We observe that in certain two-player repeated games of incomplete information, where information may be incomplete on both sides, it is possible for an informed player to signal his status as an informed player to the other without revealing any information about the choice of chance. The key to obtaining such a class of games is to relax the assumption that the players’ moves are observable. We show that in such cases players can achieve a kind of signaling that is (...) “zero-knowledge”, in the sense that the other player becomes convinced that her opponent is informed without ever learning the choice of chance. Moreover, such “zero-knowledge signaling” has all of the statistical properties associated with zero-knowledge proofs in intereactive protocols. In particular, under the general assumption that moves are unobservable, such signaling leads to a class of equilibria in repeated games that are separatingin regard to the status of player 1–informed or uninformed–but only for player 2; any other player in a network, being unable to observe the moves of player 2, remains uncertain as to the status of player 1. (shrink)

As privacy concerns among consumers rise, service providers increasingly want to provide services that support privacy enhancing technologies. At the same time, online service providers must be able to protect themselves against misbehaving users. For instance, users that do not pay their bill must be held accountable for their behavior. This tension between privacy and accountability is fundamental, however a tradeoff is not always required. In this article we propose the concept of a time capsule, that is, a verifiable encryption (...) with timed and revocable decryptability. The time capsule together with its related protocols offer support of privacy while retaining strong accountability. In our scheme an honest user may enjoy full anonymity, but dishonest users who do not pay their bill have their identity revealed. In contrast to existing revocable anonymity systems, our proposed scheme requires less trust in an external authority, while simultaneously making accountability easier (and less costly) to achieve. (shrink)

Arrow’s information paradox features the most radical kind of information asymmetry by diagnosing an inherent conflict between two parties inclined to exchange information. In this paper, we argue that this paradox is more richly textured than generally supposed by current economic discussion on it and that its meaning encroaches on philosophy. In particular, we uncovers the ‘epistemic’ and more genuine version of the paradox, which looms on our cognitive lives like a sort of tax on curiosity. Finally, we sketch the (...) relation between Arrow’s information paradox and the notion of zero-knowledge proofs in cryptography: roughly speaking, zero-knowledge proofs are protocols that enable a prover to convince a verifier that a statement is true, without conveying any additional information. (shrink)

I discuss the knowledge account of legal proof in Moss (2023) and develop an alternative. The unifying thread throughout this article are reflections on the beyond reasonable doubt (BRD) standard of proof. In Section 1, I will introduce the details of Moss’s account and how she motivates it via the BRD standard. In Section 2, I will argue that there are important disanalogies between BRD and knowledge that undermine Moss’s argument. There is however another motivation for (...) the knowledge account: combined with auxiliary claims, that is probabilistic knowledge and moral encroachment, it can provide a general solution to the puzzle of statistical evidence. Section 3 spells out the details. In Section 4, I suggest to combine the knowledge account with pragmatic encroachment, instead of moral encroachment, in order to stay clear of the thorny issues whether corporations have moral rights. In Section 5, I argue that the verdicts of Moss’s account in cases of false justified beliefs and non-luminous knowledge conflict with the BRD standard and thus call for abandoning the account. Based on the social function of the BRD standard, I suggest a replacement for the knowledge account that is also just as potent as a general solution for the puzzle of statistical evidence. While I will grant that knowledge is neither always necessary nor always sufficient for convictions, I will argue that the concept of knowledge nonetheless plays a significant and ineliminable role in legal decision-making. (shrink)

ABSTRACT In this paper we define two logics, KLn and BLn, and present tableau-based decision procedures for both. KLn is a temporal logic of knowledge. Thus, in addition to the usual connectives of linear discrete temporal logic, it contains a set of unary modal connectives for representing the knowledge possessed by agents. The logic BLn is somewhat similar; it is a temporal logic that contains connectives for representing the beliefs of agents. In addition to a complete formal definition (...) of the two logics and their decision procedures, the paper includes a brief review of their applications in AI and mainstream computer science, correctness proofs for the decision procedures, a number of worked examples illustrating the decision procedures, and some pointers to further work. (shrink)

Despite recent controversies surrounding the principle that knowledge entails truth (KT), this paper aims to prove that the principle is true. It offers a proof of (KT) in the following sense. It advances a deductively valid argument for (KT), whose premises are, by most lights, obviously true. Moreover, each premise is buttressed by at least two supporting arguments. And finally, all premises and supporting arguments can be rationally accepted by people who don’t already accept (KT).

These questions arise from any attempt to discover an epistemology for mathematics. This collection of essays considers various questions concerning the nature of justification in mathematics and possible sources of that justification. Among these are the question of whether mathematical justification is _a priori_ or _a posteriori_ in character, whether logical and mathematical differ, and if formalization plays a significant role in mathematical justification.

This volume of essays addresses the main problem confronting an epistemology for mathematics; namely, the nature and sources of mathematical justification. Attending to both particular and general issues, the essays, by leading philosophers of mathematics, raise important issues for our current understanding of mathematics. Is mathematical justification a priori or a posteriori? What role, if any, does logic play in mathematical reasoning or inference? And of what epistemological importance is the formalizability of proof? The editor, Michael Detlefsen, has brought (...) together an outstanding collection of essays, only one of which has previously appeared. It will be essential for philosophers and historians of mathematics, as well as philosophically inclined logicians and philosophers interested in the nature of reasoning and justification. A companion volume entitled Proof, Logic and Formalization, edited by Michael Detlefsen, is also available from Routledge. (shrink)

In epistemology, the concept of knowledge is of distinctive interest. This fact is also reflected in the discussion of epistemic value, which focuses to a large extend on the value problem of knowledge. This discussion suggests that knowledge has an outstanding value among epistemic standings because its value exceeds the value of its constitutive parts. I will argue that the value of knowledge is not outstanding by presenting epistemic standings of checking, transferring knowledge, and proving (...) in court, whose values exceed the value of knowledge in certain contexts. Moreover, the values of these other epistemic standings do not always rely on the value of knowledge. In terms of value, knowledge is not an outstanding epistemic concept. Hence, in terms of value we cannot find support for the privileged position that knowledge enjoys in epistemology. (shrink)

This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing (...) skills. This book is most successful in a small, seminar style class. Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers For all readers interested in abstract mathematics. (shrink)

In the third Meditation once having arrived at the conclusion that a perfect being exists, Descartes infers that this perfect being could not be a deceiver. I maintain that there is no valid way he can move from his conclusion that a perfect being exists to the conclusion that this being cannot be a deceiver. In order to see the difficulties with this inference it is necessary to examine the use of the idea of perfection in the argument for the (...) existence of the perfect being, but I will not otherwise concern myself with the validity of the argument for the existence of God. (shrink)

We give a uniform proof of the theorems of Yao and Beigel–Tarui representing ACC predicates as constant depth circuits with MODm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {MOD}_{m}$$\end{document} gates and a symmetric gate. The proof is based on a relativized, generalized form of Toda’s theorem expressed in terms of closure properties of formulas under bounded universal, existential and modular counting quantifiers. This allows the main proofs to be expressed in terms of formula classes instead of (...) Boolean circuits. The uniform version of the Beigel–Tarui theorem is then obtained automatically via the Furst–Saxe–Sipser and Paris–Wilkie translations. As a special case, we obtain a uniform version of Razborov and Smolensky’s representation of AC0[p]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {AC}^{0}[p]$$\end{document} circuits. The paper is partly expository, but is also motivated by the desire to recast Toda’s theorem, the Beigel–Tarui theorem, and their proofs into the language of bounded arithmetic. However, no knowledge of bounded arithmetic is needed. (shrink)

Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We (...) also show that some of what mathematicians take to be deductive knowledge is in fact non-deductive. 1 Introduction2 Why It Might Matter3 Two Further Examples and Preliminaries4 An Exclusive Epistemic Virtue of Proof?5 Analyses of Knowledge6 The Inductive Basis of Deduction7 Physical to Mathematical Linkages8 Conclusion. (shrink)

An enormous intellectual adventure. In this groundbreaking new book, the American biologist Edward O. Wilson, considered to be one of the world's greatest living scientists, argues for the fundamental unity of all knowledge and the need to search for consilience --the proof that everything in our world is organized in terms of a small number of fundamental natural laws that comprise the principles underlying every branch of learning. Professor Wilson, the pioneer of sociobiology and biodiversity, now once again (...) breaks out of the conventions of current thinking. He shows how and why our explosive rise in intellectual mastery of the truths of our universe has its roots in the ancient Greek concept of an intrinsic orderliness that governs our cosmos and the human species--a vision that found its apogee in the Age of Enlightenment, then gradually was lost in the increasing fragmentation and specialization of knowledge in the last two centuries. Drawing on the physical sciences and biology, anthropology, psychology, religion, philosophy, and the arts, Professor Wilson shows why the goals of the original Enlightenment are surging back to life, why they are reappearing on the very frontiers of science and humanistic scholarship, and how they are beginning to sketch themselves as the blueprint of our world as it most profoundly, elegantly, and excitingly is. (shrink)

This paper reveals and corrects a flaw in Nozick’s account of knowledge via inference. First, two counterexamples are provided by considering cases which would not typically be regarded as instances of knowledge although they are counted as such by Nozick’s theory. Then the general form of these counterexamples is given. From this it is apparent that the counterexamples show that Nozick’s theory fails to take account of cases in which the subject infers q from p, but in counterfactual (...) situations some proposition other than p would entail q. In view of this, the theory is then revised to eliminate the counterexamples. (shrink)

In this paper I shall present a method for proving determinacy from large cardinals which, in many cases, seems to yield optimal results. One of the main applications extends theorems of Martin, Steel and Woodin about determinacy within the projective hierarchy. The method can also be used to give a new proof of Woodin's theorem about determinacy in L.The reason we look for optimal determinacy proofs is not only vanity. Such proofs serve to tighten the connection between large cardinals (...) and descriptive set theory, letting us bring our knowledge of one subject to bear on the other, and thus increasing our understanding of both. A classic example of this is the Harrington-Martin proof that -determinacy implies -determinacy. This is an example of a transfer theorem, which assumes a certain determinacy hypothesis and proves a stronger one. While the statement of the theorem makes no mention of large cardinals, its proof goes through 0#, first proving that-determinacy ⇒ 0# exists,and then that0# exists ⇒ -determinacyMore recent examples of the connection between large cardinals and descriptive set theory include Steel's proof thatADL ⇒ HODL ⊨ GCH,see [9], and several results of Woodin about models of AD+, a strengthening of the axiom of determinacy AD which Woodin has introduced. These proofs not only use large cardinals, but also reveal a deep, structural connection between descriptive set theoretic notions and notions related to large cardinals. (shrink)

This is a collection of twenty-seven essays written by its author between 1962 and 1989 on topics in the history of science, the philosophy of science, and "the relevance of scientific practice to other parts of philosophy and culture". Twenty-one have been previously published, the remainder hitherto aired only as public presentations. The papers are gathered under six section-headings, including "Explanation," "Hume's Problem," "Logic and Causality," "Machines and Practices," "Scientific Knowledge--Its Scope and Limits," and "Science and Subjectivity"; yet their (...) actual range is both more diverse and less in keeping with prevailing currents in the philosophy of science than these tidily familiar rubrics suggest. "Explanation," for example, flirts with mainstream subject-matter in a much deserved encomium to Hempel's contributions in philosophy of science that reaches beyond the titular subject to the whole of Hempel's work. The section also embraces a discussion of General Systems Theory that distinguishes a doctrinaire, a prioristic approach to the study of science from a pragmatic-pluralistic version, urging the ills of the former and the virtues of the latter. It culminates in two presentations of the view that the theory of evolution rests on "circumstantial evidence" only as it involves the "logical fallacy" of "the inference of causes from effects" : the one is a historical piece on the little-known nineteenth-century naturalist, Phillip Henry Gosse, highlighting his creationistic "Omphalos" theory of the origins of biological species and the fossil record; the other is a short treatment of some conceptual issues involved in the creationist controversy. If the remaining five sections are not so heterogeneous in the scatter of subjects on which their articles touch, they are for the most part more idiosyncratic in the issues they address, the questions they raise, and the answers they suggest. Typical are "On Being in the Same Place at the Same Time," an argument for the ultimacy of subjectivity on the basis of relativity theory, and "Truth and Presence," explicating the attempt of Gaston Bachelard to blend science and poetry as complementary aspects of the human imagination. Sometimes they are also eyebrow-raising. "The Paradox of Induction and the Inductive Wager," would "show the impossibility of... logical proof [of the principle of induction]... by locating it among the paradoxes". Caw's case for paradox is simply that if inductive inference is legitimate then our past inability to justify such inference warrants the inductive conclusion that we shall never be able to justify it. But even if nothing else were suspect in this argument, its force is presumably at most probabilistic, making it hard to see how it could establish the "impossibility" of anything. Another paper, "Three Logics, or the Possibility of the Improbable," concerns "the logic of incredible events", touting the merits of so construing the natural world that events with zero probability occasionally occur and initiate spontaneous causal chains. Yet it is thoroughly unclear what interpretation of probability theory could both license identifying uncaused with impossible events and yet allow that such events may occur. Still another, "Rethinking Intentionality," includes the puzzling contention that "there can't be a science of intention because science presupposes intention". Unlike these last examples, most of the essays in the collection are provocative rather than upsetting, bearing the earmark of the independent, iconoclastic, speculative mind from which they spring, a former physicist not aligned with any of the current schools in philosophy of science, and more influenced by the classic giants of the Western philosophical tradition and by Hegel, Husserl, Heidegger, and Sartre than by empiricist philosophers of science or the recent analytic tradition. Thus, it is no surprise that the issues Caws addresses are nonstandard, and that his manner of addressing them embodies a looser, more broad-stroked, more humanistic, and more metaphysically self-conscious approach than is common in recent mainstream philosophy of science. This orientation doubtless accounts, too, for the somewhat subjective-idealistic stance, the view that one cannot definitively progress beyond one's own sensations and ideas, argued in "Yorick's World or the Universe in a Single Skull," and manifest in the tone, substance, and central thrust of a number of the essays in the collection. It is thus appropriate that Caws should have borrowed from this title to name the anthology itself.-Robert B. Barrett, Washington University in St. Louis. (shrink)

Existing discussions of legal proof address a host of apparently disparate questions: What does it take to prove a fact beyond a reasonable doubt? Why is the reasonable doubt standard notoriously elusive, sometimes considered by courts to be impossible to define? Can the standard of proof by a preponderance of the evidence be defined in terms of probability thresholds? Why is statistical evidence often insufficient to meet the burden of proof? -/- This paper defends an account of (...) proof that addresses each of these questions. Where existing theories take a piecemeal approach to these puzzles, my theory develops an insight that unifies them—namely, the thesis that legal proof requires knowledge. Although this thesis may seem radical at first, I answer several common objections to it, and I argue that it does better than several competing accounts when it comes to making sense of our intuitions about what legal proof requires. (shrink)

The first aim of this paper is to prove a topological completeness theorem for a weak version of Stalnaker’s logic KB of knowledge and belief. The weak version of KB is characterized by the assumption that the axioms and rules of KB have to be satisfied with the exception of the axiom (NI) of negative introspection. The proof of a topological completeness theorem for weak KB is based on the fact that nuclei (as defined in the framework of (...) point-free topology) give rise to a profusion of topological belief operators that are compatible with the familiar topological knowledge operator. Thereby a canonical topological model for weak KB can be constructed. For this canonical model a truth lemma for the K and B holds such that a completeness theorem for KB can be proved in the familiar way. The second aim of this paper is to show that the topological interpretation of knowledge K comes along with a complete Heyting algebra of belief operators B that all fit the knowledge operator K in the sense that the pairs (K, B) satisfy all axioms of weak KB. This amounts to a pluralistic relation between knowledge and belief: Knowledge does not fully determine belief, rather it designs a conceptual space for belief operators where different (competing) belief operators coexist. (shrink)

This paper reveals and corrects a flaw in Nozick’s account of knowledge via inference. First, two counterexamples are provided by considering cases which would not typically be regarded as instances of knowledge although they are counted as such by Nozick’s theory. Then the general form of these counterexamples is given. From this it is apparent that the counterexamples show that Nozick’s theory fails to take account of cases in which the subject infers q from p, but in counterfactual (...) situations some proposition other than p would entail q. In view of this, the theory is then revised to eliminate the counterexamples. (shrink)

Several justification logics have been created, starting with the logic LP, [1]. These can be thought of as explicit versions of modal logics, or of logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. We begin by sketching the basics of justification logics and their relations with modal logics. Then we move to new material. Modal logics come in various strengths. For their corresponding justification (...) logics, differing strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

Despite increasing the presence of ‘ethics talk’ in business and management curricula, the ability of business ethics educators to question the system and support the development of morally responsible agents is debatable. This is not because of a lack of care or competence; rather, this situation points towards a more general tendency of education to become focused on economic growth, as Nussbaum claims. Revisiting the nature of ethics education, I argue that much moral learning occurs through the imagination, and not (...) solely through the rational mind. Individuals are complex, and a great part of what we are lies below the threshold of consciousness. In this respect, ethics education must take into account the psyche and its influence on conscious behaviour, which can best be apprehended through the imagination. Echoing Jung’s concerns about unconscious and indiscriminate masses, I thus explore how imagination and creative material contribute to enhancing both self-knowledge and ethical reflection in the context of organisational life and business education. I especially consider how moral development and social awareness are tied up with individual psychological understanding, and argue that Jung’s analytical psychology offers insightful tools to explore our individuality. (shrink)

Common knowledge of a proposition A can be characterized by the following infinitary conjunction: everybody knows A and everybody knows that everybody knows A and everybody knows that everybody knows that everybody knows A and so on. We present a survey of deductive systems for the logic of common knowledge. In particular, we present two different Hilbert-style axiomatizations and two infinitary cut-free sequent systems. Further we discuss the problem of syntactic cut-elimination for common knowledge. The paper concludes (...) with a list of open problems. (shrink)

Written for any motivated reader with a high-school knowledge of mathematics, and the discipline to follow logical arguments, this book presents the proofs for revolutionary impossibility theorems in an accessible way, with less jargon and notation, and more background, intuition, examples, explanations, and exercises.

Could it be right to convict and punish defendants using only statistical evidence? In this paper, I argue that it is not and explain why it would be wrong. This is difficult to do because there is a powerful argument for thinking that we should convict and punish defendants using statistical evidence. It looks as if the relevant cases are cases of decision under risk and it seems we know what we should do in such cases (i.e., maximize expected value). (...) Given some standard assumptions about the values at stake, the case for convicting and punishing using statistical evidence seems solid. In trying to show where this argument goes wrong, I shall argue (against Lockeans, reliabilists, and others) that beliefs supported only by statistical evidence are epistemically defective and (against Enoch, Fisher, and Spectre) that these epistemic considerations should matter to the law. To solve the puzzle about the role of statistical evidence in the law, we need to revise some commonly held assumptions about epistemic value and defend the relevance of epistemology to this practical question. (shrink)

This chapter discusses Kant's 1763 "possibility proof" for the existence of God. I first provide a reconstruction of the proof in its two stages, and then revisit my earlier argument according to which the being the proof delivers threatens to be a Spinozistic-panentheistic God—a being whose properties include the entire spatio-temporal universe—rather than the traditional, ontologically distinct God of biblical monotheism. I go on to evaluate some recent alternative readings that have sought to avoid this result by (...) arguing that the relevant facts about real modality can be ultimately grounded in God’s powers or thoughts – or that Kant just leaves the grounding relations mysterious. I argue that the textual and philosophical costs of each of these alternative readings are formidable. The chapter concludes with a discussion of the fate of the proof in the critical period. Some commentators think that it disappears altogether, or that it is downgraded such that it produces a mere regulative idea of God as the most real being. I suggest that the proof survives but that the mode of assent it licenses towards its conclusion changes from knowledge to a certain kind of Belief (Glaube). (shrink)

What determines whether the procedures for proving the affirmative statement of God's existence may be called a proof? Certainly, it is necessary that all premises be true and that a reliable inference schemata be applied. One premise appears to be the most critical in the theistic argument. This premise is the principle of sufficient reason. I hold the view that the principle of sufficient reason cannot be found among the premises of any metaphysical explanation of reality, so I suggest (...) that the terms “proof” and “argument” not be used. Instead, we could speak of ways of acquiring discursive knowledge of God and ways of indirect substantiation of God's existence. (shrink)

What determines whether the procedures for proving the affirmative statement of God's existence may be called a proof? Certainly, it is necessary that all premises be true and that a reliable inference schemata be applied. One premise appears to be the most critical in the theistic argument. This premise is the principle of sufficient reason. I hold the view that the principle of sufficient reason cannot be found among the premises of any metaphysical explanation of reality, so I suggest (...) that the terms “proof” and “argument” not be used. Instead, we could speak of ways of acquiring discursive knowledge of God and ways of indirect substantiation of God's existence. (shrink)

A new understanding of Kant’s theory of a priori knowledge and his natural philosophy emerges from Jeffrey Edwards’s mature and penetrating study. In the Third Analogy of Experience, Kant argues for the existence of a dynamical plenum in space. This argument against empty space demonstrates that the dynamical plenum furnishes an a priori necessary condition for our experience and knowledge of an objective world. Such an a priori existence proof, however, transgresses the limits Kant otherwise places on (...) transcendental arguments in the _Critique of Pure Reason_ because it establishes a _material_ transcendental condition of possible experience. This finding motivates Edwards to examine the broader context of Kant’s views about matter, substance, causal influence, and physical aether in connection with the developmental history of his theory of transcendental idealism. Against the backdrop of early modern metaphysics and contemporaneous physical theory, Edwards explicates the origins of the Third Analogy in Kant’s early work on the metaphysics of nature. The argument against empty space presented in the Third Analogy reveals a central aspect of Kant’s transcendental theory of experience that Edwards explains lucidly. By clarifying the epistemological standpoint at issue in the Third Analogy, he shows that the fundamental revisions to which Kant subjects his theory of knowledge in the _Opus postumum_ not only originate in his precritical metaphysics of nature but are developments of an argument central to the _Critique of Pure Reason_ itself. Edwards’s work is important to scholars working in the history of philosophy and the history and philosophy of science, as well as to Kant specialists. (shrink)

Several justification logics have evolved, starting with the logicLP, (Artemov 2001). These can be thought of as explicit versions of modal logics, or logics of knowledge or belief, in which the unanalyzed necessity (knowledge, belief) operator has been replaced with a family of explicit justification terms. Modal logics come in various strengths. For their corresponding justification logics, differing strength is reflected in different vocabularies. What we show here is that for justification logics corresponding to modal logics extending T, (...) various familiar extensions are actually conservative with respect to each other. Our method of proof is very simple, and general enough to handle several justification logics not directly corresponding to distinct modal logics. Our methods do not, however, allow us to prove comparable results for justification logics corresponding to modal logics that do not extend T. That is, we are able to handle explicit logics of knowledge, but not explicit logics of belief. This remains open. (shrink)

A new understanding of Kant’s theory of a priori knowledge and his natural philosophy emerges from Jeffrey Edwards’s mature and penetrating study. In the Third Analogy of Experience, Kant argues for the existence of a dynamical plenum in space. This argument against empty space demonstrates that the dynamical plenum furnishes an a priori necessary condition for our experience and knowledge of an objective world. Such an a priori existence proof, however, transgresses the limits Kant otherwise places on (...) transcendental arguments in the _Critique of Pure Reason_ because it establishes a _material_ transcendental condition of possible experience. This finding motivates Edwards to examine the broader context of Kant’s views about matter, substance, causal influence, and physical aether in connection with the developmental history of his theory of transcendental idealism. Against the backdrop of early modern metaphysics and contemporaneous physical theory, Edwards explicates the origins of the Third Analogy in Kant’s early work on the metaphysics of nature. The argument against empty space presented in the Third Analogy reveals a central aspect of Kant’s transcendental theory of experience that Edwards explains lucidly. By clarifying the epistemological standpoint at issue in the Third Analogy, he shows that the fundamental revisions to which Kant subjects his theory of knowledge in the _Opus postumum_ not only originate in his precritical metaphysics of nature but are developments of an argument central to the _Critique of Pure Reason_ itself. Edwards’s work is important to scholars working in the history of philosophy and the history and philosophy of science, as well as to Kant specialists. (shrink)

In this paper, the traditional view that argumentum ad ignorantiam is a logical fallacy is challenged, and lessons are drawn on how to model inferences drawn from knowledge in combination with ones drawn from lack of knowledge. Five defeasible rules for evaluating knowledge-based arguments that apply to inferences drawn under conditions of lack of knowledge are formulated. They are the veridicality rule, the consistency of knowledge rule, the closure of knowledge rule, the rule of (...) refutation and the rule for argument from ignorance. The basic thesis of the paper is that knowledge-based arguments, including the argument from ignorance, need to be evaluated by criteria for epistemic closure and other evidential rules that are pragmatic in nature, that need to be formulated and applied differently at different stages of an investigation or discussion. The paper helps us to understand practical criteria that should be used to evaluate all arguments based on knowledge and/or ignorance. (shrink)

This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on (...) the complexities of the process of formalisation. Chapter 3 looks into the relationship between proofs and the development of the mathematical concepts that feature in them. I deploy Waismann's notion of open texture in the case of mathematical concepts, and discuss both Lakatos and Kneebone's dialectical philosophies of mathematics. I then argue that we can apply work from conceptual engineering to the relationship between formal and informal mathematics. The fourth chapter argues for the importance of mathematical knowledge-how and emphasises the primary role of the activity of proving in securing mathematical knowledge. In the final chapter I develop an account of mathematical knowledge based on virtue epistemology, which I argue provides a better view of proofs and mathematical rigour. (shrink)

This paper argues that we should reject G. E. Moore’s anti-skeptical argument as it is presented in “Proof of an External World.” However, the reason I offer is different from traditional objections. A proper understanding of Moore’s “proof” requires paying attention to an important distinction between two forms of skepticism. I call these Ontological Skepticism and Epistemic Skepticism. The former is skepticism about the ontological status of fundamental reality, while the latter is skepticism about our empirical knowledge. (...) Philosophers often assume that Moore’s response to “external world skepticism” deals exclusively with the former, not the latter. But this is a mistake. I shall argue that Moore’s anti-skeptical argument targets an ontological form of skepticism. Thus, the conclusion is an ontological claim about fundamental reality, while the premises are epistemic claims. If this is correct, then the conclusion outstrips the scope of its premises and proves too much. (shrink)

EN In his “Logic, Language, and Knowledge” Chateaubriand denounces the tyranny of belief , but takes some positions on knowledge and justification which seem to be too exacting. The fact that Chateaubriand derives constraints on the notion of justification by a close parallel to the notion of proof makes it unnecessarily loaded with the individual, rather than with the collective perspective. His position seems to leave little room for common knowledge, collective knowledge and usual common-sense (...) knowledge, and absolutely no room for explaining how people take correct decisions based on apparently faulty notions of knowledge and justification. -/- PT Em “Logic, Language, and Knowledge” Chateaubriand denuncia a tirania da crença , mas toma posições sobre conhecimento e justificação que parecem demasiado exigentes. O fato de Chateaubriand derivar condições sobre a noção de justificação a partir de uma estreita analogia com a noção de prova torna a noção de justiticação desnecessariamente carregada com a perspectiva indivídual, em detrimento da perspectiva coletiva. Sua posição parece deixar pouco espaço para noções como conhecimento comum, conhecimento coletivo e senso comum, e absolutamente nenhum espaço para explicar como as pessoas tomam decisões corretas com base em noções aparentemente errôneas de conhecimento e de justificação. (shrink)

The four theistic proofs of Monologion are based on the categories of being per se and being per aliud. This article analyses them through a comparative approach. The categories of per se and per aliud are compared with the categories of substance (ti) and function (yong) as touched on the first chapter of the Rectifying Ignorance (正蒙 Zhengmeng) of Zhang Zai (1020–1077), an exponent of neo-Confucianism. In fact, the two pairs of categories explain the relationship between an absolute, the supreme (...) nature (summum) or the Great Void (太虚 taixu) and the sensible world. Through the comparison, this article highlights the fundamental function of being per aliud in the rational knowledge of the supreme nature that exists per se and provides new insights into the process of derivation of being per aliud from the being per se.Contribution: This article, through the comparison with the Chinese philosophical tradition, intends to offer a new perspective on the understanding of the Anselmian categories of being per se and being per aliud. (shrink)

This chapter contains sections titled: Context: Hunting from an Anishinabe Perspective Teachings on Hunting Hunting and Awareness Notes.