Agustin Rayo

‘Years ago, when I was young and reckless, I believed that there was such a thing as an all-inclusive domain. Now I have come to see the error of my ways’. The source of this mistake was a view that might be labeled ‘Tractarianism’. Tractarians believe that language is subject to a _metaphysical_ constraint. In order for an atomic sentence to be true, there needs to be a certain kind of correspondence between the semantic structure of the sentence and the ‘metaphysical structure’ of reality. The purpose of this chapter is to explain why Tractarianism is mistaken, and what an anti-Tractarian should say about absolutely general quantification.

This chapter defends a metasemantic account of vagueness, which is based on the following three theses: (1) The meaningfulness of our sentences depends on the prevalence of suitable linguistic conventions; (2) Whether or not a convention prevails in a given population need not be an all-or-nothing matter — it can come in degrees; (3) Whereas conventions about how to use sentences involving only attributions of vague predicates to clear cases are often prevalent to a very high degree, conventions about how to use sentences involving attributions of vague predicates to borderline cases are prevalent, if at all, to lesser degrees.

Here is an account of logical consequence inspired by Bolzano and Tarski. Logical validity is a property of arguments. An argument is a pair of a set of interpreted sentences (the premises) and an interpreted sentence (the conclusion). Whether an argument is logically valid depends only on its logical form. The logical form of an argument is fixed by the syntax of its constituent sentences, the meanings of their logical constituents and the syntactic differences between their non-logical constituents, treated as variables. A constituent of a sentence is logical just if it is formal in meaning, in the sense roughly that its application is invariant under permutations of individuals.1 Thus ‘=’ is a logical constant because no permutation maps two individuals to one or one to two; ‘∈’ is not a logical constant because some permutations interchange the null set and its singleton. Truth functions, the usual quantifiers and bound variables also count as logical constants. An argument is logically valid if and only if the conclusion is true under every assignment of semantic values to variables (including all non-logical expressions) under which all its premises are true. A sentence is logically true if and only if the argument with no premises of which it is the conclusion is logically valid, that is, if and only if the sentence is true under every assignment of semantic values to variables. An interpretation assigns values to all variables.

In his excellent book Thin Objects, Øystein Linnebo develops a conception of objecthood that allows for thin objects: objects whose ‘existence does not make a substantial demand on the world’ (p. 4). His proposal is premised on the Fregean dictum that to be an object is to be the referent of a possible singular term (p. 22). As a result, much of Linnebo's argumentation is focused on defending a ‘thin’ conception of reference, which is liberal enough to allow for thin objects. This paper is a critique of Linnebo's conception of reference.

The goal of this paper is to develop a theory of content for vague language. My proposal is based on the following three theses: (1) language-mastery is not rulebased— it involves a certain kind of decision-making; (2) a theory of content is to be thought of instrumentally—it is a tool for making sense of our linguistic practice; and (3) linguistic contents are only locally defined—they are only defined relative to suitably constrained sets of possibilities. CiteULike    Connotea    Del.icio.us    What's this?

It would be good to have a Bayesian decision theory that assesses our decisions and thinking according to everyday standards of rationality — standards that do not require logical omniscience (Garber 1983, Hacking 1967). To that end we develop a “fragmented” decision theory in which a single state of mind is represented by a family of credence functions, each associated with a distinct choice condition (Lewis 1982, Stalnaker 1984). The theory imposes a local coherence assumption guaranteeing that as an agent's attention shifts, successive batches of "obvious" logical information become available to her. A rule of expected utility maximization can then be applied to the decision of what to attend to next during a train of thought. On the resulting theory, rationality requires ordinary agents to be logically competent and to often engage in trains of thought that increase the unification of their states of mind. But rationality does not require ordinary agents to be logically omniscient.