Somekawa's K-groups and Voevodsky's Hom groups (preliminary version)

We construct a surjective homomorphism from Somekawa's K-group associated to a finite collection of semi-abelian varieties over a perfect field to a corresponding Hom group in Voevodsky's triangulated category of effective motivic complexes.Comment: 15 page

Kant’s post-1800 Disavowal of the Highest Good Argument for the Existence of God

I have two main goals in this paper. The first is to argue for the thesis that Kant gave up on his highest good argument for the existence of God around 1800. The second is to revive a dialogue about this thesis that died out in the 1960s. The paper is divided into three sections. In the first, I reconstruct Kant’s highest good argument. In the second, I turn to the post-1800 convolutes of Kant’s Opus postumum to discuss his repeated claim that there is only one way to argue for the existence of God, a way which resembles the highest good argument only in taking the moral law as its starting point. In the third, I explain why I do not find the counterarguments to my thesis introduced in the 1960s persuasive

A Dilemma for Mathematical Constructivism

In this paper I argue that constructivism in mathematics faces a dilemma. In particular, I maintain that constructivism is unable to explain (i) the application of mathematics to nature and (ii) the intersubjectivity of mathematics unless (iii) it is conjoined with two theses that reduce it to a form of mathematical Platonism. The paper is divided into five sections. In the first section of the paper, I explain the difference between mathematical constructivism and mathematical Platonism and I outline my argument. In the second, I argue that the best explanation of how mathematics applies to nature for a constructivist is a thesis I call Copernicanism. In the third, I argue that the best explanation of how mathematics can be intersubjective for a constructivist is a thesis I call Ideality. In the fourth, I argue that once constructivism is conjoined with these two theses, it collapses into a form of mathematical Platonism. In the fifth, I confront some objections

Holomorphic Removability of Julia Sets

Let $f(z) = z^2 + c$ be a quadratic polynomial, with c in the Mandelbrot set. Assume further that both fixed points of f are repelling, and that f is not renormalizable. Then we prove that the Julia set J of f is holomorphically removable in the sense that every homeomorphism of the complex plane to itself that is conformal off of J is in fact conformal on the entire complex plane. As a corollary, we deduce that the Mandelbrot Set is locally connected at such c.Comment: 48 pages. 9 PostScript figure

Kant, the Practical Postulates, and Clifford’s Principle

In this paper I argue that Kant would have endorsed Clifford’s principle. The paper is divided into four sections. In the first, I review Kant’s argument for the practical postulates. In the second, I discuss a traditional objection to the style of argument Kant employs. In the third, I explain how Kant would respond to this objection and how this renders the practical postulates consistent with Clifford’s principle. In the fourth, I introduce positive grounds for thinking that Kant would have endorsed this principle