arbitrarily select the first of these possibilities, and imagine briefly where it might lead, if pursued in the future by admiring detractors. Meillassoux comes from the circle of Badiou, and some of Badiou’s most ardent admirers are found in Latin America. So, let’s imagine that towards mid-century some ingenious reversers of Meillassoux emerge in that portion of the Spanish-speaking world. Just for fun, let’s call them Castro and Chávez. And in order to avoid any confusion with the present-day politicians of those names, we will stipulate that Meillassoux’s great successors are both women. The philosopher Castro (we will suppose she comes from Peru) reverses Meillassoux’s argument that the ancestral or diachronic are what most threaten the human-world correlate. Instead, she claims that the diachronic does not threaten the correlate at all, and that we must instead look at space as what ruins the correlate and demands a strange new realism. What would such a philosophy look like? In order to determine this, we might ask what price Meillassoux pays for doing it the opposite way. As I see it, he pays in two separate ways. One is that laws of nature for him are contingent over time . The laws of nature apply to the universe as a whole at any given moment, and would be changed globally if they are ever changed at all. The second price he pays is that Meillassoux has no mereology , or theory of parts and wholes. Everything for him is on the level of the given, or immanent in experience, with the sole proviso that the laws governing this immanence might change without notice at any given moment. In reversing Meillassoux, Castro makes the following claims in the preface to her stunning debut book of 2045, The Cosmos and its Neighborhoods , rapidly translated from Spanish into all the languages of the world: Despite his brilliant analysis of the contingency of laws of nature over time, Meillassoux gets two important assumptions wrong. First, he allows for only one set of contingent laws to govern nature as a whole. Second, he allows laws to govern only the world that is immanent in experience, and thereby fails to explore the contingency among part-whole relations. In this book I will argue, first, that the laws of nature vary in any given instant between one region of the universe and the next; and second, that the world is made up of layers of parts and wholes that are also contingent with respect to one another. Those are the words of Castro. This may sound like a hopeless free-for-all of chaos, yet the book somehow succeeds in drawing some compelling deductions about how laws must vary from one place or level in the world to the next. Trapped in the limited horizon of 2011, and not yet inspired by the heavily balkanized political and technological situation of 2050 that somehow lends additional credence to Castro’s vision, we can only vaguely grasp what such a philosophy might look like. After this reversal of Meillassoux by Castro, the usual pattern leads us to expect a radicalization by Chávez, a young Argentine student of Castro. How could the already strange theories of Castro be radicalized? Perhaps as follows, in a disturbing new book entitled The Implosion of the Neighborhoods , which argues as follows: Castro was right to shift the Meillassouxian framework of contingency from time to space. However, in this respect she retained a surprisingly traditional opposition between the two. In this book I will show that time and space collapse into one another. This may sound too much like the discredited four-dimensional block universe of twentieth century physics and philosophy. However, the four-dimensional universe is a model biased in favor of space, merely adding an extra dimension to the commonsense spatial continuum while stipulating that the serial passage of time is an illusion. In this book I will argue instead for a one-dimensional space-time modeled after our experience of time, in which there is no simultaneous co-existence at all between different parts of the universe, or ‘neighborhoods’ as my esteemed teacher Castro has called them. Instead, the various portions of the universe link to one another by succession rather than by coexistence. Buenos Aires, New York, and Amsterdam do not exist simultaneously in the same landscape, but one after the other in the mind of some observer, and this observer can only be an observer much larger than any human. Against Meillassoux’s notion of a virtual God that does not exist now but might exist in the future, I will argue for an actual God that surveys the universe in sequence, thereby generating the illusion of spatial diversity and even the illusion of individual minds located within that diversity. Once this divine observer dies, the universe as a whole must perish. Again, these ideas are so bizarre that we of 2011 can barely comprehend them, just as Aristotle would have had a difficult time grasping the theories of Descartes. We could then perhaps imagine a further reversal of this theory, emanating from the intellectually resurgent Philippines of the twenty-second century. The Filipino School might argue that the universe is already dead, given the collapse of its spatial richness into the serial observations of a flimsy and mortal God. The virtual universe does not yet exist, but might exist in fully spatial form in the future, and this would require the death of God and the resulting liberation of God’s succession of images as independent, spatially situated realities. With a bit of sharpening, we might be able to make all of these imaginary thinkers more intuitively clear. Along with the history of philosophy, there might arise a new discipline generating imaginary futures for philosophy. The richness of Meillassoux’s system comes not from the fact that he is plausibly right about so many things, but because his philosophy offers such a treasury of bold statements ripe for being radicalized or reversed. He is a rich target for many still-unborn intellectual heirs, and this is what gives him the chance to be an important figure. NOTES 1. Quentin Meillassoux, After Finitude . Trans. R Brassier. (London: Continuum, 2008.) Page 5. The word “correlationism” does not appear in his doctoral thesis. As Meillassoux informed me in an email of February 8, 2011, he first coined this term in 2003 or 2004, while editing for publication a lecture he had given at the École normale supérieure on a day devoted to the theme of “Philosophy and Mathematics,” an event including Alain Badiou as one of the participants. 2. Graham Harman, Quentin Meillassoux: Philosophy in the Making . (Edinburgh: Edinburgh University Press, forthcoming 2011). 3. In an email of December 6, 2010, Meillassoux clarifies that in After Finitude he only deduces the impossibility of a “universal contradiction,” not of a determinate contradiction. In the same email he suggests that he can also prove the latter, though the proof is somewhat lengthier than the one found in After Finitude . 4. After Finitude (18-26), in the passage falling between the two sets of triple asterisks. These pages were sent by Meillassoux to translator Ray Brassier (in French) during the translation process, and do not appear in the original French version of the book. 5. Graham Harman, “Quentin Meillassoux: A New French Philosopher.” Philosophy Today 51.1 (2007): Pages 104-117. The passage where I raise the question of space can be found in the first column of page 107. 6. Vernes is first cited on p. 95 of After Finitude . See Jean-René Vernes, Critique de la raison aléatoire, ou Descartes contra Kant . (Paris: Aubier, 1982).  . (shrink)

Normality Does Not Equal Mental Health: The Need to Look Elsewhere for Standards of Good Mental Health is the first book to question the equation of psychological normality and mental health. It is also the first book to take contemporary psychiatry and clinical psychology to task for deeply flawed thinking when they accept the diagnostic system propounded by the DSM, which reifies syndromes into alleged “mental disorders.” Where Thomas Szasz argued that “mental disorders” are myths, Bartlett makes the much more (...) damaging charge that reifying mental disorders involves a provable form of fallacious thinking, producing a variety of epistemological nonsense. /// -/- -/- The author weighs the evidence, and with strict logic, compelling evidence, and careful analysis, challenges the current paradigm of mental health theorists and practitioners. Never has the case against the standard of psychological normality and against the non-scientific creation of “mental disorders” been made with such boldness, multidisciplinary knowledge, solid scholarship, and clarity of language. /// -/- -/- Normality Does Not Equal Mental HealthAlthough the need to question psychological normality as a satisfactory standard of good mental health has been staring us in the face for a long time, no one, clinical professional or scholar, has had the courage or the intellectual willingness to face with unflinching honesty the shortcomings and disappointments of psychological normality and to propose that we should look elsewhere for standards of good psychological health. /// -/- -/- Contemporary psychiatry and clinical psychology, on the contrary, base their conception of mental health on the standard of psychological normality. This supposition has come to be accepted uncritically and without question, and yet it has become fundamental to current clinical theory and practice, and forms the core of the psychiatric classification system of the DSM, which has become today’s diagnostic authority. /// -/- -/- While touting today’s scientific gold standard of “evidence-based” research, DSM’s authoritative classification of “mental disorders” is itself hardly “evidence-based,” for it is recognized, but seldom emphasized, that the majority of DSM’s “mental disorders” have no known empirical, organic basis. /// -/- -/- Normality Does Not Equal Mental Health takes DSM to task not only for its failure to adhere to today’s evidence-based standard, but for its failure to rein in its highly speculative diagnostic labeling, in accordance with the modern paradigm of rigorous science, which repudiates metaphorical reifications whose alleged validity rests only on the voting preferences of a professional membership. /// -/- -/- The book is a carefully argued critique of the dominant assumption in current psychiatry and clinical psychology that psychological normality is fundamental to mental health and therefore good. In place of this unsatisfactory presumption, Normality Does Not Equal Mental Health proposes a positive and constructive revision in our understanding of mental health and of our conception of mental disorders. (shrink)

Patient-centered care is now recognized as a clinical method and ideal model for patient – health professional relationships, and many definitions have influenced its evolution. Overall the patient-centered care literature has provided relatively little to define patient-centered care at the level of the patient-professional relationship. Additionally, patient-centered care lacks grounding in ethical theory. This thesis asserts that theoretical concepts from the ethics of care can provide a stronger conceptual basis for patient-centered care.This thesis begins with a critical interpretive review (...) of the patient-centered care literature, yielding 12 articles that previously introduced new theoretical and definitional work on patient-centered care and patient-centered communication. Six common themes and ideas were discovered, and include Engaging the Patient as a Whole Person, Recognizing and Responding to Emotions, Fostering a Therapeutic Alliance, Promoting an Exchange of Information, Sharing Decision Making, and Enabling Self-Management and Patient Navigation. These elements were then compared to key elements of the ethics of care. This thesis argues that feminists have good reason to consider care as a type of moral duty, and it describes how this duty functions. This thesis also argues that a duty to care is triggered when caregivers are presented with particular substantive forms of vulnerability. Specifically, this thesis argues that vulnerable subjects whose constitutive needs are at risk require particular moral obligations. The links between the ethics of care and patient-centered care are discussed, including how an ethics of care response ought to function in the health care context. Finally, the cases of J.J. and Makayla Sault, two aboriginal girls who refused chemotherapy in favour of traditional aboriginal healing practices, are analyzed. This thesis offers a short scoping review of the bioethics discourse surrounding these cases. A review of this discourse revealed several common themes, which included the peripheral importance of culture and history, the equating of best interests with survival, the supremacy of science-based medicine, and the impartial application of ethical principles. This thesis recommends that health care professionals apply an ethics of care approach to similar ethical dilemmas in the future, which involves shifting one's ethical focus to the central relationships of the case, understanding the unique perspective of the patient's narrative, and promoting a care-based rather than a justice-based approach to problem-solving. (shrink)

Reflecting Alan Robinson's fundamental contribution to computational logic, this book brings together seminal papers in inference, equality theories, and logic programming. It is an exceptional collection that ranges from surveys of major areas to new results in more specialized topics. Alan Robinson is currently the University Professor at Syracuse University. Jean-Louis Lassez is a Research Scientist at the IBM Thomas J. Watson Research Center. Gordon Plotkin is Professor of Computer Science at the University of Edinburgh. Contents: Inference. Subsumption, A Sometimes (...) Undervalued Procedure, Larry Wos, Ross Overbeek, and Ewing Lusk. The Markgraf Karl Refutation Procedure, Hans Jurgen Ohlbach and Jorg H. Siekmann. Modal Logic Should Say More than it Does, Melvin Fitting. Interactive Proof Presentation, W. W. Bledsoe. Intelligent Backtracking Revisited, Maurice Bruynooghe. A Science of Reasoning, Alan Bundy. Inductive Inference of Theories from Facts, Ehud Y. Shapiro. Equality. Solving Equations in Abstract Algebras: A Rule-based Survey of Unification, Jean-Pierre Jouannaud and Claude Kirchner. Disunification: A Survey, Hubert Comon. A Case Study of the Completion Procedure: Proving Ring Commutativity Problems, Deepak Kapur and Hantao Zhang. Computations in Regular Rewriting Systems I and II, Girard Huet and JeanJacques Levy. Unification and ML Type Reconstruction, Paris Kanellakis, Harry Mairson, and John Mitchell. Automatic Dimensional Analysis, Mitchell Wand. Logic Programming. Logic Programming Schemes and Their Implementations, Keith Clark. A Near-Horn Prolog for Compilation, Donald Loveland and David Reed. Unfold/Fold Transformations of Logic Programs, P. A. Gardner and J. C. Shepherdson. An Algebraic Representation of Logic Program Computations, Andrea Corradini and Ugo Montanari. Theory of Disjunctive Logic Programs, Jack Minker, Arcot Rajasekar, and Jorge Lobo. Bottom-Up Evaluation of Logic Programs, Jeffrey Naughton and Raghu Ramakrishnan. Absys, the First Logic Programming Language: A View of the Inevitability of Logic Programming, E. W. Elcock. (shrink)

In the last decade the concept of context has been extensivelyexploited in many research areas, e.g., distributed artificialintelligence, multi agent systems, distributed databases, informationintegration, cognitive science, and epistemology. Three alternative approaches to the formalization of the notion ofcontext have been proposed: Giunchiglia and Serafini's Multi LanguageSystems (ML systems), McCarthy's modal logics of contexts, andGabbay's Labelled Deductive Systems.Previous papers have argued in favor of ML systems with respect to theother approaches. Our aim in this paper is to support these arguments (...) froma theoretical perspective. We provide a very general definition of ML systems, which covers allthe ML systems used in the literature, and we develop a proof theoryfor an important subclass of them: the MR systems. We prove variousimportant results; among other things, we prove a normal form theorem,the sub-formula property, and the decidability of an importantinstance of the class of the MR systems. The paper concludes with a detailed comparison among the alternativeapproaches. (shrink)

The metaverse concept constructs a virtual world parallel to the real world. The social economic dynamics model establishes a systematic model for social economic dynamics simulation that integrates macroeconomy and microeconomy based on modeling mechanism of the new theory of value by analogy with Newtonian mechanics and the modeling approach of Agent-based computational economics. This article describes the SED model’s modeling mechanisms, modeling rules, and behavior equations. At the same time, this article introduces the methods, testing standards, and some (...) typical cases about using the SED model to generate the economic digital twin systems. By doing so, we hope to demonstrate that the method of computer simulation experiment based on the SED model is a scientific empirical method, which has more advantages than the existing empirical research methods in economics. The SED model, which can be fully used to form an economic engine and construct a virtual economic system by digital twin method, can be integrated with the extant physical engine in the metaverse concept to build a virtual world consisting of physics, economy, culture, and politics that is close to and coexists with reality. (shrink)

This article presents a comparative theory of subjective argument strength simple enough for application. Using the axioms and corollaries of the theory, anyone with an elementary knowledge of logic and probability theory can produce an - at least minimally rational - ranking of any set of arguments according to their subjective strength, provided that the arguments in question are descriptive ones in standard form. The basic idea is that the strength of argument A as seen by (...) person x is a function of three values: x ’s degree of belief in the premisses of A; x ’s degree of belief in the conclusion of A under the assumption that all premisses of A are true; and x ’s belief in the conclusion of A under the assumption that not all premisses of A are true. (shrink)

Kripke’s work on modal logic has been immensely influential. It hardly needs remarking that this is not his only work. Here we address his pioneering applications of fixpoint constructions to the theory of truth, and related work by others. In his fundamental paper on this he explicitly described a modal version, applying a fixpoint construction world by world within a modal frame. This can certainly be carried out, and doubtless has been somewhere. Others have suggested a variety of other (...) extensions such as using the unit interval as the underlying space of truth values, or using a four valued logic instead of three, or various combinations of these. When many similar formal constructions have been proposed, one naturally asks what is the common core. Is there some setting in which things can be proved once and for all, with the various specific proposals seen as applications of this common core. In fact this is the case, with bilattices providing the desired structure. Much of such a development has already appeared in some form or other. It is the purpose of this article to bring everything together, and also add a few things. We present general results that, more or less, have everything currently in the fixpoint literature as special cases. Fortunately this does not make things more complicated, since the underlying proofs are essentially the same as they have always been. It is just that they are being carried out in generality rather than in specificity. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THE QUEST FOR AN ADEQUATE PROPORTIONALIST THEORY OF VALUE RoNALD H. McKINNEY, S.J. U'IWversity of Scranton Scranton, Pennsylvania EDWARD VACEK shrewdly observes that proportionalism attempts to synthesize the crucial insights of both the teleologist and the deontologist.1 Indeed, Vacek provides a fine summary of this achievement. However, he reflects that the most underdeveloped feature of proportionalism is its value theory by which we are enabled to know (...) how to resolve conflict situations.2 Richard McCormick, among others, has attempted to meet this deficiency by ·adopting John Finnis' notion of associated basic goods. In this essay, I will show how such an ·approach fails to remain true to the basic aims of proportionalism. Nor should this come as a surprise, since Finnis is himself indebted to one of McCormick's archopponents, Germain Grisez. Moreover, I will attempt to outline the elements involved in a non-hierarchfoal theory of value which I will argue to be the only adequate alternative to McCormick 's attempted solution. Deontologists argue that certain acts are right or wrong regardless of the ·consequences. Proportionalists, however, are opposed to such notions as an " intrinsically evil " act or an "absolute" duty, since they recognize the existence of moral dilemmas. A moral dilemma arises whenever there is a situation in which pre-moral values •are in conflcit, i.e., whatever choice one makes will result in the omission or harm of one or other of the values at stake. According to the proportionl Edward Vacek, "Proportionalism: One View of the Debate," Theological Studies 46/2 (June, 1985), 289. 2 Va.eek, 302. 56 PROPORTIONALIST THEORY OF VALUE 57 alist reformulation of the principle of double effect, the permission or oausrution of ontic evil is not necessarily a moral evil as long as there is a proportionate reason justifying,such an action, e.g., when a father shoots an!intruder threatening to harm his family. McCormick's initial description of the requirements of proportionate reason [s ias follows: "a) a v1alue at least equal to that sacrificed is at 1 stake; b) there is no less harmful way of protecting ithe value here and now; c) the manner of its protection here and now will not undermine it in the long run." 8 McCormick argues that it simply will not do to claim that the ontic evil permitted or caused in a conflict situation is always only indirectly intended.4 For, in many instances, this simply is not true. Moreover, he would argue that to intend an end is not necess1arily to desire it as deontologists suppose. What justifies the ontic evil resulting from such actions, then, is solely the proportionate reason for which it is allowed or caused. There are some obvious criticisms that have been hurled at this proportionalist proposal for resolving conflict situations: I) that it leaves itself open to the practical, if not theoretical, difficulty of weighing different values;!2) that it results in the possibility of many resolutions that could go counter to our normal moral intuitions; 8) that there exists an inherent fallibility in the calcul,ation of long-range consequences; and 4) that this uncertainty might easliy promote an undesirable attitude of skeptical relativism. It is perhaps the onslaught of these and other criticisms which prompted McCormick to adopt Finnis' theory of associated basic goods. Lisa Cahill,argues that this new theory constitutes an "abandonment" of McCormick's prior proposal.5 To understand how this new theory leads to inevitable s Richard McCormick, ".Ambiguity in Moral Choice," Doing Evil To Achieve Good: Moral Choice in Oonfiict Situations, eds. R. McCormick and P. Ramsey (Chicago: Loyola U. Press, 1978), 45. 4 McCormick, 35-38. 5 Lisa Cahill, "Theology, Utilitarianism, and Christian Ethics," Theologica,I Studies 42/4 (Dec., 1981), 618-24. 58 RONALD H. MCKINNEY, S.J. inconsistency for McCormick, we must first examine Finnis' position itself. Finnis' Theory of Basic Goods By "value," Finnis refers to any " general form of good that oan be participated iin or realized in indefinitely many ways on indefinitely many occasions." 6 Basic values, moreover, refer to ·intrinsic goods that are desired for their own sake (NL, 62, 65). They are good not because they are... (shrink)

A generalized Schrödinger equation containing correction terms to classical kinetic energy, has been derived in the complex vector space by considering an extended particle structure in stochastic electrodynamics with spin. The correction terms are obtained by considering the internal complex structure of the particle which is a consequence of stochastic average of particle oscillations in the zeropoint field. Hence, the generalised Schrödinger equation may be called stochastic Schrödinger equation. It is found that the second order correction terms are similar to (...) corresponding relativistic corrections. When higher order correction terms are neglected, the stochastic Schrödinger equation reduces to normal Schrödinger equation. It is found that the Schrödinger equation contains an internal structure in disguise and that can be revealed in the form of internal kinetic energy. The internal kinetic energy is found to be equal to the quantum potential obtained in the Madelung fluid theory or Bohm statistical theory. In the rest frame of the particle, the stochastic Schrödinger equation reduces to a Dirac type equation and its Lorentz boost gives the Dirac equation. Finally, the relativistic Klein–Gordon equation is derived by squaring the stochastic Schrödinger equation. The theory elucidates a logical understanding of classical approach to quantum mechanical foundations. (shrink)

In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the (...) value t is treated as designated, the above logic is a “common denominator” for Kleene and Łukasiewicz 3-valued logics, which represent its two different “determinizations”. In turn, the weak semantics—where both t and u are treated as designated—represents such a “common denominator” for two major 3-valued paraconsistent logics. We give sound and complete, cut-free sequent calculi for both versions of the logic generated by the rough set Nmatrix. Then we derive from these calculi sequent calculi with the same properties for the various “determinizations” of those two versions of the logic (including Łukasiewicz 3-valued logic). Finally, we show how to embed the four above-mentioned determinizations in extensions of the basic rough set logics obtained by adding to those logics a special two-valued “definedness” or “crispness” operator. (shrink)