Kant discovered a philosophical problem with mathematical proof. Despite being a priori , its methodology involves more than analytic truth. But what else is involved? This problem is widely taken to have been solved by Frege’s extension of logic beyond its restricted (and largely Aristotelian) form. Nevertheless, a successor problem remains: both traditional and contemporary (classical) mathematical proofs, although conforming to the norms of contemporary (classical) logic, never were, and still aren’t, executed by mathematicians in a way that transparently reveals (...) why these proofs—written in the vernacular to this very day—succeed in conforming to those norms. (shrink)

The view that logic is true independently of a subject matter is criticized—enlarging on Quine's criticisms and adding further ones. It is then argued apriori that full reflective understanding of logic and deductive reasoning requires substantial commitment to mathematical entities. It is emphasized that the objectively apriori connections between deductive reasoning and commitment to mathematics need not be accepted by or even comprehensible to a given deductive reasoner. The relevant connections emerged only slowly in the history of logic. But they (...) can be recognized retrospectively as implicit in logic and deductive reasoning. The paper concludes with discussion of the relevance of its main argument to Kant's question—how is apriori knowledge of a subject matter possible? (shrink)

My goal in this paper is to develop our understanding of the role the imagination plays in Kant’s Critical account of geometry, and I do so by attending to how the imagination factors into the method of reasoning Kant assigns the geometer in the First Critique. Such an approach is not unto itself novel. Recent commentators, such as Friedman (1992) and Young (1992), have taken a careful look at the constructions of the productive imagination in pure intuition and highlighted the (...) importance of the imagination’s activity for securing the universality of geometry knowledge. Specifically, as their respective examinations bring to light, it is only with due attention to the imagination that we can make sense of how a .. (shrink)

In the Introduction to the Transcendental Dialectic, of the Critique of Pure Reason, Kant presents a conception of error. In the (Jäsche) Logic, he also deals with the problem of error, albeit in a different way. This paper aims at exposing this difference and arguing that, in the (Jäsche) Logic, error is explained moreconsistently and suitably than it is in the Transcendental Dialectic. It begins by considering judgment as the place of truth, falsehood and error, and inquiring into the cognitive (...) faculties that take part in its framing. These faculties, whose roles cannot be interchanged, are the sensibility, passive and receptive, and the understanding, active and spontaneous. Erroneous judgment springs from the unnoticed influence of sensibility on understanding, which makes theunderstanding hold merely subjective grounds of judgment to be objective ones. This unnoticed influence is conceived, in the Transcendental Dialectic, in such a way that sensibility is, in a certain sense, held to be the determining ground of error, as if it were an active faculty, whereas that influence is conceived in the (Jäsche) Logic in such a way that the understanding itself is regarded as the source and author of error. This authorship agrees with the conception of the understanding as submitted to prescriptive laws, which is contained in the very definition of Pure General Logic, as a science of the a priori laws of how the understanding ought to think. (shrink)

: Convinced that logic has a history and that its history always manages to surprise the philosophers, Claude Imbert has devoted much of her work to the study of the Stoic school and of the late-nineteenth-century German logician Gottlob Frege. In the fifth chapter of her book Pour une histoire de la logique, she examines the trajectory of Frege's awareness of what his new logic entails, in particular the way it subverts the project of Kant.

According to Kant in the Prolegomena, the natural kind proposition (GYM) "Gold is a yellow metal" is analytically true, necessary, and a priori. Saul Kripke and Hilary Putnam have argued that on the contrary propositions such as (GYM) are neither analytic, nor necessary, nor a priori. The Kripke-Putnam view is based on the doctrine of "scientific essentialism" (SE). It is a direct consequence of SE that propositions such as (GE) "Gold is the element with atomic number number 79" are metaphysically (...) necessary and a posteriori. Were Kant to travel by time-machine to the present and to consider (GE), however, he would regard it as metaphysically contingent; and even if he were able to admit it as necessary, it would be synthetic a priori, and not a posteriori. In these ways, the conflict between Kant and the scientific essentialists is a sharply-defined one: if the essentialists are right, then the Kantian theory of meaning, necessity, and a priori knowledge is wrong; but if Kant is right, then SE is wrong. As a prolegomenon to the development and defense of Kant's positive theory of natural kind propositions, this paper undertakes a Kantian critique of SE. Following the Introduction, the paper has three sections. The first section spells out the main theses and assumptions of SE. The second section, setting aside the semantic and logical components of SE, focuses on its epistemic and metaphysical components and offers four Kantian arguments against them. The final section offers Kantian "diagnoses" of the flaws in SE exposed by the four critical arguments. (shrink)

We are republishing these classic works in affordable, high quality, modern editions, using the original text and artwork.

Does logic describe something or not? If not, is it a normative or practical discipline? Is there a radical division between the practical or normative level and the theoretical or descriptive level? A discipline is theoretical, we may say, if its main propositions contain descriptive expressions, such as “is” or “have”, but no normative expressions, such as “ought”, “ought not” or “may”. A discipline is normative if its main propositions are of the form “it ought to be”. Theoretical propositions express (...) what is, whereas practical propositions express what should be. So a theoretical discipline is descriptive and a normative discipline is prescriptive, but what does a theoretical discipline describe? (shrink)

Overview -- Locke's internal sense and Kant's changing views -- Personal identity amd its problems -- Rationalalist metaphysics of mind -- Consciousness, self-consciousness, and cognition -- Strands of Argument in the Duisburg Nachlass -- A transcendental deduction for a priori concepts -- Synthesis : why and how? -- Arguing for apperception -- The power of apperception -- "I-think" as the destroyer of rational psychology -- Is Kant's theory consistent? -- The normativity objection -- Is Kant's thinker (as such) a free (...) and responsible agent? -- Kant our contemporary. (shrink)

In his critical works of the 1780's, Kant claims, seemingly inconsistently, that (1) theoretical and practical reason are one and the same reason, applied differently, (2) that he still needs to show that they are, and (3) that theoretical and practical reason are united. I first argue that current interpretations of Kant's doctrine of the unity of reason are insufficient. But rather than concluding that Kant’s doctrine becomes coherent only in the Critique of Judgment, I show that the three statements (...) are compatible, providing a new and more coherent account of Kant's 1780's doctrine of the unity of reason. (shrink)

Gödel's philosophical views were to a significant extent influenced by the study not only of Leibniz or Husserl, but also of Kant. Both Gödel and Kant aimed at the secure foundation of philosophy, the certainty of knowledge and the solvability of all meaningful problems in philosophy. In this paper, parallelisms between the foundational crisis of metaphysics in Kant's view and the foundational crisis of mathematics in Gödel's view are elaborated, especially regarding the problem of finding the “ secure path of (...) a science” for both mathematics and philosophy. Gödel's temporal subjectivism and metaphysical conceptual objectivism are presented as positively or negatively motivated by Kant's viewpoints. A remark on Gödel's collapse of modalities (in accordance with the collapse of objective time) is added. (shrink)

Kant soutient qu'une table complète et systématique des catégories peut être établie selon le « fil conducteur » des fonctions logiques du jugement. La première partie de cet article est une exposition de l'argument kantien. La deuxième partie est un examen de quelques-unes des objections formulées à l'encontre du « fil conducteur » de Kant. Je conclus que l'appropriation contemporaine de la doctrine kantienne des catégories est désormais divisée entre deux problèmes distincts : celui du contenu conceptuel (ou non) de (...) la perception, et celui des structures conceptuelles présupposées par une image scientifique particulière du monde. (shrink)

This is a lightly edited version of my comments on Brandom’s Lecture 2, as delivered in Prague at the “Prague Locke Lectures” in April, 2007. I try to say why Brandom’s proposed demarcation is significant, by placing it in a broader context of demarcation proposals from Kant to the twentieth century. I then raise some questions about the basic ingredients of Brandom’s demarcation—the notions of PP-sufficiency and VP-sufficiency—and question whether the vocabulary of conditionals, Brandom’s paradigm for logical vocabulary, can be (...) universal-LX. (shrink)

Kant identifies knowledge [Wissen], belief [Glaube], and opinion [Meinung] as our three primary modes of “holding-to-be-true” [Fürwahrhalten]. He also identifies opinion as making up the greatest part of our cognition. After a preliminary sketch of Kant’s system of propositional attitudes, this paper will explore what he says about the norms governing opinion and empirical hypotheses. The final section will turn to what, in the Critique of Pure Reason and elsewhere, Kant refers to as “General Applied Logic”. It concerns the “contingent (...) conditions of the subject, which can hinder or promote” good inquiry; and, though rarely mentioned in the secondary literature, it offers Kant’s methodological alternative to the traditional epistemological goal of finding “a sufficient and at the same time general criterion of truth”. (shrink)

I argue that §§15–20 of the B-Deduction contain two independent arguments for the applicability of a priori concepts, the first an argument from above, the second an argument from below. The core of the first argument is §16's explanation of our consciousness of subject-identity across self-attributions, while the focus of the second is §18's account of universality and necessity in our experience. I conclude that the B-Deduction comprises powerful strategies for establishing its intended conclusion, and that some assistance from empirical (...) psychology might well have produced a completely successful argument. (shrink)

Kant stresses the regulative status of teleological attributions, but sometimes he seems to treat teleology as a constitutive condition for biology. To clarify this issue, the concept of natural purpose and its role for biology are examined. I suggest that the concept serves an identificatory function: it singles out objects as natural purposes, whereby the special science of biology is constituted. This relative constitutivity of teleology is explicated by means of a distinction of levels: on the object level of biological (...) science, teleology is taken as constitutive, though it is merely regulative on the philosophical meta level. This distinction also concerns the place of Aristotelian teleology in Kant: on the object level, the Aristotelian view is accepted, whereas on the meta level, as agnostic stance is taken concerning teleology. (edited). (shrink)

Both Kant and Dilthey distinguish between cognition and knowledge, but they do so differently in accordance with their respective theoretical interests. Kant's primary cognitive interest is in the natural sciences, and from this perspective the status of psychology is questioned because its phenomena are not mathematically measurable. Dilthey, by contrast, reconceives psychology as a human science.For Kant, knowledge is conceptual cognition that has attained certainty by being part of a rational system. Dilthey also links knowledge with certainty; however, he derives (...) the latter from life-experience rather than from reason. Dilthey's psychology begins with the self-certainty of lived experience and life-knowledge, but this turns out to fall short of cognitive understanding. In the final analysis, both Kant and Dilthey move beyond psychology to arrive at self-understanding. Because of his doubts about introspection, Kant replaces psychology with a pragmatic anthropology to provide a communal framework for self-understanding. Dilthey supplements psychology with other human sciences as part of a project of anthropological reflection. (shrink)

In this paper, I examine Kant’s famous objection to the ontological argument: existence is not a determination. Previous commentators have not adequately explained what this claim means, how it undermines the ontological argument, or how Kant argues for it. I argue that the claim that existence is not a determination means that it is not possible for there to be non-existent objects; necessarily, there are only existent objects. I argue further that Kant’s primary target is not ontological arguments as such (...) but the metaphysical view they presuppose: that God necessarily exists in virtue of his essence being contained in, or logically entailed by, his essence. I show that this view of divine necessity requires the assumption that existence is a determination, and I show that Descartes and Leibniz are implicitly committed to this in their published versions of the ontological argument. I consider the philosophical motivations for the claim that existence is a determination and then I argue that Kant’s argument in the Critique of Pure Reason only undermines some of them. (shrink)

This paper has two purposes. (1) To justify the claim that there is an important distinction underlying the saying/showing distinction of the Tractatus; the distinction which Kant characterises as that between historical and rational knowledge. (2) To argue that it is because the Tractatus accepts Frege/Russell logic as a complete representation of all thought according to laws, that what is shown cannot be recognised as knowledge. This is done by interpolating Frege's logical innovations between the views of Kant and Wittgenstein (...) on logic and mathematics. (shrink)

This paper discusses Immanuel Kant’s views on the role of experiments in natural science, focusing on their relationship with hypotheses, laws of nature, and the heuristic principles of scientific enquiry. Kant’s views are contrasted with the philosophy of experiment that was first sketched by Francis Bacon and later developed by Robert Boyle and Robert Hooke. Kant holds that experiments are always designed and carried out in the light of hypotheses. Hypotheses are derived from experience on the basis of a set (...) of heuristic principles. The function of experiments is testing hypotheses in order to either reject them as false, or else to transform them into empirical laws of nature. To this end, we must integrate the hypotheses that are confirmed by experiments with the a priori principles which are the foundations of natural science. Compared with Bacon, Boyle, and Hooke, Kant has elaborate views on the one hand, on how our theoretical and pre-theoretical assumptions bear on experimental practice, and on the other hand, on how the results of experimental activity can be integrated with theories to advance our knowledge of nature. However, Kant overstates the dependence of experiments on theories. (shrink)

This book is the first detailed study of Kant's method of 'transcendental reflection' and its use in the Critique of Pure Reason to identify our basic human cognitive capacities, and to justify Kant's transcendental proofs of the necessary a priori conditions for the possibility of self-conscious human experience. Kenneth Westphal, in a closely argued internal critique of Kant's analysis, shows that if we take Kant's project seriously in its own terms, the result is not transcendental idealism but (unqualified) realism regarding (...) physical objects. Westphal attends to neglected topics - Kant's analyses of the transcendental affinity of the sensory manifold, the 'lifelessness of matter', fallibilism, the semantics of cognitive reference, four externalist aspects of Kant's views, and the importance of Kant's Metaphysical Foundations for the Critique of Pure Reason - that illuminate Kant's enterprise in new and valuable ways. His book will appeal to all who are interested in Kant's theoretical philosophy. (shrink)

In an earlier article (s. J Gen Philos Sci 40:341–355, 2009), I have rejected an interpretation of Aristotle’s syllogistic which (since Patzig) is predominant in the literature on Aristotle, but wrong in my view. According to this interpretation, the distinguishing feature of perfect syllogisms is their being evident. Theodor Ebert has attempted to defend this interpretation by means of objections (s. J Gen Philos Sci 40:357–365, 2009) which I will try to refute in part [1] of the following article. I (...) want to show that (1) according to Aristotle’s Prior Analytics perfect and imperfect syllogisms do not differ by their being evident, but by the reason for their being evident, (2) Aristotle uses the same words to denote proofs of the validity of perfect and imperfect syllogisms („ apodeixis “, “ deiknusthai ” etc.), (3) accordingly, Aristotle defines perfect syllogisms not as being evident, but as “requiring nothing beyond the things taken in order to make the necessity evident“, i.e. as not “requiring one or more things that are necessary because of the terms assumed, but that have not been taken among the propositions” ( APr. I. 1), (4) the proofs by which the validity of perfect assertoric syllogisms can be shown according to APr. I. 4 are based on the Dictum de omni et nullo , (5) the fact that Aristotle describes these proofs only in rough outlines corresponds to the fact that his proofs of the validity of other fundamental rules are likewise produced in rough outlines, e.g . his proof of the validity of conversio simplex in APr. I. 2, which usually has been misunderstood (also by Ebert): (6) Aristotle does not prove the convertibility of E -sentences by presupposing the convertibility of I -sentences; only the reverse is true. (shrink)

This volume includes three previously untranslated transcripts of Kant's logic lectures.