Previous research reported that in processing structurally ambiguous sentences comprehenders often preserve an initial incorrect analysis even after adopting a correct analysis following structural disambiguation. One criticism is that the sentences tested in previous studies involved referential ambiguity and allowed comprehenders to make inferences about the initial interpretation using pragmatic information, suggesting the possibility that the initial analysis persisted due to comprehenders' pragmatic inference but not to their failure to perform complete reanalysis of the initial misanalysis. Our study (...) investigated this by testing locally ambiguous relative clause sentences in Japanese, in which the initial misinterpretation contradicts the correct interpretation. Our study using a self-paced reading technique demonstrated evidence for the persistence of the initial analysis with this structure. The results from an eye-tracking study further suggested that the phenomenon directly reflected the amount of support given to the initial incorrect analysis prior to disambiguating information: The more supported the incorrect main clause analysis was, the more likely comprehenders were to preserve the analysis even after the analysis was falsified. Our results thus demonstrated that the preservation of the initial analysis occurs not due to referential ambiguities but to comprehenders' difficulty to fully revise the highly supported initial interpretation. (shrink)

The frame problem is a fundamental challenge in AI, and the Lucas-Penrose argument is supposed to show a limitation of AI if it is successful at all. Here we discuss both of them from a unified Gödelian point of view. We give an informational reformulation of the frame problem, which turns out to be tightly intertwined with the nature of Gödelian incompleteness in the sense that they both hinge upon the finitarity condition of agents or systems, without which their alleged (...) limitations can readily be overcome, and that they can both be seen as instances of the fundamental discrepancy between finitary beings and infinitary reality. We then revisit the Lucas-Penrose argument, elaborating a version of it which indicates the impossibility of information physics or the computational theory of the universe. It turns out through a finer analysis that if the Lucas-Penrose argument is accepted then information physics is impossible too; the possibility of AI or the computational theory of the mind is thus linked with the possibility of information physics or the computational theory of the universe. We finally reconsider the Penrose’s Quantum Mind Thesis in light of recent advances in quantum modelling of cognition, giving a structural reformulation of it and thereby shedding new light on what is problematic in the Quantum Mind Thesis. Overall, we consider it promising to link the computational theory of the mind with the computational theory of the universe; their integration would allow us to go beyond the Cartesian dualism, giving, in particular, an incarnation of Chalmers’ double-aspect theory of information. (shrink)

We prove that any 1-closed (see def 1.1) model of the Π 2 consequences of PA satisfies ¬Cons PA which gives a proof of the second Godel incompleteness theorem without the use of the Godel diagonal lemma. We prove a few other theorems by the same method.

The implicit content associated with incomplete definite descriptions is contributed in the form of definite descriptions of situations. A definite description of this kind is contributed by a small structure in the syntax, which is interpreted, in general terms, as ‘the situation that bears R to s’.

According to the displacement model of secularization, religious-theological concepts, themes, and values have been reinterpreted in non-religious contexts without fully dispensing with the religious content. Secularization is thus incomplete. The incomplete secularization argument can be used as a lens through which to read Ethan Kleinberg’s deconstructive approach to the past. In his narrative, as reconstructed here, deconstruction promises to bring us closer to a secular relationship to the past than the ontological realism Kleinberg says still dominates contemporary historical (...) theory. By contrasting Kleinberg’s analysis with Hayden White’s, whose oeuvre can be read as structured by the idea of incomplete secularization and a wish to liberate history from religious themes in order to enable a direct confrontation with meaninglessness, I argue that Kleinberg’s deconstructive approach does not fulfill its promise. Rather, it opens up a post-secular historiography in which religious themes might find a place at the very heart of historical reasoning. (shrink)

If r is a reducibility between sets of numbers, a natural question to ask about the structure ? r of the r-degrees containing computably enumerable sets is whether every element not equal to the greatest one is branching (i.e., the meet of two elements strictly above it). For the commonly studied reducibilities, the answer to this question is known except for the case of truth-table (tt) reducibility. In this paper, we answer the question in the tt case by showing that (...) every tt-incomplete computably enumerable truth-table degree a is branching in ? tt . The fact that every Turing-incomplete computably enumerable truth-table degree is branching has been known for some time. This fact can be shown using a technique of Ambos-Spies and, as noticed by Nies, also follows from a relativization of a result of Degtev. We give a proof here using the Ambos-Spies technique because it has not yet appeared in the literature. The proof uses an infinite injury argument. Our main result is the proof when a is Turing-complete but tt-incomplete. Here we are able to exploit the Turing-completeness of a in a novel way to give a finite injury proof. (shrink)

This article draws on key models of monitoring and blockholding articulated in the incomplete contracts theory of the firm. Under incomplete contracts theory, different governance systems have incentive structures that entail different tradeoffs—tradeoffs between ownership concentration and liquidity, between monitoring and management initiative, and between private rent-seeking and activity benefiting shareholders as a group. The tradeoffs delimit opportunities for productive cross-reference. More specifically, blockholder systems, such as those in Europe, subsidize monitoring by permitting blockholders to reap private benefits (...) of control through self-dealing and insider trading. Market systems, such as those in the United States and Britain, regulate such private rent-seeking toward the end of maintaining an institutional framework that supports diffuse share ownership and liquid trading markets. It follows that a legal framework conducive to blockholding may be ill-equipped to foster dispersed equity ownership and thick trading markets and that a legal framework conducive to liquid trading markets may have properties that discourage blockholding. This gives rise to questions for law reform agendas on both sides of the Atlantic. In the United States, proponents ask for deregulation of controls on institutional investors, looking to encourage blockholding and more effective monitoring. In Europe, proponents ask for stronger securities regulation, looking to encourage deeper trading markets. This article suggests that each reform program may lead to disappointing results because neither assures conforming adjustments to the pertinent actors’ incentives. Alternatively, strict reforms that materially change prevailing incentive patterns could perversely destabilize workable arrangements without assuring the appearance of more effective alternatives. (shrink)

Without making any reference to traditional linguistic disciplines such as presupposition, implicature and indirect speech acts, this article analyzes how and what implicit meanings were constructed, structured and negotiated through an ambulance request call to the119 call center in Yamagata, Japan in 2011, while enhancing the cogency of the empirical approach independent from analytical theories. Through the occasioned taxonomic analysis of the occasioned semantics of the caller and the call-taker regarding the dispatch, the analysis captured definitive evidence on how a (...) negative response was created from the call-taker’s categorization process. It reveals the process in which the rejection was determined from the talk by the call-taker that was oriented toward and constructed by the conceptual knowledge of motion, which was formulated as ‘walk’. A three-part-list structure was created, which formulated ‘emesis’ into the category of a symptom, but not into that of an illness. The analysis reports that the call-taker’s method of occasioned semantics was operative and systematically patterned. Based on the results of the analysis, with linguistic evidence, the article critically argues that the rejection of an ambulance request was due in large part to the call-taker’s method of categorization when asking questions, which provides an alternative account to that of a previously reported analysis. (shrink)

Using video recordings of draft meetings conducted as part of an intramural basketball program as data, this conversation analytic study examines the use of an incomplete utterance in a joint evaluative activity. In particular, we focus on how the participants, volunteer coaches, who meet to draft players for their respective teams, produce a syntactically incomplete utterance as a means to critically assess a player, a non-present third party to the interaction. Analysis reveals that the participants use an (...) class='Hi'>incomplete utterance as part of dispreferred design; it allows them to withhold articulating overt criticism of others. By trailing off where the criticism is due, the participants display reluctance to verbalize what is to be said and treat its articulation as delicate. The syntactic structure of the utterance that includes a contrastive conjunction and accompanying embodied actions such as head shakes help them convey a critical stance. We examine the use of incomplete utterances in both agreement and disagreement sequences; the recipients display their unproblematic understanding of the critical assessment and respond by providing their own assessments that either affiliate or disaffiliate with the conveyed critical stance. (shrink)

Can one give an account of a perfectly just society without invoking principles governing our responses to injustice? My claim is that addressing this question puts us in a position to reveal ambiguities and problems with the way in which Rawls draws the ideal/nonideal theory distinction that have so far gone unnoticed. In the first part of my paper, I demonstrate that Rawls’s original definition of the ideal/nonideal theory distinction is ambiguous as it is composed of two different conceptual distinctions, (...) before clarifying the distinctions involved, paying particular attention to the unfamiliar distinction between primary and secondary principles. I then show that we can best account for what Rawls is actually doing at the level of ideal and nonideal theory by invoking this distinction between primary and secondary principles. This result sets the stage for my argument in the second part. I first explain why Rawls does not have access to an understanding of the strict compliance condition that can account for the irrelevance of secondary principles for a complete account of the principles regulating a perfectly just basic structure. I then point out that there is a tension between what Rawls claims to be doing at the level of ideal theory and what he is actually doing at the level of ideal theory. On this basis, I argue that Rawls’s ideal conceptions of justice are incomplete because they do not encompass secondary principles. The Conclusion unpacks the contributions this article makes to the ideal/nonideal theory debate. (shrink)

The dissertation gives a second-order-logic-based explanation of modal incompleteness. The leading concept is that modal incompleteness is to be explained in terms of the incompleteness of standard second-order logic, since modal language is basically a second-order language. The development of Kripke-style semantics for modal logic has been underpinned by the conjecture that all modal systems are characterizable by classes of frames defined by first-order conditions on a binary relation. However, the discovery of certain incomplete modal systems has undermined the (...) all-encompassing feature of Kripke-style approach. There are logics not determined by any class of Kripke frames at all. ;In the dissertation I investigate a normal incomplete sentential modal system due to J. F. A. K. Van Benthem, and I address both the formal and the philosophical facets of modal incompleteness from the vantage point that modal logic is essentially second-order in its nature. Modal systems can be analyzed in terms of structures with a domain of second-order individuals that are assigned under an interpretation to propositional variables within languages of sentential modal logic. Hence, the phenomenon of there being incomplete modal systems can be accounted for through the incompleteness of standard second-order logic. ;Since second-order logic plays a crucial role in the explanation, Quine's animadversions upon second-order logic and in particular his views that second-order logic is 'Set Theory in Sheep's Clothing' are examined. Against Quine's stance I will seek to show that a vindication of second-order logic can be gotten provided a proper due is given to the sharp distinction between the logical notion of set which is the concern of second-order logic and the iterative notion of set which lies within the realm of set theory. (shrink)

Quantum mechanics is seen to be incomplete not because it cannot explain the correlations that characterize entanglement without invoking either non-locality or realism, both of which, despite special relativity or no-go theorems, are at least conceivable. Quantum mechanics is incomplete, in a perhaps broader than hidden variable sense, because it fails to address within its theoretical structure the question of how even a single particle, by being in a given quantum state, causes the frequency distribution of measurement values (...) specified by the state. This incompleteness of quantum mechanics as it is currently conceived is both fundamental and indefeasible. Failure to address the question of how the states of entangled particles are given effect to yield the correlations they specify is simply a particular albeit attention arresting instance of this incompleteness. But if that is so then quantum mechanics cannot be held to be inconsistent with locality. (shrink)

Available from UMI in association with The British Library. ;This thesis investigates the application of the theory of Conceptual Structures to an Experience Base model, which is a question-answering system for a knowledge base of pseudo-natural language statements of everyday experience. This thesis progresses to extend the fundamental principles carried from the experience base, to develop a framework for Reasoning by Analogy. Both methodologies are implemented, and uncertainty in the models is handled using the theory of Support Logic. ;Incompleteness of (...) information, uncertainty of data and the need for a definite structure to the way in which rules and data interact, are aspects which must be dealt with if the experience base is to succeed. One more aspect is the knowledge representation which dictates the ease with which processing may be performed upon it. Conceptual graphs are used to store information used by an Experience Base. Control of the reasoning is effected by plausible inference reinforced by the theory of Support Logic for handling uncertainty. The knowledge base is a set of initially completely disparate islands of knowledge, which the system automatically clusters into coherent groups in an associative network. ;The principles evolved from research into experience bases lead to the conception, development and implementation of a computational framework for Analogical Reasoning. The reasoning is performed between domains of knowledge rather than within a single domain as in case-based reasoning, and operates on pseudo-natural language statements as for the experience base. It relies on relation-based structure mapping and includes a sophisticated mechanism for translating between the new problem and the analogue. The strong connection between this work and metaphor interpretation is also investigated, together with ideas on how to negotiate with the apparent multitude of types of analogical reasoning. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:To Paul Lachance, ioculator Domini1. IntroductionWith the expression “inner experience” we refer to a complex linguistic and philosophical problem which is present even in the most recent theology. If, in general, this concept expresses the experience of something which is perceived by an individual in the absence of external stimulus or observable sensations, in Christian and mystical tradition it indicates more precisely the action and the transformation which God (...) arouses in the inner conscience. I propose investigating the specific way the Provençal Franciscan Pierre de Jean Olieu used this concept and presented it, both philosophically and theologically, in a small collection of writings which critical tradition has defined in various ways, but which I continue defining, with a term which maintains a Franciscan suggestion, as opuscula.1 These short devotional texts were written by Olieu and his followers in both Provençal and in Latin, and explicitly addressed the Beguins of the so-called “poverty houses,” as well as the laity which congregated around the Franciscan Order.2 Unlike the prayers and treatises concerning prayer by Olieu, these texts are not completely set but are conceived and written as models of continuous meditation on the part of the reader.3 In view of the critique I am editing, I here furnish a list of these texts, with the aim of updating the incomplete lists complied by Efrem Bettoni4 and Antonio Ciceri:5Cavalier armat Exercens se sacris orationibus et meditationibus Informatio Petri Ioannis De 14 gradibus amoris gratiosi 12De [12/10] gradibus humilitatis 13Grases de vera penitentia 14Modus quomodo quilibet potest referre gratias Deo de Beneficiis ab eo receptis Brevis monitio ad amorem Dei obtinendum 17Remedia contra temptationes spirituales De 7 sentimentis Christi Jhesu 20 Tractatus de 7 tentationibus 21Tractatulus de fugiendis, desiderandis, meditandis 22This approach is particularly interesting, because it is my conviction that, in these texts the author focuses on the paths and transformations of conscience, on the inter-communication of them and on the potential of repeating and recreating, autonomously, an uninterrupted process of spiritual transformation and strengthening. In this sense, as we will see, the concept of “inner experience” is central to the opuscula and, anticipating the results of my analysis, I can say that being in a significant position of the spiritual and meditative path delineated by the text, it constitutes its structural core. Such a placement finds meaning and justification within the philosophical, theological and apocalyptical reflections of the author.23 For Olieu, inwardness and outer activity, although remaining distinct, are balanceable and organizable in a reassemblage founded on devotio. We can say that the devotion of the reader, confirmed and strengthened by the inner experience of his personal reflection on mercy, is the element which allows this reassembling. We will see in what sense we can speak about an element of fracture and an entirely new forma mentis, which opens the way to modern secular spirituality.2. Inner Experience and the Structure of the opusculaI begin with the text entitled Informatio ad virtutum opera. This could be considered the manifesto text of the opuscula, because in this work Pierre de Jean Olieu clarifies the principle subject of the meditations offered to the reader, and proposes a stylistic, structural model which is respected, more or less precisely, in all the other texts of the corpus. This structure is very simple: the author lists twenty-eight subjects which the reader is invited to reflect upon during his personal endeavor towards virtuous perfection. The text is divided in two parts: the first presents fourteen orderly reflections centered on pedagogical-moral subjects like the meditation on God and the Passion of Christ, on the example of the Saints, the awareness of one’s sins, and on the coming of the Day of Judgement; in the second, the author.. (shrink)

_ Source: _Volume 53, Issue 2-4, pp 221 - 248 One of the peculiarities of Peter Abelard’s analysis of incomplete and non-assertive sentences is his use of the notion of desire: in both _Dialectica_ and _Glosses on Peri hermeneias_ the terms _desiderium_ and _desidero_ move to the foreground side by side with _optatio, expectatio, suspensio_ and the related verbs. Desire plays a structural role in Abelard’s descriptions of the compositional way in which the linguistic message is received, changing (...) step by step from incomplete to complete: the person who receives the incomplete message desires to get further information through other words since he knows that the purpose of such words or sequences of words is to combine with other words in order to form a complete sentence. On the other hand, the expression of the speaker’s attention to his inner affections renders the same semantic content a different complete sentence. (shrink)

An ordered field is said to be Scott complete iff it is complete with respect to its uniform structure. Zakon has asked whether nonstandard real lines are Scott complete. We prove in ZFC that for any complete Boolean algebra B which is not (ω, 2)-distributive there is an ultrafilter U of B such that the Boolean ultrapower of the real line modulo U is not Scott complete. We also show how forcing in set theory gives rise to examples of Boolean (...) ultrapowers of the real line which are not Scott complete. (shrink)

In speaking of empirical science as a self-correcting process one implies that a proposition accepted in accordance with the rules of procedure may have to be eliminated later according to these very rules. Taking this for granted one realizes that a particular empirical science, say physics, should be defined in terms of rules of method rather than as a system of propositions representing our knowledge at a given time. Obviously both the science of Galileo and Newton and the science of (...) Einstein and Bohr are called ''physics'' and we do not regard this as a mere equivocation. It may, however, be objected that a definition of a science in terms of rules of method is incompatible with the view that a science consists of a set of propositions. To meet this objection I propose that we distinguish between the structure of a science as defined in terms of the rules of method and the corpus of this science at a given time, i.e., the set of propositions accepted at this time in accordance with the rules of method of this science. The relation between the structure of a science and the corpus of a science is similar to that obtaining between the structure of a legal order, e.g., American law, which is defined by the rules of the process of legislation in the broadest sense and the legal norms which are the corpus of law at a given time. It should then be noted that the assertion that a certain proposition belongs to a given science is incomplete without a time-index. The scientist changes the corpus of his science either by introducing new propositions to it or by eliminating propositions which were previously accepted and did not stand further control. The significance of whatever else he does in the course of his inquiry can be determined only in the light of this selection. There are two stages in this process of selection. The first is exclusively concerned with meanings as such. The scientist has to ascertain that a given aggregate of words represents a proposition, that this proposition contains only objective meanings, that it is not self-contradictory, that it belongs to the subject-matter of the particular science. The second phase of the selection, exhibited in scientific procedure in the strict sense, applies only to such propositions which have passed this preexamination. We shall call those rules of method in terms of which the first stage of selection is defined rules of the language of science and those rules in terms of which the second stage is defined rules of the procedure of science. In this paper I shall try to show how important it is to distinguish clearly between these two types of rules. I shall first deal with the rules of the language of science and confine myself to sciences dealing with the physical world. (shrink)

This article presents and compares various algebraic structures that arise in axiomatic unsharp quantum physics. We begin by stating some basic principles that such an algebraic structure should encompass. Following G. Mackey and G. Ludwig, we first consider a minimal state-effect-probability (minimal SEFP) structure. In order to include partial operations of sum and difference, an additional axiom is postulated and a SEFP structure is obtained. It is then shown that a SEFP structure is equivalent to an effect algebra with an (...) order determining set of states. We also consider σ-SEFP structures and show that these structures distinguish Hilbert space from incomplete inner product spaces. Various types of sharpness are discussed and under what conditions a Brouwer complementation can be defined to obtain a BZ-poset is investigated. In this case it is shown that every effect has a best lower and upper sharp approximation and that the set of all Brouwer sharp effects form an orthoalgebra. (shrink)

The structural abstract discusses the features of modern post-non-classical scientific discourse, according to which all kinds of scientific and religious knowledge are simplified mental construction of a complex objective reality. All accumulated religious knowledge is a combination of various theoretical models of divine reality, the performance of which was checked by centuries of experience of mystical connection with the Lord. According to the requirements of scientific and religious discourse on incompleteness of knowledge, all religious texts of the Bible, the (...) Koran, the Torah, etc. are not carriers of absolutely probable knowledge. The sacred reality they describe is far more complex. The structural abstract reveals the originality of the subject and object of religious narration and the special nature of the mystical fact. The empirical basis of Christian knowledge is the books of the Old and New Testaments, which set the initial basis of Christian knowledge. The array of interpretations of sacred knowledge, accumulated over two thousand years of the Christianity development, it constitutes the main volume in the system of Christian knowledge. Christian theology provides a comprehensive understanding of Christian doctrine and its historical development. A special role is played by mystical knowledge-management-experiencing, the knowledge of God in the structure of Christian knowledge. The peculiarity of knowledgemanagement-experiencing determines that it comes directly from God. Theology can be achieved in the course of many years of practical work of an ascetic. The mystical side of knowledge-management is the experience of a direct connection with the Lord, which is difficult to convey in words. Secret knowledge-management exists only in real time in the existential reality of sacred experience. The structural abstract distinguishes two types of metaphysical knowledge – Western and Eastern metaphysics. Western metaphysics is considered to be the universal, most developed type of philosophical rational knowledge, the main goal of which is to develop a theoretical model of the fundamental reality, what is the God. It is reasonable to call Eastern metaphysics the metaphysics of the Path originating in the middle of the first millennium BC in India (Brahmanism, Buddhism, Jainism, etc.) and China (Taoism). Orthodoxy is the Christian version of the metaphysics of the Path, while Sufism is in Islam. Everything is subordinated to the liberation of the ascetic from worldly desires and the achievement of a mystical connection with God in Eastern metaphysics. The metaphysics of the Path includes three components – theoretical construction of the God, difficult practical actions (the Path) and the secret knowledge-management of the God, which are considered in inseparable unity. The Orthodox version of the metaphysics of the Path is one of the most developed in Eastern metaphysics.The texts of Western and Eastern metaphysics differ considerably. The works of Western metaphysicians appeal to the human mind and are predominantly speculative. The writings of Eastern metaphysicians try to reproduce the mental reality of the Path of merit of Enlightenment to a large extent. If rational knowledge of the fundamental foundations of the universe prevails in Western metaphysics, then Orthodox metaphysics is guided by the desire to enter the mystical space of divine reality. (shrink)

It has been suggested by Clark Glymour that the spatio-temporal structure of the universe might be underdetermined by all observational data that could ever, theoretically, be gathered. It is possible for two spacetimes to be observationally indistinguishable (OI) yet topologically distinct. David Malament extended the argument for the underdetermination of spacetime structure by showing that under quite general conditions (such as the absence of any closed timelike curves) a spacetime will always have an OI counterpart (at least in weak sense). (...) Because the plight of the cosmologist seemed to be so discouraging in this regard, Malament considered the relationship between global properties and OI spacetimes. This information is helpful to the cosmologist. It allows, in principle, one to reject some spacetime models based on observational evidence. In this paper, I consider the relationship between variants of geodesic incompleteness and different senses (some old and some new) of OI. In light of the findings, it seems that (for the most part) the predicament of the cosmologist is not good. Quite generally, versions of geodesic incompleteness are not conserved even under the strongest formulations of OI. (shrink)

Normal mathematical culture is overwhelmingly concerned with finite structures, finitely generated structures, discrete structures (countably infinite), continuous and piecewise continuous functions between complete separable metric spaces, with lesser consideration of pointwise limits of sequences of such functions, and Borel measurable functions between complete separable metric spaces.

We consider structural completeness in modal logics. The main result is the necessary and sufficient condition for modal logics over K4 to be hereditarily structurally complete: a modal logic λ is hereditarily structurally complete $\operatorname{iff} \lambda$ is not included in any logic from the list of twenty special tabular logics. Hence there are exactly twenty maximal structurally incomplete modal logics above K4 and they are all tabular.

Reference [12] introduced a novel formula to formula translation tool that enables syntactic metatheoretical investigations of first-order modallogics, bypassing a need to convert them first into Gentzen style logics in order torely on cut elimination and the subformula property. In fact, the formulator tool,as was already demonstrated in loc. cit., is applicable even to the metatheoreticalstudy of logics such as QGL, where cut elimination is unavailable. This paper applies the formulator approach to show the independence of the axiom schema ☐A (...) → ☐∀ A of the logics M3and ML3 of [17, 18, 11, 13]. This leads to the conclusion that the two logics obtained by removing this axiom are incomplete, both with respect to their natural Kripke structures and to arithmetical interpretations. In particular, the so modified ML3 is, similarly to QGL, an arithmetically incomplete first-order extension of GL, but, unlike QGL, all its theorems have cut free proofs. We also establish here, via formulators, a stronger version of the disjunction property for GL and QGL without going through Gentzen versions of these logics. (shrink)

This paper presents a precise semantics for incomplete predicates such as “ready”. Incomplete predicates have distinctive logical properties that a semantic theory needs to accommodate. For instance, “Tipper is ready” logically implies “Tipper is ready for something”, but “Tipper is ready for something” does not imply “Tipper is ready”. It is shown that several approaches to the semantics of incomplete predicates fail to accommodate these logical properties. The account offered here defines contexts as structures containing an element (...) called a proposition set, which contains atomic propositions and negations of atomic propositions. The condition under which “Tipper is ready” is true in a context is defined in terms of the contents of the proposition set for the context. On this account, the content of the context pertinent to a conversation must be determined not by what speakers have in mind but by relations of objective relevance. (shrink)

The notion of interaction and interaction machines, developed by Peter Wegner, includes the comparison between incompleteness of interaction machines and Gödel incompleteness. However, this comparison is not adequate, because it combines different notions and different sources of incompleteness. In particular, it merges syntactic with two senses of semantic completeness, and results about truth with results about provability and their consequences . The comparison also overlooks structural differences in the way diagonalization produces incompleteness. More generally, the comparison is unlikely because (...) interaction incompleteness is supposed to come from a system's involvement with its environment, whereas Gödel incompleteness comes from a system's involvement with itself. (shrink)

We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, more specifically, emphasises (...) its refined composition and rigorous internal structure. (shrink)

In this paper we study structural properties of n-c. e. Q-degrees. Two theorems contain results on the distribution of incomparable Q-degrees. In another theorem we prove that every incomplete Q-degree forms a minimal pair in the c. e. degrees with a Q-degree. In a further theorem it is proved that there exists a c. e. Q-degree that is not half of a minimal pair in the c. e. Q-degrees.

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal (...) logic of linear discrete time with gaps follows. (shrink)

Economics prefers complete explanations: general over partial equilibrium, microfoundational over aggregate. Similarly, probabilistic accounts of causation frequently prefer greater detail to less as in typical resolutions of Simpson’s paradox. Strategies of causal refinement equally aim to distinguish direct from indirect causes. Yet, there are countervailing practices in economics. Representative-agent models aim to capture economic motivation but not to reduce the level of aggregation. Small structural vector-autoregression and dynamic stochastic general-equilibrium models are practically preferred to larger ones. The distinction between (...) exogenous and endogenous variables suggests partitioning the world into distinct subsystems. The tension in these practices is addressed within a structural account of causation inspired by the work of Herbert Simon’s, which defines cause with reference to complete systems adapted to deal with incomplete systems and piecemeal evidence. The focus is on understanding the constraints that a structural account of causation places on the freedom to model complex or lower-order systems as simpler or higher-order systems and on to what degree piecemeal evidence can be incorporated into a structural account. (shrink)

Particularly during the 1940s, Robert Merton developed a loosely knit methodological program including such key concepts as "structure and functional analysis" and "middle range theories" which provided guidance for sociological work over several decades and which retains some considerable relevance today. However, there are inconsistencies and incompletions in this program which have become more problematic over time. The paper questions the depth of these difficulties and also points out that in the historical circumstances of a limited stimulus provided by the (...) paucity of critique written at the time and Robert Merton's operational style, it is not surprising that difficulties were not attended to. Key Words: Merton • methodological program • classics in sociology • functional analysis • middle-range theory. (shrink)

Various theories of referent are critically but briefly surveyed from the perspective of structural realism; a constructivist version of structural realist account of referent is outlined, and its implications for history of science and for descriptive metaphysics are briefly indicated.

This essay will move toward a phenomenology of “more” in ten steps. 1st, situates the investigation within the tradition of Husserlian phenomenological practice, then 2nd draws upon Husserl’s own experience of doing phenomenology. 3rd considers some initial aspects of the structure of the lived experience of “more” and 4th is about the number series, while 5th addresses the primal experience of time, space, and movement. 6th focuses on the phenomenological notion of horizons, then 7th turns to the related question of (...) transcendence. 8th takes a critical look at a particular conceptual model sometime used in thinking about the experience of “more”; 9th briefly brings out one of the ethical implications of this critique; and finally, 10th highlights some of the ways in which the research documented here is itself still incomplete and demands “more”.Este ensayo se moverá hacia una fenomenología de "más" en diez pasos. El prime-ro, sitúa la investigación dentro de la tradición de la práctica fenomenológica husserliana; luego, el segundo se basa en la propia experiencia de Husserl de hacer fenomenología; el tercero considera algunos aspectos iniciales de la estructura de la experiencia vivida de "más" y el cuarto es sobre la serie numérica, mientras que el quinto aborda la experiencia primordial de tiempo, espacio y movimiento. El sexto se centra en la noción fenomenológica de horizontes; después el séptimo pasa a la cuestión relacionada con la trascendencia. El octavo echa una mirada crítica a un modelo conceptual particular usado en algún momento para pensar sobre la experiencia de "más"; el noveno destaca brevemente una de las implicaciones éticas de esta crítica;y, finalmente, el décimo resalta algunas de las formas en las que la investigación aquí documentada todavía está incompleta y exige "más". (shrink)

This article examines some aspects of the natural philosophy of Juan Gallego de la Serna, royal physician to the Spanish kings Philip III and Philip IV. In his account of animal generation, Gallego criticizes widely accepted views: (1) the view that animal seeds are animated, and (2) the alternative view that animal seeds, even if not animated, possess active potencies sufficient for the development of animal souls. According to his view, animal seeds are purely material beings. This, of course, raises (...) the question of how living beings can arise from inanimate matter. Gallego is aware that two other thinkers who understood animal seeds as purely material beings, Duns Scotus and the Louvain-based physician Thomas Feyens, did not solve this problem. Gallego’s solution makes use of the notion of incomplete entities developed by the Spanish Jesuit Francisco Suarez. While Suarez applies this notion to soul and body in order to explain why souls have a natural tendency towards organic bodies and organic bodies have a natural tendency towards souls, Gallego applies this notion to the natural tendency of animal seeds towards each other and towards further substances in their respective environment. In his view, this natural tendency of animal seeds to incorporate further substances explains that origin of material structures complex enough to constitute an animal soul. (shrink)

This paper will apply post-structural semiotic theories to study the texts of Gödel's first incompleteness theorem. I will study the texts’ own articulations of concepts of ‘meaning’, analyze the mechanisms they use to sustain their senses of validity, and point out how the texts depend (without losing their mathematical rigor) on sustaining some shifts of meaning. I will demonstrate that the texts manifest semiotic effects, which we usually associate with poetry and everyday speech. I will conclude with an analysis (...) of how the picture I paint relates to an ethics of mathematical production. (shrink)

A possible relevant meaning of Hilbert’s program is the following one: “give a constructive semantic for classical mathematics”. More precisely, give a systematic interpretation of classical abstract proofs about abstract objects, as constructive proofs about constructive versions of these objects.If this program is fulfilled we are able “at the end of the tale” to extract constructive proofs of concrete results from classical abstract proofs of these results.Dynamical algebraic structures or geometric theories seem to be a good tool for doing this (...) job. In this setting, classical abstract objects are interpreted through incomplete concrete specifications of these objects.The structure of axioms in geometric theories gives rise in a natural way to distributive lattices and pointfree topological spaces. Abstract objects correspond to classical points of these pointfree spaces.We shall insist on the Zariski spectrum of distributive lattices and commutative rings and give a constructive interpretation of the Krull dimension.We underline the fact that many abstract objects in classical mathematics can be viewed as points of spectral spaces corresponding to distributive lattices whose definition is concrete and natural.Two important facts are to be stressed.First, abstract proofs about points of these pointfree spaces can very often be reread as constructive proofs about constructible subsets of these spaces.Second, function spaces on these pointfree spaces are often explicitly used in elegant abstract theories. The structure of these function spaces is fully constructive: indeed by the compactness theorem, “all is finite”. The constructive rereading of the abstract proofs is in this setting is nothing but the simple constatation that abstract proofs use correctly axioms.RésuméUne manière pertinente de revisiter le Programme de Hilbert serait la suivante: « donner une sémantique constructive pour les mathématiques classiques ». Plus précisément donner une interprétation systématique des preuves classiques abstraites au sujet des objets abstraits, en terme de preuves constructives au sujet de contreparties constructives de ces objets abstraits.Si ce programme est rempli, nous sommes capables « à la fin de l’histoire » d’extraire des preuves constructives de résultats concrets à partir des preuves classiques abstraites de ces résultats.Les structures algébriques dynamiques, ou ce qui revient à peu près au même les théories géométriques, semblent être un bon outil pour réaliser ce travail. Dans cette optique, les objets abstraits des mathématiques classiques sont remplacés par des spécifications incomplètes mais concrètes de ces mêmes objets.La structure des théories géométriques donne naissance de manière naturelle à des treillis distributifs et à des espaces topologiques sans points. Les objets abstraits utilisés par les mathématiques classiques correspondent aux points classiques de ces espaces sans points.Dans cet article, nous illustrerons ce phénomène principalement avec le spectre de Zariski des treillis distributifs et celui des anneaux commutatifs, en indiquant notamment un équivalent constructif de la notion de dimension de Krull.Nous insistons sur le caractère extrêmement général de l’interpétation des objets abstraits idéaux des mathématiques classiques comme des points d’espaces spectraux associés à des treillis distributifs qui sont définis de façon naturelle et concrète.Souligons deux faits d’expérience importants.Tout d’abord, les preuves abstraites au sujet des points de ces espaces sans points peuvent en général être relues comme des preuves concernant les parties constructibles de ces espaces.Enfin, les espaces de fonctions continues sur ces espaces sans points sont souvent utilisés dans d’élégantes théories abstraites. Ces espaces de fonctions sont bien définis constructivement. Cela tient au « théorème de compacité » qui nous dit que dans le cadre en question « tout est fini ». La relecture constructive des preuves abstraites n’est alors rien d’autre que la constatation que les axiomes géométriques sont utilisés de manière correcte. (shrink)

A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper approaches the problem by presenting an analysis of the notion of an elementary physical proposition. The notion is shown to be realized in standard formulations of the theory and to illuminate the significance of proofs of the impossibility of hidden variable extensions. In the interpretation of quantum mechanics that (...) emerges from this analysis, the philosophically distinctive features of the theory derive from the fact that it seeks to represent a reality of which complete knowledge is essentially unattainable. (shrink)

We show: for every noncomputable c.e. incomplete c-degree, there exists a nonspeedable c-degree incomparable with it; The c-degree of a hypersimple set includes an infinite collection of \-degrees linearly ordered under \ with order type of the integers and consisting entirely of hypersimple sets; there exist two c.e. sets having no c.e. least upper bound in the \-reducibility ordering; the c.e. \-degrees are not dense.

An efficient method of value assessment of a set of exchangeable alternatives A = a1,a2, ? ,an is presented. It particularly applies to situations where certain preferences may be easily evaluated or are already known, while other binary comparisons may not at once be available. Further applications are to ranking partial tournaments and the emergence and the characterisation of organisational hierarchy. By sequentially performing transitively efficient assessments of uncompared pairs, an initial weakly acyclical preference structure in A is transformed into (...) an ordering of A in echelons. We call these nicely surveyable preference structures echelon orders. Theoretical properties of echelon orders are investigated, including a characterisation and a numerical representation. (shrink)

In previous work I argued against (i) the likelihood of finding a theoretically sound foundation for the linked/convergent distinction and (ii) the utility of the distinction even if a sound theoretical basis could be found. Here I subject Douglas Walton’s comprehensive discussion of the linked/convergent distinction found in Argument Structure: A Pragmatic Theory to careful scrutiny and argue that at best Walton’s theory remains incomplete and that attempts to fill out the details will run afoul of at least one (...) of the problems adduced above—i.e., result in either a theoretically unsound distinction or a theoretically sound, but unnecessary distinction. (shrink)

What are scientific theories and how should they be represented? In this article, I propose a causal–structural account, according to which scientific theories are to be represented as sets of interrelated causal and credal nets. In contrast with other accounts of scientific theories (such as Sneedian structuralism, Kitcher’s unificationist view, and Darden’s theory of theoretical components), this leaves room for causality to play a substantial role. As a result, an interesting account of explanation is provided, which sheds light on (...) explanatory unification within a causalist framework. The theory of classical genetics is used as a case study. 1 Introduction2 The Theory of Classical Genetics3 Three Philosophical Accounts of the Theory of Classical Genetics3.1 The structuralist account3.2 Kitcher’s unificationism3.3 Darden and theory change in science4 A Common Lacuna: Where is Causality?5 Woodward’s Interventionist Account of Causation6 Causal Bayes Nets and Their Interrelations6.1 Causal Bayes nets6.2 Relations among causal nets6.3 Credal nets and their interrelations7 The Theory of the Gene and its Causal Graph8 A First Exemplar: Stem Length in Pea Plants8.1 Three crosses on stem length in pea plants8.2 The causal graph for stem length in pea plants8.3 Morgan’s explanatory principles and the credal net for stem length in pea plants9 Explaining Mendel’s Crosses: A Causal–Structural Account10 Monohybrid Crosses with Complete Dominance11 Exemplars,Explanatory Patterns, Generic Credal Nets, and Mechanism Schemas12 Incomplete Dominance13 Anomalies14 Multi-hybrid Crosses with Independent Assortment15 Multi-hybrid Crosses with Linkage and Crossing-Over16 Double Crossing-Over and the Linear Order of the Gene17 Causal–Structural Explanation18 Explanatory Unification19 Concluding Remarks. (shrink)

Let Δ be a set of formulas. In this paper we study the following question: under what assumptions on Δ, the concept “a complete Δ-type p over B does not fork over A ⊆ B” behaves well. We apply the results to the structure theory of ω1-saturated models.

This book offers a thorough reanalysis of Charles Darwin's Origin of Species, which for many people represents the work that alone gave rise to evolutionism. Of course, scholars today know better than that. Yet, few resist the temptation of turning to the Origin in order to support it or reject it in light of their own work. Apparently, Darwin fills the mythical role of a founding figure that must either be invoked or repudiated. The book is an invitation to (...) move beyond what is currently expected of Darwin's magnum opus. Once the rhetorical varnish of Darwin's discourses is removed, one discovers a work of remarkably indecisive conclusions. The book comprises two main theses: The Origin of Species never remotely achieved the theoretical unity to which it is often credited. Rather, Darwin was overwhelmed by a host of phenomena that could not fit into his narrow conceptual framework. In the Origin of Species, Darwin failed at completing the full conversion to evolutionism. Carrying many ill-designed intellectual tools of the 17th and 18th centuries, Darwin merely promoted a special brand of evolutionism, one that prevented him from taking the decisive steps toward an open and modern evolutionism. It makes an interesting read for biologists, historians and philosophers alike. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Argumentative Structure of Kant’s Metaphysical Foundations Of Natural ScienceEric Watkinsone of kant’s most fundamental aims is to justify Newtonian science. However, providing a detailed explanation of even the main structure of his argument (not to mention the specific arguments that fill out this structure) is not a trivial enterprise. While it is clear that Kant’s Critique of Pure Reason (1781), his Metaphysical Foundations of Natural Science (1786), and (...) his unpublished (and incomplete) Opus postumum should in some way constitute the core of this justification, it is less clear how each of these works does so in detail. In this paper I shall first argue that the standard view of the relationship between the Critique of Pure Reason and the Metaphysical Foundations of Natural Science (hereafter simply Metaphysical Foundations) is mistaken. I shall then present my own interpretation of how the Metaphysical Foundations contributes to the justification of Newtonian science. Finally, I shall conclude by considering an important interpretation of the argument of the Metaphysical Foundations developed by Michael Friedman. However, it is first necessary to present briefly Kant’s conception of science (in particular what conditions a body of knowledge must satisfy for Kant in order to be considered science proper) as well as Kant’s own understanding of the relevant differences between his projects in the first Critique, the Metaphysical Foundations, and the Opus postumum.Kant’s conception of science is rather strict if measured by contemporary standards. For in the preface to the Metaphysical Foundations Kant establishes three substantive conditions that a body of knowledge must satisfy in order to be considered science proper.1 (1) It must not consist in empirical principles, [End Page 567] but rather must be obtained solely from pure, a priori principles;2 (2) It must be apodictically certain;3 (3)4 It must be a systematically ordered whole (which means that its various propositions must be related as, for example, antecedents and consequents).5 After stating these conditions, Kant then argues that all natural science proper requires a pure part upon which its apodictic certainty is based. In other words, satisfaction of the first condition immediately implies satisfaction of the second condition as well.6 Accordingly, these three conditions (and the first one in particular) imply that natural science proper requires (or rather presupposes) a justification by something distinct from it that Kant calls a metaphysics of nature.7 But what exactly does a metaphysics of nature encompass? Kant distinguishes two different parts of the metaphysics of nature: a transcendental part and a special part. A metaphysics of nature [End Page 568] is transcendental insofar as it concerns “the laws that make the concept of nature in general possible, even without relation to any determinate object of experience, and [insofar as it is] thus indeterminate with respect to the nature of this or that thing in the sensible world,” whereas a metaphysics of nature is special to the extent that “it is concerned with a special nature of this or that kind of thing of which an empirical concept is given, but so that except for what lies in this concept no other empirical principle is used for knowledge thereof.”8 In short, a transcendental metaphysics, revealing how experience in general is possible, is not supposed to presuppose an empirical concept, whereas a special metaphysics does make such an assumption insofar as it is concerned with the special natures of things.How do the three works cited above relate to Kant’s distinction between a transcendental and a special metaphysics of nature? In the preface to the Metaphysical Foundations Kant clearly indicates that he intends the Metaphysical Foundations to constitute the special metaphysics of nature. Although he does not explicitly refer to the first Critique in the preface, it is also relatively clear that he sees it (or at least the ‘System of Pure Reason’ that Kant foresees as following upon it and as incorporating its fundamental results)9 as constituting [End Page 569] the transcendental part of a metaphysics of nature.10 The Principles of Pure Understanding (‘Grundsätze des reinen Verstandes’) in the Transcendental Analytic argue for what could naturally be described as “laws... (shrink)

Ignorance and incompleteness -- The instrumental model of talking : how to talk about talk -- Open questions, confirmation questions, and how to choose -- Which sentence-type to use when asking them -- Quantifiers, wh-expressions, and manners of interpretation -- Syntactic structure -- On the questioning speech-acts and the kinds of ignorance they -- Address.

This article addresses the problematic relation between Michel Henry’s phenomenology of life and ethics. More specifically, it asks whether Henry’s account of the self’s transcendental birth in the immanent self-generation of life allows for a sense of individual responsibility. I begin by discussing Henry’s generation of the self and show how the historical essence of the self is structured according to the antinomy of affectivity. I then show how, for Henry, this history of life is full and yet incomplete. (...) Accordingly, life is attracted to growth and this growth happens insofar as living beings proceed through a series of stages of despair. I develop these stages by looking at Henry’s analyses of anxiety, desire, and humility in relation to Kierkegaard. I argue that even though there is already an initial sense of responsibility at work in the earliest stirrings of anxiety, it is only in humility that the self comes to know who it truly is and how it ought to relate to others. Cet article se penche sur la relation problématique entre la phéno-ménologie de la vie et l’éthique de Michel Henry. Plus spécifiquement, nous nous demandons si l’explication de la naissance trans-cendantale du soi dans l’auto-génération immanente de la vie que propose Henry permet de rendre compte d’un sens de la responsabilité personnelle. Nous débutons avec une analyse de la génération du soi chez Henry et montrons comment l’essence historique du soi est structurée selon l’antinomie de l’affectivité. Nous montrons en-suite comment, pour Henry, cette histoire du soi est pleine bien qu’incomplète. En conséquence, la vie est attirée par la croissance, et cette croissance se produit dans la mesure où les êtres vivants passent à travers une série de stades du désespoir. Nous dévelop-pons ces divers stades en nous tournant vers les analyses que fait Henry de l’angoisse, du désir, et de l’humilité en relation avec Kierkegaard. Nous soutenons que même s’il y a déjà un sens initial de la responsabilité à l’oeuvre dans le premier éveil de l’angoisse, c’est seulement en atteignant le stade de l’humilité que le soi en vient à savoir qui il est vraiment et comment il doit se rapporter aux autres. (shrink)

If we want to say what “fundamentality” means, we have to start by approaching what we generally see at the empty place of the predicate “____ is fundamental”. We generally talk about fundamental entities and fundamental theories. At this article, I tried to make a metaphysical approach of what is for something to be fundamental, and I also tried to talk a little bit of fundamental incomplete and complete theories. To do that, I start stating the notion of “entity” (...) and looking at the difference at perceived entities. The difference led us to talk about the entities’ structures and their powers, and about the supervenience between these last two. The supervenience talk made us to see the fight between emergentism and reductionism as the difference between the irreducibility of laws and the reducibility of powers and structures to lower-order domains. Then, we conclude that “fundamentality” is a mereological relation – a relation that a whole structure has to a certain combination of its structural parts or that a power has to a certain combination of its constituent powers – of to be identical and to exist in virtue of them. (shrink)

ABSTRACTWhat is the relationship between structure and agency? French philosopher Michel Foucault weighed in on this question, and I argue that some of his writings indicate that he held views that were strongly structuralist. If I am correct in my interpretation of Foucault in these works, was he right to think this? Is there evidence in his work that perhaps agents do have more influence than his concept of structuralism can account for? I suggest that this is the case and (...) will argue that Foucault's structuralist views are incomplete and result in an incoherence. I then offer a critical realist account of structure and agency which seems to be able to resolve the incoherence and thus offers a better explanation of the evidence that Foucault provides. (shrink)