Kant: Logical Form

For Kant, the human cognitive faculty has two sub-faculties: sensibility and the understanding. Each has pure forms which are necessary to us as humans: space and time for sensibility; the categories for the understanding. But Kant is careful to leave open the possibility of there being creatures like us, with both sensibility and understanding, who nevertheless have different pure forms of sensibility. They would be finite rational beings and discursive cognizers. But they would not be human. And this raises a (...) question about the pure forms of the understanding. Does Kant leave open the possibility of discursive cognizers who have different categories? Even if other discursive cognizers might not sense like us, must they at least think like us? We argue that textual and systematic considerations do not determine the answers to these questions and examine whether Kant thinks that the issue cannot be decided. Consideration of his wider views on the nature and limits of our knowledge of mind shows that Kant could indeed remain neutral on the issue but that the exact form his neutrality can take is subject to unexpected constraints. The result would be an important difference between what Kant says about discursive cognizers with other forms of sensibility and what he is in a position to say about discursive cognizers with other forms of understanding. Kantian humility here takes on a distinctive character. (shrink)

This book develops a textually grounded reconstruction of Kant’s argument in the Metaphysical Deduction. The argument proceeds in three steps, developing, first, a concept of judgment on which to base the table of logical functions, next a concept of synthesis of intuition that explains the content of the categories, and finally a concept of the understanding on which the categories belong a priori to the same faculty through which we judge. -/- The investigation presented here is an argumentative reconstruction of (...) Kant’s text. The text in question is the "Guiding Thread to the Discovery of all Pure Concepts of the Understanding" in both the 1781 (A) and 1787 (B) editions of the Critique of Pure Reason (A64-83/B89-113). To illuminate Kant’s reflections in this chapter, the reconstruction also draws on passages from elsewhere in the Critique, from Kant’s writings after the Critique, as well as notes from his Nachlass and student transcriptions of lectures he held during and subsequent to writing the Critique. Four passages, in particular, are of central importance: (i) the retrospective description of the task of the Metaphysical Deduction at B159, (ii) the retrospective description of the procedure of the "Guiding Thread" at A299/B355f., (iii) the section "On the A Priori Grounds for the Possibility of Experience" in the A-edition Transcendental Deduction of the Categories (A95-110), and (iv) §§15-21 in the B-edition Transcendental Deduction (B128-148). -/- The present interpretation of the Metaphysical Deduction thus emerges from a detailed and comprehensive analysis of the "Guiding Thread" that draws on related passages from the indicated portion of Kant’s corpus and, especially, on the aforementioned four passages from the Critique. Viewing these texts together and in a specific relation to one another suggests a reading which leaves little room for doubt. This sort of textually sensitive but charitable reconstruction helps to bring out the enduring force and interest of Kant’s philosophical position. [For Dennis Schulting's review for "Kantian Review" see under "External Links" below.] -/- -- -/- Wie hier durch textnahe und argumentative Rekonstruktion erstmals gezeigt wird, entwickelt Kant in der Metaphysischen Deduktion in drei Schritten: (i) einen Begriff des Urteils, auf dem die Tafel logischer Funktionen beruht; (ii) einen Begriff der Synthesis der Anschauung, der die Inhalte der Kategorien erklärt; und (iii) einen Begriff des Verstandes, demzufolge die Kategorien a priori zu demselben Vermögen gehören, durch das wir auch urteilen. -/- Die vorliegende Untersuchung ist eine argumentative Rekonstruktion von Kants Text. Der rekonstruierte Text ist der „Leitfaden der Entdeckung aller reinen Verstandesbegriffe" auf A 64 bis 83 / B 89 bis 113 der Kritik der reinen Vernunft in ihren beiden Auflagen von 1781 (A) und 1787 (B). Zudem werden andere, für ein Verständnis der Überlegungen in diesem Kapitel erforderliche oder zumindest erhellende Textstellen aus der Kritik herangezogen; aus Schriften, die Kant nach der Kritik geschrieben hat; sowie schließlich aus Kants Nachlass-Notizen und aus Nachschriften zu seinen Vorlesungen jeweils seit der Entstehungszeit der Kritik. Von entscheidender Bedeutung sind dabei vor allem vier weitere Passagen der Kritik selbst: i) die rückblickende Beschreibung der Aufgabe der Metaphysischen Deduktion auf B 159, ii) die rückblickende Beschreibung des Vorgehens im „Leitfaden" auf A 299/B 355 f., iii) der Abschnitt „Von den Gründen a priori zur Möglichkeit der Erfahrung" auf A 95 bis 110 der Transzendentalen Deduktion der Kategorien in der ersten Auflage und schließlich iv) die §§ 15 bis 21 auf B 128 bis 148 der Transzendentalen Deduktion der Kategorien in der zweiten Auflage der Kritik. -/- Vor dem Hintergrund einer umfassenden und detaillierten Analyse des „Leitfadens", bei Hinzuziehung verwandter Stellen aus dem umgrenzten Textbestand und nicht zuletzt bei Berücksichtigung des Verhältnisses des „Leitfadens" zu den genannten vier Passagen der Kritik legt sich eine Interpretation der Metaphysischen Deduktion nahe, die sich nur schwer bestreiten lässt, sobald diese Texte einmal gemeinsam betrachtet und auf eine bestimmte Weise zueinander ins Verhältnis gesetzt werden. Dabei kann eine durchgehend wohlwollende, argumentative Rekonstruktion dazu beitragen, auch die philosophische Überzeugungskraft der Position Kants deutlich zu machen. [Für Dennis Schultings Rezension für "Kantian Review" siehe unten unter "External Links".]. (shrink)

A critical discussion of Lu-Adler's chapter on Kant's mature view of pure general logic. I sketch an alternative interpretation of its formality on which Kant would hold no deduction is possible of this logic's laws.

This paper formalizes part of the cognitive architecture that Kant develops in the Critique of Pure Reason. The central Kantian notion that we formalize is the rule. As we interpret Kant, a rule is not a declarative conditional stating what would be true if such and such conditions hold. Rather, a Kantian rule is a general procedure, represented by a conditional imperative or permissive, indicating which acts must or may be performed, given certain acts that are already being performed. These (...) acts are not propositions; they do not have truth-values. Our formalization is related to the input/ output logics, a family of logics designed to capture relations between elements that need not have truth-values. In this paper, we introduce KL3 as a formalization of Kant’s conception of rules as conditional imperatives and permissives. We explain how it differs from standard input/output logics, geometric logic, and first-order logic, as well as how it translates natural language sentences not well captured by first-order logic. Finally, we show how the various distinctions in Kant’s much-maligned Table of Judgements emerge as the most natural way of dividing up the various types and sub-types of rule in KL3. Our analysis sheds new light on the way in which normative notions play a fundamental role in the conception of logic at the heart of Kant’s theoretical philosophy. (shrink)

There are two ways interpreters have tended to understand the nature of the laws of Kant’s pure general logic. On the first, these laws are unconditional norms for how we ought to think, and will govern anything that counts as thinking. On the second, these laws are formal criteria for being a thought, and violating them makes a putative thought not a thought. These traditions are in tension, in so far as the first depends on the possibility of thoughts that (...) violate these laws, and the second makes violation impossible. In this essay I develop an interpretation of Kant’s pure general logic that overcomes this tension. It accounts for the possibility of logical mistakes, as the first tradition does, while still establishing the absolute impossibility of logical aliens, as the second tradition does. I then argue that the formalist insight that illogical exercises of the understanding are not alternative ways coherent thoughts could have been, but are mere confusions, is fundamental for achieving a proper understanding of the absolute normativity of the laws of pure general logic. (shrink)

It’s widely accepted that normativity is not subject to truth values. The underlying reasoning is that truth values can only be predicated of descriptive statements; normative statements are prescriptive, not descriptive; thus truth value predicates cannot be assigned to normative statements. Hence, deonticity lacks logical semantics. This semantic monism has been challenged over the last decades from a series of perspectives that open the way for legal logics with imperative semantics. In the present paper I will go back to Kant (...) and review his understanding of practical judgments, presenting it as supported by a pluralistic semantics. From this perspective a norm of Law is a logical expression that includes as content a generic description of a possible behavior by a generality of juridical agents, and assigns to that content the assertion of its obligatory character, accompanied by a disincentive for non-compliance. From this perspective legal norms can be syntactically formalized and assigned appropriate semantic values in such terms that they can be incorporated into valid inferential schemes. The consequence is that we can put together legal logics that handle both the phenomenal and the deontic dimensions of legality. (shrink)

This chapter spells out in detail how Kant’s thinking about logic during the critical period shapes the account of philosophy that he gives in the Critiques. Tolley explores Kant’s motivations behind his formation of the idea of a new “transcendental” logic, drawing out in particular how he means to differentiate it from the traditional “merely formal” approaches to logic, insofar as transcendental logic investigates not just the basic forms of the activity of thinking but also its basic contents. Kant’s understanding (...) of both of these logics directly factor into the first Critique’s more general project of the critique of reason in particular, as not just a capacity for a certain kind of thinking (inferring), but as a possible source of a priori cognition. (shrink)

The aim of this paper is to provide a dynamic interpretation of Kant’s logical hylomorphism. Firstly, various types of the logical hylomorphism will be illustrated. Secondly, I propose to reevaluate Kant’s constitutivity thesis about logic. Finally, I focus on the design of logical norms as specific kinds of artefacts.

As is well known, the linguistic/philosophical reflection on natural kind terms has undergone a remarkable development in the early seventies with Putnam and Kripke’s essentialist approaches, touching upon different aspects of Kan’s slant. Preliminarily, however, it might be useful to review some of the theoretical stages in Locke and Leibniz’s approaches on natural kind terms in the light of contemporary reflections, to eventually pinpoint Kant’s contribution and see how some commentators have placed it within the theory of direct reference. Starting (...) with textual evidence even from the logical corpus, in the present essay I will attempt to discuss some of the arguments dismissing Kant’s adherence to this view. These assume that in his approach to the semantics of natural kind Kant appears to be still holding on to a nominalist/conceptualist position, though he seems to be well aware of a few key issues for the theorists of direct reference. (shrink)

The aim of Kant’s Sources in Translation is to retrieve the rich intellectual world that influenced Kant’s philosophical development. In its first stage, the series makes available the most important textbooks Kant used throughout his long teaching career. Many of these textbooks are in Latin or in German and remain inaccessible to Anglophone readers. Lacking this material, however, it is difficult to appreciate Kant’s originality and process of philosophical maturation, for readers are unable to understand what prompted Kant to introduce (...) a distinction, offer a qualification, attack a position, or develop a new thesis. This background is essential to understand the genesis of Kant’s thought. -/- This volume provides a translation of Georg Friedrich Meier’s Auszugaus der Vernunftlehre, the textbook that serves not only as the basis for Kant’s lectures on logic and related Reflexionen but is also crucial for studying the so-called Jäsche Logic of 1800, which is redacted from the marginal and interleave notes found in Kant’s personal copy of Meier’s book. Given the recent growth in scholarship on Kant’s logic, normative epistemology, and the psychology of belief, this volume makes a major contribution to contemporary debates in the field. (shrink)

In this chapter, I discuss some problems of Kant’s logic corpus while recognizing its richness and potential value. I propose and explain a methodic way to approach it. I then test the proposal by showing how we may use various mate- rials from the corpus to construct a Kantian demonstration of the formal rules of thinking (or judging) that lie at the base of Kant’s Metaphysical Deduction. The same proposal can be iterated with respect to other topics. The said demonstration (...) will have cleared the path for such iterations. (shrink)

The paper sets out from Göodel's question about primitive concepts, in connection with Gödel's proposal of the employment of phenomenological method. The author assumes that the answer that can be found in Kant is relevant as a starting point. In a modification of the approach by K. Reich, a reconstruction of Kant's "deduction'' of logical forms of judgment is presented, which serve Kant as the basis for his "metaphysical deduction of categories'' including substantiality and causality. It is proposed that different (...) aspects of Kant's "original unity of self-consciousness'' as applied and attached to concrete representations step by step yield different forms of concepts, judgments, and inferences. Categorical, hypothetical and disjunctive judgments are shown to be gradually strengthening the conditions of bringing our representations under the "objective unity of consciousness", and in this way gradually implementing logical laws. The corresponding concepts of substantiality, causality, and mutual influence appear to be grounded in the primitive forms of our thinking. (shrink)

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

Among Immanuel Kant's most influential contributionsto philosophy is his development of the transcendental argument. InKant's conception, an argument of this kind begins with a compellingpremise about our thought, experience, or knowledge, and then reasonsto a conclusion that is a substantive and unobvious presupposition andnecessary condition of this premise. The crucial steps in thisreasoning are claims to the effect that a subconclusion or conclusionis a presupposition and necessary condition of a premise. Such anecessary condition might be a logically necessary condition, butoften (...) in Kant's transcendental arguments the condition is necessary inthe sense that it is the only possible explanation for the premise,whereupon the necessity might be weaker than logical. Typically, thisreasoning is intended to be a priori in some sense, eitherstrict or more relaxed. The conclusion of the argument is often directed againstskepticism of some sort. For example, Kant's Transcendental Deductiontargets Humean skepticism about the applicability of a priorimetaphysical concepts, and his Refutation of Idealism takes aim atskepticism about external objects. These two transcendental argumentsare found in the Critique of Pure Reason, butsuch arguments are found throughout Kant's works, for example inthe Critique of Practical Reason, in the Critiqueof the Power of Judgment, and in the OpusPosthumum. This article focuses on theTranscendental Deduction, the Refutation of Idealism, and more recenttranscendental arguments such as P. F. Strawson's that areinspired by these two examples. (shrink)

Among Kant's innovations in the understanding of logic (‘general logic’) were his claims that logic had no content of its own, but was the form of the thought of any possible content, and that the unit of meaning, the truth-bearer, judgement, was essentially apperceptive. Judging was implicitly the consciousness of judging. This was for Kant a logical truth. This article traces the influence of the latter claim on Fichte, and, for most of the discussion, on Hegel. The aim is to (...) understand the relations among self-consciousness, reason and freedom in the idealist tradition. (shrink)

Against the standard interpretation of Kant's ‘Copernican revolution’ as the prioritization of epistemology over ontology, I argue in this paper that his critique of traditional metaphysics must be seen as a farewell to the perfectionism on which early modern rationalist ontology and epistemology are built. However, Kant does not simply replace ‘perfection’ with another fundamental concept of normativity. More radically, Kant realizes that it is not simply ideas but only the relation of ideas that can be subject to norms, and (...) thus he shifts the focus from the reality of ideas to the validity of judgments. Section 1 of this paper clarifies the pre-Kantian role of the concept of perfection and examines Kant's critical response to that concept. Section 2 identifies Kant's point of departure from the Cartesian ‘way of ideas.’ Section 3 explains the key problem of his novel account of epistemic normativity. I conclude that Kant's anti-perfectionism must be seen as the driving force behind his ‘Copernican revolution’ in order to fully appreciate his mature account of epistemic normativity. (shrink)

In §12 of his 1837 magnum opus, the Wissenschaftslehre, Bolzano remarks that “In the new logic textbooks one reads almost constantly that ‘in logic one must consider not the material of thought but the mere form of thought, for which reason logic deserves the title of a purely formal science’” (WL §12, 46).1 The sentence Bolzano quotes is his own summary of others’ philosophical views; he goes on to cite Jakob, Hoffbauer, Metz, and Krug as examples of thinkers who held (...) that logic abstracts from the matter of thought and considers only its form. Although Bolzano does not mention Kant by name here, Kant does of course hold that “pure general logic”, what Bolzano would consider logic in the traditional sense (the theory of propositions, representations, inferences, etc.), is formal. As Kant remarks in the Introduction to the 2nd edition of Kritik der reinen Vernunft , (pure general) logic is “justified in abstracting – is indeed obliged to abstract – from all objects of cognition and all of their differences; and in logic, therefore, the understanding has to do with nothing further than itself and its own form” (KrV, Bix).2. (shrink)

Le texte traduit ici est tiré d’un recueil réunissant plusieurs écrits du philosophe allemand Franz Brentano (1838-1917) et publié en 1925 par son disciple Alfred Kastil sous le titre Essai sur la connaissance. La pièce maîtresse du recueil est un manuscrit de Brentano intitulé « À bas les préjugés ! », portant le sous-titre : « Une exhortation pour inciter l’époque actuelle à renoncer, dans l’esprit de Bacon et de Descartes, à tous les a priori aveugles » (1903). Nous avons (...) traduit la première partie de ce texte, dans laquelle Brentano s’attaque simultanément au common sense du philosophe écossais Thomas Reid et aux jugements synthétiques a priori d’Immanuel Kant. Cet extrait constitue l’un des rares documents dans lesquels Brentano expose sans détours son opposition radicale à un certain kantisme et, plus largement, à toute forme de constructivisme. Brentano s'attaque à l'idée kantienne du synthétique a priori, en jetant les bases d'un programme gnoséologique dont l'axe central est l'exhibition des sources empiriques de nos concepts fondamentaux (substance, cause, être, nécessité, etc.). Ce programme sera développé à son tour par Carl Stumpf ('Erkenntnislehre', 1939). (shrink)

According to a widely held view, a Kantian intuition functions like a singular term. I argue that this view is false. Its apparent plausibility, both textual and philosophical, rests on attributing to Kant a Fregean conception of judgment. I show that Kant does not hold a Fregean conception of judgment and argue that, as a consequence, intuition cannot be understood on analogy with singular terms.

I defend the thesis that Kantian analytic judgments are about objects (as opposed to concepts) against two challenges raised by recent scholars. First, can it accommodate cases like “A two-sided polygon is two-sided”, where no object really falls under the subject-concept as Kant sees it? Second, is it compatible with Kant’s view that analytic judgments make no claims about objects in the world and that we can know them to be true without going beyond the given concepts? I address these (...) challenges in two steps. First, given Kant’s distinction between an object in general = x from an object of sensible intuition, I argue that analytic judgments are about objects in the former sense, no matter whether the purported objects can be given in our intuition. Second, using Kant’s method of representing certain logical relations of concepts with such figures as circles, I construct a model to show that analytic truths are truths about objects in general = x and yet can be determined solely by the intensional relation between the given concepts plus certain Kantian-logical laws. Analytic truths are thus shown as formal in the Kantian sense that they do not presuppose the purported objects as givable in our intuition. This account of the formality of analytic truths captures Kant’s diagnosis of the Leibnizian illusion that we can make material claims about the world by analytically true judgments. (shrink)

In the wake of Kant, logicians seemed to have adhered to the idea that what is distinctive of logic is its “formality”. In the paper, I discuss the distinction Kant draws between formality and generality of logic and argue that he ultimately conflates the two notions. I argue further that Kant's views on the formality of logic rest on a series of non trivial assumptions concerning the nature of cognition. I document the way in which these assumptions were received in (...) his successors. In the second part of the paper I focus on Bolzano's criticism of the Kantian position and his redefinition of the notion of form. I argue that while what contemporary, post-Tarskian philosophers generally understand as the formality of logic ought to be traced back to Bolzano there are also important differences between the two positions. (shrink)

It is a received view that Kant’s formal logic (or what he calls “pure general logic”) is thoroughly intensional. On this view, even the notion of logical extension must be understood solely in terms of the concepts that are subordinate to a given concept. I grant that the subordination relation among concepts is an important theme in Kant’s logical doctrine of concepts. But I argue that it is both possible and important to ascribe to Kant an objectual notion of logical (...) extension according to which the extension of a concept is the multitude of objects falling under it. I begin by defending this ascription in response to three reasons that are commonly invoked against it. First, I explain that this ascription is compatible with Kant’s philosophical reflections on the nature and boundary of a formal logic. Second, I show that the objectual notion of extension I ascribe to Kant can be traced back to many of the early modern works of logic with which he was more or less familiar. Third, I argue that such a notion of extension makes perfect sense of a pivotal principle in Kant’s logic, namely the principle that the quantity of a concept’s extension is inversely proportional to that of its intension. In the process, I tease out two important features of the Kantian objectual notion of logical extension in terms of which it markedly differs from the modern one. First, on the modern notion the extension of a concept is the sum of the objects actually falling under it; on the Kantian notion, by contrast, the extension of a concept consists of the multitude of possible objects—not in the metaphysical sense of possibility, though—to which a concept applies in virtue of being a general representation. While the quantity of the former extension is finite, that of the latter is infinite—as is reflected in Kant’s use of a plane-geometrical figure (e.g., circle, square), which is continuum as opposed to discretum, to represent the extension in question. Second, on the modern notion of extension, a concept that signifies exactly one object has a one-member extension; on the Kantian notion, however, such a concept has no extension at all—for a concept is taken to have extension only if it signifies a multitude of things. This feature of logical extension is manifested in Kant’s claim that a singular concept (or a concept in its singular use) can, for lack of extension, be figuratively represented only by a point—as opposed to an extended figure like circle, which is reserved for a general concept (or a concept in its general use). Precisely on account of these two features, the Kantian objectual extension proves vital to Kant’s theory of logical quantification (in universal, particular and singular judgments, respectively) and to his view regarding the formal truth of analytic judgments. (shrink)

In this paper I discuss Kant's and Bolzano's differing perspectives on ordinary natural language. I argue that Kant does not see ordinary language as providing semantically organized content and that, as a result, Kant does not believe that ordinary language is sufficiently well-developed to support philosophical analysis and definition. By contrast, for Bolzano, the content given in ordinary language are richly structured entities he calls 'propositions in themselves'. This contrast in views is used to explain Bolzano's criticism of Kant's belief (...) that definition is impossible for philosophical concepts. It is also used to explain Bolzano's criticism of Kant's methods of exposition of philosophical concepts. (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)

In the Critique of Pure Reason, Kant defends the mathematically deterministic world of physics by arguing that its essential features arise necessarily from innate forms of intuition and rules of understanding through combinatory acts of imagination. Knowing is active: it constructs the unity of nature by combining appearances in certain mandatory ways. What is mandated is that sensible awareness provide objects that conform to the structure of ostensive judgment: “This (S) is P.” -/- Sensibility alone provides no such objects, so (...) the imagination compensates by combining passing point-data into “pure” referents for the subject-position, predicate-position, and copula. The result is a cognitive encounter with a generic physical object whose characteristics—magnitude, substance, property, quality, and causality—are abstracted as the Kantian categories. Each characteristic is a product of “sensible synthesis” that has been “determined” by a “function of unity” in judgment. -/- Understanding the possibility of such determination by judgment is the chief difficulty for any rehabilitative reconstruction of Kant’s theory. I will show that Kant conceives of figurative synthesis as an act of line-drawing, and of the functions of unity as rules for attending to this act. The subject-position refers to substance, identified as the objective time-continuum; the predicate-position, to quality, identified as the continuum of property values (constituting the second-order type named by the predicate concept). The upshot is that both positions refer to continuous magnitudes, related so that one (time-value) is the condition of the other (property-value). -/- Kant’s theory of physically constructive grammar is thus equivalent to the analytic-geometric formalism at work in the practice of mathematical physics, which schematizes time and state as lines related by an algebraic formula. Kant theorizes the subject–predicate relation in ostensive judgment as an algebraic time–state function. When aimed towards sensibility, “S is P” functions as the algebraic relation “t → ƒ(t).”. (shrink)

Elqayam & Evans' (E&E's) critique of normativism is related to an inherently philosophical question: Is thinking a normative affair? Should thinking be held accountable towards certain norms? I present the historical and philosophical origins of the view that thinking belongs to the realm of normativity and has a tight connection with logic, stressing the pivotal role of Kant in these developments.

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)

In an earlier article (see J Gen Philos Sci (2009) 40: 357-372) I have discussed the arguments brought forward by Michael Wolff against the interpretation given in the commentary by Ebert and Nortmann on Aristotle's syllogistic theory (Aristoteles Analytica Priora Buch I, übersetzt und erläutert von Theodor Ebert und Ulrich Nortmann. Berlin 2007) and against the critique of Kant's adaption of the syllogistic logic. I have dealt with Wolff's arguments concerning (Ebert/Nortmann's interpretation of) Aristotle in the paper mentioned and with (...) his attempts to defend his critique in this subsequent article (part 1; see J Gen Philos Sci (2010) 41: 215-231). Part 2 (the paper below) is concerned with Wolffs renewed attempts to defend Kant as a logician. In particular I point out that if, as Wolff claims, the nota notae relation in Kant is restricted to subordinated concepts, then it can hardly serve as a principle for syllogistic logic, as Kant claims. Against Wolff's attempts to defend Kant's claim that o-propositions are simpliciter convertible, I point out two arguments: (1) Even if Kant, following the Vernunftlehre by Meier, has assumed that an o-proposition can be turned into an i-proposition (by adding the negation sign to the predicate), this conversion is useless for the reduction to first figure syllogisms since we are no longer dealing with three syllogistic terms but with four. (2) It is quite unlikely that Kant has a conversion of this type in mind since the texts of his students always talk of the group of either the particular propositions or else of the negative propositions. Given Kant's mistakes concerning the convertibility simpliciter of o-propositions, it is no wonder that he overlooks the special status of the moods Baroco and Bocardo. Wolffs attempts to provide Kant with what he claims are direct proofs for these moods can be shown to rely on a reductio ad impossibile. Kant mistook what are parts of the proofs for the validity of moods in figures two to four as parts of these moods themselves. Wolff—who tries to defend Kant on this point—is forced to an artificial and unconvincing reading of the Kantian texts. (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)

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)

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 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)

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)

In the Critique of Pure Reason, Kant conceives of general logic as a set of universal and necessary rules for the possibility of thought, or as a set of minimal necessary conditions for ascribing rationality to an agent . Such a conception, of course, contrasts with contemporary notions of formal, mathematical or symbolic logic. Yet, in so far as Kant seeks to identify those conditions that must hold for the possibility of thought in general, such conditions must hold a fortiori (...) for any specific model of thought, including axiomatic treatments of logic and standard natural deduction models of first-order predicate logic. Kant's general logic seeks to isolate those conditions by thinking through – or better, reflecting on – those conditions that themselves make thought possible. (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)

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)

The exercise of judgement is an aspect of human endeavour from our most mundane acts to our most momentous decisions. In this book Wayne Martin develops a historical survey of theoretical approaches to judgement, focusing on treatments of judgement in psychology, logic, phenomenology and painting. He traces attempts to develop theories of judgement in British Empiricism, the logical tradition stemming from Kant, nineteenth-century psychologism, 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 judgement with twentieth-century phenomenological accounts. He also shows that the psychological, logical and phenomenological dimensions of judgement are not only equally important but fundamentally interlinked in any complete understanding of judgement. His book will interest a wide range of readers in history of philosophy, philosophy of the mind and psychology. (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)

In this collection of essays Béatrice Longuenesse considers the three aspects of Kant's philosophy, his epistemology and metaphysics of nature, his moral philosophy and his aesthetic theory, under one unifying standpoint: Kant's conception of our capacity to form judgements. She argues that the elements which make up our cognitive access to the world - what Kant calls the 'human point of view' - have an equally important role to play in our moral evaluations and our aesthetic judgements. Her discussion ranges (...) over Kant's account of our representations of space and time, his conception of the logical forms of judgements, sufficient reason, causality, community, God, freedom, morality, and beauty in nature and art. Her book will appeal to all who are interested in Kant and his thought. (shrink)

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.

One of the central and most distinctive theses of Kant’s philosophy of mathematics is that mathematical knowledge is synthetic. In this context, synthetic judgments are defined in opposition to analytic ones, whose predicate concept is “contained in” the subject. Kant’s thesis has often been attacked as indefensible, but just as frequently critics have complained that the thesis itself, and even the analytic/synthetic distinction on which it rests, are simply unintelligible. Thus, even prior to questions of its correctness, the Kantian doctrine (...) has been rejected as unclear, based on general skepticism that there is a real distinction of “containment”—or indeed any tolerably clear distinction at all—between analytic and synthetic judgments. (shrink)