We shall address from a conceptual perspective the duality between algebra and geometry in the framework of the refoundation of algebraic geometry associated to Grothendieck’s theory of schemes. To do so, we shall revisit scheme theory from the standpoint provided by the problem of recovering a mathematical structure A from its representations \ into other similar structures B. This vantage point will allow us to analyze the relationship between the algebra-geometry duality and the structure-semiotics duality. Whereas in classical algebraic geometry (...) a certain kind of rings can be recovered by considering their representations with respect to a unique codomain B, Grothendieck’s theory of schemes permits to reconstruct general rings by considering representations with respect to a category of codomains. The strategy to reconstruct the object from its representations remains the same in both frameworks: the elements of the ring A can be realized—by means of what we shall generally call Gelfand transform—as quantities on a topological space that parameterizes the relevant representations of A. As we shall argue, important dualities in different areas of mathematics can be understood as particular cases of this general pattern. In the wake of Majid’s analysis of the Pontryagin duality, we shall propose a Kantian-oriented interpretation of this pattern. We shall use this conceptual framework to argue that Grothendieck’s notion of functor of points can be understood as a “relativization of the a priori” that generalizes the relativization already conveyed by the notion of domain extension to more general variations of the corresponding domains. (shrink)

McDowell'sMind and Worldis a commentary on a traditional, dualist, epistemology which puzzles over, and offers accounts of, a fundamental division between mental, subjective items, and nonmental, objective items in experience. The principal responses to that tradition which McDowell considers are those of Davidson's coherentism, Evans's form of realism, and Kant; but it is Kant's famous B75 text which occupies centre stage:‘Gedanken ohne Inhalt sind leer; Anschauungen ohne Begriffe sind blind’. (Thoughts without content are empty; intuitions without concepts are blind).

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)

Kant claims that an intuitive understanding—such as God would possess—could cognize things in themselves. This claim has prompted many interpreters of Kant's theoretical philosophy to propose that things in themselves correspond to how an intuitive understanding would cognize things. In contrast, I argue that Kant's theoretical philosophy does not endorse the common proposal that all things in themselves correspond to how an intuitive understanding would cognize things. Instead, Kant's theoretical philosophy maintains that things in themselves might or might not correspond (...) to how an intuitive understanding would cognize things. I then consider whether Kant's moral philosophy and theory of reflecting judgment might provide alternative grounds for claiming that we should regard things in themselves as corresponding to how an intuitive understanding would cognize things. I argue that Kant's moral philosophy does not provide such grounds, but his theory of reflecting judgment does. Thus, interpretations of Kant's transcendental idealism should attend to the differences between Kant's theoretical philosophy, moral philosophy, and theory of reflecting judgment in assessing the relationship between intuitive understanding and things in themselves. (shrink)

The idea that noumena or things in themselves causally affect our sensibility, and thus provide us with sensations, has been rejected on two basic grounds: It is unintelligible because distinguishes between appearance and reality in such a way that things cannot in principle appear as they really are, and it requires applying the concept of causality trans-phenomenally, contra Kant’s Schematism. I argue that noumenal causality is intelligible and is required out of fidelity to Kant’s texts and doctrines. Kant’s theory of (...) meaning and his transcendental reflection on sensibility show how Kant legitimately can speak about, and determine that, our passive sensibility must be causally affected by noumena. Kant’s analysis of agency shows that Kant’s practical philosophy requires noumenal causality, both from a first- and from a third-person perspective. These points ground my criticisms of Buchdahl and Allison’s view of affection, and Strawson and Sandberg’s view of meaning. (shrink)

Lucy Allais argues that we can better understand Kant's transcendental idealism by taking seriously the analogy of appearances to secondary qualities that Kant offers in theProlegomena. A proper appreciation of this analogy, Allais claims, yields a reading of transcendental idealism according to which all properties that can appear to us in experience are mind-dependent relational properties that inhere in mind-independent objects. In section 1 of my paper, I articulate Allais's position and its benefits, not least of which is its elegant (...) explanation of how the features of objects that appear to us are transcendentally ideal while still being ‘empirically’ real. In section 2, I contend that there are elements of Allais's account that are problematic, yet also inessential, to what I view to be the core contribution of her analysis. These elements are the views that the properties that appear to human beings are not really distinct from properties that things have ‘in themselves’ and that Kant embraced a relational account of perception. In section 3, I return to the core of Allais's reading and argue that, despite its multiple virtues, it cannot make sense of key features of Kant's idealism. (shrink)

According to Kant, there is some doctrine, which he sometimes calls 'empirical realism,' such that it was doubted by Descartes, denied by Berkeley, and endorsed by Kant himself. It may be doubted whether there really is such a doctrine or, if there is, whether it takes the form Kant seems to say it does. For instance, if empirical realism is taken as the assertion that familiar objects like tables and chairs exist, then this doctrine was neither seriously doubted by Descartes, (...) nor denied by Berkeley. If empirical realism is the view that such objects are mind-independent, then it was clearly denied by Berkeley, but was neither seriously doubted by Descartes, nor straightforwardly endorsed by Kant. Kant's assertion thus presents us with a puzzle: what might empirical realism be? The primary aim of this paper will be to reconstruct Kant's own narrative of the historical relationship between Descartes, Berkeley, and himself, in order to identify the doctrine Kant calls 'empirical realism.' I argue that the empirical realism which Descartes doubted, Berkeley denied, and Kant endorsed is the doctrine that the concept of extended substance has legitimate application. (shrink)

This article presents a metaphysical approach to the interpretation of the role of things-in-themselves in Kant’s theoretical philosophy. This focuses upon identifying their transcendental function as the grounding of appearances. It is interpreted as defining the relation of appearing as the grounding of empirical causality. This leads to a type of dual-aspect account that is given further support through a detailed examination of two sections of Kant’s first Critique. This shows the need to embed this dual-aspect account within a two-perspective (...) framework. The resulting picture is contrasted with the main rival theories and objections are addressed. (shrink)

In the interpretation of Kant’s transcendental idealism, a textual stalemate between two camps has evolved: two-world interpretations regard things in themselves and appearances as two numerically distinct entities, whereas two-aspect interpretations take this distinction as one between two aspects of the same thing. I try to develop an account which can overcome this dispute. On the one hand, things in themselves are numerically distinct from appearances, but on the other hand, things in themselves can be regarded as they exist in (...) themselves and as they appear. This reveals a mutual entailment of both accounts. Finally, I suggest that this approach most naturally leads to a kind of ‘phenomenalism’, but of a sort not normally attributed to Kant. (shrink)

A well-known trilemma faces the interpretation of Kant’s theory of affection, namely whether the objects that affect us are empirical, noumenal, or both. I argue that according to Kant, the things that affect us and cause representations in us are not empirical objects. I articulate what I call the Causal Power Argument, according to which empirical objects cannot affect us because they do not have the right kind of power to cause representations. All the causal powers that empirical objects have (...) are moving powers, and such powers can only have spatial effects. According to Kant, however, the representations that arise in us as a result of the affection of our sensibility are non-spatial. I show that this argument is put forward by Kant in a number of passages, and figures as a decisive reason for rejecting empirical affection and instead endorsing affection by the things in themselves. (shrink)

McDowell's Mind and World is a commentary on a traditional, dualist, epistemology which puzzles over, and offers accounts of, a fundamental division between mental, subjective items, and nonmental, objective items in experience. The principal responses to that tradition which McDowell considers are those of Davidson's coherentism, Evans's form of realism, and Kant; but it is Kant's famous B75 text which occupies centre stage:‘Gedanken ohne Inhalt sind leer; Anschauungen ohne Begriffe sind blind’..

I begin by considering a question that has driven much scholarship on transcendental idealism: are appearances numerically identical to the things in themselves that appear, or numerically distinct? I point out that much of the debate on this question has assumed that this is equivalent to the question of whether they are the same objects, but go on to provide textual, historical, and philosophical evidence that “object” (Gegenstand) and “thing” (Ding) have different meanings for Kant. A thing is a locus (...) of intensively gradable causal force, reality. I argue that appearances and things in themselves are not identical as objects, because the very concept of object-identity is tied, for Kant, to the concept of an intellect that would cognize the numerical identity of the objects in question. Because no intellect can be both discursive and intellectual, no intellect could cognize the numerical identity of objects across the phenomenal/noumenal divide, and thus the claim that they are identical has no content. However, the very same things, the same reality, can be given to our sensible intellects, and to divine intuitive intellect, as two non-overlapping domains of objects. Identity readers are thus shown to be right about the same thing relation, while non-identity readers are vindicated on the numerical identity of objects. (shrink)

In this thesis I provide an interpretation of Kant's theories of knowledge, nature, and being in order to argue that Kant's ontology is a productive ontology: it is a theory of being that includes a notion of production. I aim to show that Kant's epistemology and philosophy of nature are based on a theory of being as productivity. The thesis contributes to knowledge in that it considers in detail Kant's ontology and theory of being, topics which have generally been ignored (...) or misunderstood. In arguing for Kant's productive ontology, I argue against Heidegger's interpretation of Kant, which states that Kant understands being as "produced permanent presence" or as divinely created materiality. Based on Kant's definition of being as positing, I argue, by contrast to Heidegger, that Kant understands being as the original productive relation between subject and object. This can also be expressed as the relation between formality and materiality, or between epistemic conditions and existence, that is productive of objects of experience. Being is not producedness but a relation of productivity, through which both subject and object are themselves productive. The subject is productive in its spontaneity, and nature, determined as dynamical interaction, is interpreted as productive. The subject, I will argue, does not understand nature as produced, but approaches it with a comportment towards its production as object of experience. Because of its own subjective productivity - spontaneity or "life" - the subject has a "productive comportment" towards nature. Ontology, I claim, concerns the realm of the productive relation of being, the realm of the relation between epistemic conditions and existence, and therefore the realm of possible experience. This marks Kant as divergent not only from what Heidegger calls "the ontology of the extant", but also from the concept-based ontology of the German rationalists. The general aims of the thesis are, first, to argue that being for Kant is the original relation between subject and object, and that ontology concerns this relation; second, to argue that ontology and being are understood in terms of production and productivity; and third, to argue that Heidegger is wrong to ascribe to Kant an understanding of being as "produced pennanent presence". I approach these aims by examining a number of Kant's texts in detail, focusing particularly on Kant's theses about existence and being in The One Possible Basis for a Demonstration of the Existence of God and the Critique of Pure Reason; on Kant's philosophy of nature and dynamical matter in the Transcendental Analytic and Metaphysical Foundations of Natural Science; on Kant's doctrine of experience and objectivity in the Transcendental Deductions; on ontological reflection and the productive comportment of "life" in the Critique of Judgment; and on Kant's final theory of matter, life and production in the Opus Postumum. (shrink)