Colonius suggests that, in using standard set theory as the language in which to express our computational-level theory of human memory, we would need to violate the axiom of foundation in order to express meaningful memory bindings in which a context is identical to an item in the list. We circumvent Colonius's objection by allowing that a list item may serve as a label for a context without being identical to that context. This debate serves to highlight the value of (...) specifying memory operations in set theoretic notation, as it would have been difficult if not impossible to formulate such an objection at the algorithmic level. (shrink)

Starting from Marr's ideas about levels of explanation, a theory of the data structures and access processes in human memory is demonstrated on 10 tasks. Functional characteristics of human memory are captured implementation-independently. Our theory generates a multidimensional task classification subsuming existing classifications such as the distinction between tasks that are implicit versus explicit, data driven versus conceptually driven, and simple associative (two-way bindings) versus higher order (threeway bindings), providing a broad basis for new experiments. The formal language clarifies the (...) binding problem in episodic memory, the role of input pathways in both episodic and semantic (lexical) memory, the importance of the input set in episodic memory, and the ubiquitous calculation of an intersection in theories of episodic and lexical access. (shrink)

Groups are only real, and only serve as a basis for collective action, when their members perceive them to be real. For a computational model to have analytic fidelity and predictive validity it, therefore, needs to engage with the psychological reality of groups, their internal structure, and their structuring by the social context in which they function.

Mercier & Sperber (M&S) argue for their argumentative theory in terms of communicative abilities. Insights can be gained by extending the discussion beyond human reasoning to rodent and robot navigation. The selection of arguments and conclusions that are mutually reinforcing can be cast as a form of abductive reasoning that I argue underlies the construction of cognitive maps in navigation tasks.

This paper suggests that Dante’s writings on language provide elements for the construction of a philosophy of language. The main emphasis is on the theoretical treatment of language in De Vulgari Eloquentia, but it also considers La Vita Nouva and Il Convivio, earlier works providing insights into the development of Dante’s views on the nature and use of language. De Vulgari Eloquentia is an extended justification for the use of a vernacular language capable of treating the worthiest topics in a (...) manner appropriate to them. Two main purposes of language are to instruct and delight. Dante shows that others must be addressed in a language they understand, but if it is to lift them, it must have a beauty and power beyond them. (shrink)

The central questions addressed in this paper are: (1) how are forms related to predication? And (2) what role do forms and predication play in the discovery and articulation of truth? The first section of the paper provides—in broad strokes—a synopsis of Plato’s account of forms. The second section considers predication in relation to forms showing that the existence and nature of forms is a necessary condition for predication, and that Plato’s account of predication is consistent with, in fact, anticipates, (...) Aristotle’s treatment of reality in the Categories. The conclusion of the paper is that forms and predication are central to philosophical hermeneutics, to the discovery and articulation of truth. (shrink)

The argument of this paper is that the Aristotelian analysis of justice and related concepts provides the best framework for understanding the structure and importance of justice in Dante’s Commedia. After giving a synopsis of the principle features of Aristotle’s account of justice in Book 5 of the Nicomachean Ethics, I consider a few scenes from the Inferno, the Purgatorio, and the Paradiso, showing how the punishments and rewards Dante describes are based on the Aristotelian analysis of justice. Finally, I (...) show that Dante, following Aristotle’s views on the metaphysics of the human person, recognizes that argument alone is inadequate to the task of educating the reader on the proper care of the soul, and that Dante’s effective use of images, makes the abstract Aristotelian concept of justice vivid and attractive, and its opposite repulsive. (shrink)

The argument of this paper is that the Aristotelian analysis of justice and related concepts provides the best framework for understanding the structure and importance of justice in Dante’s Commedia. After giving a synopsis of the principle features of Aristotle’s account of justice in Book 5 of the Nicomachean Ethics, I consider a few scenes from the Inferno, the Purgatorio, and the Paradiso, showing how the punishments and rewards Dante describes are based on the Aristotelian analysis of justice. Finally, I (...) show that Dante, following Aristotle’s views on the metaphysics of the human person, recognizes that argument alone is inadequate to the task of educating the reader on the proper care of the soul, and that Dante’s effective use of images, makes the abstract Aristotelian concept of justice vivid and attractive, and its opposite repulsive. (shrink)

Cui bono? Cherchez la femme! These ancient maxims offer counsel to the investigator of an unsolved murder or some inexplicable pattern of behaviour. They advise the pursuit of what has come more recently to be known as a form of lateral thinking. The puzzle may not best be solved by an intensification of the examination of the immediate data. The primary clue may lie out of sight somewhere further back. Financial advantage or sexual attraction, which does not show up as (...) a feature of the immediate situation, may be the hidden motive of the traditionally male agent's actions. When that is recognized, the otherwise inexplicable phenomena may become intelligible. (shrink)

The appearance of two new editions of the Choephoroi in 1986 has prompted me to reexamine the theatrical logic of the recognition scene. Anthony Bowen's student edition offers a curious contrast. Bowen is alert to the music of the choruses, and describes them as ‘a feast in themselves’ . He remarks with reference to the strophic verse that ‘it is surprising how well these works have come down to us’ . When he discusses the staging, however, he no longer finds (...) the text well preserved, and follows Fraenkel in disposing of the footprints. Three interpolations, a total of nine lines, have to be struck out . A. F. Garvie's scholarly edition broadly accepts the extant text, but does not – I wish to argue – yet grasp the theatrical logic of the writing. (shrink)

In 1931 the mathematical logician Kurt Godel published a revolutionary paper that challenged certain basic assumptions underpinning mathematics and logic. A colleague of Albert Einstein, his theorem proved that mathematics was partly based on propositions not provable within the mathematical system and had radical implications that have echoed throughout many fields. A gripping combination of science and accessibility, Godel’s Proof by Nagel and Newman is for both mathematicians and the idly curious, offering those with a taste for logic and (...) philosophy the chance to satisfy their intellectual curiosity. (shrink)

The central thesis of this treatment of Aristotle's philosophy of mind is that Aristotle's writings contain a coherent theory of perception which is explanatory of a variety of psychological activities such as sense perceiving, imagining, remembering, dreaming and thinking. The approach taken rejects the developmental theory of Jaeger and others, and assumes that the psychological theses found in the De Anima and the Parva Naturalia form a continuous exposition of one psychological theory.

This work is a critical history of ancient Greek accounts of pleasure from the pre-Socratics down to Epicurus and the early Stoics. Four natural divisions may be distinguished: The pre-Platonic background containing the didactic tradition, the physiological tradition, and the evaluative accounts of Democritus, Socrates, and Aristippus; Plato's theory and its development; Aristotle's theory, including a discussion of the views of Speusippus and Eudoxus; and, the post-Aristotelian accounts of Epicurus and the early Stoics.

Many natural and technological systems are complex, with organizational structures that exhibit characteristic patterns but defy concise description. One effective approach to analyzing such systems is in terms of repeated topological motifs. Here, we extend the motif concept to characterize the dynamic behavior of complex systems by introducing developmental motifs, which capture patterns of system growth. As a proof of concept, we use developmental motifs to analyze the developmental cell lineage of the nematode Caenorhabditis elegans, revealing a new perspective (...) on its complex structure. We use a family of computational models to explore how biases arising from the dynamics of the developmental gene network, as well as spatial and temporal constraints acting on development, contribute to this complex organization. © 2010 Wiley Periodicals, Inc. Complexity 16: 48‐57, 2011. (shrink)

A proof of Fermat’s last theorem is demonstrated. It is very brief, simple, elementary, and absolutely arithmetical. The necessary premises for the proof are only: the three definitive properties of the relation of equality (identity, symmetry, and transitivity), modus tollens, axiom of induction, the proof of Fermat’s last theorem in the case of n = 3 as well as the premises necessary for the formulation of the theorem itself. It involves a modification of Fermat’s approach of infinite (...) descent. The infinite descent is linked to induction starting from n = 3 by modus tollens. An inductive series of modus tollens is constructed. The proof of the series by induction is equivalent to Fermat’s last theorem. As far as Fermat had been proved the theorem for n = 4, one can suggest that the proof for n ≥ 4 was accessible to him. An idea for an elementary arithmetical proof of Fermat’s last theorem (FLT) by induction is suggested. It would be accessible to Fermat unlike Wiles’s proof (1995). (shrink)

1. Fairness is about the just distribution of society's resources, and in ML, the main resource being distributed is model performance, e.g. the translation quality produced by machine translation...

Anayltical study of epistemology in Indian philosophy.

The article investigates whether Hobbes’s political theory gives us reason to expect the systematic subordination of women. It argues that who dominates whom is a matter of victory in the quest to pull allies into ordered alliances. The primary means of gaining allies—force and wiles—depend on both skill-fitness and affective fitness. The analyses suggest that it is sex-linked and gender-linked differences in affective fitness—particularly in the intensity of men’s desire to use religious wiles—that most plausibly explain the subjection of women, (...) both across the spectrum of states of nature and within civil societies. Although Hobbes’s political theory enables us to make sense of how it happened, there is nothing in that theory that either necessitates or should cause us to expect the systematic subordination of women. (shrink)

Some sufficient conditions on a Symmetric Monoidal Closed category K are obtained such that a diagram in a free SMC category generated by the set A of atoms commutes if and only if all its interpretations in K are commutative. In particular, the category of vector spaces on any field satisfies these conditions . Instead of diagrams, pairs of derivations in Intuitionistic Multiplicative Linear logic can be considered . Two derivations of the same sequent are equivalent if and only if (...) all their interpretations in K are equal. In fact, the assignment of values to atoms is defined constructively for each pair of derivations. Taking into account a mistake in R. Voreadou's proof of the “abstract coherence theorem” found by the author, it was necessary to modify her description of the class of non-commutative diagrams in SMC categories; our proof of S. Mac Lane conjecture also proves the correctness of the modified description. (shrink)

A sequent calculus methodology for systems of agency based on branching-time frames with agents and choices is proposed, starting with a complete and cut-free system for multi-agent deliberative STIT; the methodology allows a transparent justification of the rules, good structural properties, analyticity, direct completeness and decidability proofs.

In “The Gettier Problem and Legal Proof,” I argue that epistemic conditions that undermine knowledge in Gettier-type cases also potentially undermine legal verdicts. For this reason, I argue, there is a deeper connection between knowledge and legal proof than is typically presupposed or argued for in the scholarly legal literature. To support these claims, I present several examples illustrating how conditions that render epistemically justified beliefs merely accidentally true (and thus disqualify them as cases of genuine knowledge) may (...) also render evidentially well-supported verdicts merely accidentally true for similar reasons. Such “Gettierized” verdicts, I contend, fail to realize the epistemic goal or aim of legal proof. Thus I conclude there, legal proof includes something like a knowledge requirement—in the sense that legal verdicts aim not only at truth and sufficient evidential support but also, as with knowledge, at an appropriate connection between their truth and justifying evidential support. (shrink)

Contents include: Foreword Editor's Preface Introduction by the Editor Preface Introduction BOOK ONE: The Objective Problem Concerning the Truth of Christianity Introductory Remarks Chapter I: The Historical Point of View 1. The Holy Scriptures 2. The Church 3. The Proof of the Centuries for the Truth of Christianity Chapter II: The Speculative Point of View BOOK TWO: The Subjective Problem, The Relation of the Subject to the Truth of Christianity, The Problem of Becoming a Christian PART ONE: Something About (...) Lessing Chapter I: An Expression of Gratitude Chapter II: Theses Possibly or Actually Attributable to Lessing 1. The subjective existing thinker has regard to the dialectics of the process of communication 2. The existing subjective thinker is in his existential relation to the truth as negative as he is positive; he has a much humor as he has essential pathos; and he is constantly in process of becoming, i.e. he is always striving 3. Lessing has said that accidental historical truths can never serve as proofs for eternal truths of the reason; and that the transition by which it is proposed to base an eternal truth upon historical testimony is a leap 4. Lessing has said that, if God held all truth in His right hand, and in His left the lifelong pursuit of it, he would choose the left hand A. A logical system is possible B. An existential system is possible PART TWO: How the Subjectivity of the Individual Must be Qualified in Order that the Problem May Exist for Him Chapter I: The Task of Becoming Subjective. The conclusion that would be forced upon ethics if the attainment of subjectivity were not the highest task confronting a human being—Considerations left out of account in connection with the closer understanding of this—Examples of thinking directed towards becoming subjective Chapter II: The Subjective Truth, Inwardness; Truth is Subjectivity Appendix. A Glance at the Contemporary Effort in Danish Literature Chapter III: Real or Ethical Subjectivity—The Subjective Thinker 1. Existence and Reality 2. Possibility as higher than Reality—Reality as higher than Possibility—Poetic and Intellectual Ideality—Ethical Ideality 3. The Simultaneity of the Individual Factors of Subjectivity in the Existing Subject—The Constrast between this Simultaneity and the Speculative Process 4. The Subjective Thinker—his Task, his Form, his Style Chapter IV: The Problem of the Fragments: How can an Eternal Happiness be based upon Historical Knowledge? Section I. For Orientation in the Plan of the Fragments 1. That the point of departure was taken in the pagan consciousness, and why 2. The importance of a preliminary agreement concerning what Christianity is, before there can be any question of mediating between Christianity and speculative thought. The absence of such an agreement favors the proposal of medication, while at the same time making any mediation illusory; the presence of such an agreement precludes mediation 3. The problem of the Fragments viewed as a problem, introductory not to Christianity, but to becoming a Christian Section II. The Problem Itself. The eternal happiness of the individual is decided in time through the relationship to something historical, which is furthermore of such a character as to oinclude in its composition that which by virtue of its essence cannot become historical, and must therefore become such by virtue of the absurd A. Existential Pathos 1. The Initial Expression for Existential Pathos: the absolute direction (respect) toward the absolute telos, expressed in action through the transformation of the individual's existence Aesthetic Pathos—The deceptiveness of the principle of mediation—The medieval monastic movement—The simultaneous maintenance of an absolute relationship to the absolute telos and a relative relationship to the relative ends 2. The Essential Expression for Existential pathos: Suffering—Fortune and misforutne as the expression for an aesthetic view of life, in constradistinction to suffering as the expression of a religious view (illustrated by reference to the religious discourse)—The Reality of suffering (humor)—The reality of suffering in the last instance as evidence for the possession by the existing individual of a relationship to an eternal happiness—The illusion of religiosity—The category of Anfechtung—The primary ground and significance of the religious suffering: The dying away from the life of immediacy while still remaining in the finite—An edifying divertisement—Humor as an incognito for religiosity 3. The Decisive Expression for existential pathos: Guilt—That the investigation goes backward instead of forward—The eternal recollection of guilt is the highest expression for the relation between the consciousness of guilt and an eternal happiness—Lower expressions for the consciousness of guilt, and corresponding forms of satisfaction—Self-imposted penance—Humor—The religiosity of hidden inwardness Intermediate Clause between A and B B. The Dilectical 1. The dialectical contradiction which constitutes the breach: to expect an eternal happiness in time through a relationship to something else in time 2. The dialectical constradiction that an eternal happiness is based upon something historical 3. The dialectical contradiction that the historical fact here in question is not a simple historical fact, but is constituted by that which only against its nature can become historical, hence by virtue of the absurd Appendix to B. The retroactive effect of the dialectical upon the pathetic, and the factor simultaneously present in the pathos (a) The consciousness of sin (b) The possibililty of offense (c) The smart of sympathy Chapter V. Conclusion. About Childish Christianity Appendix. For an Understanding with the Reader First and Last Declaration Notes Index Originally published in 1941. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905. (shrink)

This introduction to the basic ideas of structural proof theory contains a thorough discussion and comparison of various types of formalization of first-order logic. Examples are given of several areas of application, namely: the metamathematics of pure first-order logic (intuitionistic as well as classical); the theory of logic programming; category theory; modal logic; linear logic; first-order arithmetic and second-order logic. In each case the aim is to illustrate the methods in relatively simple situations and then apply them elsewhere in (...) much more complex settings. There are numerous exercises throughout the text. In general, the only prerequisite is a standard course in first-order logic, making the book ideal for graduate students and beginning researchers in mathematical logic, theoretical computer science and artificial intelligence. For the new edition, many sections have been rewritten to improve clarity, new sections have been added on cut elimination, and solutions to selected exercises have been included. (shrink)

Talk about God is often the source of controversy. Theists and atheists are equally passionate when making their stand for or against belief in God. In this book, a wide range of philosophers of religion have come together to discuss how serious talk about God ought to be conducted for theists and atheists alike in what should be their common pursuit for truth. The essays both address methodological questions and provide a range of concrete samples of serious God-talk, spanning from (...) political, religion, and classical proofs of God's existence to the problem of evil. (Series: Nordic Studies in Theology / Nordische Studien zur Atheism, Vol. 4) [Subject: Religious Studies]Ã?Â?Ã?Â? (shrink)

Part 1. Plan of This Commentary -- From an Epigram by Filangieri against Improvement in the Art of War -- On Encouragements for Agriculture -- On the Conversion of Rulers to Peace -- On the Salutary Revolution Which Filangieri Foresaw -- On the Union of Politics and Legislation -- On the Influence Which Filangieri Attributes to Legislation -- On the State of Nature, the Formation of Society, and the True Goal of Human Associations -- On Errors in Legislation -- Some (...) Remarks by Filangieri on the Decline of Spain -- On Filangieri's Observations about France -- On the Decline Filangieri Predicted for England -- Part 2. Object of this Second Part -- On the Black Slave Trade -- On Population -- Continuation of the Same Subject -- On Malthus's System Relating to Population -- Some Writers Who Have Exaggerated M. Malthus's System -- On a Contradiction by Filangieri -- On the Division of Properties -- On the Grain Trade -- On Agriculture as a Source of Wealth -- On the Protection Given Industry -- A New Proof of Filangieri's Fundamental Mistake -- On Guilds and Masters -- On Privileges for Industry -- On Taxation -- Part 3. On Criminal Prosecution Confided Exclusively to a Magistrate -- On Secret Indictments -- On Denunciation -- New Thoughts on the Idea of Giving Each Citizen the Right to Prosecute -- New Thoughts on the Idea of Giving Each Citizen the Right to Prosecute -- On the Right to Prosecute Given to Servants, When It Is a Question of Crimes against Society -- That the Prosecuting Magistrate Should Be Responsible, If Not for the Truth, at Least for the Legitimacy of the Accusation -- On Prisons -- On the Shortening of Legal Procedures -- On Defense Witnesses -- On Judgment by Juries -- On the Death Penalty -- On Convict Labor -- On Deportation -- Part 4. On Education -- On Religion -- Of the Growth of Polytheism -- On the Priesthood -- On the Mysteries -- Conclusion. (shrink)

A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.

A survey of works on automatic theorem-proving in the ussr 1964-1970. the philosophical problems are not touched.

The Curry-Howard isomorphism states an amazing correspondence between systems of formal logic as encountered in proof theory and computational calculi as found in type theory. For instance, minimal propositional logic corresponds to simply typed lambda-calculus, first-order logic corresponds to dependent types, second-order logic corresponds to polymorphic types, sequent calculus is related to explicit substitution, etc. The isomorphism has many aspects, even at the syntactic level: formulas correspond to types, proofs correspond to terms, provability corresponds to inhabitation, proof normalization (...) corresponds to term reduction, etc. But there is more to the isomorphism than this. For instance, it is an old idea---due to Brouwer, Kolmogorov, and Heyting---that a constructive proof of an implication is a procedure that transforms proofs of the antecedent into proofs of the succedent; the Curry-Howard isomorphism gives syntactic representations of such procedures. The Curry-Howard isomorphism also provides theoretical foundations for many modern proof-assistant systems (e.g. Coq). This book give an introduction to parts of proof theory and related aspects of type theory relevant for the Curry-Howard isomorphism. It can serve as an introduction to any or both of typed lambda-calculus and intuitionistic logic. Key features - The Curry-Howard Isomorphism treated as common theme - Reader-friendly introduction to two complementary subjects: Lambda-calculus and constructive logics - Thorough study of the connection between calculi and logics - Elaborate study of classical logics and control operators - Account of dialogue games for classical and intuitionistic logic - Theoretical foundations of computer-assisted reasoning · The Curry-Howard Isomorphism treated as the common theme. · Reader-friendly introduction to two complementary subjects: lambda-calculus and constructive logics · Thorough study of the connection between calculi and logics. · Elaborate study of classical logics and control operators. · Account of dialogue games for classical and intuitionistic logic. · Theoretical foundations of computer-assisted reasoning. (shrink)

This article explores the relationships between legal proof and fundamental epistemic concepts such as knowledge and justification. A survey of the legal literature reveals a confusing array of seemingly inconsistent proposals and presuppositions regarding these relationships. This article makes two contributions. First, it reconciles a number of apparent inconsistencies and tensions in accounts of the epistemology of legal proof. Second, it argues that there is a deeper connection between knowledge and legal proof than is typically argued for (...) or presupposed in the legal literature. This connection is illustrated through a discussion of the Gettier problem in epistemology. It is argued that the gap or disconnect between truth and justification that undermines knowledge in Gettier cases also potentially undermines the success of legal verdicts. (shrink)