Officially, for Kant, judgments are analytic iff the predicate is "contained in" the subject. I defend the containment definition against the common charge of obscurity, and argue that arithmetic cannot be analytic, in the resulting sense. My account deploys two traditional logical notions: logical division and concept hierarchies. Division separates a genus concept into exclusive, exhaustive species. Repeated divisions generate a hierarchy, in which lower species are derived from their genus, by adding differentia(e). Hierarchies afford a straightforward sense of containment: (...) genera are contained in the species formed from them. Kant's thesis then amounts to the claim that no concept hierarchy conforming to division rules can express truths like '7+5=12.' Kant is correct. Operation concepts ( ) bear two relations to number concepts: and are inputs, is output. To capture both relations, hierarchies must posit overlaps between concepts that violate the exclusion rule. Thus, such truths are synthetic. (shrink)

This compelling reevaluation of the relationship between logic and knowledge affirms the key role that the notion of judgement must play in such a review. The commentary repatriates the concept of judgement in the discussion, banished in recent times by the logical positivism of Wittgenstein, Hilbert and Schlick, and the Platonism of Bolzano. The volume commences with the insights of Swedish philosopher Per Martin-Löf, the father of constructive type theory, for whom logic is a demonstrative science in which judgement is (...) a settled feature of the landscape. His paper opens the first of four sections that examine, in turn, historical philosophical assessments of judgement and reason; their place in early modern philosophy; the notion of judgement and logical theory in Wolff, Kant and Neo-Kantians like Windelband; their development in the Husserlian phenomenological paradigm; and the work of Bolzano, Russell and Frege. The papers, whose authors include Per Martin-Löf, Göran Sundholm, Michael Della Rocca and Robin Rollinger, represent a finely judged editorial selection highlighting work on philosophers exercised by the question of whether or not an epistemic notion of judgement has a role to play in logic. The volume will be of profound interest to students and academicians for its application of historical developments in philosophy to the solution of vexatious contemporary issues in the foundation of logic. ​. (shrink)

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)

Within eighteenth-century debates on animal cognition we can distinguish at least three main theoretical positions: (i) Buffon’s mechanism, (ii) Reimarus’ theory of instincts, and (iii) the sensationalism of Condillac and Leroy. In this paper, I adopt a philosophical perspective on this debate and argue that in order to fully understand the justification Buffon, Reimarus, Condillac, and Leroy gave for their respective theories, we must pay special attention to the theoretical virtues these naturalists alluded to while justifying their position. These theoretical (...) virtues have received little to no attention in the literature on eighteenth-century animal cognition, but figure prominently in the justification of the mechanist, instinctive, and sensationalist theories of animal behavior. Through my philosophical study of the role of theoretical virtues in eighteenth-century debates on animal cognition, we obtain a deeper understanding of how theoretical virtues were conceptualized in eighteenth-century science and how they influenced the justification of theories of animal cognition. (shrink)

This article explains Kant’s claim that sciences must take, at least as their ideal, the form of a ‘system’. I argue that Kant’s notion of systematicity can be understood against the background of de Jong & Betti’s Classical Model of Science (2010) and the writings of Georg Friedrich Meier and Johann Heinrich Lambert. According to my interpretation, Meier, Lambert, and Kant accepted an axiomatic idea of science, articulated by the Classical Model, which elucidates their conceptions of systematicity. I show that (...) Kant’s critique of the mathematical method is compatible with his adherence to this axiomatic conception of science. I further show that systematicity furthers traditionally accepted logical ideals of scientific knowledge, which explains why Meier and Kant think that sciences must be ‘systematic’. (shrink)

Ernst Mayr argued that the emergence of biology as a special science in the early nineteenth century was possible due to the demise of the mathematical model of science and its insistence on demonstrative knowledge. More recently, John Zammito has claimed that the rise of biology as a special science was due to a distinctive experimental, anti-metaphysical, anti-mathematical, and anti-rationalist strand of thought coming from outside of Germany. In this paper we argue that this narrative neglects the important role played (...) by the mathematical and axiomatic model of science in the emergence of biology as a special science. We show that several major actors involved in the emergence of biology as a science in Germany were working with an axiomatic conception of science that goes back at least to Aristotle and was popular in mid-eighteenth-century German academic circles due to its endorsement by Christian Wolff. More specifically, we show that at least two major contributors to the emergence of biology in Germany—Caspar Friedrich Wolff and Gottfried Reinhold Treviranus—sought to provide a conception of the new science of life that satisfies the criteria of a traditional axiomatic ideal of science. Both C.F. Wolff and Treviranus took over strong commitments to the axiomatic model of science from major philosophers of their time, Christian Wolff and Friedrich Wilhelm Joseph Schelling, respectively. The ideal of biology as an axiomatic science with specific biological fundamental concepts and principles thus played a role in the emergence of biology as a special science. (shrink)

In his table of judgements, Kant added infinity as a third quality. An infinite judgement ‘All S are non-P’ is said to differ from the affirmative ‘All S are P’ because it ascribes a negative predicate; and it differs from the negative ‘No S is P’ because it has a richer content. The present paper puts three interpretations of this surplus content to six tests. Among other things, it is examined whether these interpretations marry up with Kant’s solution to the (...) first antinomy, his conception of analyticity and the principle of complete determination. The unpleasant conclusion is that none of the interpretations can make its mark as the most adequate one. It thus remains unclear what Kant had in mind when positioning infinite judgements besides affirmative and negative ones. (shrink)

In this essay, I investigate Baumgarten’s doctrine of the six perfections of knowledge (wealth, magnitude, truth, clarity, certainty, and life), which is famously one of the most characteristic and enigmatic features of his philosophy. Recent scholarship has almost unanimously stressed the rhetorical background of the categories. Instead, I argue that Baumgarten elaborates his theory in close relationship with coeval philosophy. To support this claim, I examine the position of some Thomasian philosophers, such as Johann Liborius Zimmermann, who had indicated a (...) list of criteria similar to that of Baumgarten. Moreover, I analyse the distinction between formal and material perfections, tracing it back to the Wolffian milieu. On these bases, I propose a new reconstruction of Baumgarten’s doctrine, with particular attention to its aesthetic application. Finally, I outline the reception of the six categories in the late German Enlightenment until Kant. (shrink)

There is an emerging consensus among interpreters that in his Critical writings Kant ascribes unconscious representations to the mind. The nature and extent of this ascription over the course of Kant’s philosophical development is however not well understood. I argue that from his earliest published writings Kant consistently ascribes unconscious representations to the mind; that some of these representations are unconscious in the strong sense that they are not available to introspection; and that Kant extends his commitment to unconscious representations (...) by ascribing to the mind unconscious acts of judging and reasoning. (shrink)

Philosophers after Leibniz used a technical idiom to classify and explain the nature of mental content. Substantive philosophical claims were formulated in terms of this vocabulary, including claims about the nature of mental representations, concepts, unconscious mental content, and consciousness. Despite its importance, the origin and development of this vocabulary is insufficiently well understood. More specifically, interpreters have failed to recognize the existence of two distinct and influential versions of the post-Leibnizian idiom. These competing formulations used the same technical terms (...) and taxonomic relations but assigned different connotations to those terms and employed different criteria for their application. This paper explains the two most influential versions of the post-Leibnizian idiom. (shrink)

The present paper argues for the relevance of Immanuel Kant and the German Enlightenment to contemporary social epistemology. Rather than distancing themselves from the alleged ‘individualism’ of Enlightenment philosophers, social epistemologists would be well-advised to look at the substantive discussion of social-epistemological questions in the works of Kant and other Enlightenment figures. After a brief rebuttal of the received view of the Enlightenment as an intrinsically individualist enterprise, this paper charts the historical trajectory of philosophical discussions of testimony as a (...) source of knowledge, via such philosophers as C. Thomasius, C. A. Crusius, J. M. Chladenius, G. F. Meier, and finally Kant. Building on recent work on Kant's epistemology of testimony, the paper considers Kant's broader contributions to social epistemology. This includes an analysis of Kant's comments on the social basis of contingent epistemic standards, e.g. in the sciences, as well as on problems arising from the management of what Kant calls the growing ‘volume of knowledge’. Special attention is paid to the relation between Kant's views and contemporary problems arising both in the context of education and from our increased reliance on scientific experts. (shrink)

Immanuel Kant is often regarded as an exponent of the ‘individualist’ tradition in epistemology, according to which testimony is not a fundamental source of knowledge. The present paper argues that this view is far from accurate. Kant devotes ample space to discussions of testimony and, in his lectures on logic, arrives at a distinct and stable philosophical position regarding testimony. Important elements of this position consist in (a) acknowledging the ineliminability of testimony; (b) realizing that testimony can establish empirical knowledge (...) with certainty; (c) establishing a presumptive principle regarding the acceptance of testimony; (d) arguing for a symmetry between knowledge based on experience and knowledge based on testimony. Rejecting testimony as a fundamental source of knowledge merely on the basis that no theoretically necessary ground for its truth can be given, would, as Kant puts it, indicate ‘a lack of moral interest’. Such ‘incredulity’ would be a form of ‘logical egoism’: it demonstrates an unwillingness or inability to think oneself in the place of others, yet this we must do if we are to trust our own judgements. While Kant strongly endorses testimony as a source of empirical knowledge, he does, however, make one important restriction: ‘Propositions of reason’ (Vernunftwahrheiten), such as universal moral principles, may not be adopted on the basis of testimony. I argue that this distinction, between testimonial knowledge of empirical matters of fact and individual knowledge of propositions of reason, is an important element of Kant’s epistemology of testimony, as it explains how his strong endorsement of testimony as a source of knowledge can be squared with his equally strong demand for intellectual autonomy. Finally, I comment on the overall implications of this account for Kant’s discussion, elsewhere in his work, of the public nature of communication. (shrink)

This review of contemporary discussions of Kantian philosophy of mathematics is timed for the publication of the essay Kant’s Philosophy of Mathematics. Volume 1: The Critical Philosophy and Its Roots (2020) edited by Carl Posy and Ofra Rechter. The main discussions and comments are based on the texts contained in this collection. I first examine the more general questions which have to do not only with the philosophy of mathematics, but also with related areas of Kant’s philosophy, e. g. the (...) question: What is intuition and singular term? Then I look at more specific questions, e. g.: What is the subject of arithmetic and what is the significance of diagrams in mathematical reasoning? As a result, the reader is presented with a fairly complete overview of modern discussions which can be used as an introduction to the problem field of Kant’s philosophy of mathematics. (shrink)

The present paper argues for the relevance of Immanuel Kant and the German Enlightenment to contemporary social epistemology. Rather than distancing themselves from the alleged ‘individualism’ of Enlightenment philosophers, social epistemologists would be well-advised to look at the substantive discussion of social-epistemological questions in the works of Kant and other Enlightenment figures. After a brief rebuttal of the received view of the Enlightenment as an intrinsically individualist enterprise, this paper charts the historical trajectory of philosophical discussions of testimony as a (...) source of knowledge, via such philosophers as C. Thomasius, C. A. Crusius, J. M. Chladenius, G. F. Meier, and finally Kant. Building on recent work on Kant's epistemology of testimony, the paper considers Kant's broader contributions to social epistemology. This includes an analysis of Kant's comments on the social basis of contingent epistemic standards, e.g. in the sciences, as well as on problems arising from the management of what Kant calls the growing ‘volume of knowledge’. Special attention is paid to the relation between Kant's views and contemporary problems arising both in the context of education and from our increased reliance on scientific experts. (shrink)

This paper considers Kant's understanding of conceptual representation in light of his view of geometry.

is true, there is a truth-maker (e.g., a fact) with which it is identical and the truth of the former consists in its identity with the latter. The theory is best understood as a reaction to the correspondence theory, according to which the relation of truth-bearer to truth-maker is correspondence. A correspondence theory is vulnerable to the nagging suspicion that if the best we can do is make statements that merely correspond to the truth, then we inevitably fail to capture (...) the reality they are about and thus fall short of the truth we aim at. An identity theory is designed to overcome this suspicion. (shrink)

This dissertation concerns the methodology Kant employs in the first two sections of the Groundwork of the Metaphysics of Morals (Groundwork I-II) with particular attention to how the execution of the method of analysis in these sections contributes to the establishment of moral metaphysics as a science. My thesis is that Kant had a detailed strategy for the Groundwork, that this strategy and Kant’s reasons for adopting it can be ascertained from the Critique of Pure Reason (first Critique) and his (...) lectures on logic, and that understanding this strategy gains us interpretive insight into Kant’s moral metaphysics. At the most general level of methodology, Kant says there are four steps for the establishment of any science: 1) make distinct the idea of the natural unity of its material 2) determine the special content of the science 3) articulate the systematic unity of the science 4) critique the science to determine its boundaries The first two of these steps are accomplished by the genetically scholastic method of analysis, paradigmatically the method whereby confused and obscure ideas are made clear and distinct, thereby logically perfecting them and transforming them into possible grounds of cognitive insight that are potentially complete and adequate to philosophical purposes. The analysis of Groundwork I is a paradigmatic analysis that makes distinct what is contained in common understanding, i.e. its Inhalt or intension, making distinct the higher partial concepts that together define the concept of morality. The analysis of Groundwork II is an employment more specifically of the method of logical division, which makes distinct what is contained under the concept, i.e. its Umfang, by which the extension or object of morality is determined. Part I introduces Kant’s conception of moral metaphysical science and why he took it to be in need of establishment, explains the general method for establishing science and the scholastic method of analysis by which its first two steps are to be accomplished, then provides an interpretation of Groundwork I as an execution of this method. Part II details Kant’s determination of the special content of moral science in Groundwork II in relation to the central problem for moral metaphysics – how synthetic a priori practical cognition is possible. (shrink)

Modern philosophy is often seen as characterized by a shift of focus from the things themselves to our knowledge of them, i.e., by a turn to the subject and subjectivity. The philosophy of Immanuel Kant is seen as the site of the emergence of the idea of a subject that constitutes the object of knowledge, and thus plays a central role in this narrative. This study examines Kant’s theory of knowledge at the intersection between the history of science and the (...) history of the modern subject, on the one hand, and in the tension between modern experimental and mathematical science and more traditional Aristotelian conceptions of epistemic perfection, on the other. The dissertation consists of four chapters. In the first chapter, I examine Kant’s concept of experience, and its relation both to Early Modern experimentalism and to the Wolffian tradition. In the second chapter, I argue that Kant adheres to a broadly Aristotelian conception of epistemic perfection – the ideal of understanding – but transforms this ideal into the self-understanding of reason, where reason can only have insight into the products of its own activity. In the third chapter, I use Kant’s conception of space and time to exemplify such products of reason, and argue that, for Kant, space and time are constructively generated representations that function as principles for ordering empirical knowledge. In the fourth and final chapter, I examine Kant’s conception of the subject, and situate it in relation to both the long history of the modern subject and German Enlightenment philosophy. Whereas the modern philosophical conception of the subject is usually taken to combine an ‘I’ functioning as the subject to which mental acts are attributed and an ‘I’ that has the ability to immediately perceive itself as the subject of these acts, I argue that Kant reconceives this relation between the ‘I’ and its acts as a purely intellectual self-relation. The unity of the ‘I’ is not a perceived unity, but a unity brought about by the intellect. (shrink)