I examine the division of labor between the Metaphysical Deduction (MD) and the Transcendental Deduction (TD). Against a common reading, I argue that the MD is insufficient to prove the a priori origin of the categories. For both Kant and his main opponent, namely Hume, the question of whether the categories have an a priori origin in the pure understanding is inseparable from the question of whether they have objective validity. Since the MD does not establish the (...) objective validity of the categories, it cannot establish their a priori origin either. The MD is nevertheless an indispensable part of Kant's project because it lays the argumentative groundwork for the proof structure of the TD and because it provides the systematic plan for the future metaphysics of experience. (shrink)

This chapter contains section titled: The Metaphysical Deduction.

This article focuses on the interpretation of the metaphysical deductions of the higher cognitive faculties in Gabriele Gava’s Kant’s Critique of Pure Reason and the Method of Metaphysics. The aim is to assess the role that Kant’s general logic plays in these metaphysical deductions, the consequences for the analysis of the faculties, and the place of general logic in Gava’s overall theoretical analysis of Kant’s first Critique.

In lieu of an abstract, here is a brief excerpt of the content:Concepts, Judgments, and Unity in Kant's Metaphysical Deduction of the Relational Categories CHARLES NUSSBAUM 1. INTRODUCTION TO ANY ATTENTIVEREADERof the section of the Critique of Pure Reason' known as the "Metaphysical Deduction of the Categories" (A67/B92-A83/B to9), one paragraph in that section stands out particularly by virtue of its special importance for Kant's developing argument: The same function Which gives unity to the various representations (...) in ajudgment also gives unity to the mere synthesis of various representations in an intuition; and this unity, in its most general expression, we entitle the pure concept of the understanding. The same understanding, through the same operations by which in concepts, by means of analytical unity, it produced the logical form of a judgment, also introduces a transcendental content into its representations, by means of the synthetic unity of the manifold of intuition in general.... (CPR A79/B loS) The importance of this paragraph is, however, more than equaled by its difficulties, which center on the question of how the function which operates by means of analytical unity can be the same as one that operates by means of the synthetic unity of the manifold of intuition in general. Put shortly, the problem is this. If the functions are really the same, then how do we distinguish at all between analytic and synthetic operations? But if they are different, then how can these forms of judgment serve as a clue for the discovery of the categories? ' Immanuel Kant, Critiqueof Pure Reason, trans. Norman KempSmith (London: Macmillan and Co., Ltd., 1963).Hereafter CPR. [89] 9~ JOURNAL OF THE HISTORY OF PHILOSOPHY 28:1 JANUARY 1990 The results of this dilemma which can be observed in the literature are not surprising: commentators tend to grasp one horn or the other. They either emphasize the difference between analysis and synthesis, and reject or dilute the claims as to sameness of function; or they take seriously Kant's argument concerning sameness of functions, and try to minimize the difference between analysis and synthesis. The major twentieth-century representant of the former approach is Kemp Smith," and of the latter, Paton. 3 This latter approach has found a formidable contemporary champion in the person of Henry Allison. By Allison's own admission,4 however, his position on this controversial topic was suggested (in part) by arguments first put forward over fifty years ago by Klaus Reich in a most remarkable book entitled Die Volls~ndigkeit der Kantischen Urteilstafel, 5 a book, by the way, also greatly admired by Paton. 6 In the first section of this paper I will try to show that Reich's arguments are rather more subtle than Allison apparently takes them to be, and that Reich is one commentator who attempts to go between the horns of the dilemma described above, and who essays an interpretation of our crucial paragraph that unifies its seemingly divergent tendencies. In the second section of the paper I will introduce some interpretive elements of my own. 2. Let us begin by reacquainting ourselves with Kant's notion of analytical unity, one aspect of this debate which is not particularly controversial and is largely agreed upon by all parties. For Kant, analytical unity is the sort of unity achieved by all general concepts (conceptus communes) insofar as they abstract from all differences that subsist between the objects under them, or the lower concepts subordinated to them. 7 A general concept unifies these objects or concepts by means of a common mark or set of marks. Thus Kant's example at CPR A69/B94 of the unification of bodies under the concepts 'body' and 'divisible' is a perfectly representative instance of unification via analytical unity, as the function upon which such concepts "rest." Let us note that the " Norman KempSmith,A CommentarytoKant's "Cr/t~rueofPureReason"(NewYork:HumanitiesPress, 196~). 3 H.J. Paton, Kant's MetaphysicofExperience, 2 vols.(London:George Allenand Unwin,Ltd., 1936). 4 Henry Allison,Kant's TranscendentalIdealum (NewHaven:YaleUniversityPress, 1983), 144 n. 3o. Hereafter KTI. 5 KlausReich,Die Vollst~ndigkeitderKantischenUrteilstafel,3rd. ed. (Hamburg: Meiner, 1986). Hereafter VKU. 6 Paton, Kant's Metaphysic, 1:302. Kant, we should note, does not makethis important logicaldistinctionbetweensubordination... (shrink)

The paper explores a deductive-nomological account of metaphysical explanation: some truths metaphysically explain, or ground, another truth just in case the laws of metaphysics determine the latter truth on the basis of the former. I develop and motivate a specific conception of metaphysical laws, on which they are general rules that regulate the existence and features of derivative entities. I propose an analysis of the notion of ‘determination via the laws’, based on a restricted form of logical entailment. (...) I argue that the DN-account of ground can be defended against the well-known objections to the DN-approach to scientific explanation. The goal of the paper is to show that the DN-account of metaphysical explanation is a well-motivated and defensible theory. (shrink)

Kant’s Metaphysical Deduction of the Categories justifies their apriority, i.e. that their contents originate in the understanding itself, while the Transcendental Deduction justifies their objectivity, both in that they purport to represent objects of experience and that they do so successfully. The apriority of the categories, as explained in terms of acts of synthesis required for having sensible intuitions of objects, is justified by establishing their generic identity with logical functions of judgment, i.e. acts of judgment required (...) for referring concepts to objects. The objective purport of the categories is justified by establishing that sensible intuitions fall under them. To finally justify that the categories represent successfully, i.e. that the objects of our intuitions fall under them, it is established that the representations of space and time do, namely by showing that the features addressed in their Metaphysical Expositions, too, are to be explained in terms of acts of synthesis. (shrink)

My aim is to demonstrate the specificities and differences between transcendental deduction of concepts and deduction of the fundamental principles of pure practical reason in Kant’s metaphysics. First of all it is necessary to examine Kant’s attitude to the metaphysics of his time and the problem of its new justification. Kant in his philosophy explicated not only the theoretical world of cognition, but also the practical world of freedom. Accordingly, the fundamental means of proving metaphysics’ claims are the (...) deduction of pure concepts of understanding and the deduction of the principles of pure practical reason. The underlying premises of the Kantian project of reviving metaphysics, “the Copernican Turn”, the critical methods and basic principles of transcendental idealism also provide the methodological basis of transcendental deduction, a new method of proving the claims of metaphysics in various spheres of human being. Proceeding from the above, I analyse the essence, structure and the peculiarities as well as the differences between the deduction of experience and the deduction of freedom. I single out the following features of the two types of deduction. First, theoretical use of reason is aimed at objects while practical reason is aimed at noumena, the foundations of will and freedom. Second, the transcendental deduction of space and time, as well as the deduction of categories, is preceded by transcendental reduction, which is absent in the deduction of freedom. Third, Kant orients the methodological movement of deductions in opposite directions. Theoretical deduction proceeds from pure forms of sensible intuition to concepts of understanding and thence to fundamental principles. Practical deduction proceeds from a priori principles to the concepts of the metaphysics of morals and thence to moral feelings. Fourth, deduction in the theoretical sphere forbids speculative reason to go beyond experience. Practical deduction has pointed to the intelligible world and has proved its “legitimacy”. (shrink)

In this paper I explore the ways in which Alexander of Aphrodisias employs and develops so-called ‘common notions’ as reliable starting points of deductive arguments. He combines contemporary developments in the Stoic and Epicurean use of common notions with Aristotelian dialectic, and axioms. This more comprehensive concept of common notions can be extracted from Alexander’s commentary on Metaphysics A 1–2. Alexander puts Aristotle’s claim that ‘all human beings by nature desire to know’ in a larger deductive framework, and adds weight (...) to Aristotle’s use of the common understanding of the notion of ‘wisdom’. Finally I will indicate how these upgraded common notions are meant to play an important role in the general framework of metaphysics as a science. (shrink)

This chapter contains sections titled: Introduction Apperception Representations of Objects Universality and Necessity Logical Forms of Judgment and Categories The Second Step of the B‐Deduction A Final Word.

This work offers a new understanding of Kant on the freedom of the will. Voeller looks in detail at the _Groundwork of the Metaphysics of Morals_ and the _Critique_ _of Practical Reason_ against the background of Kant's critical philosophy as a whole.

This work offers a new understanding of Kant on the freedom of the will. Voeller looks in detail at the Groundwork of the Metaphysics of Morals and the Critique of Practical Reason against the background of Kant's critical philosophy as a whole.

This article analyzes Aristotle's argument on form as the primary substance and principle in Metaphysics Zeta 17 from the point of departure of the sense-perceptible substances subject to the becoming.

This article introduces the first English translation of one of Tanabe’s early essays on metaphysics. It questions the relation of the universal to the particular in context of logic, phenomenology, Neo-Kantian epistemology, and classical metaphysics. Tanabe provides his reflections on the nature of the concept of universality and its constitutive relation to phenomenal particulars through critical analyses of the issue as it is discussed across various schools of philosophy including: British Empiricism, the Marburg School, the Austrian School, the Kyoto School, (...) and Platonism. In this essay, Tanabe reveals his ability to think metaphysically the ground for the possibility of reasoning and dares to voice his own thought beyond references to the most prominent thinkers of his time from distinct intellectual traditions in both the east and the west. This essay, therefore, demonstrates that his strong tendency to move beyond the received epistemology and phenomenology of the European intellectual tradition to metaphysics was already present in the early days of his academic life and thereby marks a more general contribution of the Kyoto School of Philosophy to distinct European schools of thought in the early twentieth century. (shrink)

In these comments, I share some remarks concerning two main points lying at the core of Gava’s book Kant’s Critique of Pure Reason and the Method of Metaphysics: Gava’s reconstruction and account of a transcendental deduction, its relation to a metaphysical deduction, and more specifically his reading of the B-Deduction. I will discuss Gava’s arguments in order to highlight the key tenets of his interpretation and raise questions related to (1) the meaning and scope of the (...) notion of ‘transcendental’; and (2) the commitment to – and the extent of – what we might call ‘cognitive constructivism’. (shrink)

Fichte argues that the conclusion of Kant’s transcendental deduction of the categories is correct yet lacks a crucial premise, given Kant’s admission that the metaphysical deduction locates an arbitrary origin for the categories. Fichte provides the missing premise by employing a new method: a genetic deduction of the categories from a first principle. Since Fichte claims to articulate the same view as Kant in a different, it is crucial to grasp genetic deduction in relation to (...) the sorts of deduction that Kant offers. I propose to interpret genetic deduction as the simultaneous fulfillment of two tasks: answering the question quid facti by deriving the categories from the I and answering the question quid juris by establishing our entitlement to the categories as conditions of experience. While the second task represents Fichte’s agreement with Kant’s transcendental deduction, the first reflects his correction of Kant’s metaphysical deduction. (shrink)

This paper has two specific goals. The first is to demonstrate that the theorem in MetaphysicsΘ 9, 1051a24-27 is not equiva-lent to Euclid’s Proposition 32 of book I (which contradicts some Aristotelian commentators, such as W. D. Ross, J. L. Heiberg, and T. L. Heith). Agreeing with Henry Mendell’s analysis, I ar-gue that the two theorems are not equivalent, but I offer different reasons for such divergence: I propose a pedagogical-philosoph-ical reason for the Aristotelian theorem being shorter than the Euclidean (...) one (and the previous Aristotelian versions). Aristotle wants to emphasize the deductive procedure as a satisfactory method to discover scientific knowledge. The second objective, opposing some consensus about geometrical deductions/theo-rems in Aristotle, is to briefly propose that the theorem, exactly as we found it in Metaphysics and without any emendation to the text (therefore opposing Henry Mendell’s suggested amend-ments), allows the ancient philosopher to demonstrate that universal mathematical knowledge is in potence in geometrical figures. This tentatively proves that Aristotle emphasizes that geometrical deduction is sufficient to actualize mathematical knowledge. (shrink)

This essay partly builds on and partly criticizes a striking idea of Dieter Henrich. Henrich argues that Kant's distinction in the first Critique between the question of fact (quid facti) and the question of law (quid juris) provides clues to the argumentative structure of a philosophical "Deduction". Henrich suggests that the unity of apperception plays a role analogous to a legal factum. By contrast, I argue, first, that the question of fact in the first Critique is settled by the (...) Metaphysical Deduction, which establishes the purity of origin of the Categories, and, second, that in the second Critique, the relevant factum is the Fact of Reason, which amounts to the fact that the Moral Law is pure in origin. (shrink)

The traditional No-Miracles Argument (TNMA) asserts that the novel predictive success of science would be a miracle, and thus too implausible to believe, if successful theories were not at least approximately true. The TNMA has come under fire in multiple ways, challenging each of its premises and its general argumentative structure. While the TNMA relies on explaining novel predictive success via the truth of the theories, we put forth a deductive version of the No-Miracles argument (DNMA) that avoids inference to (...) the best explanation entirely. Instead, a relatively simple empirical framework and a probabilistic analysis can accomplish the ambitious goals of the TNMA while entirely sidestepping its problems. This close-but-distinct argument has many independent strengths and comparatively few weaknesses. Indeed, objections tailored specifically to the DNMA reveal surprising insights into how exactly NMAs are neither circular nor question-begging, as has been widely speculated. (shrink)

In the Critique of Practical Reason, Kant presents the moral law as the sole ‘fact of pure reason’ that neither needs nor admits of a deduction to establish its authority. This claim may come as a surprise to many readers of his earlier Groundwork of the Metaphysics of Morals. In the last section of the Groundwork, Kant seemed to offer a sketch of just such a ‘deduction of the supreme principle of morality’ . Although notoriously obscure, this sketch (...) shows that Kant hoped to base the moral law in the freedom that rational agents can claim as members of the ‘intelligible world’ that transcendental idealism makes available to us. In contrast, the second Critique abandons all aspirations of deriving morality from more basic notions of freedom and practical rationality. (shrink)

Bruce Waller has defended a deductive reconstruction of the kinds of analogical arguments found in ethics, law, and metaphysics. This paper demonstrates the limits of such a reconstruction and argues for an alternative. non-deductive reconstruction. It will be shown that some analogical arguments do not fit Waller's deductive schema, and that such a schema does not allow for an adequate account of the strengths and weaknesses of an analogical argument. The similarities and differences between the account defended herein and the (...) Trudy Govier's account are discussed as well. (shrink)

Bruce Waller has defended a deductive reconstruction of the kinds of analogical arguments found in ethics, law, and metaphysics. This paper demonstrates the limits of such a reconstruction and argues for an alternative. non-deductive reconstruction. It will be shown that some analogical arguments do not fit Waller's deductive schema, and that such a schema does not allow for an adequate account of the strengths and weaknesses of an analogical argument. The similarities and differences between the account defended herein and the (...) Trudy Govier's account are discussed as well. (shrink)

In a discussion of Sherlock Holmes’ “science of deduction” and the related “method of exclusion,” I show that Holmes’ claim that his inferences are deductive makes sense, if we consider his theoretical presuppositions. So, it is more accurate to say that he tries to reduce abduction to deduction than that he confuses them. His theoretical framework, albeit inadequate as a theory of empirical reasoning, can be seen as a basic model of classical (symbolic) AI. The main problems of (...) this approach are surveyed, and abduction is brought into play as both a better characterization of Holmes’ inferences and a better guide for building AI systems. This is a good background for raising the question of creativity because, according to Peirce, it relates to abduction in a substantial way. Is Sherlock Holmes creative? Can machines be creative? An affirmative answer to the second question might be given by a “logic of discovery” but the problem remains that inventing such a logic already presupposes creativity. (shrink)

The argument of the Transcendental Deduction of the Categories in the Critique of Pure Reason is the deepest and most far-reaching in philosophy. In his new book, Robert Howell interprets main themes of the Deduction using ideas from contemporary philosophy and intensional logic, thereby providing a keener grasp of Kant's many subtleties than has hitherto been available. No other work pursues Kant's argument through every twist and turn with the careful, logically detailed attention maintained here. Surprising new accounts (...) of apperception, the concept of an object, the logical functions of thought, the role of the Metaphysical Deduction, and Kant's relations to his Aristotelian-Cartesian background are developed. Howell makes a precise contribution to the discussion of most of the disputed issues in the history of Deduction interpretation. Controversial in its conclusions, this book demands the attention of all who take seriously the task of understanding Kant's work and evaluating it dispassionately. (shrink)

Henry E. Allison presents an analytical and historical commentary on Kant`s transcendental deduction of the pure concepts of the understanding in the Critique of Pure Reason. He argues that, rather than providing a new solution to an old problem, it addresses a new problem, and he traces the line of thought that led Kant to the recognition of the significance of this problem in his 'pre-critical' period. In addition to the developmental nature of the account of Kant`s views presented (...) here, two distinctive features of Allison's reading of the deduction are a defense of Kant`s oft criticized claim that the conformity of appearances to the categories must be unconditionally rather than merely conditionally necessary and an insistence that the argument cannot be separated from Kant`s transcendental idealism. (shrink)

I defend an interpretation of the first Critique’s category of totality based on Kant’s analysis of totality in the third Critique’s Analytic of the mathematical sublime. I show, firstly, that in the latter Kant delineates the category of totality — however general it may be — in relation to the essentially singular standpoint of the subject. Despite the fact that sublime and categorial totality have a significantly different scope and function, they do share such a singular baseline. Secondly, I argue (...) that Kant’s note (in the first Critique’s metaphysical deduction) that deriving the category of totality requires a special act of the understanding can be seen as a ‘mark’ of that singular baseline. This way, my aesthetical ‘detour’ has the potential of revealing how the subjective aspects of object-constitution might be accounted for in the very system of the categories (of quantity) itself. (shrink)

Deductive inference is usually regarded as being “tautological” or “analytical”: the information conveyed by the conclusion is contained in the information conveyed by the premises. This idea, however, clashes with the undecidability of first-order logic and with the (likely) intractability of Boolean logic. In this article, we address the problem both from the semantic and the proof-theoretical point of view. We propose a hierarchy of propositional logics that are all tractable (i.e. decidable in polynomial time), although by means of growing (...) computational resources, and converge towards classical propositional logic. The underlying claim is that this hierarchy can be used to represent increasing levels of “depth” or “informativeness” of Boolean reasoning. Special attention is paid to the most basic logic in this hierarchy, the pure “intelim logic”, which satisfies all the requirements of a natural deduction system (allowing both introduction and elimination rules for each logical operator) while admitting of a feasible (quadratic) decision procedure. We argue that this logic is “analytic” in a particularly strict sense, in that it rules out any use of “virtual information”, which is chiefly responsible for the combinatorial explosion of standard classical systems. As a result, analyticity and tractability are reconciled and growing degrees of computational complexity are associated with the depth at which the use of virtual information is allowed. (shrink)

Any theory of explanation must account for the explanatory successes of statistical scientific theories. This should not be done by endorsing determinism. These considerations have been taken as sufficient ground for rejecting the demand on explanations to be deductive. The arguments for doing so, in Coffa (1974) and Salmon (1977, 1984, 1988), are, however, not persuasive. Deductivism is a viable position. Considering that doubts can be raised against the explanatory validity of probabilistic causal relations and the intuitive plausibility of deductivism, (...) it is also a recommendable position, though elaboration is needed in accounting for some of the uses of statistical theories in explanations. (shrink)

According to the deductive-nomological account of ground, a fact A grounds another fact B in case the laws of metaphysics determine the existence of B on the basis of the existence of A. Accounts of grounding of this particular variety have already been developed in the literature. My aim in this paper is to sketch a new version of this account. My preferred account offers two main improvements over existing accounts. First, the present account is able to deal with necessitarian (...) as well as non-necessitarian cases of grounding by acknowledging the existence of two types of metaphysical laws. I will argue that we should assume that metaphysical laws come in the necessitarian as well as in the non-necessitarian varietyclosely paralleling the distinction between strict and non-strict laws in the philosophy of science. The second main improvement of the present account is that this account is able to provide an explanation of why the laws of metaphysics have a direction built into them. I will argue that we should characterize metaphysical laws with the help of Theodore Sider’s (2011) notion of structure, which is a descendent of David Lewis’s (1983) notion of naturalness. According to the account of metaphysical laws developed in this paper, metaphysical laws express in their antecedents either perfectly structural truths or more structural truths than in their consequents. Since on Sider’s account structural features of reality are fundamental features of reality, the account is able to explain as to why the laws of metaphysics take us from the fundamental to the derivative. (shrink)

The syllogistic mnemonic known by its first two words Barbara Celarent introduced a constellation of terminology still used today. This concatenation of nineteen words in four lines of verse made its stunning and almost unprecedented appearance around the beginning of the thirteenth century, before or during the lifetimes of the logicians William of Sherwood and Peter of Spain, both of whom owe it their lasting places of honor in the history of syllogistic. The mnemonic, including the theory or theories it (...) encoded, was prominent if not dominant in syllogistics for the next 700 years until a new paradigm was established in the 1950s by the great polymath Jan Łukasiewicz, a scholar equally at home in philosophy, classics, mathematics, and logic. Perhaps surprisingly, the then-prominent syllogistic mnemonic played no role in the Łukasiewicz work. His 1950 masterpiece does not even mention the mnemonic or its two earliest champions William and Peter. The syllogistic mnemonic is equally irrelevant to the post-Łukasiewicz paradigm established in the 1970s and 1980s by John Corcoran, Timothy Smiley, Robin Smith, and others. Robin Smith’s comprehensive 1989 treatment of syllogistic does not even quote the mnemonic’s four verses. Smith’s work devotes only 2 of its 262 pages to the mnemonic. The most recent translation of Prior Analytics by Gisela Striker in 2009 continues the post-Łukasiewicz paradigm and accordingly does not quote the mnemonic or even refer to the code—although it does use the terminology. Full mastery of modern understandings of syllogistic does not require and is not facilitated by ability to decode the mnemonic. Nevertheless, an understanding of the history of logic requires detailed mastery of the syllogistic mnemonic, of the logical theories it spawned, and of the conflicting interpretations of it that have been offered over the years by respected logicians such as De Morgan, Jevons, Keynes, and Peirce. More importantly, an understanding of the issues involved in decoding the mnemonic might lead to an enrichment of the current paradigm—an enrichment so profound as to constitute a new paradigm. After presenting useful expository, bibliographic, hermeneutic, historical, and logical background, this paper gives a critical exposition of Smith’s interpretation. (shrink)

In this article, the author proposes to reconstruct Kant's "transcendental deduction" without in any way making use of the results of the so-called "metaphysical" one. His suggestion is that what Kant baptizes "pure concepts" or "categories" are in fact not "concepts" at all, strictly speaking, but rather the very forms of judgment from which these "concepts" were supposed to have been derived in the "metaphysical deduction". The task of the "transcendental" deduction is, then, to show (...) that such forms of judgment can legitimately be applied to empirical contents: to demonstrate, in other words, the possibility of empirical knowledge. (shrink)

The purpose of this paper is first to explain a general notion of transcendental deductions, of which the Kantian are special cases; next to show, and to illustrate by examples from Kant’s work, that no transcendental deduction can be successful; and thirdly to put one of Kant’s achievements in its proper light by substituting for his spurious distinction between metaphysical exposition and transcendental deduction, a revised notion of metaphysical exposition and of the philosophical tasks arising out (...) of it. (shrink)

In this book, Alison Laywine considers the mystery of the Transcendental Deduction in Immanuel Kant's Critique of Pure Reason. What is it supposed to accomplish and how? Laywine argues that Kant's peculiar adaptation of his early account of a world is the key to this mystery. Collecting evidence from the Critique and other writings by Kant--in order to identify what he took himself to be doing on his own terms--she holds that Kant deliberately adapted elements of his early metaphysics (...) both to set the agenda of the Deduction and to carry it out. Laywine highlights how the most important metaphysical element in Kant's thought was his early account of a world; a world is not just the sum-total of all substances created by God, but a whole unified by the universal laws of community prescribed by God that externally relate any given substance to all others. From this conception of a world, Kant then extracted a way to conceive key elements in the Deduction: experience as the whole of all possible appearances unified by the universal laws human understanding gives to nature. (shrink)

I OFFER AN ANALYSIS OF DESCARTES'S COGITO WHICH IS RADICALLY NOVEL WHILE INCORPORATING MUCH AVAILABLE INSIGHT. BY ENLARGING FOCUS FROM THE DICTUM ITSELF TO THE REASONING OF DOUBT, DREAMING AND DEMON, I DEMONSTRATE A CLOSE PARALLEL TO THE LOGIC OF THE LIAR PARADOX. THIS HELPS TO EXPLAIN FAMILIAR PARADOXICAL FEATURES OF DESCARTES'S ARGUMENT. THE ACCOUNT PROVES TO BE TEXTUALLY ELEGANT AND, MOREOVER, HAS CONSIDERABLE INDEPENDENT PHILOSOPHICAL PLAUSIBILITY AS AN ACCOUNT OF MIND AND SELF.

In standard model theory, deductions are not the things one models. But in general proof theory, in particular in categorial proof theory, one finds models of deductions, and the purpose here is to motivate a simple example of such models. This will be a model of deductions performed within an abstract context, where we do not have any particular logical constant, but something underlying all logical constants. In this context, deductions are represented by arrows in categories involved in a general (...) adjoint situation. To motivate the notion of adjointness, one of the central notions of category theory, and of mathematics in general, it is first considered how some features of it occur in set-theoretical axioms and in the axioms of the lambda calculus. Next, it is explained how this notion arises in the context of deduction, where it characterizes logical constants. It is shown also how the categorial point of view suggests an analysis of propositional identity. The problem of propositional identity, i.e., the problem of identity of meaning for propositions, is no doubt a philosophical problem, but the spirit of the analysis proposed here will be rather mathematical. Finally, it is considered whether models of deductions can pretend to be a semantics. This question, which as so many questions having to do with meaning brings us to that wall that blocked linguists and philosophers during the whole of the twentieth century, is merely posed. At the very end, there is the example of a geometrical model of adjunction. Without pretending that it is a semantics, it is hoped that this model may prove illuminating and useful. (shrink)

I take up Kant's remarks about a " transcendental deduction" of the "concepts of space and time". I argue for the need to make a clearer assessment of the philosophical resources of the Aesthetic in order to account for this transcendental deduction. Special attention needs to be given to the fact that the central task of the Aesthetic is simply the "exposition" of these concepts. The Metaphysical Exposition reflects upon facts about our usage to reveal our commitment (...) to the idea that these concepts refer to pure intuitions. But the legitimacy of these concepts still hangs in the balance: these concepts may turn out to refer to nothing real at all. The subsequent Transcendental Exposition addresses this issue. The objective validity of the concepts of space and time, and hence their transcendental deduction, hinges on careful treatment of this last point. (shrink)

Hegel often says that his "logic" is meant to replace metaphysics. Since Hegel's Science of Logic is so different from a standard logic, most commentators have not treated the portion of that work devoted to logical forms as relevant to this claim. This paper argues that Hegel's discussion of logical forms of judgment and syllogism is meant to be the foundation of his reformation of metaphysics. Implicit in Hegel's discussion of the logical forms is the view that the metaphysical (...) concepts discussed in Books I and II of the Science of Logic supervene on the role of subject and predicate terms in the logical forms discussed in Book III. Hegel thus has an explanation for the nature and significance of metaphysical concepts that resembles Kant's "metaphysical deduction," according to which the categories can be derived from the table of judgments. Though Hegel's metaphysics is often supposed to be influenced by Kant, prevailing interpretations do not show how Hegel's fine-grained treatment of logical forms is relevant to his critical view of metaphysics. The present interpretation provides a model for Hegel's explanation of metaphysical concepts, as well as a new picture of the structure of his Science of Logic that emphasizes the priority of its Doctrine of the Concept. (shrink)

In recent years philosophy of science has seen a resurgence of interest in metaphysical issues, especially those concerning laws, causation,and explanation. Although this book takes only the latter two words for its title, it is also about laws of nature. It is divided into three sections: the first is on causation, the second is on laws, and the third is on explanation: this is entirely appropriate because the debates about them are closely related. Ever since Hume argued that causation (...) is nothing more than regularities, laws have been more respectable than causes in philosophy. Perhaps this is also because science is replete with specially named laws which seem to play a central role in theories and explanations. Yet, as many philosophers have recently pointed out, contrary to Russell’s famous pronouncement that causation is a relic of a bygone age (quoted p. 3 by Psillos), the contemporary special sciences are very much concerned with the identification and investigation of all manner of causal structures. This raises the question of whether the apparent causal powers attributed to kinds in the special sciences are anything over and above a way of talking about the result of the operations of physical laws governing their microconstituents. Hence the logical empiricist’s project of showing how the laws of the special sciences reduce to those of physics. On their view, explanation, and in particular causal explanation, is nothing more than argument using the laws of nature as premises. However, this coveringlaw model of explanation has been subjected to intense criticism, and there have been attempts to construct alternatives that rely on the idea that to explain an event is to cite its real cause, where this cause need not be subsumed under any law. Since the demise of logical empiricism, or at least the waning of its influence, there has been a proliferation of theories about laws, causation and explanation, many of which differ radically from one another. (shrink)

Drawing upon Martin-Löf’s semantic framework for his constructive type theory, semantic values are assigned also to natural-deduction derivations, while observing the crucial distinction between consequence among propositions and inference among judgements. Derivations in Gentzen’s format with derivable formulae dependent upon open assumptions, stand, it is suggested, for proof-objects, whereas derivations in Gentzen’s sequential format are proof-acts.