Martin offers an intriguing account of nineteenth century challenges to the traditional theory of judgment as a synthesis of subject and predicate (the synthesis theory)--criticisms motivated largely by the problem posed by existential judgments, which need not have two terms at all. Such judgments led to a theory of "thetic" judgments, whose essential feature is to "posit" something, rather than to combine terms (as in synthetic judgment). I argue, however, that Kant's official definition of judgment already implicitly recognizes the importance (...) of positing, and that its (otherwise confusing) abstract generality actually affords Kant's own logic an adequate way to accommodate existential judgments within the traditional synthesis theory. Preservation of a synthetic account of judgment is also found to be independently important for Kant's larger aims in the theory of cognition. (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)

Charles Peirce is often credited for being among the first, perhaps even the first, to develop a scientific metaphysics of indeterminism. After rejecting the received view that Peirce developed his views from Darwin and Maxwell, I argue that Peirce's view results from his synthesis of Immanuel Kant's critical philosophy and George Boole's contributions to formal logic. Specifically, I claim that Kant's conception of the laws of logic as the basis for his architectonic, when combined with Boole's view of probability, yields (...) Peirce's metaphysics of probabilistic laws. Indeterminism provides, therefore, an excellent illustration of how Peirce attempted to use logic to clarify metaphysical problems.Since everyone must have conceptions of things in general, it is most important that they should be carefully constructed. I shall enter into no criticism of the different methods of metaphysical research, but shall merely say that in the opinions of several great thinkers, the only successful mode yet lighted upon is that of adopting our logic as our metaphysics. (W1: 490, 1866)2. (shrink)

This paper explores Kant’s views about the logical form of “I think”-judgments. It is shown that according to Kant, in an important class of cases the prefix “I think” does not contribute to the assertoric, truth-conditional content of judgments of the form “I think that P.” Thus, judgments of this type are often merely judgments that P. The prefix “I think” does mention the subject and his thought, but it does not make the complex judgment a judgment about the subject (...) and his or her thought. Kant argues that there is a distinctive kind of self-consciousness that is adequately expressed by means of this non-assertoric “I think.” The paper explains that understanding Kant’s ideas on the logic of “I think”-judgments is fruitful both for discussions in contemporary analytic philosophy and for an adequate understanding of Kant’s philosophy. (shrink)

The concept of necessity plays a central role in Kant's philosophy, but seems to lead to severe paradoxes. On the one hand he states: ‘Notwendigkeit und strenge Allgemeinheit sind sichere Kennzeichen einer Erkenntnis a priori’. On the other hand he talks also about ‘notwendig (d. i. nach einer Regel)’, which means ‘necessary according to the empirical natural laws’. However, he never states explicitly the distinction between these two different concepts of necessity. Either Kant's philosophy is inconsistent or we have to (...) assume that he indeed interchanges two different concepts, even if he does not tell us that there is a difference between synthetic apriori necessity and natural necessity. This paper defends the hypothesis of two different necessities and then shows how this strategy makes possible a rational reconstruction of Kant's epistemology. (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 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)

I shall make two main claims. My first main claim is that Frege started out with a view of logic that is closer to Kant’s than is generally recognized, but that he gradually came to reject this Kantian view, or at least totally to transform it. My second main claim concerns Frege’s reasons for distancing himself from the Kantian conception of logic. It is natural to speculate that this change in Frege’s view of logic may have been spurred by a (...) desire to establish the logicality of the axiom system he needed for his logicist reduction, including the infamous Basic Law V. I admit this may have been one of Frege’s motives. But I shall argue that Frege also had a deeper and more interesting reason to reject his early Kantian view of logic, having to do with his increasingly vehement anti-psychologism. (shrink)

In the 82/2 (2000) issue of this journal, Michael Friedman has offered a stimulating discussion of my recent book, Kant and the Capacity to Judge. His conclusion is that on the whole I fail to do justice to what is most revolutionary about Kant's natural philosophy, and instead end up attributing to Kant a pre-Newtonian, Aristotelian philosophy of nature. This is because, according to Friedman, I put excessive weight on Kant's claim to have derived his categories from a set of (...) logical forms of judgment which he inherits from a traditional Aristotelian logic. In taking Kant at his word on this point, I fail to give their full import to Kant's insights into the newly discovered applications of mathematical concepts and methods to the science of nature. (shrink)

Let me start with a well-known story. Kant held that logic and conceptual analysis alone cannot account for our knowledge of arithmetic: “however we might turn and twist our concepts, we could never, by the mere analysis of them, and without the aid of intuition, discover what is the sum [7+5]” (KrV, B16). Frege took himself to have shown that Kant was wrong about this. According to Frege’s logicist thesis, every arithmetical concept can be defined in purely logical terms, and (...) every theorem of arithmetic can be proved using only the basic laws of logic. Hence, Kant was wrong to think that our grasp of arithmetical concepts and our knowledge of arithmetical truth depend on an extralogical source—the pure intuition of time (Frege 1884, §89, §109). Arithmetic, properly understood, is just a part of logic. (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.

Wayne Martin traces attempts to develop theories of judgment in British Empiricism, the logical tradition stemming from Kant, nineteenth-century psychologism, recent experimental neuropsychology, and the phenomenological tradition associated with Brentano, Husserl and Heidegger. His reconstruction of vibrant but largely forgotten nineteenth-century debates links Kantian approaches to judgment with twentieth-century phenomenological accounts. He also shows that the psychological, logical and phenomenological dimensions of judgment are not only equally important, but fundamentally interlinked.

In this paper I lay the foundations for an understanding of one of Fichte's most neglected and least understood texts: the late lecture course on Transcendental Logic. I situate this work in the context of Fichte's lifelong struggle with the problem of understanding the relation between logic and philosophy – a problem that I show to figure centrally both in Fichte's own revolutionary thinking and in his response to Kant's notorious denunciation of the Wissenschaftslehre. By attending to this context we (...) can understand Fichte's philosophical ambitions in the late lectures: a critique of particular doctrines of general logic; a critique of the conception of thought presupposed both by the traditional logic and by Kant himself; and a new conception of the relation between logic and the philosophical theory of experience. (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.

Fregean predicates applied to Fregean objects are merely defined by a "timeless" deductive order of sentences. They cannot provide sufficient structure in order to explain how names can refer to objects of intuition and how predicates can express properties of substances that change in time. Therefore, the accounts of Wilson and Quine, Prior and Brandom for temporal judgments fail -- and a new reconstruction of Kant's transcendental logic, especially of the analogies of experience, is needed.

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)

Kant used transcendental reflection to distinguish in judgment what belongs to its form and what to its material. Regarding the form of judgment, Buchdahl's work highlights the analogies between the different levels of judgment in Kant's transcendental ontology. He uses the explicit contingency of judgments of the system of nature to illuminate the contingency of judgments of objects in general. In the Critique of pure reason, Kant had left much of the work of judgment to the unconscious imagination. Fichte and (...) Schelling attempted to make conscious and determinate the work of the unconscious imagination, but found themselves unable to avoid a reflexive regress in trying to objectify and provide a foundation for the activity of the self in judgment. Buchdahl also clarifies the role Kant gave to the object in judgment, as the indeterminate 'thinghood' remaining once all forms of cognition are abstracted. Fichte represented this objective side of consciousness as the not-I, as the limit of the activity of the I, as an unconscious, alien element within consciousness. Schelling struggled to illuminate this unconscious object in judgment, to provide a construction of nature, without dissolving its positive presence into abstract formulations. In pursuing relentlessly Kant's critique of judgment, Fichte and Schelling exposed its opaque points and problematized the ambition to build a complete system of philosophy. (shrink)

Here I revisit Bolzano's criticisms of Kant on the nature of logic. I argue that while Bolzano is correct in taking Kant to conceive of the traditional logic as a science of the activity of thinking rather than the content of thought, he is wrong to charge Kant with a failure to identify and examine this content itself within logic as such. This neglects Kant's own insistence that traditional logic does not exhaust logic as such, since it must be supplemented (...) by a transcendental logic that will in fact study nothing other than thought's content. Once this feature of Kant's views is brought to light, a much deeper accord emerges between the two thinkers than has hitherto been appreciated, on both the nature of the content that is at issue in logic and the sense of logic's generality and formality. (shrink)

One of the characteristic features of contemporary logic is that it incorporates the Frege-Russell thesis according to which verbs for being are multiply ambiguous. This thesis was not accepted before the nineteenth century. In Aristotle existence could not serve alone as a predicate term. However, it could be a part of the force of the predicate term, depending on the context. For Kant existence could not even be a part of the force of the predicate term. Hence, after Kant, existence (...) was left homeless. It found a home in the algebra of logic in which the operators corresponding to universal and particular judgments were treated as duals, and universal judgments were taken to be relative to some universe of discourse. Because of the duality, existential quantifier expressions came to express existence. The orphaned notion of existence thus found a new home in the existential quantifier. (shrink)

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

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)