Matti Eklund

Rudolf Carnap's 1930s philosophy of logic, including his adherence to the principle of tolerance, is discussed. What theses did Carnap commit himself to, exactly? I argue that while Carnap did commit himself to a certain multitude thesis—there are different logics of different languages, and the choice between these languages is merely a matter of expediency—there is no evidence that he rejected a language-transcendent notion of fact, contrary to what Warren Goldfarb and Thomas Ricketts have prominently argued. (In fact, it is obscure just what Goldfarb and Ricketts claim about Carnap). Toward the end I critically discuss Michael Friedman's suggestion that Carnap believed in a relative a priori

My theme here will be vagueness. But first recall Quine’s arguments for the indeterminacy of translation and the inscrutability of reference. (I will presume these arguments to be familiar.) If Quine is right, then there are radically different acceptable assignments of semantic values to the expressions of any language: different assignments of semantic values that for all that is determined by whatever it is that determines semantic value are all acceptable, and all equally good. Quine even argued that the indeterminacy is so radical that some sentences are true under some acceptable assignments but false under others.1 Still, Quine does not allow intermediate truth-values or truthvalue gaps. (As I will put it, avoiding the disjunctive formulation: does not allow that there are sentences which are neuter.) Quine holds on to classical logic and bivalence and requires each acceptable assignment to be classical and bivalent.2.

I will here present a number of problems concerning the idea that there is ontological vagueness, and the related claim that appeal to this idea can help solve some vagueness-related problems. A theme underlying the discussion will be the distinction between vagueness specifically and indeterminacy more generally (and, relatedly, the distinction between ontological vagueness and ontological indeterminacy). Even if the world is somehow ontologically indeterminate it by no means follows that it is, properly speaking, ontologically vague.1..

A central element in neo-Fregean philosophy of mathematics is the focus on abstraction principles, and the use of abstraction principles to ground various areas of mathematics. But as is well known, not all abstraction principles are in good standing. Various proposals for singling out the acceptable abstraction principles have been presented. Here I investigate what philosophical underpinnings can be provided for these proposals; specifically, underpinnings that fit the neo-Fregean's general outlook. Among the philosophical ideas I consider are: general views on a priori justification; the idea of abstraction as reconceptualization, the idea that truth is prior to reference in the sense associated with Frege's context principle; and various broadly relativistic views. The conclusions are by and large negative.

In (2001), (2003), and elsewhere, Ted Sider presents two arguments concerning the existential quantifier which are justly central to the recent discussion of metaontology. What we will call Sider's indeterminacy argument is an attempted reductio of the suggestion that the existential quantifier might be semantically indeterminate. What we will call Sider's naturalness argument is an argument for the claim that the semantic value of the existential quantifier is the most eligible existence-like meaning there is, à la David Lewis' eligibility theory of meaning. We will argue that these arguments cannot be jointly maintained: Sider must give up at least one. Before arguing this, we will present Sider's two arguments in a bit more detail, and discuss their relationship. A few remarks on the broader significance of our conclusions are in order at the outset. One may think that since one successful argument for a given conclusion is sufficient the point that Sider's arguments cannot both work is purely academic. But we think that Sider's two arguments at bottom reflect different ways of thinking about metaphysics. Moreover, we think that it is only the naturalness argument that promises to deliver all that Sider wants when it comes to metaontology, and it is only the indeterminacy argument that promises to deliver all that Sider wants when it comes to ontology