Famously, Kant describes space and time as infinite “given” magnitudes. An influential interpretative tradition reads this as a claim about phenomenological presence to the mind: in claiming that space and time are given, this reading holds, Kant means to claim that we have phenomenological access to space and time in our original intuitions of them. In this paper, I argue that we should instead understand givenness as a metaphysical notion. For Kant, space and time are ‘given’ in virtue of three (...) related facts: (i) they are necessary grounds of the existence of all other spatial and temporal possibilities; (ii) in virtue of being such grounds, they are metaphysically linked to all other represented spatiotemporal things; and (iii) as representations, space and time issue from the nature of our faculty of sensibility rather than from an arbitrary act of choice. Understanding givenness in this non-epistemological way helps us recover what is plausible in both ‘intellectualist’ and ‘anti-intellectualist’ readings of the Transcendental Aesthetic. Anti-intellectualists are correct that space and time are given in mere sensibility, but intellectualists are correct that we depend on the understanding for consciousness of space and time. (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)

Kant holds that some nonhuman animals “are acquainted with” objects, despite lacking conceptual capacities. What does this tell us about his theory of human cognition? Numerous authors have argued that this is a significant point in favour of Nonconceptualism—the claim that, for Kant, sensible representations of objects do not depend on the understanding. Against this, I argue that Kant’s views about animal minds can readily be accommodated by a certain kind of Conceptualism. It remains viable to think that, for Kant, (...) humans’ sensible representations necessarily represent objects as temporally structured in ways that allow us to have thoughts about them, and such representations are produced, and could only be produced, by the understanding. This allows Conceptualists to maintain that humans’ sensible representations depend on the understanding, while accepting that animals have sensible representations of objects too. We must, therefore, reassess both the warrant for Nonconceptualism and the shape Conceptualist readings must take. (shrink)

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

In this essay, I specify types of representational content that can be attributed to Kant’s account of representation. The more specific aim is to examine which of these types of content can be regarded as possible without the application of concepts. In order to answer the question, I proceed as follows. First, I show how intuition (in Kant’s sense) can be seen as providing indexical content independently of empirical concepts. Second, I show in what sense the generation of spatial content (...) can be regarded as non-categorial. A key distinction is that a perceptual examination of an object can be understood as thoroughly sensible and particular, whereas a conceptual determination always grasps the object via its generalisable features. Third, I propose that the faculties of sensibility and understanding are not only separable in principle, but that their contributions remain in a certain sense separate in actual cognition as well. This is to say that a conceptual determination of an object does not entail that the object ceases to be non-conceptually available to the perceiver, which further suggests the autonomy of sensibility and its perceptual content. Finally, I raise difficulties in attributing non-conceptual representational content to Kant’s judgment-centered stance on representation and experience, only to emphasise how these difficulties easily lead to a misappreciation of Kant’s fundamental distinction between sensibility and understanding and their unique cognitive contributions. (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)

The subject of this article is a powerful objection to the non-conceptualist interpretation of Kant’s transcendental deduction of the categories. Part of the purpose of the deduction is to refute the sort of scepticism according to which there are no objects of empirical intuition that instantiate the categories. But if the non-conceptualist interpretation is correct, it does not follow from what Kant is arguing in the transcendental deduction that this sort of scepticism is false. This article explains and assesses a (...) number of possible responses to this objection. (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 this paper, I discuss the debate on Kant and nonconceptual content. Inspired by Kant’s account of the intimate relation between intuition and concepts, McDowell (1996) has forcefully argued that the relation between sensible content and concepts is such that sensible content does not severally contribute to cognition but always only in conjunction with concepts. This view is known as conceptualism. Recently, Kantians Robert Hanna and Lucy Allais, among others, have brought against this view the charge that it neglects the (...) possibility of the existence of essentially nonconceptual content that is not conceptualised or subject to conceptualisation. Their critique of McDowell amounts to nonconceptualism. However, both views, conceptualist and nonconceptualist, share the assumption that intuition is synthesised content in Kant’s sense. My interest is not in the validity of the philosophical positions of conceptualism or nonconceptualism per se. I am particularly interested in the extent to which the views that McDowell and Hanna and Allais respectively advance are true to Kant, or can validly be seen as Kantian positions. I argue that although McDowell is right that intuition is only epistemically relevant in conjunction with concepts, Hanna and Allais are right with regard to the existence of essentially nonconceptual content (intuitions) independently of the functions of the understanding, but that they are wrong with regard to non-conceptualised intuition being synthesised content in Kant’s sense. Kantian conceptualists (Bowman 2011; Griffith 2012; Gomes 2014) have responded to the recent nonconceptualist offensive, with reference to A89ff./B122ff. (§13)—which, confusingly, the nonconceptualists also cite as evidence for their contrary reading—by arguing that the nonconceptualist view conflicts with the central goal of the Transcendental Deduction, namely, to argue that all intuitions are subject to the categories. I contend that the conceptualist reading of A89ff./B122ff. is unfounded, but also that the nonconceptualists are wrong to believe that intuitions as such refer strictly to objects independently of the functions of the understanding, and that they are mistaken about the relation between figurative synthesis and intellectual synthesis. I argue that Kant is a conceptualist, albeit not in the sense that standard conceptualists assume. Perceptual knowledge is always judgemental, though without this resulting in the standard conceptualist claim that, necessarily, all intuitions or all perceptions per se stand under the categories (strong conceptualism). I endorse the nonconceptualist view that, for Kant, perception per se, i.e. any mere or ‘blind’ intuition of objects (i.e. objects as indeterminate appearances) short of perceptual knowledge, does not necessarily stand under the categories. Perception is not yet perceptual knowledge. In this context, I point out the common failure in the literature on the Transcendental Deduction, both of the conceptualist and nonconceptualist stripe, to take account of the modal nature of Kant’s argument for the relation between intuition and concept insofar as cognition should arise from it. (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)

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.

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 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)

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)

The book addresses two main areas of Kant’s theoretical philosophy: the doctrine of transcendental idealism and various central aspects of the arguments from the Metaphysical and Transcendental Deductions, as well as the relation between the deduction argument and idealism. -/- Among the topics covered are the nature of objective validity, the role and function of transcendental logic in relation to general or formal logic, the possibility of contradictory thoughts, the meaning of the Leitfaden at A79 and the unity of cognition, (...) the two-steps-in-one-proof interpretation and categorial instantiation, categorial illusion, Strawson’s transcendental argument, the persistently perplexing question of the derivation of the categories, and the relation between apperception, objectivity, judgement, and idealism. -/- With regard to idealism in particular, the focus is on the metaphysical two-aspect interpretation and its problems, on the merits and demerits of the controversial phenomenalist reading of Kant’s idealism, and on the topic of subjectivism and epistemic humility. -/- In all of the aforementioned topics, the book presents wholly novel interpretations compared to the standard or mainstream interpretations. (shrink)

In this essay, I focus on two questions. First, what is Kant's understanding of the sense in which our faculties form a unified system? And, second, what are the implications of this for the metaphysical relationships between the faculties within this system? To consider these questions, I begin with a brief discussion of Longuenesse's groundbreaking work on the teleological unity of the understanding as the faculty for judgment. In doing so, I argue for a generalization of Longuenesse's account along two (...) dimensions. The result is a picture of our faculties as forming a teleological system—unified under the overarching aims of reason as the highest rational faculty. Then I discuss the recent debate between “additive” and “transformative” interpretations of the relationship between sensibility and the understand- ing, before proposing that we should interpret Kant as endorsing a moderate form of the “transformative” reading, which captures important elements of both the “additive” and the “transformative” account. (shrink)

There is no consensus concerning how to understand the ‘two-step proof structure’ (§§15–20, 21–7) of the Transcendental Deduction in the B-edition of the Critique of Pure Reason. This disagreement invites a closer examination of what Kant might have meant by a ‘transcendental deduction’. I argue that the transcendental deduction consists of three tasks that parallel Kant’s broader project of a ‘critique’ of pure reason; first, an origin task to justify reason’s authority to use them; second, an analytical task that determines (...) the conditions under which this authority can be legitimately exercised; and third, a dialectical task to determine the conditions under which this authority cannot be legitimately exercised. So long as we continue to read the B-Deduction solely in terms of its two-step proof structure, we overlook how Kant’s notion of ‘critique’ constitutes the real grounds for his argumentative strategy there. (shrink)

This paper provides a novel reconstruction of Kant’s argument for transcendental idealism in the Transcendental Aesthetic. This reconstruction relies on two main contentions: first, that Kant accepts the then-ubiquitous view that all cognition is either from grounds or consequences, a view he props up by drawing a distinction between logical and real grounds; second, that Kant, like most of his contemporaries, holds that our representations are the most immediate grounds of our cognition. By stressing these elements, the most threatening objection (...) to Kant’s argument can be avoided, namely, the claim that Kant ignores the possibility that our representations of space and time are subjective in origin, but objective as regards their applicability. My reconstruction shows that this so-called neglected alternative objection is based on a conceptual confusion about the nature of a priori cognition. (shrink)

Kant’s published arguments for the non-spatiotemporality of things in themselves have not been well received. I argue that Kant has available to himself an argument for the non-spatiotemporality of things in themselves that is premised upon a disparity between the compositional structure of the intelligible world and the structure of space and time. I argue that Kant was unwaveringly committed to the premises of this argument throughout his career and that he was aware of their idealistic implications. I also argue (...) that this argument is consistent with Kant’s restrictive mature epistemology. If my argument is successful, then even if Kant’s published arguments for transcendental idealism fail, we need not regard his ambitious metaphysical project as a failure. (shrink)

Prolegomena §38 is intended to elucidate the claim that the understanding legislates a priori laws to nature. Kant cites various laws of geometry as examples and discusses a derivation of the inverse-square law from such laws. I address 4 key interpretive questions about this cryptic text that have not yet received satisfying answers: How exactly are Kant's examples of laws supposed to elucidate the Legislation Thesis? What is Kant's view of the epistemic status of the inverse-square law and, relatedly, of (...) the legitimacy of the geometric derivation of that law? Whose account of laws, the understanding, and space is Kant critiquing in the passage? What positive account of the relationship between laws, the understanding, and space is Kant offering in the passage? My answer to depends crucially on my answers to –. As I interpret Kant, he holds that a wide range of a priori laws—including geometric laws, the inverse-square law, and the universal laws discussed in the Analytic of Principles—are ‘grounded’ in categorial syntheses rather than the intrinsic nature of the space given to us in pure intuition. (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)

In this article I respond to Sacha Golob's critique of my stance on Kantian nonconceptualism, objectivity, and animal perception of spatial particulars.

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)

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)

I draw on Carl Stumpf’s essay “Psychologie und Erkenntnistheorie”, and his precocious On the Psychological Origin of the Idea of Space, to set out a charge he raises against Kant’s fo...

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)

I defend a novel interpretation of Kant's conceptualism regarding the contents of our perceptual experiences. Conceptualist interpreters agree that Kant's Deduction aims to prove that intuitions require the categories for their spatiality and temporality. But conceptualists disagree as to which features of space and time make intuitions require the categories. Interpreters have cited the singularity, unity, infinity, and homogeneity of space and time. But this is incompatible with Kant's Aesthetic, which aims to prove that these same features qualify space and (...) time as intuitions, not concepts. On my interpretation, the feature is objectivity. Space and time are objective, in that they ground our judgments in geometry and mechanics. (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)