A discrete version of the Mishou theorem. II

In 2007, H. Mishou obtained a joint universality theorem for the Riemann zetafunction ζ(s) and the Hurwitz zeta-function ζ(s, α) with transcendental parameter α. The theorem states that a pair of analytic functions can be simultaneously approximated by the shifts ζ(s + iτ ) and ζ(s + iτ, α), τ ∈ R. In 2015, E. Buivydas and the author established a version of this theorem in which the approximation is performed by the discrete shifts ζ(s + ikh) and ζ(s + ikh, α), h > 0, k = 0, 1, 2.... In the present study, we prove joint universality for the functions ζ(s) and ζ(s, α) in the sense of approximation of a pair of analytic functions by the shifts ζ(s + ik ^β h) and ζ(s + ik ^β h, α) with fixed 0 < β < 1.     

Fregean Facts

Two important Fregean ideas appear to conflict. The first is that a thought can be decomposed in different ways, and the second is that a thought is constituted by the senses of its constituents. This paper is a defense of Dummett’s suggestion of a way to reconcile between those two theses through the claim that although the same thought can be structured in different ways by different sentences; one of the structures is privileged. My defense focuses on the charge raised by Levine (Ratio (new series), XIX, 43–63, 2006) that Dummett’s claim about the privileged structure of a thought conflicts with the Slingshot argument. I show that this charge is misconceived; a careful examination of the Slingshot argument’s methodology reveals that Dummett’s claim does not conflict with it.     

Non-Realist Cognitivism,Truth and Objectivity

In On What Matters, Derek Parfit defends a new metaethical theory, which he calls non-realist cognitivism. It claims that (i) normative judgments are beliefs; (ii) that some normative beliefs are true; (iii) that the normative concepts that are a part of the propositions that are the contents of normative beliefs are irreducible, unanalysable and of their own unique kind; and (iv) that neither the natural features of the reality nor any additional normative features of the reality make the relevant normative beliefs true. The aim of this article is to argue that Parfit’s theory is problematic because its defenders have no resources to make sense of the nature of normative truth, which is an essential element of their view. I do this by showing how the traditional theories of truth are not available for the non-realist cognitivists.     

Necessarily Incompatible Consistent Wants

This paper argues that the wants or desires of a person can be consistent with each other and still necessarily incompatible with each other and for interesting reasons. It is argued here that this problem is not rare and that there is no solution in sight.