A central theme in the foundational debates in the early Twentieth century in response to the paradoxes was to invoke the notion of the indefinite extensibility of certain concepts e,g. definability (the Richard paradox) and class (the Zermelo-Russell contradiction). Dummett has recently revived the notion, as the real lesson of the paradoxes and the source of Frege's error in basic law five of the Grundgesetze. The paper traces the historical and conceptual evolution of the concept and critices Dummett's argument (...) that the proper lesson of the paradoxes is that set theory is a theory of indefinitely extensible domains. (shrink)

Poincaré in a 1909 lecture in Göttingen proposed a solution to the apparent incompatibility of two results as viewed from a definitionist perspective: on the one hand, Richard’s proof that the definitions of real numbers form a countable set and, on the other, Cantor’s proof that the real numbers make up an uncountable class. Poincaré argues that, Richard’s result notwithstanding, there is no enumeration of all definable real numbers. We apply previous research by Luna and Taylor on Richard’s paradox, (...) indefinite extensibility and unrestricted quantification to evaluate Poincaré’s proposal. We emphasize that Poincaré’s solution involves an early recourse to indefinite extensibility and argue that his proposal, if it is to completely avoid Richard’s paradox, requires rejecting absolutely unrestricted quantification: Richard’s paradox provides a context in which paradox seems inescapable if unrestricted quantification is possible. In proposing his solution to the apparent conflict between Richard’s and Cantor’s results, Poincaré employs temporal expressions whose exact meaning he does not clarify. We suggest an interpretation of these expressions in terms of order of availability and briefly discuss its explanatory power in topics like paradoxes, limitation theorems and indefinite extensibility. (shrink)

This paper discusses Simpson's paradox and the problem of positive relevance in probabilistic causality. It is argued that Cartwright's solution to Simpson's paradox fails because it ignores one crucial form of the paradox. After clarifying different forms of the paradox, it is shown that any adequate solution to the paradox must allow a cause to be both a negative cause and a positive cause of..

What value should we put on our chances of obtaining a good? This paper argues that, contrary to the widely accepted theory of von Neumann and Morgenstern, the value of a chance of some good G may be a nonlinear function of the value of G. In particular, chances may have diminishing marginal utility, a property that is termed chance uncertainty aversion. The hypothesis that agents are averse to uncertainy about chances explains a pattern of preferences often observed in the (...) Ellsberg paradox. While these preferences have typically been taken to refute Bayesian decision theory, it is shown that chance risk aversion is perfectly compatible with it. (shrink)

Clinicians have a convention whereby symptoms are subjective statements 'as told by' patients, whereas signs are outwardly observable facts. Yet both first-person reports and third-person observations are theory laden and can bias conclusions. Two aspects of the oft-mentioned unreliability of reports are the subject's interpretation of them and the experimenter's assumptions when translating introspective reports into scientifically useful characterizations. Meticulous training of introspectors can address their mischief, whereas investigators can become more attentive to their own theory-laden biases. In the case (...) of hallucinations, for example, ignoring some customary third-person constructs and focusing on the visual experience itself has led to fresh explanations of visual symptoms based on cortical physiology rather than conceptual categories. Constructs that historically have ignored the subject's state of mind are also problematic; an example is the so-called resting state during metabolic brain imaging, long believed to reflect a blank mental slate. Introspective reports, not accepted literally but properly interpreted and revised by investigators as necessary, are legitimate sources of data. (shrink)

A coherent theory of relations was a critical part of Russell’s metaphysics. In Appearance and Reality Bradley posed a problem that sits squarely in the way of any doctrine of “external” relations. Russell, determined to advance such a doctrine, tried several times to find a way around the paradox and apparently believed he had succeeded by making use of one of his inventions, the theory of logical types.Gilbert Ryle and Alan Donagan have advanced an argument that I read, over (...) the objections of its authors, as a special case of Bradley’s. In this paper I argue that the ad hoc solution suggested by Donagan to the special problem is one that Russell had already indicated a willingness to accept but that the general problem of the paradox remains.What finally prevents Russell from solving the paradox is a combination of his refusal to abandon the claim that relations are constituents of facts and the necessity of distinguishing a relational fact from its converse. Following some hints that Russell left, I do some reconstruction, showing how the theory of types would (and should) have been applied had Russell followed through on his own insights. The result, I suggest, is a truly Russellian theory that escapes Bradley’s paradox. (shrink)

In 1898, Peirce delivered a series of lectures titled Reasoning and the Logic of Things. Peirce scholars have found the first of those lectures—titled “Philosophy and the Conduct of Life”—especially perplexing.Some scholars have a decidedly negative assessment of Peirce’s lecture. Cornelis de Waal, for example, maintains that Peirce’s claims in the lecture are doubtful. He states that “Peirce... takes a radical stance, arguing emphatically that science should stay away from ‘matters of vital importance,’ moral problems among them, thereby denying the (...) validity of a science of ethics”. He goes on to say that “on Peirce’s account, the ethics of inquiry seems to preclude ethical inquiry. The scientific.. (shrink)

Forrester claims to have shown that a contradiction can be derived from a set of two apparently innocuous moral rules together with standard deontic logic, a principle for adverbial detachment, and a statement of fact. Let l be a system of laws that has the following as immediate consequences: It is obligatory* that Smith not murder Jones. It is obligatory; that, if Smith murders Jones, then Smith murders Jones gently.

Nāgārjuna’s doctrine of emptiness, his ideas on “two truths” and language, and his general method of arguing are presented clearly by him and can be stated without paradox. That the dialetheists today can restate his beliefs in paradoxical ways does not mean that Nāgārjuna argued that way; in fact, their restatements misrepresent and undercut his arguments.

I argue that the duty of confidentiality is relative, not absolute; and that it is primarily a matter for the professional judgment of the reflective health practitioner to determine in the particular case whether competing public interests (or other compelling reasons) override that duty. I have supported that account with an analysis of medical practice as a recourse role and with an account of law that emphasises not only its duty‐imposing character but also, and crucially, an embedded liberty to depart (...) from the plain requirements of a primary legal rule where in the conscientious judgment of the addressee of that law, there is ‘damn good reason’ to do so. This account of the moral nullification of law at the outer limits appears to be descriptively accurate over a wide range of law and normatively appealing not only to democratic citizens but also to professionals such as doctors and lawyers whose role involves testing the law on moral grounds and who should be ready to do so, if but only if, they believe in the good faith exercise of professional judgment that the outcome mandated by the literal application of the legal rule is inconsistent with the moral mission of their role. The argument is illustrated with cases from American and English courts which, perhaps, render plausible the otherwise paradoxical notion that the law itself admits of departures from the legal rules. (shrink)

In 1905, Richard discovered his paradox of definability, and in a letter written that year he presented both the paradox and a solution to it.Soon afterwards, Poincaré endorsed a variant of Richard?s solution.In this paper, I critically examine Richard?s and Poincaré?s ways out.I draw on an objection of Peano?s, and argue that their stated solutions do not work.But I also claim that their writings suggest another way out, different from their stated solutions, and different from the orthodox Tarskian (...) approach.I argue that this second solution does not prevent the return of the paradox. (shrink)

A paradox can be defined as an unacceptable conclusion derived by apparently acceptable reasoning from apparently acceptable premises. Many paradoxes raise serious philosophical problems, and they are associated with crises of thought and revolutionary advances. The expanded and revised third edition of this intriguing book considers a range of knotty paradoxes including Zeno's paradoxical claim that the runner can never overtake the tortoise, a new chapter on paradoxes about morals, paradoxes about belief, and hardest of all, paradoxes about truth. (...) The discussion uses a minimum of technicality but also grapples with complicated and difficult considerations, and is accompanied by helpful questions designed to engage the reader with the arguments. The result is not only an explanation of paradoxes but also an excellent introduction to philosophical thinking. (shrink)

To be religious in the sense which Kierkegaard calls ?religiousness A? involves one, according to him, in a paradox. If we take the terms in which he describes this paradox in ordinary senses, it is not clear what this paradox consists of. If we take the terms in a technical sense, the description of being religious involves a paradox. But the paradox is of such a nature that it is now logically impossible that anyone should (...) be religious. If we attach a slightly different meaning to Kierkegaard's terms, being religious is possible but does not involve a paradox. Also on this interpretation, religious conduct becomes indistinguishable from non?religious conduct. (shrink)

The paradox of 'the One and the Many' might, more generally, be understood as the paradox of relationship. In order for there to be relationship there must be at least two parties in relation. The relation must, at once, hold the parties apart (otherwise they would collapse into unity) while holding them together (otherwise relationship itself would cease). It must do so, further, without itself becoming a third party which would then, itself, need to be related. This paper (...) considers this paradox as we find it manifest in the theories of quantum physics, the Socratic pursuit of universals, and, finally, at the very heart of human personhood - where we discover it at the core of interpersonal relationships, existential anxiety, and social distress. It is suggested, in the end, that though reason cannot resolve the terms of this paradox, there is a potential solution to the existential problems that spring from it, a solution lying in what Jesus calls, simply, 'faith.'. (shrink)

Discusses Soren Kierkegaard's use of irrationality in his pseudonymous writings to bolster important truths about rationality.

Gottlob Frege's Grundgesetze der Arithmetik, or Basic Laws of Arithmetic, was intended to be his magnum opus, the book in which he would finally establish his logicist philosophy of arithmetic. But because of the disaster of Russell's Paradox, which undermined Frege's proofs, the more mathematical parts of the book have rarely been read. Richard G.

Do logical paradoxes, like Eubulides’s Liar Paradox (the claim that the sentence “I am now lying” is true if and only if it is false), have any “existential” significance or are they mere brain puzzles for the mathematically minded? The paper argues that Randall Jarrell’s poem, “Eighth Air Force”, contains a poetic use of Eubulides’ Liar Paradox, spoken by Pontius Pilate’s wife in her statements about the “murder” of Jesus, in order to capture, symbolically, the inherent universal duplicity (...) (inauthenticity) of human life, specifically, the fact that human life, even in its true statements about fundamental moral-existential issues, is an inseparable blend of “truth” and “lies.”. (shrink)

: HIPAA is often described as a privacy rule. It is not. In fact, HIPAA is a disclosure regulation, and it has effectively dismantled the longstanding moral and legal tradition of patient confidentiality. By permitting broad and easy dissemination of patients’ medical information, with no audit trails for most disclosures, it has undermined both medical ethics and the effectiveness of medical care.

Although most scholars trace the Liar Paradox to Plato’s contemporary, Eubulides, the paper argues that Plato builds something very like the Liar Paradox into the very structure of his dialogues with significant consequences for understanding his views. After a preliminary exposition of the liar paradox it is argued that Plato builds this paradox into the formulation of many of his central doctrines, including the “Divided Line” and the “Allegory of the Cave” and the “Ladder of Love”. (...) Thus, Plato may have been the first to formulate the view that Graham Priest calls dialetheism, roughly, the view that some contradictions are, in an illuminating way, inescapable and true. The paper argues that Plato builds this Liar paradox into the formulation of his signature views because he holds that the attempt by finite human beings to theorize about transcendent realities results in the simultaneous necessity, and impossibility, of transgressing the limits of language—leading to the paradoxes. Finally, it is argued that the existence of these paradoxes in these Platonic doctrines is the direct result of an intrinsic hermeneutical circle in Plato’s aforementioned signature views. (shrink)

One of Marx‘s and Engels‘ main claims (hereafter ―original Marxism) in their account of the historical ―inevitability of the collapse of capitalism is that one‘s material (economic) conditions, not one‘s ideas, arguments or philosophy, determines one‘s ―consciousness and actions. However, the self-reference in this characterization of philosophical views generates a paradox analogous to the 7th century B.C. Epimenides ―Liar paradox. The Epimenides-paradox arises when Epimenides, a Cretan, states that all Cretans are liars. Epimenides-statement is paradoxical in the (...) sense that if it is true then it is false. Similarly, the Marxist claim that all philosophers who purport to state the cause of all social changes must be wrong, where Marx and Engels are themselves philosophers stating just such a claim, generates a paradox analogous to the ― Epimenides Liar paradox. This leads to what Engels himself calls a―false consciousness, i.e., a failure to understand the true causes of social change. This paradox can only be escaped by abandoning at least one of original Marxism‘s core doctrines. (shrink)

The purpose of this note is to present a strong form of the liar paradox. It is strong because the logical resources needed to generate the paradox are weak, in each of two senses. First, few expressive resources required: conjunction, negation, and identity. In particular, this form of the liar does not need to make any use of the conditional. Second, few inferential resources are required. These are: (i) conjunction introduction; (ii) substitution of identicals; and (iii) the inference: (...) From ¬(p ∧ p), infer ¬ p. It is, interestingly enough, also essential to the argument that the ‘strong’ form of the diagonal lemma be used: the one that delivers a term λ such that we can prove: λ = ¬ T(⌈λ⌉); rather than just a sentence Λ for which we can prove: Λ ≡ ¬T(⌈Λ⌉). The truth-theoretic principles used to generate the paradox are these: ¬(S ∧ T(⌈¬S⌉); and ¬(¬S ∧ ¬T(⌈¬S⌉). These are classically equivalent to the two directions of the T-scheme, but they are intuitively weaker. The lesson I would like to draw is: There can be no consistent solution to the Liar paradox that does not involve abandoning truth-theoretic principles that should be every bit as dear to our hearts as the T-scheme. So we shall have to learn to live with the Liar, one way or another. (shrink)

Charles Sanders Peirce proposed two different solutions to the Liar Paradox. He proposed the first in 1865 and the second in 1869. However, no one has yet noted in the literature that Peirce rejected his 1869 solution in 1903. Peirce never explicitly proposed a third solution to the Liar Paradox. Nonetheless, I shall argue he developed the resources for a third and novel solution to the Liar Paradox.In what follows, I will first explain the Liar Paradox. (...) Second, I will briefly rehearse Peirce's 1865 solution and his reasons for rejecting it.1 Third, I will review his 1869 solution and his reasons for rejecting it in 1903. Lastly, I will propose a novel solution to the Liar Paradox by drawing upon Peirce's later.. (shrink)

As is well-known, the formal system in which Frege works in his Grundgesetze der Arithmetik is formally inconsistent, Russell's Paradox being derivable in it. This system is, except for minor differences, full second-order logic, augmented by a single non-logical axiom, Frege's Axiom V. It has been known for some time now that the first-order fragment of the theory is consistent. The present paper establishes that both the simple and the ramified predicative second-order fragments are consistent, and that Robinson arithmetic, (...) Q, is relatively interpretable in the simple predicative fragment. The philosophical significance of the result is discussed. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:January 22, 2009 (8:41 pm) G:\WPData\TYPE2802\russell 28,2 048red.wpd russell: the Journal of Bertrand Russell Studies n.s. 28 (winter 2008–09): 127–42 The Bertrand Russell Research Centre, McMaster U. issn 0036-01631; online 1913-8032 YABLO’S PARADOX AND RUSSELLIAN PROPOSITIONS Gregory Landini Philosophy / U. of Iowa Iowa City, ia 52242–1408, usa [email protected] Is self-reference necessary for the production of Liar paradoxes? Yablo has given an argument that self-reference is not necessary. (...) He hopes to show that the indexical apparatus of self-reference of the traditional Liar paradox can be avoided by appealing to a list, a consecutive sequence, of sentences correlated one-one withnaturalnumbers.Yabloopens his “Paradox without Self-Reference” (Analysis, 1993) with the assumption that there is a sequence such that: Snz: “(;k)(k > n.!. True Sk)” Each sentence on Yablo’s list is supposed to be correlated one-one with number n. Each sentence is supposed to say that for every natural number kz greater than n, the k-th sentence on the list is not true. By comparing Yablo’s construction to an analogous construction with early Russellian propositions, we show that Yablo has failed to generate a paradox. 1. vicious circularity in yablo’s paradox S elf-reference has been taken to be the source of paradoxes. Poincaré and Russell are commonly associated with this thesis. In an amusing passage, the mathematician Jourdain recalls something of the dialogue between them: Nearly all mathematicians agreed that the way to solve these paradoxes was simply not to mention them; but there was some divergence of opinion as to how they were to be unmentioned. It was clearly unsatisfactory merely not to mention them. Thus Poincaré was apparently of the opinion that the best way of avoiding such awkward subjects was to mention that they were not to be mentioned. But [as Russell put it] “one might as well, in talking to a man with January 22, 2009 (8:41 pm) G:\WPData\TYPE2802\russell 28,2 048red.wpd 128 gregory landini 1 Philip Jourdain, The Philosophy of Mr. B*rtr*nd R*ss*llz (London: Allen & Unwin, 1918), p. 77. Russell is quoted from “Mathematical Logic as Based on the Theory of Types” (1908), LK, p. 63. 2 “On ‘Insolubilia’ and Their Solution By Symbolic Logic”, in B. Russell, Essays in Analysis, ed. Douglas Lackey (London: Allen & Unwin, 1973), p. 196. 3 I believe that this is Russell’s view in 1906. See Gregory Landini, “Russell’s Separation of the Logical and Semantic Paradoxes”, Revue internationale de philosophie 58 (2004): 257–94 (issue titled “Russell en héritage / Le centenaire des Principes”, ed. Philippe de Rouilhan). a long nose, say: ‘When I speak of noses, I except such as are inordinately long’, which would not be a very successful eTort to avoid a painful topic.”1 Poincaré maintained that one should exclude the oTending cases and therebyavoid“viciouscircles”ofself-referencewhichgenerateparadoxes. Russell objected: We may illustrate this by what M. Poincaré says concerning Richard’s paradox. Having Wrst put E = “all numbers deWnable in a Wnite number of words” we arrive at a paradox, due, says M. Poincaré, to our having included a number only deWnable in a Wnite number of words by means of E. This vicious circle he proposes to avoid by deWning E as “all numbers deWnable in a Wnite number of words without mentioning Ey”. To the uninitiated, this deWnition looks more circular than ever.2 Russell held that some paradoxes such as those of classes require, in order to exclude oTending cases without mentioning them, a “reconstruction of logical Wrst principles”. Others, such as Richard’s, are to be dismissed because they involve confused and viciously circular notions of “deWnability ”.3 Is self-reference necessary for paradoxes? The question is not well crafted. There are quite diTerent notions ofz “self-reference” involved in paradoxes. The self-reference involved in the Liar “This sentence is false” is provided by an apparatus of indexicals. This apparatus is quite distinct from the self-reference involved in Russell’s early ontology of propositions (as mind- and language-independent states of aTairs). This is an ontological self... (shrink)

Central to the liar paradox is the phenomenon of 'self-reference'. The paradox typically begins with a sentence like: -/- (L): (L) is not true -/- Historically, doubts about the intelligibility of self-reference have been quite common. In some sense, though, these doubts were answered by Kurt Gödel's famous 'diagonal lemma'. This paper surveys some of the methods by which self-reference can be achieved, focusing first on purely syntactic methods before turning attention to the 'arithmetized' methods introduced by Gödel. (...) It's primary lesson is that we need to be more careful than we usually have been about self-reference. (shrink)

Is the point of belief and assertion invariably to think or say something true? Is the truth of a belief or assertion absolute, or is it only relative to human interests? Most philosophers think it incoherent to profess to believe something but not think it true, or to say that some of the things we believe are only relatively true. Common sense disagrees. It sees many opinions, such as those about matters of taste, as neither true nor false; it takes (...) it as obvious that some of the truth is relative. Mark Richard's accessible book argues that when it comes to truth, common sense is right, philosophical orthodoxy wrong. The first half of the book examines connections between the performative aspects of talk, our emotions and evaluations, and the conditions under which talk and thought qualifies as true or false. It argues that the performative and expressive sometimes trump the semantic, making truth and falsity the wrong dimension of evaluation for belief or assertion. Among the topics taken up are: racial slurs and other epithets; relations between logic and truth; the status of moral and ethical talk; vagueness and the liar paradox. The book's second half defends the idea that much of everyday thought and talk is only relatively true or false. Truth is inevitably relative, given that we cannot work out in advance how our concepts will apply to the world. Richard explains what it is for truth to be relative, rebuts standard objections to relativism, and argues that relativism is consistent with the idea that one view can be objectively better than another. The book concludes with an account of matters of taste and of how it is possible for divergent views of such matters to be equally valid, even if not true or false. When Truth Gives Out will be of interest not only to philosophers who work on language, ethics, knowledge, or logic, but to any thoughtful person who has wondered what it is, or isn't, for something to be true. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Killing Our Way Out of ViolenceEngaging Wrangham's The Goodness ParadoxChris Haw (bio) and Richard Wrangham (bio)Wrangham's Goodness Paradox (GP) offers excellent anthropological research for mimetic theorists interested in the questions of human evolution and violence. It theorizes a framework of how group killing played a selective function in the emergence of our species, but it leaves open plenty of questions and concerns for productive, critical dialogue. Wolfgang Palaver (...) has written a short affirmation of the book, and Melvin Konner reviewed it for The Atlantic.1 But as one who has taken keen interest in the evolutionary and theological dimensions of mimetic theory,2 I offer here a longer engagement with the book and the author. I begin by extrapolating Wrangham's argument, I offer some critique, and then I share an edited version of my extended conversation with him.Wrangham's overall paradox is that humanity emerged through killing our way out of violence. More precisely, proactive coalitionary killing against aggressive, alpha-male individuals selected out, in a genetic pressure over hundreds of thousands of years, the more temperamental threads of Homo, resulting in a species (sapiens) who are relatively more domesticated and docile.3 [End Page 63]The argument proceeds as follows. First: Domestication is a real, genetic thing. Various domesticated species tend to share an odd, seemingly unrelated set of features called a "domestication syndrome." This refers to some combination of phenotype differences as compared to nondomesticated cousins: reduced skeleton mass, reduced/rounder cranium sizes and jaw lines, floppier ears, white patches of fur, extended juvenility, more frequent fertile periods, males with greater approximation to female characteristics, and so on. Beneath all these is a genetic reduction in "reactive aggression," which is the propensity for violence related to irascibility and short-fused tempers.Two: Domestication can happen intentionally or just randomly in nature. Humans have domesticated foxes in quick succession, breeding only ones with reduced reactive aggression, resulting in a domestication syndrome.4 The same seems to have happened slowly, with increasing intentionality over time, in the domestication of wolves into dogs. (This perhaps first began with the natural selection of wolves who were least aggravated by getting near humans to eat their camp detritus.) But domestication can also happen outside the human sphere, as in bonobos, who are basically a domesticated cousin of chimpanzees—evidenced not only in their reduced aggression but in their own domestication syndrome.5 This happened, he argues, largely through contingent, niche ecological features related to landscape, dramatic climate variations, and changes in competition over food.Three: It has long been asked whether humans are a "domesticated" species or whether such a thought is just anthropocentrism. The answer is definitely yes, but who domesticated us? A traditional answer, of course, was that God made us (or that some humans are properly domesticated, and others savage); but what if we ask in a more specifically scientific, causal framework? One early anthropologist posed that perhaps some now-extinct super-species domesticated us.6 Wrangham's answer is that we unintentionally domesticated ourselves by persistently killing off the genetic lines of the most aggressive individuals. This has resulted in Homo sapiens being basically a domesticated version of Homo neanderthalensis, erectus, and so on. Girard's not-unrelated answer is that religion domesticated us. By "religion" Girard means an integrated pattern of chaotic/exceptional and ordered/normal behaviors that contain violence, mediated through our mimetic capacity: chaotic mimetic violence restrained and channeled through mimetic ritual, taboo, and myth. This created an increasing feedback loop that exercised and intensified our mimetic capacity while protecting against its dangerous excess. Whatever the case, compared with our hominin cousins, the human phenotype shows strong signs of a domestication [End Page 64] syndrome: reduced cranium and jaw sizes, smaller skeleton mass, and a likely decreased reactive aggression in comparison to previous Homo.Fourth, and finally: Wrangham argues this domestication is related to a long, prehuman arc of transition, throughout the mid-Pleistocene (the Pleistocene ranges from about 2 million years ago to the thawing of the last ice age, 12,000 years ago), from older alpha-dominance patterns to tyrannies of egalitarian patriarchy. Wrangham draws upon hunter... (shrink)

Ultralogic as Universal? is a seminal text in non-classcial logic. Richard Routley presents a hugely ambitious program: to use an 'ultramodal' logic as a universal key, which opens, if rightly operated, all locks. It provides a canon for reasoning in every situation, including illogical, inconsistent and paradoxical ones, realized or not, possible or not. A universal logic, Routley argues, enables us to go where no other logic—especially not classical logic—can. Routley provides an expansive and singular vision of how a universal (...) logic might one day solve major problems in set theory, arithmetic, linguistics, physics, and more. It circulated in typescript in the late 1970s before appearing as the Appendix to Exploring Meinong's Jungle and Beyond. With engaging, forceful prose, unsparing criticism of entrenched institutions, and many tantalizing proof sketches, Ultralogic? has had a major influence on the development of paraconsistent and relevant logic. This new edition makes this work available for a modern audience, newly typeset and corrected, along with extensive notes, and new commentary essays. (shrink)

This essay argues that the engagement with Greece and Rome after The Will to Knowledge allowed Foucault to bring clarity to his conception of limited freedom in complex societies. The Classical fulfilled this function paradoxically by being jarringly different from and integral to the discourses of modern sexuality. Foucault’s engagement with the Classical in The Use of Pleasure and The Care of the Selfcontinued his established method of uncovering the development of a discourse, or set of discourses, over time. He (...) thereby demonstrated the historical specificity of understandings of sexuality and the self. It follows that if the ancient self was a historical construct, then the modern self must also be such. But Foucault’s Classical engagement leads him to an innovative position in which the disciplinary dynamics of ancient self-knowledge offer a practical philosophy. Foucault’s Greek philosophy could have effects through two related mechanisms: the care of the self through askesis and the speaking of truth to power through parresia. Through the rigors of askesis, the self can be rendered an object of analysis and hence a critical position external to the self can be achieved. Externality allows the philosopher to exercise parresia since the constraints of society have been surpassed and consequently offers a prospect of agency and a measure of freedom. The second part of the essay questions the extent of that freedom by reading Foucault against Tacitus, particularly the Agricola and the mutinies episode in the Annales. These episodes show the limitations of parresia and how parresia is bound into the workings of imperial power. In the Tacitean model, externality is a viable political stance, but is problematic ethically. The essay concludes by contrasting Foucauldian and Tacitean models of historical change. (shrink)

Part I : The metaphysics of spoilers. A brief history of spoilers -- What are spoilers? -- Things that can never be spoiled -- What else can be spoiled? -- Vagueness and spoilers -- Part II : The ethics of spoilers. Is it bad to spoil? -- The badness of spoiling -- When is it wrong to spoil? -- When you should spoil -- The timing of spoilers -- The ethics of spoiler alerts -- Part III: The pragmatics of spoilers. (...) Paradoxes of spoiling -- Spoiling remakes and some other tricky cases -- Are our reactions to spoilers justified? -- Culture, relativism, and spoilers -- What to do when you encounter someone who spoils. (shrink)

This essay recounts a fascinating if complicated piece of Anglo-American debate. My aim is to reach a conclusion about the importance of the notion of changing one's normative position as part of the act of giving sufficient consideration for a legal contract. In several journals and textbooks between 1894 and 1918 the major contract scholars of the time, e.g., Langdell, Anson, Pollock, Williston, Ames, and Corbin, discussed a special example which was thought to reveal a paradox in the common (...) law of consideration. The problem had shown itself in the textbooks of Pollock in England and Langdell in the United States. The example is of two contracts made by three persons in which one contract with the third party repeats the content of an existing contract with the second party. It would appear that the party at the pivot experiences no new detriment in merely performing, or promising to perform, his pre-existing duty. If so, such oblique contracts with third parties must fail for want of consideration extended from the first party. About this difficulty the experts were anything but agreed. The cases were not consistent. At the root of this uncertainty is an ambivalence about the concept of consideration itself. Should it be conceived in terms of normative relations and changes of moral position or should it be conceived in valuative terms, as harms and benefits? The differences of opinion about the legal validity of oblique contracts is explained by this ambiguity, one which the common lawyer has not yet resolved. (shrink)

Objectivity in the sciences is a much-touted yet problematic concept. It is sometimes held up as characterising scientific knowledge, yet operational definitions are diverse and call for such paradoxical genius as the ability to see without a perspective, to predict repeatability, to elicit nature’s own self-revelation, or to discern the structure of reality with inerrancy. Here we propose a positive and general definition of objectivity based on work in the Reformational philosophy tradition. We recognise a suite of relation-frames–ways in which (...) things function and relate to each other, which can be analytically distinguished in the process of conceptual abstraction. These relation-frames also ground the diverse aspects of scientific analysis within which relationships and properties may be abstracted from entities and systems. We argue that objectivity can be understood as characteristic of representations that attempt to portray a subject in an earlier relation-frame than that in which it characteristically functions. In short, objectivity is projection. This proposal is exemplified from mathematics and the natural sciences and some possible objections to it are considered, as well as its extension to the social sciences. (shrink)

IT HAS BEEN characteristic of metaphysics, since the beginning of philosophy, to deny the reality of time. The characteristics ascribed to it by unreflective people, particularly that of passage, have seemed so puzzling and paradoxical that the metaphysical temperament has preferred to banish time altogether rather than embrace those paradoxes. Thus Parmenides, the earliest metaphysician, denied reality to all time and becoming, leaving his bleak and changeless conception of reality to be perfected by his pupil Zeno. Plato, too, declared that (...) reality can only be the eternal, describing the strange passage of time in which we mortals live as nothing but that eternity's moving image. Among modern philosophers Spinoza sounded the same note, being unable to think of any reality in which time, by itself, could make a difference, while Immanuel Kant reduced it to a mere form of sensibility. Among recent thinkers McTaggart comes at once to mind, with his proofs that the concept of time is simply self-contradictory. (shrink)

David Hume is an ardent supporter of the practice of religions toleration. For Hume, toleration forms part of the background that makes progress in philosophy possible, and it accounts for the superiority of philosophical thought in England in the eighteenth century. As he puts it in the introduction to the Treatise: “the improvements in reason and philosophy can only be owing to a land of toleration and of liberty” (T Intro.7; SBN xvii).1 Similarly, the narrator of part 11 of the (...) First Enquiry comments: -/- Our conversation began with my admiring the singular good fortune of philosophy, which, as it requires entire liberty above all other privileges, and chiefly flourishes from the free opposition of sentiments and argu­ mentation, received its first birth in an age and country of freedom and toleration. (EHU 11.2; SBN 132) -/- The toleration to which Hume refers is broader than religious toleration, but in the context of the eighteenth century, religious toleration is clearly the paradigm case. Indeed, religious toleration represents one of the key accomplishments of the culminating event of Hume’s History of England: the Glorious Revolution of 1688. -/- Yet even though religious toleration forms the background of philosophy in general—or perhaps just because it does so—Hume offers precious few arguments for it, and they are, for the most part, given implicitly rather than as formal argu­ ments. Nevertheless, we can distinguish three different, though interrelated, lines of support for toleration in Hume’s thought: (i) an argument based on a general skepticism; (ii) an argument based on a contempt for organized religion; and (iii) a pragmatic argument based on the need for peace and orderly government. From our point of view, what is striking about all of these argument is how un-Lockean they are: Hume does not rely on the idea of a fundamental conceptual separation of church and state, nor on a natural right to freedom of conscience that character­izes writers working in the Lockean tradition. However, of the arguments he gives, only the last, I will argue, has any hope to provide a useful case for toleration. (shrink)

Curry claims that the positive paradox principle, ` A ⊃ in his elementary statement presentation, ‘is valid in any normal interpretation’ . By previous definition, ‘an interpretation of a system S is a normal interpretation just when the proposition A is true when and only when ` A’ . But his argument to normal validity is interestingly, and relevantly, invalid.

This book is a critical and analytical survey of the major attempts, in modern philosophy, to deal with the phenomenon of intentionality—those of Descartes, Brentano, Meinong, Husserl, Frege, Russell, Bergmann, Chisholm, and Sellars. By coordinating the semantical approaches to the phenomenon, Dr. Aquila undertakes to provide a basis for dialogue among philosophers of different persuasions. "Intentionality" has become, since Franz Brentano revived its original medieval use, the standard term describing the mind's apparently paradoxical capacity to relate itself to objects existing (...) in the world. One approach to the phenomenon emphasizes the mental act. The author argues that the most adequate account involves elements of both approaches. Contemporary treatments tend to formulate problems of intentionality primarily in terms of logic and semantics rather than those of metaphysics and phenomenology. Dr. Aquila's effort to coordinate these approaches will make his book useful to students both of analytical philosophy of mind and also of phenomenology. (shrink)

Journal of Human Values, Volume 28, Issue 3, Page 209-220, September 2022. It is paradoxical to make a moral statement and, in the same breath, disavow commitment to it. Following G. E. Moore, who first identified an analogous paradox—albeit, in the case of factual statements and disavowal of belief in them—these are called Moore paradoxical statements. Richard Hare argues that in order to determine whether an ‘ought’ is a moral one, one only needs to examine if this attitudinal adherence (...) necessarily accompanies the judgement in question. If not, Moore paradoxicality hits and the ‘ought’ in question is not a moral ‘ought’. Hare’s test poses a problem for Joseph Raz who argues that normative terms such as ‘ought’ have the same meaning in legal and moral statements. Raz, however, acknowledges a dilemma this brings in its wake: It is possible to make legal statements without necessarily endorsing them, which creates a presumption against these being equivalent to moral statements. To tackle the dilemma, Raz challenges the very idea of commitment to normative statements by arguing that it is also possible to make detached moral judgements. This paper argues that Raz’s idea of ‘detached normative statements’ falters in that the purported examples of detached normative statements Raz uses turn out upon closer examination to be non-normative statements using either norm-relative or non-normative ‘oughts’. (shrink)

Genetic epistemology analyzes the growth of knowledge both in the individual person (genetic psychology) and in the socio-historical realm (the history of science). But what the relationship is between the history of science and genetic psychology remains unclear. The biogenetic law that ontogeny recapitulates phylogeny is inadequate as a characterization of the relation. A critical examination of Piaget's Introduction à l'Épistémologie Généntique indicates these are several examples of what I call stage laws common to both areas. Furthermore, there is at (...) least one example of a paradoxical inverse relation between the two — geometry. Both similarities and differences between the two domains require an explanation, a developmental explanation. Although such an explanation seems to be psychological in nature, it is not merely empirical but also normative (since psychology is both factual and normative according to Piaget). Hence genetic epistemology need not be reduced to psychology (narrowly conceived), but rather should be seen as being both empirical and normative and thus similar to certain types of contemporary philosophy of science. (shrink)

Jacques Lacan was a notoriously difficult and idiosyncratic thinker. But is there any value in his hermetically difficult style? By highlighting certain crucial elements of his practice, I show how Lacan enlists the notion of difficulty to press home that he did not want his readers to understand directly. Instead, as Foucault and Althusser explain so well, Lacan wished for his readers and auditors to discover themselves as subjects of desire through reading him. Indeed, in miming the language of the (...) unconscious, Lacan believed he could throw into sharp relief the notion of the unconscious itself and, paradoxically, better express himself. This temporary detour through misunderstanding indicates the programmatic value of difficulty itself. By commenting on the comedic aspect of Lacan's difficult literary dandyism, I also seek to playfully remind the reader that Lacan was a master of comedy and irony and that it is only by adopting a comparative literary approach to his work that we can appreciate how his theory of misunderstanding is at the heart of his conceptualization of madness and psychosis, allowing us to see how, for Lacan, the subject is ontologically sick. (shrink)

Theories of Truth provides a clear, critical introduction to one of the most difficult areas of philosophy. It surveys all of the major philosophical theories of truth, presenting the crux of the issues involved at a level accessible to nonexperts yet in a manner sufficiently detailed and original to be of value to professional scholars. Kirkham's systematic treatment and meticulous explanations of terminology ensure that readers will come away from this book with a comprehensive general understanding of one of philosophy's (...) thorniest set of topics. -/- Included are discussions of the correspondence, coherence, pragmatic, semantic, performative, redundancy, appraisal, and truth-as-justification theories. There are also chapters or sections of chapters on the liar paradox, three-valued logic, Field's critique of Tarski, Davidson's program, Dummett's theory of linguistic competence, satisfaction, recursion, the extension/intension distinction, and an explanation of how theories of justification, properly understood, differ from theories of truth. -/- A persistent theme is that philosophers have too often failed to recognize that not all theories of truth are intended to answer the same question. When the various questions are made distinct, it is apparent that many of the "debates" in this field are really cases of philosophers talking past one another. There is much less disagreement within the field than has commonly been thought. (shrink)

The desirability of what actually occurs is often influenced by what could have been. Preferences based on such value dependencies between actual and counterfactual outcomes generate a class of problems for orthodox decision theory, the best-known perhaps being the so-called Allais Paradox. In this paper we solve these problems by extending Richard Jeffrey's decision theory to counterfactual prospects, using a multidimensional possible-world semantics for conditionals, and showing that preferences that are sensitive to counterfactual considerations can still be desirability maximising. (...) We end the paper by investigating the conditions necessary and sufficient for a desirability function to be an expected utility. It turns out that the additional conditions imply highly implausible epistemic principles. (shrink)

Reductio arguments are notoriously inconclusive, a fact which no doubt contributes to their great fecundity. For once a contradiction has been proved, it is open to interpretation which premise should be given up. Indeed, it is often a matter of great creativity to identify what can be consistently given up. A case in point is a traditional paradox of the infinite provided by Galileo Galilei in his Two New Sciences, which has since come to be known as Galileo’s (...) class='Hi'>Paradox. It concerns the set of all numbers, N: since to every number there is a corresponding square, there are as many squares as numbers. But since there are non-squares between the squares, “all numbers, comprising the squares and the non-squares, are greater than the squares alone”, i.e. there must be fewer numbers in the set of all squares S than in N. Thus N is both equal to and greater than S. This is a contradiction, so one of the premises must be given up: the question is, which one? (shrink)