Kant: Transcendental Logic

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)

I reconstruct the notion of significance [_Sinnhaftigkeit_] in the later Husserl, with attention to his conceptions of judgment and transcendental logic. My analysis is motivated by the idea that an account of significance can help to connect analytic, Anglo-American conceptions of meaning as a precise, law-governed phenomenon investigated via linguistic analysis and Continental European conceptions of meaning in a broader “existential” sense. I argue that Husserl’s later work points to a transcendental-logical conception of a founding level of _significance_ [_Sinnhaftigkeit_] prior (...) to language, and that this conception meets characteristically analytic demands for precision and governance by logical constraints. At the same time, since it is based in descriptions of perceptual intentionality at the level of essential possibility, it leaves room for an account of meaning as a partially undetermined phenomenon of lived experience, and not just of our language and concepts, and thereby meets the characteristically Continental demand to take at face value meaning’s vagueness and indeterminacy in everyday human life. (shrink)

This paper looks at dialectical inferences as they relate to Hegel’s modal metaphysics, closely examining the Actuality section of Hegel’s Science of Logic and positing a reading of Hegel’s modal actualism that engages with two strains of secondary commentary. Responding to commentators, we make the case that Hegel’s ‘das Logische’ avoids presupposing possibility’s being prior to actuality insofar as actuality and the derivation of possibility is considered as the in-itselfness of actuality, an implicit inner moment whereby actuality further determines itself. (...) Actuality is immediate yet derived as an identity from the logic of inner and outer. If actuality as immediacy is explicit/outer, then its opposition, its implicitness/innerness, has to be possibility in the logic of modality. In order to conceive of actuality as existence, and particularly as an emerging process, we must already conceive the problem of presupposing an alien form within the logic of actuality. (shrink)

Los noumena son, en principio, conceptos límites. En el corpus kantiano encontramos múltiples de ellos, cuyo papel es decisivo en el tratamiento de la metafísica anterior, así como en la propuesta de metafísicas alternativas. Kant, sin embargo, no se detiene a explicarnos de dónde surgen esos conceptos y dónde irían. La presente investigación sugiere que a partir del concepto de nota (Merkmal) presentada en la KrV y desarrollada en la Jäsche Logik, podemos comprender estos noumena como las notas analíticas, suficientes, (...) esenciales y primitivas de las ideas de la razón, tanto teóricas como prácticas. (shrink)

Foucault found the starting point of modern European philosophy to be the construction of “man” as both an empirical fact and a transcendental operator. The aim is to show how this construction was made possible by an underlying strategical handling of the concept of matter. Some restrictions imposed on the materiality of knowledge-contents became key in explaining how actual men could gain access to transcendental knowledge. The paper focuses on Husserl and Kant as meaningful turning points of this transcendental discourse. (...) However, the relevance of their dematerializing strategies will be shown to lay beyond their historic-cultural meaning, since they can also provide a way of dealing with knowledge experiences that can be critical even towards modernity’s characteristic anthropocentrism. (shrink)

The infinite judgement has long been forgotten and yet, as I am about to demonstrate, it may be urgent to revive it for its critical and productive potential. An infinite judgement is neither analytic nor synthetic; it does not produce logical truths, nor true representations, but it establishes the genetic conditions of real objects and the concepts appropriate to them. It is through infinite judgements that we reach the principle of transcendental logic, in the depths of which all reality can (...) emerge in its material and sensible singularity, making possible all generalization and formal abstraction. (shrink)

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)

It is often claimed that the structure of the Transcendental Logic is modeled on the Wolffian division of logic textbooks into sections on concepts, judgments, and inferences. While it is undeniable that the Transcendental Logic contains elements that are similar to the content of these sections, I believe these similarities are largely incidental to the structure of the Transcendental Logic. In this essay, I offer an alternative and, I believe, more plausible account of Wolff’s influence on the structure of the (...) Transcendental Logic, one that puts the focus on his empirical psychology rather than his logic. In particular, I argue that the structure of the Transcendental Logic is deeply indebted to a conception of purity that Wolff introduces in his empirical psychology and that this conception sheds more light on the overall structure of the Transcendental Logic than the accepted view. In section one, I outline two conceptions of purity found in Kant and trace them to similar views in Wolff. In section two, I turn to Kant’s views about logic as they are expressed in the Critique and argue that it is best to interpret Kant’s taxonomy of logic on its own terms rather than reading it through its terminological similarities to aspects of the Wolffian tradition. In section three, I argue that the second of the two conceptions of purity identified in section one is central to the structure of the Transcendental Logic. In doing so, I argue against the widespread view that this section of the Critique is modeled solely on what Kant calls pure general logic as opposed to both pure and applied general logic. I then conclude by briefly reviewing my account and considering some of its broader implications for our understanding of Kant. (shrink)

The Question of Truth in Kant’s Transcendental Logic [English] In the third section of the “Introduction” to transcendental logic, Kant dedicates a couple of paragraphs to the subject of truth (KrV B82-83). Based on this passage, Kant’s com¬mentators have justified various and sometimes contradictory interpretations of the Kantian notion of truth. However, few have analyzed the passage in its own context, that is, as part of the strategy to introduce the idea of transcendental logic. In this work, I intend to (...) take a position in this regard. I will try to show that this passage does not subscribe to the distinction between general and transcendental logic, but between analytic and dialectic logic. [Español] En la tercera sección de la “Introducción” a la lógica trascendental, Kant dedica un par de párrafos al tema de la verdad (KrV B82-83). Basándose en este pasaje, los comentaristas de Kant han justificado diversas y a veces contradictorias interpretaciones de la noción kantiana de verdad. Sin embargo, pocos han analizado el pasaje en su propio contexto, es decir, como parte de la estrategia para introducir la idea de una lógica trascendental. En este trabajo se pretende tomar postura a este respecto. Se intentará mostrar que este pasaje no abona a la distinción entre lógica general y lógica trascendental, sino entre analítica y dialéctica. (shrink)

In this paper, I consider the basis for Kant's praise of Wolff's general logic as "the best we have." I argue that Wolff's logic was highly esteemed by Kant on account of its novel analysis of the three operations of the mind (tres operationes mentis), in the course of which Wolff formulates an argument for the priority of the understanding's activity of judging.

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)

Kant's Notion of "Transcendental Truth". [English] The aim of this work is to elucidate the notion of “transcendental truth” and to show its role in the Kantian system. I will argue that this notion is in line with the traditional definition of truth, i.e., that it consists in the correspondence between knowledge and object. I will also argue that criteria of transcendental truth are provided by transcendental logic, and that it is this notion of truth what makes it possible to (...) establish the truth of a priori knowledge and delimitate the field of empirical truth. [Español] El objetivo de este trabajo es dilucidar la noción de “verdad trascendental” y mostrar su lugar en el sistema kantiano. Se defenderá que la verdad trascendental consiste, en línea con la definición tradicional de verdad, en un sentido de correspondencia entre conocimiento y objeto, que la lógica trascendental establece criterios de verdad trascendental, y que es esta noción de verdad la que permite establecer la verdad del conocimiento a priori y delimitar el territorio de la verdad empírica. (shrink)

Engaging with Kant’s transcendental logic seems to be a question of mere scholarly historical interest today. It is most commonly regarded a mixture between logic and psychology or epistemology, and by that, not a serious form of logic. Transcendental logic seems to be of no systematical impact on the concept of logic. My paper aims to disclose a different account on the endeavour of Kant’s transcendental logic in particular and of the “Critique of Pure Reason” (CPR) in general. Kant’s fundamental (...) question is in a revolutionary way aiming to ground the character of necessity of knowledge, which means to justify the claim that thinking in accordance with the forms and principles of formal logic does not lead to sheer tautologies or an unsolved contradiction, but to knowledge that is objectively valid. In a first part, I shall demonstrate the necessity and the significance of this new fundamental question of the CPR with respect to its genesis out of pre-Kantian metaphysics. A brief outline of Kant’s answer to this question, with special emphasis on his revolutionary new comprehension of logical form, will be given as well. A second part shall open up a perspective that lies beyond Kant’s standpoint with reference to Nietzsche and eventually to Hegel. I will answer the question: What knowledge do we achieve about being or actuality by means of formal logic? I will argue that Kant shows that formal logic is the logic of all technical-practical conduct but also, at least indirectly, the limitation of the technical-practical knowledge and its legitimate sphere of application. (shrink)

For Kant, ‘reflection’ is a technical term with a range of senses. I focus here on the senses of reflection that come to light in Kant's account of logic, and then bring the results to bear on the distinction between ‘logical’ and ‘transcendental’ reflection that surfaces in the Amphiboly chapter of the Critique of Pure Reason. Although recent commentary has followed similar cues, I suggest that it labours under a blind spot, as it neglects Kant's distinction between ‘pure’ and ‘applied’ (...) general logic. The foundational text of existing interpretations is a passage in Logik Jäsche that appears to attribute to Kant the view that reflection is a mental operation involved in the generation of concepts from non-conceptual materials. I argue against the received view by attending to Kant's division between ‘pure’ and ‘applied’ general logic, identifying senses of reflection proper to each, and showing that none accords well with the received view. Finally, to take account of Kant's notio.. (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)

Although Kant (1998) envisaged a prominent role for logic in the argumentative structure of his Critique of Pure Reason, logicians and philosophers have generally judged Kantgeneralformaltranscendental logics is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first-order logic. The main technical application of the formalism developed here is a formal proof that Kants logic is after all a distinguished subsystem of first-order logic, namely what (...) is known as geometric logic. (shrink)

As Ebbinghaus (1908) tells us in the opening words of his popular textbook of psychology, “psychology has a long past but only a short history.” In my opinion, there are three foundational moments in the history of psychology and, paradoxically, all three are moments of great advancement in biology. First, in the long past of psychology, psychology did not exist as such but was part of philosophy. It is extremely interesting to understand why it has been necessary, at one point (...) of time in the sixteenth century, to invent this field and to create a signifier – namely “psychology” – separate from philosophy, which enabled the field to distinguish itself from philosophy (Mengal, 2000/2001). In this century of religious violence, bare corpses lay everywhere and progresses in anatomy are major. In 1540, the German religious reformer Philippe Melanchthon publishes a book which comments the De anima of Aristotle and he completes the Aristotelian text with a long treaty of anatomy (Mengal, 2000/2001). On the basis of this new knowledge, Melanchthon attributes functions to the body which were previously reserved for the soul. The brain becomes the principal organ of sensory functions and displaces the heart as the seat of emotional life and of thought. To the Aristotelian position that all living beings, whether plant, animal, or human, to varying degrees possess a soul which organizes the body, Melanchthon opposes a dualistic anthropology which divides the human in body and soul. The two-dimensional “anthropologia” is articulated in “anatomia,” science of body, and “psychologia,” science of the soul. It is this new anthropology that is diffused into the world of the Reformation (Mengal, 2000/2001). The Dutch reformer Snellius (1594), for example, defines the body and the soul by their respective essential property: “The rational soul of man is the thought that, coupled with the body, completes man. (…) The physical things closer to natural bodies that move naturally, have an extension and for that reason occupy a space. (…) The faculty of the rational soul is the mind or will. Thought is the faculty of the soul to discourse and think about things which are and which are not.”1 (Snellius, 1594, pp. 26–27). It is as a philosopher that René Descartes proposes his dualist vision much in line with the reformist opinions. Descartes dissects animals and human cadavers and is familiar with the research on the flow of blood (Fuchs, 2001). He comes to the conclusion that the body is a complex device that is capable of moving without the soul, thus contradicting the Aristotelian doctrine of the soul. The metaphysical order, which states that the body exists by the soul, is broken. (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)

One of the principle aims of the B version of Kant’s transcendental deduction is to show how it is possible that the same “I think” can accompany all of my representations, which is a transcendental condition of the possibility of judgment. Contra interpreters such as A. Brook, I show that this “I think” is an a priori (reflected) self-consciousness; contra P. Keller, I show that this a priori self-consciousness is first and foremost a consciousness of one’s personal identity from a (...) first person point of view. (shrink)

Traditionally transcendental logic has been set apart from formal logic. Transcendental logic had to deal with the conditions of possibility of judgements, which were presupposed by formal logic. Defined as a purely philosophical enterprise transcendental logic was considered as being a priori delivering either analytic or even synthetic a priori results. In this paper it is argued that this separation from the (empirical) cognitive sciences should be given up. Transcendental logic should be understood as focusing on specific questions. These do (...) not, as some recent analytic philosophy has it, include a refutation of scepticism. And they are not to be separated from meta-logical investigations. Transcendental logic properly understood, and redefined along these theses, should concern itself with the (formal) re-construction of the presupposed necessary conditions and rules of linguistic communication in general. It aims at universality and reflexive closure. (shrink)

In this article we provide a mathematical model of Kant?s temporal continuum that satisfies the (not obviously consistent) synthetic a priori principles for time that Kant lists in the Critique of pure Reason (CPR), the Metaphysical Foundations of Natural Science (MFNS), the Opus Postumum and the notes and frag- ments published after his death. The continuum so obtained has some affinities with the Brouwerian continuum, but it also has ‘infinitesimal intervals’ consisting of nilpotent infinitesimals, which capture Kant’s theory of rest (...) and motion in MFNS. While constructing the model, we establish a concordance between the informal notions of Kant?s theory of the temporal continuum, and formal correlates to these notions in the mathematical theory. Our mathematical reconstruction of Kant?s theory of time allows us to understand what ?faculties and functions? must be in place for time to satisfy all the synthetic a priori principles for time mentioned. We have presented here a mathematically precise account of Kant?s transcendental argument for time in the CPR and of the rela- tion between the categories, the synthetic a priori principles for time, and the unity of apperception; the most precise account of this relation to date. We focus our exposition on a mathematical analysis of Kant’s informal terminology, but for reasons of space, most theorems are explained but not formally proven; formal proofs are available in (Pinosio, 2017). The analysis presented in this paper is related to the more general project of developing a formalization of Kant’s critical philosophy (Achourioti & van Lambalgen, 2011). A formal approach can shed light on the most controversial concepts of Kant’s theoretical philosophy, and is a valuable exegetical tool in its own right. However, we wish to make clear that mathematical formalization cannot displace traditional exegetical methods, but that it is rather an exegetical tool in its own right, which works best when it is coupled with a keen awareness of the subtleties involved in understanding the philosophical issues at hand. In this case, a virtuous ?hermeneutic circle? between mathematical formalization and philosophical discourse arises. (shrink)

This paper presents an interpretation of Immanuel Kant’s transcendental deduction of the categories, based primarily on the “two-step” argument of the B deduction of the Critique of Pure Reason. I undertake to show that Kant’s distinction between the “pure forms of intuition” and “pure formal intuition” is successful in its attempt to prove that all sensible intuitions presuppose the a priori categories, in a way which is compatible, I claim, with Kant’s statements (in the Aesthetic and elsewhere) that sensible intuition (...) is prior to all concepts; and therefore that the Transcendental Aesthetic presupposes the Transcendental Analytic. Thus my Interpretation is a "conceptualist" reading of the deduction, in holding that perception, as receptivity, presupposes an underlying spontaneity of the pure understanding and categories. The categories are held to be not just compatible with all possible sensible intuitions, but through their "transcendental content" constitutive of the relation of sensible intuitions to objects - and this explains how our thought can represent objects a priori. It is one of the claims of my interpretation that the logical forms of judgment of general logic derive from the pure categories of transcendental logic, rather than vice-versa. I.e. that the logical forms through which we make empirical judgments by combining analytical concepts in inner sense in time, are originally grounded in an atemporal categorial synthesis in pure intuition (i.e. in the form of time but not the dimension of time), referring an outer intuition in general to the transcendental object of intuition (as “something in general” outside sensibility or receptivity), thereby providing the synthetic unity of the manifold which “..all analysis presupposes.” My conceptualist reading of the deduction, I claim, avoids the problems associated with other conceptualist readings, for example inconsistency with the text (“Intuitions are prior to all concepts.” etc.) and blurring of the distinction between receptivity and spontaneity. In my paper I prove that the categories can correctly be held to provide the a priori unity of intuitions, notwithstanding the fact that the latter are “prior to all concepts,” because this unity is not provided by the categories as fully-fledged concepts in the empirical subject, but as the transcendental logical form of these concepts, as a unity in the pure understanding - and the categories therefore require their empirical content or application for their objective reality as concepts. I.e. the categories, as logical functions of judgment for transcendental apperception, in the pure forms of intuition, are prior to all "concepts", correctly speaking, as well as prior to all intuitions, and provide the necessary unity of both. Likewise, at the empirical level my version of conceptualism cannot be accused of blurring the distinction between receptivity and spontaneity, or sensibility and understanding, because although the transcendental content of the categories, as a logical function of judgment in the pure forms of intuition, in transcendental apperception, is in necessary relation to sensibility (in combining the manifold in the pure or formal representation of the transcendental object) their empirical content is not. - At the empirical level the divide between spontaneity (as judgment in the empirical subject) and receptivity (as the effect of transcendental synthesis and the transcendental object on outer and inner sense) remains intact. Conceptualist readings of the deduction also have to avoid infringing Kant’s requirement that the sensible manifold originally be given prior to and independently of all acts of the understanding, or otherwise to qualify the requirement in some way - e.g. by taking a Hegelian direction, such as that taken by John McDowell.1 On my reading of the deduction the sensible manifold given indeterminately in the pure forms of space and time must be given prior to the categorial synthesis of the manifold in the pure representation of the transcendental object, i.e. in the pure 'concept' of an object in general affecting sensibility. Therefore Kant’s requirement for an undetermined manifold given prior to, and independently of, all acts of the understanding (“..the manifold to be intuited must be given prior to the synthesis of understanding, and independently of it. How this takes place, remains here undetermined” [cf.B145/146]) is not infringed. In a later section of the paper, however, I will argue that the transcendental object (of intuition) does have pure theoretical reason as one of its two interacting immanent aspects, but is distinct from pure theoretical reason in the other of its (the transcendental object of intuition's) two interacting immanent aspects, i.e. pure will, which adds a Schopenhauerian element to my interpretation (which will be argued for in a way which supports Kantian optimism over Schopenhauerian pessimism however, in regard to the freedom of the will). Another perceived inconsistency in the deduction, which my interpretation can explain, is Kant’s description (in the B deduction) of the principle of the necessary synthetic unity of apperception as analytic, while in the A deduction it is described as synthetic. I explain this as a difference in the reference of terms such as “my representations” in the two versions - a transcendental reference in the B version but an empirical and transcendental reference in the A version of the principle. I also show that the first part of the two-step B deduction can correctly be characterised by Kant as analytic and the second, concluding part, synthetic (a point of dispute amongst Kant scholars) because transcendental logic (which refers to both the analytic and synthetic aspects of the principle of apperception) “does not abstract from the pure content of knowledge.” While being a “double aspect” rather than “two world” view of transcendental Idealism (because objects of intuition are comprised of both the empirical and transcendental object, i.e. transcendental referent, of intuition, my view differs significantly from the “double aspect” interpretation of Henry Allison (which distinguishes empirical reality from the “God’s eye” view). The view of transcendental idealism resulting from my reading of the deduction, I claim, allows a full empirical realism, because empirical intuitions, as objects of cognition, are the appearance of both the transcendental subject and the transcendental object (i.e. transcendental referent ) of transcendental synthesis (both as “something in general” outside sensibility or receptivity, or rather outside sensibility as receptivity). I conclude that Kant succeeds (although only with the addition of what I have called my 'Schopenhauerian element') in his attempt to prove that we have a transcendental unity of apperception which both constitutes, and is constituted by, the relation of sensible representations to objects, and that since transcendental apperception is the a priori underlying ground of empirical apperception, the categories (as the logical functions of judgment by which transcendental apperception relates sensible representations to objects) are the a priori underlying ground of all experience, and are therefore valid synthetically a priori for all objects of experience. 1 E.g. in “On Pippin’s Postscript.” European Journal of Philosophy 15:3 pp. 395-410. (shrink)