Frege's Conception of Numbers as Objects

If we are asked what, in general, it is that someone knows when he knows the meaning of a word, it seems natural enough to reply: what that word stands for. ‘Stands for’ is of course a metaphor. The phrase suggests a model or picture, of what happens when a language is instituted. The picture it suggests is this. There is an object in the world, and the word serves as a substitute for that object; as, that is, a kind of proxy: something that does duty for, or stands in place of the object.

Reference and Generality

Objects Of Thought

On Quantification and Ontology

Naturalism and Ontology.

This dissertation develops an inferentialist theory of meaning. It takes as a starting point that the sense of a sentence is determined by the rules governing its use. In particular, there are two features of the use of a sentence that jointly determine its sense, the conditions under which it is coherent to assert that sentence and the conditions under which it is coherent to deny that sentence. From this starting point the dissertation develops a theory of quantification as marking coherent ways a language can be expanded and modality as the means by which we can reflect on the norms governing the assertion and denial conditions of our language. If the view of quantification that is argued for is correct, then there is no tension between second-order quantification and nominalism. In particular, the ontological commitments one can incur through the use of a quantifier depend wholly on the ontological commitments one can incur through the use of atomic sentences. The dissertation concludes by applying the developed theory of meaning to the metaphysical issue of necessitism and contingentism. Two objections to a logic of contingentism are raised and addressed. The resulting logic is shown to meet all the requirement that the dissertation lays out for a theory of meaning for quantifiers and modal operators. Second-Order Modal Logic

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Andrew Parisi

Papers

Second-Order Modal Logic