I defend Kant’s definition of analyticity in terms of concept “containment”, which has engendered widespread scepticism. Kant deployed a clear, technical notion of containment based on ideas standard within traditional logic, notably genus/species hierarchies formed via logical division. Kant’s analytic/synthetic distinction thereby undermines the logico-metaphysical system of Christian Wolff, showing that the Wolffian paradigm lacks the expressive power even to represent essential knowledge, including elementary mathematics, and so cannot provide an adequate system of philosophy. The results clarify the extent to (...) which analyticity sensu Kant can illuminate the problem of a priori knowledge generally. (shrink)

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)

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)

There has been a significant shift in the discussion of a priori knowledge. The shift is due largely to the influence of Quine. The traditional debate focused on the epistemic status of mathematics and logic. Kant, for example, maintained that arithmetic and geometry provide clear examples of synthetic a priori knowledge and that principles of logic, such as the principle of contradiction, provide the basis for analytic a priori knowledge. Quine’s rejection of the analytic-synthetic distinction and his holistic empiricist account (...) of mathematic and logical knowledge undercut the traditional defenses of the a priori in two ways. First, one could no longer defend the view that mathematical and logical knowledge is a priori solely by rejecting Mill’s inductive empiricism. Moreover, holistic empiricism proved to be a more challenging position to refute than inductive empiricism. Second, the rejection of the analytic-synthetic distinction blocked an alternative defense of the a priori status of mathematics and logic that appealed to their alleged analyticity. (shrink)

This major publication is a history of the semantic tradition in philosophy from the early nineteenth century through its incarnation in the work of the Vienna Circle, the group of logical positivists that emerged in the years 1925-1935 in Vienna who were characterised by a strong commitment to empiricism, a high regard for science, and a conviction that modern logic is the primary tool of analytic philosophy. In the first part of the book, Alberto Coffa traces the roots of logical (...) positivism in a semantic tradition that arose in opposition to Kant's theory that a priori knowledge is based on pure intuition and the constitutive powers of the mind. In Part II, Coffa chronicles the development of this tradition by members and associates of the Vienna Circle. Much of Coffa's analysis draws on the unpublished notes and correspondence of many philosophers. The book, however, is not merely a history of the semantic tradition from Kant 'to the Vienna Station'. Coffa also critically reassesses the role of semantic notions in understanding the ground of a priori knowledge and its relation to empirical knowledge and questions the turn the tradition has taken since Vienna. (shrink)

This paper concentrates on some aspects of the history of the analytic-synthetic distinction from Kant to Bolzano and Frege. This history evinces considerable continuity but also some important discontinuities. The analytic-synthetic distinction has to be seen in the first place in relation to a science, i.e. an ordered system of cognition. Looking especially to the place and role of logic it will be argued that Kant, Bolzano and Frege each developed the analytic-synthetic distinction within the same conception of scientific rationality, (...) that is, within the Classical Model of Science: scientific knowledge as cognitio ex principiis . But as we will see, the way the distinction between analytic and synthetic judgments or propositions functions within this model turns out to differ considerably between them. (shrink)

Alfred North Whitehead (1861–1947) quotably wrote in 1929 that “the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato.”1 The same could be said, perhaps with even greater accuracy, of the twentieth-century Euro-American philosophical tradition and Immanuel Kant (1724–1804).2 In this sense the twentieth century was the post-Kantian century. Twentieth-century philosophy in Europe and the USA was dominated by two distinctive and (after 1945) officially opposed traditions: the analytic tradition and (...) the phenomenological tradition. Very simply put, the analytic tradition was all about logic and analyticity,3 and the phenomenological tradition was all about consciousness and intentionality.4 (See also “The birth of analytic philosophy,” Chapter 1; “The development of analytic philosophy: Wittgenstein and after,” Chapter 2; “American philosophy in the twentieth century,” Chapter 5; and “Phenomenology,” Chapter 15.) Ironically enough however, despite their official Great Divide, both the analytic and the phenomenological traditions were essentially continuous and parallel critical developments from an earlier dominant neo-Kantian tradition. This, by the end of the nineteenth century had vigorously reasserted the claims of Kant’s transcendental idealism against Hegel’s absolute idealism and the other major systems of post-Kantian German Idealism, under the unifying slogan “Back to Kant!” So again ironically enough, both the analytic and phenomenological traditions were alike founded on, and natural outgrowths from, Kant’s Critical Philosophy. By the end of the twentieth century however, and this time sadly rather than ironically, both the analytic and phenomenological traditions had not only explicitly rejected their own Kantian foundations and roots but also had effectively undermined themselves philosophically, even if by no means institutionally.. (shrink)

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)

Kant’s Critique of Pure Reason (KrV) presents a priori knowledge of synthetic truths as posing a philosophical problem of great import whose only possible solution vindicates the system of transcendental idealism. The work does not accord any such significance to a priori knowledge of analytic truths. The intelligibility of the contrast rests on the well-foundedness of Kant’s analytic–synthetic distinction and on his claim to objectively or correctly classify key judgments with respect to it. Though the correctness of Kant’s classification is (...) vital to his philosophical project, it has been vigorously challenged since he introduced his famous distinction of judgments. The aim of this essay is to explore several .. (shrink)

This volume provides the first ever extensive translation of the notes and fragments that survived Kant's death in 1804. These include marginalia, lecture notes, and sketches and drafts for his published works. They are important as an indispensable resource for understanding Kant's intellectual development and published works, casting new light on Kant's conception of his own philosophical methods and his relations to his predecessors, as well as on central doctrines of his work such as the theory of space, time and (...) categories, the refutations of skepticism and metaphysical dogmatism, the theory of the value of freedom and the possibility of free will, the conception of God, the theory of beauty, and much more. (shrink)

This accessible and practical edition of Kant's best introduction to his own work is designed especially for students. Assuming no prior knowledge of the Prolegomena to Any Future Metaphysics, esteemed scholar Gunter Zoller provides an extensive introduction that covers Kant's life, the origin and reception of the Prolegomena, the organization of the work, its principal arguments, and its philosophical significance. Detailed notes, a chronology, a glossary, an annotated bibliography, and two reviews of the Critique of Pure Reason--which establishes the specific (...) intellectual background of the Prolegomena--are also included. (shrink)

This new, revised edition of Kant's Prolegomena, the best introduction to the theoretical side of his philosophy, presents his thought clearly through careful attention to his original language. Also included are selections from the Critique of Pure Reason, which fill out and explicate some of Kant's central arguments (including famous sections of the Schematism and Analogies), and in which Kant himself explains his special terminology. The first reviews of the Critique, to which Kant responded in the Prolegomena, are included in (...) this revised edition. First Edition Hb (1997): 0-521-57345-9 First Edition Pb (1997): 0-521-57542-7. (shrink)

Kant's views on logic and logical theory play an important role in his critical writings, especially the Critique of Pure Reason. However, since he published only one short essay on the subject, we must turn to the texts derived from his logic lectures to understand his views. The present volume includes three previously untranslated transcripts of Kant's logic lectures: the Blumberg Logic from the 1770s; the Vienna Logic (supplemented by the recently discovered Hechsel Logic) from the early 1780s; and the (...) Dohna-Wundlacken Logic from the early 1790s. Also included is a new translation of the Jasche Logic, compiled at Kant's request and published in 1800 but which also appears to stem in part from a transcript of his lectures. Together these texts provide a rich source of evidence for Kant's evolving views on logic, on the relations between logic and other disciplines, and on a variety of topics (e.g. analysis and synthesis) central to Kant's mature philosophy. They also provide a portrait of Kant as lecturer, a role in which he was both popular and influential. This volume contains substantial editorial apparatus: a general introduction, linguistic and factual notes, glossaries of key terms (both German/English and English/German) and concordances relating Kant's lectures to Georg Frederich Meier's Excerpts from the Doctrine of Reason, the book on which Kant lectured throughout his life and in which he left extensive notes. (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)

This chapter begins with a discussion of Kant's theory of judgment-forms. It argues that it is not true in Kant's logic that assertoric or apodeictic judgments imply problematic ones, in the manner in which necessity and truth imply possibility in even the weakest systems of modern modal logic. The chapter then discusses theories of judgment-form after Kant, the theory of quantification, Frege's Begriffsschrift, C. I. Lewis and the beginnings of modern modal logic, the proof-theoretic approach to modal logic, possible world (...) semantics, correspondence theory, and modality and quantification. (shrink)

In twentieth-century Kant scholarship, few have provided an account of the analytic-synthetic distinction and of the problem of the synthetic a priori that takes into consideration the views of Kant's idealist successors such as Maimon, Fichte, Schelling, and Hegel. I first explain how Kant formulates the analytic-synthetic distinction in terms of the determinate-indeterminate distinction, which, in turn, is based on the distinction between general and transcendental logic. Kant's problem of the synthetic a priori , then, is the problem of showing (...) how the logical forms of judgment can be employed determinately (and not merely indeterminately). I then show that Maimon also formulates the distinction and the problem in the same way, and that his interpretation will shape how Fichte, Schelling, and Hegel each construe and address Kant's question, How are synthetic judgments possible a priori ? (shrink)

Kant’s analytic-synthetic distinction is often construed in terms of the question of whether or not the predicate is contained in or can be derived from the concept of the subject. Few have observed that Kant has another formulation of the distinction, a formulation that is based on the determinate-indeterminate distinction. In fact, it is this formulation that will shape the development of one of the main tasks of post-Kantian German idealism. It is my aim to explain how Kant, Maimon, and (...) Fichte each define and address the problem of the synthetic a priori in terms of the determinate-indeterminate distinction. (shrink)

This paper looks at the Kantian background in the development of the views on formal logic and contradiction in German Idealism. Assuming the post-Kantian view, I examine what Kant advanced and what he left unsettled, provoking thus the subsequent debate. I start by showing (§1) that already the pre-critical Kant questions the effectiveness of formal logic in philosophical discourse andclaims that the laws of identity and non-contradiction fall short of explaining change, opposition, and contradiction, all these being parts of reality. (...) Turning then to the first Critique, I discuss (§2) the introduction of transcendental logic as the (meta)logic of truth, consider how the tension between formal and transcendental logic is displayed in Kant’s exposition of the antinomy of pure reason (§3), and arrive at the conclusion (§4) that Kant, despite his criticism, and unlike the other great German Idealists, allows formal logic to dominate his exposition of transcendental logic. (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 effort to fit simple logical truths — like 'if it's either red or green and it's not red, then it must be green' — into Kant's account of knowledge turns up a position more subtle and intriguing than might be expected at first glance.

I. The Problem of ‘Truth’ in the Logic of Truth.

Kant''s claim that the justification of transcendental philosophy is a priori is puzzling because it should be consistent with (1) his general restriction on the justification of knowledge, that intuitions must play a role in the justification of all nondegenerate knowledge, with (2) the implausibility of a priori intuitions being the only ones on which transcendental philosophy is founded, and with (3) his professed view that transcendental philosophy is not analytic. I argue that this puzzle can be solved, that according (...) to Kant transcendental philosophy is justified a priori in the sense that the only empirical information required for its justification can be derived from any possible human experience. Transcendental justification does not rely on any more particular or special observations or experiments. Philip Kitcher''s general account of apriority in Kant captures this aspect of a priori knowledge. Nevertheless, I argue that Kitcher''s account goes wrong in the link it specifies between apriority and certainty. (shrink)

This is a critical examination of the astonishing progress made in the philosophical study of the properties of the natural numbers from the 1880s to the 1930s. Reassessing the brilliant innovations of Frege, Russell, Wittgenstein, and others, which transformed philosophy as well as our understanding of mathematics, Michael Potter places arithmetic at the interface between experience, language, thought, and the world.

In the Critique of Pure Reason Kant appears to characterize analytic judgments in four distinct ways: once in terms of “containment,” a second time in terms of “identity,” a third time in terms of the explicative–ampliative contrast, and a fourth time in terms of the notion of “cognizability in accordance with the principle of contradiction.” The paper asks: Which of these characterizations—or apparent characterizations—best captures Kant’s conception of analyticity in the first Critique? It suggests: “the second.” It argues, further, that (...) Kant’s distinction is intended to apply only to judgments of subject–predicate form, and that the fourth alleged characterization is not properly speaking a characterization at all. These theses are defended in the course of a more general investigation of the distinction’s meaning, its epistemology, and its tenability. (shrink)

In this essay I discuss Fichte's changing understanding of the a priori/a posteriori distinction from the earliest writings on the Wissenschaftslehre to the System of Ethics. I argue that Fichte moves decisively away from the Kantian conception of the a priori, due to his development of the ideal/real distinction in his elaboration of the Wissenschaftslehre. Since Fichte's conception of apriority is not Kant's, we can only understand his claim that the System of Ethics can provide an answer a priori to (...) the question: what is our duty? (shrink)

Abstract: Kant follows a substantial tradition by defining judgment so that it must involve a relation of concepts, which raises the question of why he thinks that single-term existential judgments should still qualify as judgments. There is a ready explanation if Kant is somehow anticipating a Fregean second-order account of existence, an interpretation that is already widely held for separate reasons. This paper examines Kant's early (1763) critique of Wolffian accounts of existence, finding that it provides the key idea in (...) his mature model of existential judgment, which is in fact sharply opposed to the Fregean strategy. By relating this to Kant's theory of judgment in general—in particular, to his claim for an isomorphism between the assertoric function of judgment and the category of existence—a preliminary case is made that absolute positing, far from being a marginal special case, accomplishes the primary function of judgment. This argument shows the importance of distinguishing between contexts in which Kant is treating judgment as a vehicle for inference (e.g. pure general logic) and contexts in which he is treating it, more robustly, as the cognition of an object. (shrink)

In the works of Kant and his followers, the notion of form plays an important role in explaining the apriority, necessity and certainty of logic. Bernard Bolzano (1781–1848), an important early critic of Kant, found the Kantians' definitions of form imprecise and their explanations of the special status of logic deeply unsatisfying. Proposing his own conception of form, Bolzano developed radically different views on logic, truth in virtue of form, and other matters. This essay presents Bolzano's views in the light (...) of his criticisms of the Kantian logicians. (shrink)

Strawson famously argues that Kant’s argument for the necessary conditions of experience can only be retained once freed from a priori synthesis. Strawson claims that a purely ‘analytical connexion’ between experience and the object of experience is conceptually inferable from a thoroughly analytic premise concerning the capacity for self-ascription of representations. In this paper, I take issue with the way in which Strawson construes the analyticity of the principle of self-ascription or what Kant calls the principle of transcendental apperception. More (...) particularly, I shall argue that Strawson’s unity argument, viz. his construal of the unity of consciousness, on which the principle of self-ascription depends, suffers from a modal fallacy. Whilst arguing this, I shall suggest that a priori synthesis is required even for analytic unity of consciousness to be possible. [Note: on p. 265n.19 reach should be r-each (subscript), and on p. 269 square symbol should be universal quantifier]. (shrink)

This paper reconstructs the Peircean interpretation of Kant's doctrine on the syntheticity of mathematics. Peirce correctly locates Kant's distinction in two different sources: Kant's lack of access to polyadic logic and, more interestingly, Kant's insight into the role of ingenious experiments required in theorem-proving. In this second respect, Kant's analytic/synthetic distinction is identical with the distinction Peirce discovered among types of mathematical reasoning. I contrast this Peircean theory with two other prominent views on Kant's syntheticity, i.e. the Russellian and the (...) Beckian views, and show how Peirce's interpretation of Kant solves the dilemma that each of these two views faces. I also show that Hintikka's criterion for Kant's synthetic judgments, i.e. a new individual introduced by the -instantiation rule, does not capture the most important characteristic of Peirce's theorematic reasoning, i.e. the process of choosing a correct individual. (shrink)

According to Kant, arithmetic judgements are not analytic since they are about our practice of operating with figures and things in a certain way. Hence the empiricist thesis that any meaningful assertion is either analytic or synthetic a posteriori seems to be refuted (§§ 1, 2). Using syntax and semantics of truth-conditional logic Frege nevertheless shows that arithmetic can be understood as a system of quasi-analytic sentences speaking about numbers as abstract entities (§§ 3, 4). Axiomatic set theory, however, conceals (...) the connection between (internal) truth-functional arithmetic and our (external) practice of counting and computing (§§ 5-€“7). ---” In spite of the insights truth-conditional semantics provides for a non-psychological understanding of mathematical thinking, it is neither a general theory of meaning and analyticity nor a foundation of a general sense-criterion (§§ 8, 9). (shrink)

Friedrich Albert Lange (1828?1875) author of a famous History of Materialism and Critique of Its Present Significance(1866, English transi.I?III 1877?79, repr.1925 with introduction by Bertrand Russell), was also interested in the epistemological foundations of formal logic.Part I of his intended two?volume Logische Studienwas published posthumously in 1877 by Hermann Cohen?head?of the Marburg school of neo?Kantianism.Lange, departing from Kant, claims that spatial intuition is the source of the apodeictic character not only of the truths of mathematics, but also of the truths (...) of logic.He aims at showing this by basing validity and invalidity of syllogistic inferences on an interpretation of the standard forms (of proposition in assertoric syllogistic) with the help of the five kinds of possible relations (in fact what is known today as the Gergonne?Euler relations) between extensions of concepts given to us as areas in a plane, i.e.in space.Generality is achieved by considering all possible variations within each type of spatial relation, exhibiting a connection between concept and intuition reminding Lange of the Kantian ?schema?. Lange is well aware of the contemporary English ?algebraic? logic, but he considers its approach as the appropriate one for a logic of content (Inhaltslogik)and not for a logic of extension (Umfangslogik)Lange did not live to enjoy the recognition by some leading logicians (amongst them John Venn, to whose reference in 1881 to Lange?s ?admirable Logische Studien?the present paper owes it title), nor could he respond to the many critics of his proposed foundation of logic.Its radicality as well as its broad reception (and discussion up to at least 1959) seem to entitle Lange?s Logische Studiento an, if modest, place in the history of logic in the 19th century. (shrink)

I present an argument for an interpretation of Kant's views on the nature of the ‘content [Inhalt]’ of ‘cognition [Erkenntnis]’. In contrast to one of the longest standing interpretations of Kant's views on cognitive content, which ascribes to Kant a straightforwardly psychologistic understanding of content, and in contrast as well to the more recently influential reading of Kant put forward by McDowell and others, according to which Kant embraces a version of Russellianism, I argue that Kant's views on this topic (...) are of a much more Fregean bent than has traditionally been admitted or appreciated. I conclude by providing a sketch of how a better grasp of Kant's views on cognitive content in general can help bring into sharper relief what is, and what is not, at stake in the recent debates over whether Kant accepts a particular kind of cognitive content—namely, non-conceptual content. (shrink)

The paper assesses Martin's recent logico-phenomenological account of judgment that is cast in the form of an eclectic history of judging, from Hume and Kant through the 19th century to Frege and Heidegger as well as current neuroscience. After a preliminary discussion of the complex unity and temporal modalities of judgment that draws on a reading of Titian's "Allegory of Prudence" (National Gallery, London), the remainder of the paper focuses on Martin's views on Kant's logic in general and his theory (...) of singular existential judgment in particular. The paper argues against Martin's key claims of the primacy of formal logic over transcendental logic and of the synthetic nature of judgment in Kant. It also takes issue with each of the four interpretations of singular existential judgment in Kant offered by Martin: existence as logical predicate, as copula, as thesis and as logical subject. (shrink)