Daniel Smyth

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.

This article sketches a strategy for teaching Heidegger's essay "The Origin of the Work of Art" ("Origin"). I illustrate how one can address Heidegger's Nazi affiliation while simultaneously engaging his philosophy of art on its own terms-goals that often work at cross purposes in the classroom. Like many, I read "Origin" together with Meyer Schapiro's critique of Heidegger's interpretation of a van Gogh still life of shoes, which figures so prominently in "Origin." My innovation is to pair the Heidegger/Schapiro dispute with Holocaust imagery of victims' shoes and personal effects. Such imagery serves to introduce historical and political context for the debate and to highlight methodological differences in their conceptions of the meaning, reception, and interpretation of artworks and images more generally. These differences raise big-picture questions about the norms that govern our engagements with art and the theoretical desiderata we want a philosophy of art to satisfy. The dispute between Heidegger and Scha-piro, read in conjunction with Holocaust imagery, lends these rather abstract questions a concreteness and urgency that greatly enhances classroom discussion.

I advance a novel interpretation of Kant's argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition.

A widespread interpretation of Kant's Inaugural Dissertation (ID) holds that the structure and content of intuition must be finite. I argue that this is mistaken and obscures central motivations for Kant's distinction between sensibility and intellect as well as key aspects of his idealism about spatiotemporal phenomena. Intuition, I argue, does have an infinitary structure in ID. Indeed, it is just this infinitary structure that precludes intuition from representing true unities – simples, composite substances, and totalities of substances (worlds). Focusing on this overarching concern with the representation of true unity reveals that the concrete representation of infinity is one of Kant's chief criteria for distinguishing sensibility from intellect. Moreover, it yields an interpretation of Kant's precritical idealism that places him squarely in the Leibnizian tradition: holding that, since infinitary complexes cannot enjoy true unity, the unity we represent them to have (as parts and wholes with determinate spatiotemporal boundaries) cannot be due to the objects themselves, but must rather be due to our mode of representing them. Concrete infinitary complexes, such as spatiotemporal phenomena, are thus ideal, or mind dependent, in that the unity we represent them to have is grounded in features of the mind representing them.

Our treatment of and feelings for photos seem to distinguish them from other sorts of pictures. Yet explanations of this phenomenon often suffer from a lack of technical understanding and employ terms that veil important distinctions. This paper develops a more precise way of thinking about photography by examining and critiquing Kendall Walton's admirably grounded account of " seeing through photos " as an explanation of our special feelings for them. I argue that Walton's account won't do what he wants it to and suggest that the very idea of "seeing through photos" rests on a confusion. Finally, I gesture at a different way of understanding why photos can move us in a special way. Snapshots, Perception, and Intimacy: Thoughts on the Ontology of Photos

I argue that, though humanistic study is multiply instrumentally value, it also promises a distinctive intrinsic value. This intrinsic value, however, can only be realized under certain conditions: in particular, it requires peace and quiet, a condition that is traditionally (and currently) the privilege of very few in our society. I suggest that a full commitment to promoting humanistic study at the collegiate level must therefore turn its attention to societal conditions affecting the broader community.

'Elucidations' is a (terrific!) philosophy podcast founded by Matt Teichman and based at the University of Chicago. Episodes consist of conversations with professional philosophers about aspects of their work and interests. The discussions are in-depth but are designed to be accessible to a non-professional audience (roughly: any attentive college freshman).  In this episode, Matt and I talk with Jim Conant (U.Chicago) and Jay Elliott (Bard) about the so-called "Analytic" philosophical tradition. Conant and Elliott are co-editors of the forthcoming Norton Anthology of Analytic Philosophy and we spoke about different ways to conceive of a "philosophical tradition" and other conceptual issues that arise in attempting to select tradition-defining texts in an impartial but informative manner.

'Elucidations' is a (terrific!) philosophy podcast founded by Matt Teichman and based at the University of Chicago. Episodes consist of conversations with professional philosophers about aspects of their work and interests. The discussions are in-depth but are designed to be accessible to a non-professional audience (roughly: any attentive college freshman).  In this episode, Matt and I talk with Barbara Herman (UCLA) about the much-neglected topic of gratitude as an ethical value.

'Elucidations' is a (terrific!) philosophy podcast founded by Matt Teichman and based at the University of Chicago. Episodes consist of conversations with professional philosophers about aspects of their work and interests. The discussions are in-depth but are designed to be accessible to a non-professional audience (roughly: any attentive college freshman).  In this episode, Matt and I talk with Malte Willer (U.Chicago) about non-monotonic logic and some of its applications: e.g. in moral reasoning.

Elucidations is a (terrific!) philosophy podcast founded by Matt Teichman and based at the University of Chicago.  I often join Matt to interview professional philosophers about their work and interests.  Our discussions are designed to be accessible to a broad audience (roughly: any attentive college freshman) and they're tons of fun.  In this episode, we talk with Mark Hopwood (Sewannee) about the role of love in ethical reasoning and the challenge of being faithful to the infinite individuality of another's reality.

This public talk at the Art Institute of Chicago was part of a series in which academics utilize the permanent collection in order to present their research to a broader audience. I selected Gerhard Richter's "Ice" Series (1989) as an entry point into my work on Immanuel Kant's epistemology. I suggest that the duality of harmony and unpredictability in Richter's abstracts has an analogue in Kant's view that theoretical knowledge requires (and requires nothing more than) a capacity for abstract conceptualization in concert with a receptivity to concrete particularity.

The “mathematization of nature” is a hallmark of the so-called “scientific revolution” in sixteenth- and seventeenth-century Europe.  By privileging quantitative methods for measuring and explaining natural phenomena, thinkers broke with the largely “qualitative” forms of explanation typical of the Aristotelian tradition.  Especially with the development of new mathematical methods – notably, advances in algebra, analytical geometry, and the development of infinitesimal calculus – the scope and explanatory power of natural philosophy was considerably extended.  At the same time, however, new puzzles arose about how the pristine models of abstract mathematics could apply to the messy reality of concrete nature.  This question was especially pressing in connection with new mathematics’ exploitation the notion of infinity: infinite series, infinite extensions, infinitesimally small quantities, and even infinities greater than other infinities.  Should we take the successful application of such infinitary mathematics to natural phenomena to imply that nature itself harbors an infinity of infinities?  And how must we reconceive the cognitive powers of the human mind to make room for the fact that infinity has ceased to signify the unknowable as such and has instead become a primary tool for producing scientific knowledge?  In this seminar, we will examine some of the most prominent Early Modern applications of infinitary mathematical methods in the study of natural phenomena as well as central debates about what sense, if any, can be made of these procedures and their apparent success.

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 ...

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 ...

This article sketches a strategy for teaching Heidegger's essay "The Origin of the Work of Art" ("Origin"). I illustrate how one can address Heidegger's Nazi affiliation while simultaneously engaging his philosophy of art on its own terms-goals that often work at cross purposes in the classroom. Like many, I read "Origin" together with Meyer Schapiro's critique of Heidegger's interpretation of a van Gogh still life of shoes, which figures so prominently in "Origin." My innovation is to pair the Heidegger/Schapiro dispute with Holocaust imagery of victims' shoes and personal effects. Such imagery serves to introduce historical and political context for the debate and to highlight methodological differences in their conceptions of the meaning, reception, and interpretation of artworks and images more generally. These differences raise big-picture questions about the norms that govern our engagements with art and the theoretical desiderata we want a philosophy of art to satisfy. The dispute between Heidegger and Scha-piro, read in conjunction with Holocaust imagery, lends these rather abstract questions a concreteness and urgency that greatly enhances classroom discussion.

I advance a novel interpretation of Kant’s argument that our original representation of space must be intuitive, according to which the intuitive status of spatial representation is secured by its infinitary structure. I defend a conception of intuitive representation as what must be given to the mind in order to be thought at all. Discursive representation, as modelled on the specific division of a highest genus into species, cannot account for infinite complexity. Because we represent space as infinitely complex, the spatial manifold cannot be generated discursively and must therefore be given to the mind, i.e. represented in intuition.

This is Supplementary Material to §2.4 of my book, 'Intuition in Kant: The Boundlessness of Sense' (CUP). To my knowledge, the term 'Anschauung' (and its cognates) appears just four times in Kant's corpus in connection with non-rational animals. The present discussion analyzes these passages, arguing that two are ambiguous and one is likely a student interpolation. So there is just one unambiguous record, in student lecture notes, of Kant ascribing Anschauung to non-rational animals. This is far too flimsy a textual basis for claiming that non-rational animals can enjoy Kantian Anschauungen. In light of the philosophical considerations I elaborate in the book, I conclude that it is misleading to characterize the sensible representations of non-rational animals as intuitions in Kant's sense.

This is Supplementary Material for §3.2 of my book, 'Intuition in Kant: The Boundlessness of Sense' (CUP). It analyzes Kant's teleological characterization of the relation of thought to intuition (A19/B33), using Heidegger's interpretation as a stalking horse.