Kant: Philosophy of Logic

This book provides the first comprehensive discussion regarding the role that Kant ascribes to systematicity in the sciences. It considers not only what Kant has to say on systematicity in general, but also how the systematicity requirement for science is specified in different fields of knowledge. -/- The chapters are divided into three thematic sections. Part 1 is devoted to historical context. The chapters explore precursors of Kant’s account of the systematicity of the sciences. Part 2 addresses the application of (...) systematicity to the special sciences—cosmology, physics, chemistry, logic, mathematics, the life sciences and history. Finally, Part 3 explores the systematicity of philosophy. -/- Kant and the Systematicity of the Sciences will be of interest to scholars and advanced students working on Kant and the history and philosophy of science. (shrink)

Kant’s derivation of the table of categories from logical functions of judgments in the metaphysical deduction remains one of the least convincing arguments of the Critique of Pure Reason. This article presents an alternative approach to the question of the a priori origin of the table of categories. By circumventing the metaphysical deduction, I show the possibility of demonstrating the exact functions and necessity of the twelve categorial forms as emerging from the interaction of the synthetic unity of apperception with (...) the manifold content of the a priori intuition of space and time. I argue that this a priori material of cognition imposes a constraint on the spontaneity of understanding, thus giving rise to the specific rules of synthesis that make up the table of categories. On the reading I suggest, the table of categories can be understood as expressing the a priori form of self-consciousness in the face of space and time. (shrink)

According to a common interpretation, most explicitly defended by Onora O’Neill and Patricia Kitcher, Kant held that epistemic obligations normatively depend on moral obligations. That is, were a rational agent not bound by any moral obligation, then she would not be bound by any epistemic obligation either. By contrast, in this paper, I argue that, according to Kant, some epistemic obligations are normatively independent from moral obligations, and are indeed normatively absolute. This view, which I call epistemicism, has two parts. (...) First, it claims that in the absence of other kinds of obligations, rational agents would still be bound by these epistemic obligations, i. e., that the latter are normatively independent. Second, it claims that, no matter what other obligations are at stake, rational agents are bound by these epistemic obligations, i. e., the normativity of these epistemic obligations is absolute in that it cannot be undercut by any moral or other sort of obligation. The argument turns on an exploratory reading of Kant’s remarks in “What Is Orientation in Thinking?” (1786) about the maxim of “thinking for oneself” as the “supreme touchstone of truth”. In contrast to O’Neill and Kitcher, I argue that if we interpret this maxim as stating the unifying principle of theoretical and practical reason, then we must interpret it as stating an epistemic, and not merely practical imperative. This result, I argue, vindicates epistemicism and illuminates interesting lessons about Kant’s conception of the category of “epistemic” norms. Further, it helps us make headway with Kant’s enigmatic remarks about the unity of practical and theoretical reason in the Groundwork, the first and second Critiques, and the Lectures on Logic. On my proposal, principles of the practical and theoretical uses of reason are unified through a formal epistemic principle. (shrink)

Im Folgenden stellen wir drei aktuelle Forschungsbereiche zur formalen Logik bei Kant allgemeinverständlich dar und greifen dabei auf die trans zendentale Logik nur dann zurück, wenn sie ein besseres Verständnis der formalen Logik ermöglicht: Zunächst wird Kants Beitrag zur Rezeption und Weiterentwicklung von Euler-artigen Diagrammen dargestellt. Diese Diagramme wurden in den 1990er Jahren wiederentdeckt, als formales System interpretiert und werden heute insbes. in der Didaktik, in den Kognitionswissenschaften, in der Linguistik, in KI-Bereichen wie der (Logik-basierten) Wissensrepräsentation eingesetzt, und auch in (...) der Philosophie verwendet (Kapitel 2). Mehrere Studien haben in den letzten Jahren gezeigt, dass Kant in weiten Teilen seines Systems Oppositionsverhältnisse verwendet, die der Struktur des logischen Quadrats entsprechen. Das logische Quadrat ist heute Gegenstand intensiver Forschung, da es neben der klassischen, auch die paravollständige und parakonsistente Negation abbildet (Kap. 3). Jüngst wurde zudem die Implementierbarkeit der kantischen Logik in ein formalisiertes deduktives System bewiesen. Die Bedeutung dieses Ergebnisses wird insbesondere im Hinblick auf die formalisierte Umsetzung der Sätze vom Widerspruch, vom zureichenden Grund und der Ausschließung des Mittleren erläutert (Kap. 4). Abschließend möchten wir ein paar Perspektiven für die Forschung zur formalen Logik bei Kant nennen (Kap. 5). -- -/- Note: No financial support acknowledged by the second autor (S. Kovač). (shrink)

본 연구는 칸트의 선험철학에 대한 체계론적 방법론으로 ‘사이로서의 형식’을 제안한다. 요컨대 사이로서의 형식은 규정들의 병존 관계에 대한 반성을 유기적으로 수행할 수 있는 사유 조건이다. 사이로서의 형식은 규정 관계들의 간격을 통일성 있게 반성할 (reflektierend) 수 있다는 점에서 하나의 ‘인식원리’로 작용한다. 사이성 형식을 매개로 칸 트의 주요 개념들이 임의적 간극을 형성하는 가운데 ‘공존’에 관한 규정문제가 앎의 인식 론적 지평에서 재고되고 숙고될 수 있다. 구체적으로 본 연구는 ‘칸트의 사이와 공존’을 불일치 개념들의 사이성 속에서 논한다. 칸트의 주요 철학 개념들 간에 환치될 수 없는 규정들의 (...) 경계들을 찾아, 그 사이에 ‘공존’의 의미를 체계론적으로 재사유한다. 첫 번째로 다룰 개념들은 칸트의 1770년 『교수 취임논문』에서의 ‘감성계’와 ‘지성계’의 사이성이다. 이 두 규정항들의 불일치하는 지점들 을 분석하여, 양자의 벌어진 거리 속에 공존의 가능 조건들을 반성한다. 다음으로 칸트의 ‘형이상학’과 ‘순수이성’ 간의 사이성과 공존에 관해 논구한다. 『순수이성비판』을 토대로 두 규정항들의 간극을 분석하고, 그 불일치의 사이에서 공동체 앎에 관한 인식론적 의미를 반추한다. 마지막은 ‘선험철학’과 ‘아프리오리’의 불일치와 공존이다. 마찬가지로 『순수이 성비판』에 기반하여 양자의 사이성을 고찰하고 공존의 현대적 의미를 재확립한다. (shrink)

In this article I engage with a recent debate vis-à-vis Kant’s conception of logic, which deals with whether Kant saw logical laws as normative for, or rather as constitutive of, the faculty of understanding. On the former view, logical laws provide norms for the correct exercise of the understanding; on the latter, they define the necessary structure of the faculty of understanding per se. I claim that these two positions are not mutually exclusive, as Kant held both a normative and (...) a constitutive conception of logic. I also sketch a parallelism between Kant’s conceptions of logic and of ethics: Kant’s twofold conception of logic parallels his view of moral laws as normative (for the human will) but constitutive (of a holy will). (shrink)

Dharmakīrti argues that there is no pramāṇa (valid means of cognition or source of knowledge) for a thesis that is a self-contradiction (svavacanavirodha). That is, self-contradictions such as ‘everything said is false’ and ‘my mother is barren’ cannot be known to be true or false. The contemporary scholar Tillemans challenges Dharmakīrti by arguing that we can know that self-contradictions are false by means of a formal logical inference. The aims of the paper are to answer Tillemans’ challenge from what we (...) take to be Dharmakīrti’s or Dharmakīrtian (someone who is like Dharmakīrti) perspective and to demonstrate the unique features of Dharmakīrti’s view of inference. By so doing, we show that the epistemology in relation to the formal conception of logic that underlies Tillemans’ challenge is problematic from Dharmakīrti’s or Dharmakīrtian perspective. The paper, thus, presents Dharmakīrti’s view of inference and logical reasoning as well as a Dharmakīrtian challenge to the formal conception of logic that is the dominant contemporary conception. (shrink)

A reconstruction of a formal logical deduction of Kant's table of judgments and of the other forms of Kant's "general logic" is proposed on the basis of Kant's texts, remarks and lectures. Logical unity of apperception is taken as the starting point and the reconstructed deduction proceeds only by means of analytic judgments. In distinction to Klaus Reich's approach, the forms of judgment are not derived from the definition of a judgment as relation, but "regressively", starting from quantity, in the (...) order displayed in Kant's table of judgments and on the basis of the fourfold unity of apperception (analytic, synthetic, objective, necessary) [this reconstruction is summarized in the author's paper 'Forms of Judgment as a Link between Mind and the Concepts of Substance and Cause (Kant, Gödel)', 2014). The early, negative and positive, reception of Kant's logic in works of Croatian philosophers (especially, I. K. Horváth and Š. Čučić) is presented and discussed. (shrink)

European Journal of Philosophy, Volume 29, Issue 4, Page 988-1009, December 2021.

This paper draws out and connects two neglected issues in Kant’s conception of a priori knowledge. Both concern topics that have been important to contemporary epistemology and to formal epistemology in particular: knowability and luminosity. Does Kant commit to some form of knowability principle according to which certain necessary truths are in principle knowable to beings like us? Does Kant commit to some form of luminosity principle according to which, if a subject knows a priori, then they can know that (...) they know a priori? I defend affirmative answers to both of these questions, and by considering the special kind of modality involved in Kant’s conceptions of possible experience and the essential completability of metaphysics, I argue that his combination of knowability and luminosity principles leads Kant into difficulty. (shrink)

On the few occasions that Kant addresses the subject of truth, he usually does so in relation to the problems involved in the nominal definition of truth and in the search for a truth criterion. The aim of this paper is to provide a synoptic view of the way in which Kant poses these two issues. In the first section of the paper I address the topic of the definition of truth. I begin by explaining what a definition is and (...) what does this entail for the definition of truth. I then present the consequences and problems that Kant draws from this. In the second section of the paper I develop the topic of the criterion of truth. First, I set out Kant's expectations for such criterion and show the limits he encounters. Then I provide a classification and an explanation of the truth criteria that he mentions throughout his work. -/- En las pocas ocasiones en que Kant aborda el tema de la verdad, lo suele hacer en función de los problemas implicados en la definición nominal de verdad y en la búsqueda de un criterio de verdad. El objetivo de este trabajo es ofrecer una visión sinóptica del modo en que Kant plantea estas dos cuestiones. En la primera sección del trabajo se aborda el tema de la definición de la verdad. Primero explico qué es una definición y qué implica esto para el caso de la verdad. Tras esto, expongo las consecuencias y problemas que Kant extrae al respecto. En la segunda sección del trabajo se desarrolla el tema del criterio de verdad. Para comenzar expongo las expectativas de Kant respecto de dicho criterio y los límites con que se encuentra. Tras esto ofrezco una clasificación y explicación de los criterios de verdad que menciona a lo largo de su obra. (shrink)

The article focuses on Kant's formal logic (formal theory of concepts, judgments, and inference, general methodology) in the systematic order of logical forms and presents the main characteristics of his transcendental logic (theory of categories and transcendental ideas). Kant's problem of the foundations of logic and its completeness is addressed. The relevance and influence of Kant's account of logic in the development of modern logic is outlined. The article gives a selection of primary and secondary sources.

Volume 41, Issue 1, February 2020, Page 96-97.

Volume 28, Issue 1, January 2020, Page 207-209.

Kant’s early work The False Subtlety of the Four Syllogistic Figures is typically considered a narrow, technical work still embedded in the tradition of Wolffian logic. I argue instead that it needs to be considered in light of Kant’s developing theory of cognition and his corresponding criticism of the Wolffian single faculty theory. Whereas the mature Kant criticizes the rationalists for misrepresenting the nature of sensibility, the urgent task facing him at this stage seems to have been a proper determination (...) of the nature of the understanding. On the Wolffian framework, the latter is defined in a merely nominal manner, in terms of a generic cognitive task: the distinct representation of the possible. On Kant’s view, however, distinctness entails a capacity to relate representations, which only happens in the act of judgment. Thus, the stated aim of the False Subtlety notwithstanding, the work attempts to reorganize the logical operations around the capacity to judge. In turn, by defining the higher faculty of cognition in terms of an act of relating representations, Kant wants to show that this faculty cannot stem from a power of representation that we share with non-rational animals and must instead rest on a different fundamental power, which at the time he alternatively calls “inner sense” or “consciousness”. (shrink)

ABSTRACT I suggest how a broadly Kantian critique of classical logic might spring from reflections on constructibility conditions. According to Kant, mathematics is concerned with objects that are given through ‘arbitrary synthesis,’ in the form of ‘constructions of concepts’ in the medium of ‘pure intuition.’ Logic, by contrast, is narrowly constrained – it has no objects of its own and is fixed by the very forms of thought. That is why there is not much room for developments within logic, as (...) compared to the progress in mathematics. Kant’s view of logic remains critical, though – through considerations that are effectively on the scope and limits of classical logic and which play a part in his transcendental idealism. The most important ones are to be found in his critique of the use of reductio ad absurdum proofs in metaphysics and his solutions to the ‘antinomies of pure reason.’ Arguably, these considerations carry over to mathematics as well – by way of ‘analogues’ to the antinomies – in particular in resolving infinity paradoxes. (shrink)

At A71/B96–7 Kant explains that singular judgements are ‘special’ because they stand to the general ones as Einheit to Unendlichkeit. The reference to Einheit brings to mind the category of unity and hence raises a spectre of circularity in Kant’s explanation. I aim to remove this spectre by interpreting the Einheit-Unendlichkeit contrast in light of the logical distinctions among universal, particular and singular judgments shared by Kant and his logician predecessors. This interpretation has a further implication for resolving a controversy (...) over the correlation between the logical moments of quantity (universal, particular, singular) and the categorial ones (unity, plurality, totality). (shrink)

Kant describes logic as “the science that exhaustively presents and strictly proves nothing but the formal rules of all thinking”. (Bviii-ix) But what is the source of our cognition of such rules (“logical cognition” for short)? He makes no concerted effort to address this question. It will nonetheless become clear that the question is a philosophically significant one for him, to which he can see three possible answers: those representations are innate, derived from experience, or originally acquired a priori. Although (...) he gives no explicit argument for the third answer, he seems committed to it—especially given his views on the source of pure concepts of the understanding and on the nature of logic. It takes careful preparatory work to gather all the essential materials for motivating and reconstructing Kant’s “original acquisition” account of logical cognition. I shall proceed in two sections. In section 1, I analyze Kant’s argument that pure concepts of the understanding (or intellectual concepts)—as one kind of pure cognition—must be acquired originally and a priori. My analysis partly concerns his varied attitudes toward Crusius’s and Leibniz’s versions of the nativist account of such concepts. I give special attention to how Kant characterizes the nativist account and his own “original acquisition” account in terms of “preformation” and “epigenesis”. My goal is, firstly, to tease out the sense in which Kant grants that there must be an innate ground (or preformation) for the derivation of pure concepts and, secondly, to introduce—and pave the way for answering—the question about the source of logical cognition. In section 2, in light of Kant’s reference to Locke and Leibniz as the greatest reformers of philosophy (including logic) in their times (Log, AA 9: 32), I examine the Lockean and Leibnizian approaches to logic, respectively. Both approaches are “physiological” by Kant’s standard and are directly opposed to his own strictly critical method. I explain how this methodological move shapes Kant’s view that representations of logical rules must be originally acquired a priori. This acquisition involves a kind of radical epigenesis of pure reason: unlike the acquisition of pure concepts, it presupposes no further innate ground (or preformation). This view will have important consequences for issues such as the ground of the normativity of logical rules and the boundaries of their rightful use. (shrink)

Kant rejects Leibniz’s Principle of the Identity of Indiscernibles. In quantum mechanics, Leibniz’s principle is also apparently violated. However, both ways of rejecting the PII differ significantly. In particular, Kant denies that spatiotemporal objects are unique individuals and establishes appearances as merely singular ones. The distinction between ‘unique’ and ‘singular’ individuals is crucial for the role that intuition plays in cognition: it will be shown that Kant’s way of rejecting the PII goes against the standard versions of conceptualism and non-conceptualism (...) which, in turn, points out the relevance of this issue for the understanding of transcendental idealism. Finally, the systematic relevance will be checked by defending a Kantian interpretation of quantum individuality. (shrink)

The notion of the a priori is an important legacy of Kant for modern philosophy of science. In the course of the 20th century, a variety of proposals was put forward all of which claimed to overcome the inadequacies of Kant’s original proposal of a synthetic a priori for modern science.

This article defends the view that the logical vocabulary of syllogistic is sufficient for representing the logical form of rules and laws of non-syllogistic (classical or non-classical) predicate logic. This representation requires replacement only of the descriptive vocabulary of syllogistic (i. e. of variables for terms) by non-syllogistic descriptive signs. The validity of rules and laws of modern (classical or non-classical) predicate logic rests on the validity of rules and laws which can without exception be represented in the formal language (...) of syllogistic. Expressions of this language are representations of logical form. Frege's view that relationships between logical subjects and logical predicates can be „reduced“ to relationships between functions and arguments confuses logical and grammatical subjects as well as logical and grammatical predicates. (shrink)

As Friedman has argued, Kant's argument for the ideality of space turns on the nondeductive character of geometrical reasoning in Euclid's system. Since geometry can be axiomatized, this argument fails. But ("pace" Russell) Leibniz's argument based on the unreality of constitutive relations is not thereby answered as well. I argue that what is needed in response to Leibniz is a properly post-Kantian conception of concepts as inferentially articulated. This conception, I suggest, is based on the same fundamental insight that underlies (...) the axiomatization of geometry. (shrink)

Bernard Bolzano (1781-1848) was an original and independent thinker, who left a lasting legacy in several areas of philosophy. Four such areas are singled for special attention: political philosophy, ethics and theology, logics and semantics, and mathematics. In all these areas he was far ahead of his time. He had pioneering ideas in political philosophy and in ethics and philosophy of religion, and he argued for them in a brilliantly clear way. In logic and semantics he anticipated Frege, Carnap and (...) Quine on important points, and he had intriguing, yet to be explored, ideas on intuition and other fundamental philosophical notions. In the foundations of mathematical analysis and the theory of infinite sets he anticipated Weierstrass and Cantor. (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)