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)

I examine how Kant argues for the transcendental ideality of space. I defend a reading on which Kant accepts the ideality of space because it explains our (actual) knowledge that mathematical judgments are necessarily true. I argue that this reading is preferable over the alternative suggestion that Kant can infer the ideality of space directly from the fact that we have an a priori intuition of space. Moreover, I argue that the reading I propose does not commit Kant to incoherent (...) modal views. If we carefully distinguish between different senses of modality, the fact that our spatial form of intuition is (in some sense) contingent does not undermine the claim that this form can explain how our mathematical judgments are (in some sense) necessary. (shrink)

A distinção entre filosofia e matemática enquanto modos de operação da razão tem presença marcante nos cursos de Lógica de Kant, mas igualmente articula diversas soluções de problemas no interior do pensamento crítico. No entanto, ela data do período pré-crítico, tendo se tornado bem explícita já na obra Investigação sobre a distinção dos princípios da teologia natural e da moral (1764). Quase duas décadas depois, essa distinção será retomada na “Doutrina transcendental do método”, contida na Crítica da razão pura (1781). (...) Ao contrário de Christian Wolff, que propunha uma divisão tripartite do conhecimento, distinguindo conhecimentos históricos, filosóficos e matemáticos, Kant aloca os conhecimentos filosóficos e matemáticos no interior da mesma divisão epistemológica: ambos são conhecimentos racionais. No entanto, um é conhecimento racional por conceitos (filosofia) e outro é conhecimento racional por construção de conceitos (matemática). Por meio dessa distinção e das oposições que ela comporta, Kant vai definir o método de trabalho do filósofo e do matemático e o modo de resolução de problemas específico de cada uma dessas disciplinas. Comparando os dois textos citados acima, pretendemos esclarecer os procedimentos metodológicos concebidos mediante essa distinção, e as respectivas tarefas epistemológicas que ela comporta. (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)

This paper gives an interpretation of Kant's argument for transcendental idealism in the Transcendental Aesthetic. I argue against a common way of reading this argument, which sees Kant as arguing that substantive a priori claims about mind-independent reality would be unintelligible because we cannot explain the source of their justification. I argue that Kant's concern with how synthetic a priori propositions are possible is not a concern with the source of their justification, but with how they can have objects. I (...) argue that Kant's notion of intuition needs to be understood as a kind of representation which involves the presence to consciousness of the object it represents, and that this means that a priori intuition cannot present us with a mind-independent feature of reality. (shrink)

I take up Kant's remarks about a " transcendental deduction" of the "concepts of space and time". I argue for the need to make a clearer assessment of the philosophical resources of the Aesthetic in order to account for this transcendental deduction. Special attention needs to be given to the fact that the central task of the Aesthetic is simply the "exposition" of these concepts. The Metaphysical Exposition reflects upon facts about our usage to reveal our commitment to the idea (...) that these concepts refer to pure intuitions. But the legitimacy of these concepts still hangs in the balance: these concepts may turn out to refer to nothing real at all. The subsequent Transcendental Exposition addresses this issue. The objective validity of the concepts of space and time, and hence their transcendental deduction, hinges on careful treatment of this last point. (shrink)

I argue that Kant’s transcendental idealism and Strawson’s descriptive metaphysics are both examples of what I call methodological conservativism. Methodological conservativism involves the claim that a subset of common first-order beliefs is immune to revision. I argue that there are striking differences between their respective commitments to this position, however. For Kant, his conservativism is based upon a commitment to the reliability of particular results of the sciences of his day. For Strawson, in contrast, his conservativism is based upon his (...) attempted liberation of arguments for the necessity of a certain conceptual scheme from any particular scientific commitments. In fact, for Strawson, no change in scientific commitments could displace the conceptual scheme employed to navigate the manifest world of ordinary perceptual experience. Each approach brings with it challenges with regard to how to accommodate potential scientific theory change. (shrink)

We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

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...

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)

Matthias Neuber’s book represents an important contribution to the relatively young discipline of the History of Philosophy of Science. Starting roughly in the 1980s, increasing attention has been devoted not only to the relationship between philosophy and the history of science, but to an accurate historical reconstruction of earlier projects within philosophy of science. One of the most outstanding results of these investigations has probably been the radical reshaping of the rather caricatural image of logical empiricism—for better or worse the (...) core of the philosophical heritage of many philosophers of science—summarized in the so-called ‘standard view’. By analyzing the historical, sociological, and philosophical questions surrounding logical empiricism new light has been shed on the sense of a cultural, social, and political mission that characterized it before its emigration from Europe to North America in the 1930s and 1940s. What came to be known as .. (shrink)

Kant’s treatments of incongruent counterparts have been criticized in the recent literature. His 1768 essay has been charged with an ambiguous use of the notion of ‘inner ground’, and his 1770 claim that those differences cannot be apprehended conceptually is thought to be false. The author argues that those two charges rest on an uncharitable reading. ‘Inner ground’ is equivocal only if misread as mapping onto Leibniz notion of quality. Concepts suffice to distinguish counterparts, but are insufficient to specify their (...) spatial forms. Kant’s claims are reasonable and plausible, and have been reaffirmed repeatedly in contemporary discussions of demonstrative identification. (shrink)

The paper provides a systematic account of Kant’s ‘right to be somewhere’ as introduced in the Doctrine of Right. My claim is that Kant’s concern with the concurrent existence of a plurality of corporeal agents on the earth’s surface occupies a rarely appreciated conceptual space in his mature political philosophy. In grounding a particular kind of moral relation that is ‘external’ but not property-mediated, it provides us with a fundamentally new perspective on Kant’s cosmopolitanism, which I construe as a cosmopolitanism (...) for ‘earth dwellers’. (shrink)

This is a survey of the concept of continuity. Efforts to explicate continuity have produced a plurality of philosophical conceptions of continuity that have provably distinct expressions within contemporary mathematics. I claim that there is a divide between the conceptions that treat the whole continuum as prior to its parts, and those conceptions that treat the parts of the continuum as prior to the whole. Along this divide, a tension emerges between those conceptions that favor philosophical idealizations of continuity and (...) those that are more readily available for mathematico-scientific use. (shrink)

I argue for a new delimitation of what Kant means by ‘cognition [Erkenntnis]’, on the basis of the intermediate, transitional place that Kant gives to cognition in the ‘progression [Stufenleiter]’ of our representations and our consciousness of them. I show how cognition differs from mental acts lying earlier on this progression—such as sensing, intuiting, and perceiving—and also how cognition differs from acts lying later on this progression—such as explaining, having insight, and comprehending. I also argue that cognition should not be (...) confused with ‘knowledge [Wissen]’, insofar as knowledge represents the culmination of a separate orthogonal progression of acts of ‘holding-true’. Along the way, I show how having in focus the specific progression from representation, to consciousness, to cognition (and beyond) allows us to better appreciate the architectonic significance of the progression of Kant’s analysis in the first Critique (and beyond), and also helps to illuminate the unity of Kant’s account of cognition itself across its variety of (empirical, mathematical, philosophical) forms. (shrink)

Kant uses incongruent counterparts in his work before and after 1781, but not in the first Critique. Given the relevance that incongruent counterparts had for his thought on space, and their persistence in his work during the 1780s, it is plausible to think that he had a reason for leaving them out of both editions of the Critique. Two implausible conjectures for their absence are here considered and rejected. A more plausible alternative is put forth, which explains that textual absence (...) as a result of the synthetic method of presentation intended for the Critique. (shrink)

While the critically oriented writings of Immanuel Kant remain the key theoretical grounds from which universalists challenge reduction of international rights law and protection to the practical particularities of sovereign states, Kant’s theory can be read as also a crucial argument for a human rights regime ordered around sovereign states and citizens. Consequently, universalists may be tempted to push Kant’s thinking to greater critical examination of ‘the human’ and its properties. However, such a move to more theoretical rigour in critique (...) only solidifies the subversive statism of Kant’s apparent universalism, as long as it remains embedded in his prior theory of critical philosophy that privileges a singular form of reason. Universalist theories of human rights can break with this contradiction only insofar as they also displace the right to philosophy from the subject and site of ‘civil’ man to a politics of theory where no such subject or site is guaranteed. (shrink)