Kant: Inference

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)

In the transcendental deduction, the central argument of the Critique of Pure Reason, Kant seeks to secure the objective validity of our basic categories of thought. He distinguishes objective and subjective sides of this argument. The latter side, the subjective deduction, is normally understood as an investigation of our cognitive faculties. It is identified with Kant’s account of a threefold synthesis involved in our cognition of objects of experience, and it is said to precede and ground Kant’s proof of the (...) validity of the categories in the objective deduction. I challenge this standard reading of the subjective deduction, arguing, first, that there is little textual evidence for it, and, second, that it encourages a problematic conception of how the deduction works. In its place, I present a new reading of the subjective deduction. Rather than being a broad investigation of our cognitive faculties, it should be seen as addressing a specific worry that arises in the course of the objective deduction. The latter establishes the need for a necessary connection between our capacities for thinking and being given objects, but Kant acknowledges that his readers might struggle to comprehend how these seemingly independent capacities are coordinated. Even worse, they might well believe that in asserting this necessary connection, Kant’s position amounts to an implausible subjective idealism. The subjective deduction ismeant to allay these concerns by showing that they rest on a misunderstanding of the relation between these faculties. This new reading of the subjective deduction offers a better fit with Kant’s text. It also has broader implications, for it reveals the more philosophically plausible account of our relation to the world as thinkers that Kant is defending – an account that is largely obscured by the standard reading of the subjective deduction. (shrink)

In 1870, Hermann von Helmholtz criticized the Kantian conception of geometrical axioms as a priori synthetic judgments grounded in spatial intuition. However, during his dispute with Albrecht Krause (Kant und Helmholtz über den Ursprung und die Bedeutung der Raumanschauung und der geometrischen Axiome. Lahr, Schauenburg, 1878), Helmholtz maintained that space can be transcendental without the axioms being so. In this paper, I will analyze Helmholtz’s claim in connection with his theory of measurement. Helmholtz uses a Kantian argument that can be (...) summarized as follows: mathematical structures that can be defined independently of the objects we experience are necessary for judgments about magnitudes to be generally valid. I suggest that space is conceived by Helmholtz as one such structure. I will analyze his argument in its most detailed version, which is found in Helmholtz (Zählen und Messen, erkenntnistheoretisch betrachtet 1887. In: Schriften zur Erkenntnistheorie. Springer, Berlin, 1921, 70–97). In support of my view, I will consider alternative formulations of the same argument by Ernst Cassirer and Otto Hölder. (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)

O objectivo central de Kant no texto da "Segunda Analogia da Experiência", na Crítica da Razão Pura, é o de estabelecer a condição de possibilidade da experiência de uma sucessão objectiva de fenómenos. A sucessão contingente de fenómenos ao nível da intuição converte-se na percepção objectiva de uma sequência de fenómenos apenas pela actividade sintética da imaginação de acordo com o princípio de causalidade. No texto em análise, a aplicação daquele princípio não vai além das formas a priori do espaço (...) e do tempo. Kant não afirma pois a tese de que a natureza obedece a leis causais. Finalmente, o mesmo princípio de causalidade não pode ser aplicado ao caso da afectação da sensibilidade pela "coisa em si". /// L'objective central de Kant dans le texte de la "Deuxième Analogie de l'Expérience", dans la Critique de la Raison Pure, est d'établir la condition de possibilité de l'expérience d'une succession objective de phénomènes. La succession contingente de phénomènes au niveau de l'intuition est convertie dans la perception objective d'une séquence de phénomènes seulement par l'activité synthétique de l'imagination d'accord avec le principe de causalité. Dans le contexte en analyse, l'explication de ce principe ne va pas au-delà des formes a priori de l'espace et du temps. Kant n'affirme pas donc la tèse de que la nature obéit aux lois causalles(?). Finalement, le même principe de causalité ne peut pas être appliqué au cas d'affectation de la sensibilité par la "chose en soi". /// The basic aim of Kant in the text of the "Second Analogy of Experience", in the Critic of Pure Reason, is to establish the condition of possibility of the experience of an objective succession. The Kantian thesis is that the contingent succession of appearances at the intuitional level is converted into an objective perception of a sequence only by the synthetic activity of the imagination, according to the principle of causality. In that text, the application of this principle does not go beyond the realm of the intuitional modes of space and time. Thus Kant is not aiming to establish the lawlikeness of nature. Finally, the Kantian concept of causality, as it it transcendentally derived in the Second Analogy, cannot be applied to the case of affection of the sensibility by the "thing in itself. (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)

This is a critique of Michael Wolff's ideas on Kant and Aristotle. I criticize in particular his overestimation of Kant as a logician and his claim that Aristotle wants to offer proofs for his perfect syllogisms.

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 to highlight this difference and arguing that, in the (Jäsche) Logic, error is explained more consistently 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 the understanding hold merely subjective grounds of judgment to be objective ones. In the Transcendental Dialectic, this unnoticed influence is conceived 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 in the (Jäsche) Logic that influence is conceived in such a way that the understanding itself is regarded as the source and author of error. This author 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)

It is traditionally held that our knowledge of necessity is a priori; but the familiar theories of a priori knowledge – platonism and conventionalism – have now been discredited, and replaced by either modal skepticism or a posteriori essentialism. The main thesis of this paper is that Kant's theory of a priori knowledge, when detached from his transcendental idealism, offers a genuine alternative to these unpalatable options. According to Kant's doctrine, all epistemic necessity is grounded directly or indirectly on our (...) capacity for clear and distinct rational intuition. Insight, in turn, depends upon functions of the imagination for creating “mental models” of necessary truths. This doctrine is well exemplified by Kant's account of our knowledge of simple analytic truths. (shrink)

Simple or "standard" empirical judgments--as expressed in such statements as "The rose is red" or "Socrates is mortal"--are logically basic for theoretical rationality. All the more complex forms of judgment presuppose the existence and tenability of judgments of the "standard" type. The overall aim of this study is twofold: to show how the traditional theory of standard empirical judgments--as represented by Kant's doctrine of judgment--is subject to a through-going form of skepticism that I entitle "judgmental skepticism" and to attempt to (...) develop a more adequate account of the standard empirical judgment which circumvents the central difficulties in the traditional theory. ;Part I of the study develops, and then criticizes, Kant's theory of empirical judgment. Part II of the study then attempts to develop an accurate description of the standard empirical judgment, using the critical results of part I as working clues and foils. In the last chapter of part II, what may be called a "common sense" approach to judgmental skepticism is deployed: it is claimed that the judgmental skeptic cannot challenge the tenability of all standard judgments without rational self-stultification. Accepting this auxiom, it then becomes possible simple to describe several ways in which a paradigmatic, successful, standard judgment presupposes certain instinctive or "commonsensical" cognitive abilities. The careful description of these abilities in turn provides a commonsensical or non-transcendental foundation for theoretical rationality itself. (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)

In this innovative study Patricia Kitcher argues that we can only understand the deduction of the categories in Kant's Critique of Pure Reason in terms of his attempt to fathom the psychological prerequisites of thought. Thus a consideration of his conception of psychology is essential to an understanding of his philosophy. Kitcher specifically considers Kant's claims about the unity of the thinking self; the spatial forms of human perceptions; the relations among mental states necessary for them to have content; the (...) relations between perceptions and judgment; and the limits of philosophical insight into psychological processes. (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)

Kant's philosophy of geometry rests upon his doctrine of the "schematism" which I argue is formally identical to the ability to grass the middle term of an Aristotelian syllogism. The doctrine fails to avoid obscurities which were already present in Plato, Aristotle, and Hume.

In response to Henry Allison's and Sally Sedwick's comments on my recent book, Kant and the Capacity to Judge, I explain Kant's description of the understanding as being essentially a "capacity to judge", and his view of the relationship between the categories and the logical functions of judgment. I defend my interpretation of Kant's argument in the Transcendental Deduction of the Categories in the B edition. I conclude that, in my interpretation, Kant's notions of the "a priori" and the "given" (...) are more complex and flexible than is generally perceived. Nevertheless, Kant maintains a strict distinction between receptivity and spontaneity, the "passive" and the "active" aspects of our representational capacities. This separates him from his German idealist successors, most notably Fichte and Hegel. Contrary to Sedgwick's and Allison's suggestions, I do not think that my interpretation tends to blur this distinction. (shrink)

This paper provides a comprehensive critique of Poincaré’s usage of the term intuition in his defence of the foundations of pure mathematics and science. Kant’s notions of sensibility and a priori form and Parsons’s theory of quasi-concrete objects are used to impute rigour into Poincaré’s interpretation of intuition. In turn, Poincaré’s portrayal of sensible intuition as a special kind of intuition that tolerates the senses and imagination is rejected. In its place, a more harmonized account of how we perceive concrete (...) objects is offered whereby intuitive knowledge is consistently a priori whatever the domain of application.Keywords: Immanuel Kant; Charles Parsons; Henri Poincaré; Quasi-concrete object; Sensible intuition; Sensibility. (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)

The transition in Kant's writings form a pre-critical to a critical standpoint has been thoroughly documented with regard to Kant's changing conception of metaphysics, theory of knowledge, and philosophy of mathematics. But a similar alteration in standpoint in Kant's philosophy of logic has received little or no attention. This paper documents the existence of this shift in Kant's philosophy of logic and examines its nature. The resulting analysis provides evidence for the thesis that Kant began with a strictly intensional term (...) logic and with a theory of inference based on the analytic composition of concepts, and ended with a view of logic which, while remaining fundamentally intensional and term-based, shows movement towards a logic of propositions and propositional connectives. (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)

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)

One of the perennially intriguing questions regarding Kant’s approach to the human sciences is the relation between his ‘transcendental psychology’ and empirical cognitive psychology. In this paper I compare his analysis of the a priori conditions of human cognition in the Critique of pure reason with his empirical account of the human cognitive faculties in his Anthropology from a pragmatic point of view. In comparing his approach to self-consciousness, sensibility, imagination, and understanding in these two works, I argue that Kant (...) distinguishes between the transcendental and empirical aspects of the human cognitive faculties, and regards the transcendental functions as configuring the empirical faculties of human consciousness, or as giving them the structure that they require to become faculties of cognition. I then show that the cognitive faculties of human beings may vary in their empirical operation, even while they are configured by the same transcendental structure. Finally, I characterize Kant’s transcendental psychology in the first Critique as an account of the faculties that are required for a mind to be an agent or subject of cognition, corresponding to his account of the conditions that are required universally and necessarily for something to be an object of cognition.Keywords: Immanuel Kant; Anthropology; Psychology; Cognition; Transcendental; Empirical. (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 target is not merely ontological arguments as such (...) but the larger ‘ontotheist’ metaphysics they presuppose: the view that God necessarily exists in virtue of his essence being contained in, or logically entailed by, his essence. I show that the ontotheist explanation 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 examine Kant's arguments in the Critique of Pure Reason against it. (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 chapter discusses the relation between Kant’s views on the foundations of syllogistic inference in ‘The False Subtlety of the Four Syllogistic Figures’, the views of eighteenth-century German authors who wrote on syllogism, and the conception of metaphysics that Kant developed in 1762-1764. Kant’s positions are, on the whole, rather original, even though they are not as independent from the intellectual context as Kant’s later, Critical philosophy. Despite Kant’s polemical tone, his views on syllogism are not primarily motivated by polemical (...) purposes. They are strongly influenced by his views on the method of metaphysics. (shrink)

This article reconstructs Kant's view on the existential import of categorical sentences. Kant is widely taken to have held that affirmative sentences (the A and I sentences of the traditional square of opposition) have existential import, whereas negative sentences (E and O) lack existential import. The article challenges this standard interpretation. It is argued that Kant ascribes existential import only to some affirmative synthetic sentences. However, the reasons for this do not fall within the remit of Kant's formal logic. Unlike (...) traditional logic and modern standard quantification theory, Kant's formal logic is free from existential commitments. (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 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)

This paper argues that kant's general epistemology incorporates a theory of algebra which entails a less constricted view of kant's philosophy of mathematics than is sometimes given. To extract a plausible theory of algebra from the "critique of pure reason", It is necessary to link kant's doctrine of mathematical construction to the idea of the "schematism". Mathematical construction can be understood to accommodate algebraic symbolism as well as the more familiar spatial configurations of geometry.

In an earlier article (see J Gen Philos Sei (2010) 41: 341-355) I have compared Aristotle's syllogistic with Kant's theory of "pure ratiocination". "Ratiocinia pura" („reine Vernunftschlüsse") is Kant's designation for assertoric syllogisms Aristotle has called 'perfect'. In Kant's view they differ from non-pure ratiocinia precisely in that their validity rests only on the validity of the Dictum de omni et nullo (which, however, in Kant's view can be further reduced to more fundamental principles) whereas the validity of non-pure ratiocinia (...) additionally presupposes the validity of inferences which Kant calls consequentiae immediatae. I have argued that Kant's view is in some (not in all) essential features in accordance with Aristotle's view concerning perfect syllogisms and certainly leading to a tenable and interesting logical theory. As a result I have rejected not only the interpretation of Aristotle adopted by Theodor Ebert, but also the objections he has raised against Kant's logical theory. As far as Aristotle is concerned, Ebert has attempted to defend his position in the first part of his reply to my article published in J Gen Philos Sei (2009) 40: 357-365, and I have argued against this defence in issue 1 of the J Gen Philos Sei (2010) 41: 199-213 (cf. Ebert's answer in the same issue pp. 215-231). In the following discussion I deal with Eberts defence of his criticism of Kant published in the second part of his reply to my article (see J Gen Philos Sei (2009) 40: 365-372). I shall argue, that Kant's principle 'nota notae est nota rei ipsius' and his use of technical vocabulary stand up to the objections raised by Ebert. His attempts to prove that Kant's logical theory is defective are based on several misinterpretations. (shrink)