It is often maintained that one insight of Kant's Critical philosophy is its recognition of the need to distinguish accounts of knowledge acquisition from knowledge justification. In particular, it is claimed that Kant held that the detailing of a concept's acquisition conditions is insufficient to determine its legitimacy. I argue that this is not the case at least with regard to geometrical concepts. Considered in the light of his pre-Critical writings on the mathematical method, construction in the Critique can be (...) seen to be a form of concept acquisition, one that is related to the modal phenomenology of geometrical judgement. (shrink)

Grete Hermann’s essay “Die naturphilosophischen Grundlagen der Quantenmechanik” has received much deserved scholarly attention in recent years. In this paper, I follow the lead of Elise Crull who sees in Hermann’s work the general outlines of a neo-Kantian interpretation of quantum theory. In full support of this view, I focus on Hermann’s central claim that limited spatio-temporal, and even analogically causal, representations of events exist within an overall relational structure of entangled quantum mechanical states that defy any unified spatio-temporal description. (...) In my view, Hermann also advances an important transcendental argument that perspectival spatio-temporal representations of nature have their foundations in general relational networks that are not spatio-temporal. The key point is that the adoption of a perspectival system within the general network induces the representation but only for that context. These ideas are consistent with a perspectival subject–object principle in Kant and also with Weyl’s work on Lie groups and their representations. (shrink)

In this paper I explicate the notion of “presence” [Gegenwart] as it pertains to intuition. Specifically, I examine two central problems for the position that an empirical intuition is an immediate relation to an existing particular in one’s environment. The first stems from Kant’s description of the faculty of imagination, while the second stems from Kant’s discussion of hallucination. I shall suggest that Kant’s writings indicate at least one possible means of reconciling our two problems with a conception of “presence” (...) such that perceptual and hallucinatory states might be understood as different kinds of intuition. This may not be sufficient to secure the relationalist’s claim that intuition is an immediate relation to an existing particular in one’s environment, but it does show that opposition to this claim will require further argument. (shrink)

Logic diagrams have seen a resurgence in their application in a range of fields, including logic, biology, media science, computer science and philosophy. Consequently, understanding the history and philosophy of these diagrams has become crucial. As many current diagrammatic systems in logic are based on ideas that originated in the 18th and 19th centuries, it is important to consider what motivated the use of logic diagrams in the past and whether these reasons are still valid today. This paper proposes that (...) transcendental philosophy was a key inspiration for the development of logic diagrams and that such diagrams can be employed in transcendental arguments, even after the linguistic turn. (shrink)

Ang papel na ito ay isang pilosopikong pagsusuri sa konsepto ng espasyo sa Pilipinong pananaw. Ang konsepto ng espasyo sa Pilipinong pananaw ay nagsisilbing dahilan para masabi nating tayo ay nagmamahal sa karunungang nagmula at pinagyaman ng kamalayang Pilipino. Ang konsepto ng espasyo rin ang nagpapatibay sa katwiran na naglalantad sa pangangailangan nang agarang pananaliksik ng karunungang nakaligtaan sa kanluran. Kung ang mga Hapon ay matagumpay na pinagmunihan ang 'espasyo' gamit ang mga konseptong basho, aidagara, at zettai mu tungo sa (...) pagbibigay diin sa pagkamakabayan, ang ‘espasyo’ ay magsisilbing gabay sa mga Pilipino na lumingon sa kanilang pinanggalingan upang bigyan ng linaw ang layunin sa bawat tangkang pagbuo ng masasabing makataong ‘pilosopiya natin’. Tungo sa makataong espasyo sa pag-iral ng tao, nais galugarin ng diskursong ito ang mga sumusunod na paksa: 1] Lugar ay Espasyo; 2] Sa Pagitan ng ‘Ako’ at ng ‘Ikaw’; 3] Espasyo Bilang Bukal ng Kaalaman at pagkatuto; 4] Pagbuo ng Makataong Espasyo at Pagbuwag sa mga Mapang-aping Espasyo; 5] Salaysay ng mga Karanasan Tungo sa paghulma ng Makataong Espasyo; 6] Espasyo ng/para sa mga Peminista?; 7] Sa Pagitan ng Namatay at ng Namatayan; 8] Saan Matatagpuan ang Kapayapaan? (shrink)

In this paper, I argue that although Kant’s account of empirical schemata in the Critique of Pure Reason is primarily used to explain the shared content of intuitions and empirical concepts, it is also informed by methodological problems in natural history. I argue that empirical schemata, which are rules for determining the spatiotemporal form of objects, not only serve to connect individual intuitions with concepts, but also concern the very features of objects on the basis of which they were connected (...) and ordered in taxonomic systems based on similarity of form. I then suggest that Kant likely had scientific illustrations in mind in his discussion of empirical images in the Schematism chapter and that his account of schemata can help explain the epistemic function of these images in early modern science. (shrink)

In this paper, I propose a novel interpretation of the role of the understanding in generating the unity of space and time. On the account I propose, we must distinguish between the unity that belongs to determinate spaces and times – which is a result of category-guided synthesis and which is Kant’s primary focus in §26 of the B-Deduction, including the famous B160–1n – and the unity that belongs to space and time themselves as all-encompassing structures. Non-conceptualist readers of Kant (...) have argued that this latter unity cannot be the product of categorial synthesis. While they are correct that this unity is not the product of any particular act of category-guided synthesis, I argue that conceptualists are right to nevertheless attribute this unity to the understanding. I argue that it is a result of what we can think of as the ‘original’ synthesis of understanding and sensibility themselves – it is a synthesis, moreover, in which the whole is logically prior to the parts. (shrink)

In the 3rd Analogy, Kant claims that I can perceive that things coexist by synthesizing my perceptions in an order-indifferent way. Reigning orthodoxy holds that I first successively perceive different things, and then (through some further act) determine that the things I perceive coexist. Focusing on prominent examples of this approach, I argue that these accounts fail to do justice to the order-indifferent synthesis that Kant describes: Strawson explains the synthesis in a way which renders Kant’s argument in the 3rd (...) Analogy obviously unconvincing, Watkins makes the synthesis irrelevant to Kant’s argument, while Longuenesse and Allison make the unity of the synthesis obscure. The problems with these views, I contend, show that Kant thinks the rule for synthesizing my perceptions is already operative in the successive perceptions, such that the fundamental act of perception already involves ‘objective time-determinations.’ This connects with the recent dispute about whether Kant is a conceptualist: my argument provides additional evidence that Kant is a conceptualist, while also extending the conceptualist reading to the 3rd Analogy in a novel way. For those who think conceptualism is wrong, my argument serves as a critical notice that non-conceptualists have yet to offer a satisfying interpretation of the 3rd Analogy. (shrink)

Although it has become a common place to refer to the ׳sixth problem׳ of Hilbert׳s (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert׳s project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory (...) and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a ׳vague׳ mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the ׳sixth problem׳ of 1900. (shrink)

The Univalent Foundations of Mathematics provide not only an entirely non-Cantorian conception of the basic objects of mathematics but also a novel account of how foundations ought to relate to mathematical practice. In this paper, I intend to answer the question: In what way is UF a new foundation of mathematics? I will begin by connecting UF to a pragmatist reading of the structuralist thesis in the philosophy of mathematics, which I will use to define a criterion that a formal (...) system must satisfy if it is to be regarded as a “structuralist foundation.” I will then explain why both set-theoretic foundations like ZFC and category-theoretic foundations like ETCS satisfy this criterion only to a very limited extent. Then I will argue that UF is better-able to live up to the proposed criterion for a structuralist foundation than any currently available foundational proposal. First, by showing that most criteria of identity in the practice of mathematics can be formalized in terms of the preferred criterion of identity between the basic objects of UF. Second, by countering several objections that have been raised against UF’s capacity to serve as a foundation for the whole of mathematics. (shrink)

Kant afirma que espacio y tiempo son condiciones a priori de toda experiencia, a la vez que parece comprometerse con la naturaleza euclidiana del espacio y la simultaneidad absoluta. Su defensa del carácter a priori de estas nociones pasa por considerarlas intuiciones puras, de ahí que su naturaleza newtoniana parecería tener su origen en la configuración de lo que Kant llama intuición. No obstante, como muestran ciertas discusiones recientes, no está claro qué sea la intuición en Kant y cómo se (...) determina el espacio-tiempo a partir de ella. En este artículo, me acerco al debate sobre la procedencia de la síntesis de la intuición pura que, según Kant, determinaría la estructura espacio-temporal y discuto hasta que punto tener en cuenta la participación de las categorías en esta síntesis puede tener un efecto en el compromiso que, según la propuesta kantiana, uno debería asumir con respecto a una métrica determinada a priori. Mi conclusión es que el análisis kantiano da cabida, de forma natural, a que la determinación de la métrica espacio-temporal no esté dada a priori, en el sentido de universal y necesariamente. (shrink)

Recent work on Kant’s conception of space has largely put to rest the view that Kant is hostile to actual infinity. Far from limiting our cognition to quantities that are finite or merely potentially infinite, Kant characterizes the ground of all spatial representation as an actually infinite magnitude. I advance this reevaluation a step further by arguing that Kant judges some actual infinities to be greater than others: he claims, for instance, that an infinity of miles is strictly smaller than (...) an infinity of earth-diameters. This inequality follows from Kant’s mereological conception of magnitudes (quanta): the part is (analytically) less than the whole, and an infinity of miles is equal to only a part of an infinity of earth-diameters. This inequality does not, however, imply that Kant’s infinities have transfinite and unequal sizes (quantitates). Because Kant’s conception of size (quantitas) is based on the Eudoxian theory of proportions, infinite magnitudes (quanta) cannot be assigned exact sizes. Infinite magnitudes are immeasurable, but some are greater than others. (shrink)

In his argument for the possibility of knowledge of spatial objects, in the Transcendental Deduction of the B-version of the Critique of Pure Reason, Kant makes a crucial distinction between space as “form of intuition” and space as “formal intuition.” The traditional interpretation regards the distinction between the two notions as reflecting a distinction between indeterminate space and determinations of space by the understanding, respectively. By contrast, a recent influential reading has argued that the two notions can be fused into (...) one and that space as such is first generated by the understanding through an act of synthesis of the imagination. Against this reading, this article argues that a key characteristic of space as a form of intuition is its nonconceptual unity, which defines the properties of space and is as such necessarily independent of determination by the understanding through the transcendental synthesis of the imagination. The conceptual unity that the understanding prescribes to the manifold in intuition, by means of the categories, defines the formal intuition. Furthermore, this article argues that it is the sui generis, nonconceptual unity of space, when takenas a unity for the understanding by means of conceptual determination, that first enables geometric knowledge and knowledge of spatially located particulars. (shrink)

In the Transcendental Aesthetic of the Critique of Pure Reason, Immanuel Kant famously claims that we have an a priori intuition of space as an ‘infinite given magnitude’. Later on, in the Transcendental Analytic, he seems to add that the intuition of space presupposes a synthetic activity of the transcendental imagination. Several authors have recently pointed out that these two claims taken together give rise to two problems. First, it is unclear how the transcendental imagination of a finite mind could (...) ever result in the intuition of an entity that is infinitely large. Second, Kant claims that our intuition of space has a ‘whole-prior-to-its-parts’ structure, such that its parts are given only as limitations of the whole, while synthesis is compositional and has a ‘parts-prior-to-their-whole’ structure, because it consists in first running through and then taking together the parts of a sensible manifold. I will solve these two problems by showing that Kant thought that synthesis does not always have a compositional structure but that there is also a form of ‘decomposing’ synthesis, which has a whole-prior-to-its-parts structure. Building on similarities between Kant, Edmund Husserl and G. W. F. Hegel, I will argue that infinite space is given to us in intuition by precisely such an activity of decomposition, one that allows us to differentiate between finite spatial objects and the unlimited phenomenal horizon in which they appear. (shrink)

On one reading of Kant’s account of our original representations of space and time, they are, in part, products of the understanding or imagination. On another, they are brute, sensible givens, entirely independent of the understanding. In this article, while I agree with the latter interpretation, I argue for a version of it that does more justice to the insights of the former than others currently available. I claim that Kant’s Transcendental Deduction turns on the representations of space and time (...) as determinate, enduring particulars, whose unity is both given and a product of synthesis. (shrink)

In the Critique of Pure Reason Kant appears to make incompatible claims regarding the unitary natures of what he takes to be our a priori representations of space and time. I argue that these representations are unitary independently of all synthesis and explain how this avoids problems encountered by other positions regarding the Transcendental Deduction and its relation to the Transcendental Aesthetic in that work. Central is the claim that these representations (1) contain, when characterized as intuitions and considered as (...) prior to any affections of sensibility, only an infinitude of merely possible finite spatial and temporal representations, and (2) are representations that are merely transcendental grounds for the possibilities for receiving or generating finite representations in sensibility that are determined (immediately, in the case of reception) by means of syntheses that accord with the categories. (shrink)

In this paper we provide a mathematical model of Kant’s temporal continuum that yields formal correlates for Kant’s informal treatment of this concept in theCritique of Pure Reasonand in other works of his critical period. We show that the formal model satisfies Kant’s synthetic a priori principles for time and that it even illuminates what “faculties and functions” must be in place, as “conditions for the possibility of experience”, for time to satisfy such principles. We then present a mathematically precise (...) account of Kant’s transcendental theory of time—the most precise account to date.Moreover, we show that the Kantian continuum which we obtain has some affinities with the Brouwerian continuum but that it also has “infinitesimal intervals” consisting of nilpotent infinitesimals; these allow us to capture Kant’s theory of rest and motion in theMetaphysical Foundations of Natural Science.While our focus is on Kant’s theory of time the material in this paper is more generally relevant for the problem of developing a rigorous theory of the phenomenological continuum, in the tradition of Whitehead, Russell, and Weyl among others. (shrink)

Proposition I.1 is, by far, the most popular example used to justify the thesis that many of Euclid’s geometric arguments are diagram-based. Many scholars have recently articulated this thesis in different ways and argued for it. My purpose is to reformulate it in a quite general way, by describing what I take to be the twofold role that diagrams play in Euclid’s plane geometry (EPG). Euclid’s arguments are object-dependent. They are about geometric objects. Hence, they cannot be diagram-based unless diagrams (...) are supposed to have an appropriate relation with these objects. I take this relation to be a quite peculiar sort of representation. Its peculiarity depends on the two following claims that I shall argue for: ( i ) The identity conditions of EPG objects are provided by the identity conditions of the diagrams that represent them; ( ii ) EPG objects inherit some properties and relations from these diagrams. (shrink)

The article proposes an interpretation of Kant’s notions of form of, and formal intuition of space to explain and justify the claim that representing space as object requires a synthesis. This involves identifying the transcendental conditions of the analytic unity of consciousness of this formal intuition and distinguishing between it and its content. On this reading which builds upon recent proposals, footnote B160–1n. involves no revision of the Transcendental Aesthetic: space is essentially characterized by non-conceptual features. The article also addresses (...) worries about the infinite magnitude and the unicity of space, by considering the characteristics and requirements of geometric constructions. (shrink)

One of the central debates in contemporary Kant scholarship concerns whether Kant endorses a “conceptualist” account of the nature of sensory experience. Understanding the debate is crucial for getting a full grasp of Kant's theory of mind, cognition, perception, and epistemology. This paper situates the debate in the context of Kant's broader theory of cognition and surveys some of the major arguments for conceptualist and non-conceptualist interpretations of his critical philosophy.

‘Mathematics is the science of the infinite, its goal the symbolic comprehension of the infinite with human, that is finite, means.’ Along this line, in The Open World, Hermann Weyl contrasted the desire to make the infinite accessible through finite processes, which underlies any theoretical investigation of reality, with the intuitive feeling for the infinite ‘peculiar to the Orient,’ which remains ‘indifferent to the concrete manifold of reality.’ But a critical analysis may acknowledge a valuable dialectical opposition. Struggling to spell (...) out the infinity of real numbers mathematicians come to see the active role of emptiness. Pondering over the essence of self-awareness, the Japanese philosopher Nishida Kitarō comes to see the ‘place’ where it abides as absolute nothingness. Thus, the two ways of seeing coalesce into a perspective in which infinity and nothingness mirror each other. (shrink)

The aim of this paper is to show that attention to Kant's philosophy of mathematics sheds light on the doctrine that there are two stems of the cognitive capacity, which are distinct, but equally necessary for cognition. Specifically, I argue for the following four claims: The distinctive structure of outer sensible intuitions must be understood in terms of the concept of magnitude. The act of sensibly representing a magnitude involves a special act of spontaneity Kant ascribes to a capacity he (...) calls the productive imagination. Contrary to what is assumed by many commentators, it is not the case that the Two Stems Doctrine implies that a representation is either sensible or spontaneity-dependent, but not both. Outer sensible intuitions are both sensible and spontaneity-dependent – they are sensible because they exhibit the kind of structure Kant takes to be distinctive of outer sensible intuitions, and they depend on spontaneity because they are cases of sensibly representing a magnitude. (shrink)

Are the pure intuitions of space and time, for Kant, dependent upon the understanding's activity? This paper defends the recently popular Self-Affection Thesis : namely, that the pure intuitions require an activity of self-affection—an influence of the understanding on the inner sense. Two systematic objections to this thesis have been raised: The Independence objection claims that SAT undermines the independence of sensibility; the Compatibility objection claims that certain features of space and time are incompatible with being the products of the (...) understanding's activity. I show that the resources to rebut these objections can be found in Kant's account of causal influence. (shrink)

Does Kant hold that we can have intuitions independently of concepts? A striking passage from § 13 of the Critique of Pure Reason appears to say so explicitly. However, it also conjures up a scenario where the categories are inapplicable to objects of intuition, a scenario presumably shown impossible by the following Transcendental Deduction. The seemingly non-conceptualist claim concerning intuition have therefore been read, by conceptualist interpreters of Kant, as similarly counterpossible. I argue that the passage in question best supports (...) an underappreciated middle position where intuition requires a pre-conceptual use of the understanding. Such pre-conceptual use of the understanding faces both textual and systematic objections. I show that these objections can be rebutted. (shrink)

Incongruent counterparts are pairs of objects which cannot be enclosed in the same spatial limits despite an exact similarity in magnitude, proportion, and relative position of their parts. Kant discerns in such objects, whose most familiar example is left and right hands, a “paradox” demanding “demotion of space and time to mere forms of our sensory intuition.” This paper aims at an adequate understanding of Kant’s enigmatic idealist argument from handed objects, as well as an understanding of its relation to (...) the other key supports of his idealism. The paper’s central finding is that Kant’s idealist argument from incongruent counterparts rests essentially on his theory of freedom. The surprising result sheds new light on deep and overlooked links among the pillars of transcendental idealism, pointing the way to a comprehensive and unified reading of Kant’s system of idealist arguments. (shrink)

Until recently, leading work on the philosophy of thought experiments mistakenly credited Mach with coining the term. While Ørsted’s prior use has become more widely acknowledged, there remains a c...

I argue that Kierkegaard has an account of thought experiment. While his contemporary Ørsted’s contributions to the early history of the concept of ‘thought experiment’ have been recently acknowledged, Kierkegaard’s contributions remain largely unrecognized. I argue that Kierkegaard’s method of ‘imaginary construction’ [Tanke-Experiment] aims at identifying underlying invariants in objects of experience. I outline similarities between Ørsted’s pursuit of invariants in the sciences and Kierkegaard’s fictional variations in Repetition. One implication is that Kierkegaard’s view is more scientific and methodological than (...) is standardly thought by Kierkegaard scholars, who more commonly treat imaginary construction as a literary device. A further implication is that Kierkegaard, like Ørsted, is interested in the success or failure of mental acts, rather than (or in addition to) practical action, as is more standardly associated with Kierkegaard. One original development, beyond what Kierkegaard inherits from Ørsted, is the role of thought experiments as exceptions. An exception is a case that falls outside a rule without breaking it. Exceptions can neither establish a rule nor refute its necessity; however, they turn attention to relevant principles and further determine their content. I highlight similarities between Ørsted’s account of thought experiments and Kierkegaard’s as a method of variation. (shrink)

Much recent attention has been paid to Kant’s account of the unity of space in the Critique of Pure Reason, not least because of the significant implications of that view for other key critical-period doctrines. But far less attention has been paid to the development of Kant’s account of the unity of space. This paper aims to offer a systematic account of Kant’s pre-critical account of the unity of space. On the view presented herein, Kant’s early account of the unity (...) of space is deeply rooted in his pre-critical cosmological views. In particular, I argue that Kant sees the unity of space as grounded in the cosmological unity of the world of substances, which is itself rooted in the divine conservation of all substances in relations of mutual causal dependence. I contend that the seeds of this view are present in the late 1740s and 1750s, but that this view receives its fullest and most complete expression in the 1770 Inaugural Dissertation. The final section of the paper considers the fate of Kant’s pre-critical account of the unity of space. I contend that the theory is excluded from the Critique of Pure Reason in light of the strict epistemological strictures adopted in that text. But considerable textual evidence shows that Kant continues to aver the theory throughout the 1770s and 1780s in the looser epistemic context of his lectures. I contend, then, that this theory is not abandoned at all. Rather, like Kant’s 1763 proof of the existence of God, it is epistemically demoted: it is Kant’s preferred view, but one that falls short of the demanding epistemic standards of the critical philosophy. (shrink)

Although traditionally neglected, mathematical diagrams have recently begun to attract attention from philosophers of mathematics. By now, the literature includes several case studies investigating the role of diagrams both in discovery and justification. Certain preliminary questions have, however, been mostly bypassed. What are diagrams exactly? Are there different types of diagrams? In the scholarly literature, the term “mathematical diagram” is used in diverse ways. I propose a working definition that carves out the phenomena that are of most importance for a (...) taxonomy of diagrams in the context of a practice-based philosophy of mathematics, privileging examples from contemporary mathematics. In doing so, I move away from vague, ordinary notions. I define mathematical diagrams as forming notational systems and as being geometric/topological representations or two-dimensional representations. I also examine the relationship between mathematical diagrams and spatiotemporal intuition. By proposing an explication of diagrams, I explain certain controversies in the existing literature. Moreover, I shed light on why mathematical diagrams are so effective in certain instances, and, at other times, dangerously misleading. (shrink)

Overview of the (non)conceptualism debate in Kant studies.

William James' Radical Empiricist essays offer a unique and powerful argument for direct realism about our perceptions of objects. This theory can be completed with some observations by Kant on the intellectual preconditions for a perceptual judgment. Finally James and Kant deliver a powerful blow to the representational theory of perception and knowledge, which applies quite broadly to theories of representation generally.

In this chapter I advance a moderately conceptualist interpretation of Kant’s account of the threefold synthesis in the A-Deduction. Often the first version of TD, the A-Deduction, is thought to be less conceptualist than the later B-version from 1787 (e.g. Heidegger 1991, 1995). Certainly, it seems that in the B-Deduction Kant puts more emphasis on the role of the understanding in determining the manifold of representations in intuition than he does in the A-Deduction. It also appears that in the A-Deduction (...) the seemingly pre-conceptual aspects of a priori synthesis, namely those of the synthesis of apprehension and the imagination, are more prominently featured than in the B-Deduction. And the fact that in the A-Deduction judgement does not appear to play any significant role reinforces the view that the A-Deduction is less strongly conceptualist. I believe that Kant is a conceptualist also in the A-Deduction (as much as in the B-Deduction) in the sense that all syntheses, which are expounded in the second section of the A-Deduction, must be seen as involving the categories or the understanding as the seat of the categories. However, despite some apparent strong modal claims regarding apperception in the A-Deduction, I argue that Kant is a moderate conceptualist in the sense that he allows for the real possibility that some representations are apprehended that are not subsumed or subsumable under the categories, or determined or determinable by the understanding as the seat of the categories. Not all representations must be synthesised and hence be conceptualised (by means of the categories), nor are all representations necessarily conceptualisable (by means of the categories). Often it is argued that the application of the categories must be seen as separate from or prior to conceptualisation (that is, employment of concepts in a judgement), so that the categories must be considered to apply to representations at least to the extent that the productive imagination or recognitive synthesis is involved, even if no empirical concepts are applied in an actual judgement. But it is difficult to see how categories can apply outside the context of an actual judgement in which ipso facto empirical concepts are employed, because, after all, categories are nothing but logical functions of judgement (e.g. B143). More in particular, I shall argue for the claims that (1) appearances to the contrary, all three levels of syntheses in the A-Deduction, including the synthesis of recognition, are interdependent and are not to be seen as operating singly or independently of each other, and hence of the categories; (2) ‘mere’ apprehension, or ‘mere’ intuition, is not dependent on the understanding and the application or possible application of the categories; and that (3) ‘mere’ apprehension does not even invoke a priori synthesis of apprehension and hence is as such fully lawless in terms of Kantian a priori laws. In this context, I also address Kant’s argument in the A-Deduction about the role of the imagination in the production of spatial objects and explain his apt use of the example of cinnabar to show that the kind of association that is at issue here concerns the possibility of knowledge, not the possibility of mere association, as is often assumed. (shrink)

This dissertation’s contribution consists in providing a novel interpretation of the role time plays in Kant’s transcendental idealism. A significant part of Kant scholarship on the Critiques tends to assume that time, as understood in transcendental philosophy, is solely a formal property of intuition. This assumption has led several commentators to overlook a fundamental feature of transcendental idealism, namely, that in being the most basic form of intuition time is, also, a provider of content in and for experience. In looking (...) attentively at such feature this dissertation shows that time is the activity of the self that grounds the possibility of objectivity and explores the philosophical implications of such an interpretation. In the first Chapter I conduct a comprehensive survey of relevant literature and show that it is impossible to separate general metaphysics from transcendental logic in the context of Kant’s transcendental philosophy without making serious philosophical sacrifices. I then argue, in the second Chapter, that time is not merely a formal property of intuition but is, rather, the fundamental form of intuition and that, even if space is in no way reducible to, or derivable from it, time has nonetheless primacy over space on both logical and ontological grounds. From this I argue that by time, or self-affection, Kant understands the activity of subjectivity that brings about the possibility of relating to objects through the power of imagination. In the third Chapter, I show that such relation is not left wholly undetermined and that, instead, it occurs in accordance with the layout presented by Kant in the Table of Judgments, the Table of Pure Concepts of the Understanding, the Schemata and, importantly, in the System of Principles of the Understanding. I show that only an interpretation that acknowledges the systematicity found in the Analytic section of the Critique of Pure Reason can justify the distinction drawn by Kant between the mathematical and the dynamical and conclude, from that, that time does indeed provide a specific content in and for experience to be found in the Schematism doctrine. Finally, in the fourth Chapter I broaden the philosophical scope and inquire as to whether Kant has the theoretical means to articulate something like an uncategorized schema or time-determination. I conclude that, although in the Critical period Kant can do so only problematically, in the post-Critical period there are means to do so categorically: system, as such, is a time-determination for which the understanding lacks a pure concept. (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)