Online research in philosophy

It is shown that the nonrecursive predecessors of a 1-generic degree $ are all 1-generic. As a corollary, it is shown that the 1-generic degrees are not densely ordered.

Abstract   Theories of descriptions tend to involve commitments about the ambiguity of descriptions. For example, sentences containing descriptions are widely taken to be ambiguous between de re , de dicto , and intermediate interpretations and are sometimes thought to be ambiguous between the former and directly referential interpretations. I provide arguments to suggest that none of these interpretations are due to ambiguities (or indexicality). On the other hand, I argue that descriptions are ambiguous between the above family of interpretations and what may be called ‘institutional’ as well as generic interpretations. My arguments suggest that an adequate theory of descriptions may require considerable rethinking. Most contemporary theories of descriptions appear to be committed to one or more claims about the ambiguity of descriptions that I reject in this paper. I suggest that my observations provide a reason to renew efforts to develop a theory of descriptions within a representationalist theory of interpretation. Content Type Journal Article Pages 1-16 DOI 10.1007/s11098-011-9759-5 Authors Philipp Koralus, Philosophy Department, Princeton University, 212 1879 Hall, Princeton, NJ 08544, USA Journal Philosophical Studies Online ISSN 1573-0883 Print ISSN 0031-8116.

i. Proofless text is based on a variant of ZFC with free logic. Here variables always denote, but not all terms denote. If a term denotes, then all subterms must denote. The sets are all in the usual extensional cumulative hierarchy of sets. There are no urelements.

The paper revisits Sharvy's theory of plural definite descriptions. An alternative account of plural definite descriptions building on the ideas of plural quantification and non-distributive plural predication is developed. Finally, the alternative is extrapolated to account for generic uses of definite descriptions.

Let ZF denote Zermelo-Fraenkel set theory (without the axiom of choice), and let M be a countable transitive model of ZF. The method of forcing extends M to another model M[ G] of ZF (a "generic extension"). If the axiom of choice holds in M it also holds in M[ G], that is, the axiom of choice is preserved by generic extensions. We show that this is not true for many weak forms of the axiom of choice, and we derive an application to Boolean toposes.

Definite descriptions (e.g. 'The king of France in 1997', 'The teacher of Aristotle') do not stand for particulars. Or so I will assume. The semantic alternative has seemed to be that descriptions only have meaning within sentences: i.e., that their semantic contribution is given syncategorimatically. This doesn't seem right, however, because descriptions can be used and understood outside the context of any sentence. Nor is this use simply a matter of "ellipsis." Since descriptions do not denote particulars, but seem to have a meaning in isolation, I propose that they be assigned generalized quantifiers as denotations — i.e. a kind of function, from sets/properties to propositions. I then defend the pragmatic plausibility of this proposal, using Relevance Theory. Specifically, I argue that, even taken as standing for generalized quantifiers, descriptions could still be used and understood in interpersonal communication.

A real is called properly n-generic if it is n-generic but not n+1-generic. We show that every 1-generic real computes a properly 1-generic real. On the other hand, if m > n ≥ 2 then an m-generic real cannot compute a properly n-generic real.

What, from a semantic perspective, is the difference between singular indefinite and definite descriptions? Just over a century ago, Russell provided what has become the standard philosophical response. Descriptions are quantifier phrases, not referring expressions. As such, they differ with respect to the quantities they denote. Indefinite descriptions denote existential quantities; definite descriptions denote uniquely existential quantities. Now around the 1930s and 1940s, some linguists, working independently of philosophers, developed a radically different response. Descriptions, linguists such as Jespersen held, were referring expressions, not quantifier phrases. Accordingly, descriptions differ with respect their rules of reference. Indefinite descriptions refer to „novel‟ items, definite descriptions to „familiar‟ ones. My dissertation serves as the first systematic effort to bridge the gap between these two seemingly incompatible responses. It provides a satisfactory answer to the above question which links the seemingly intractable divide between Russellians and familiarity theorists. This is achieved by utilizing two observations: Donnellan‟s observation that speakers use descriptions not only as devices of quantification but also as devices of reference, and Devitt‟s observation that these two uses, being regular, systematic, and cross-linguistic, have the status of convention in our language. Taken in conjunction, these two observations, I argue, require postulating that descriptions are semantically ambiguous. These observations compel the thoughtful theorist to maintain that descriptions have two distinct semantic functions, one quantificational and one referential. Accordingly, the semantic contrast between singular indefinite and definite descriptions is two-fold. Descriptions can contrast either quantificationally or with respect to the speaker‟s view of the audience‟s familiarity with the description‟s referent.