Modal Empiricism and Two-Dimensional Semantics

In the paper I argue that it follows from David Chalmers’ semantics and metaphysics concerning microphysical terms that microphysical identifications are strongly necessary. This result supports modal empiricism and also counts in favour of a posteriori materialism (and thus against Chalmers’ property dualism), for it blocks the conjecture that a posteriori materialism is committed to strong necessities, but there are no such modalities

Juhos' Antiphysicalism and his Views on the Psychophysical Problem

My primary aim in this paper is to discuss Bela Juhos' views on the mind-body problem and his objections to the physicalist accounts of Carnap, Neurath and Hempel in the early 1930s. In order to achieve this, I also provide some background against which his ideas can be located: I shall outline Juhos' metaphilosophical views on the nature and goal of philosophical inquiry, and the diverse accounts of the psychophysical problem in and around the Vienna Circle

Polarization, sign sequences and isotropic vector systems

We determine the order of magnitude of the $n$th $\ell_p$-polarization constant of the unit sphere $S^{d-1}$ for every $n,d \geq 1$ and $p>0$. For $p=2$, we prove that extremizers are isotropic vector sets, whereas for $p=1$, we show that the polarization problem is equivalent to that of maximizing the norm of signed vector sums. Finally, for $d=2$, we discuss the optimality of equally spaced configurations on the unit circle.Comment: 13 page

Density estimates of 1-avoiding sets via higher order correlations

We improve the best known upper bound on the density of a planar measurable set A containing no two points at unit distance to 0.25442. We use a combination of Fourier analytic and linear programming methods to obtain the result. The estimate is achieved by means of obtaining new linear constraints on the autocorrelation function of A utilizing triple-order correlations in A, a concept that has not been previously studied.Comment: 10 pages, 2 figure