Inferential Role and the Ideal of Deductive Logic

Although there is a prima facie strong case for a close connection between the meaning and inferential role of certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This distinction is closely tied to two conceptions of deductive logic, and it is the key, I argue, for understanding first the connection between meaning and inferential role, and second what the paradoxes show more generally

Proof-Theoretic Reduction As A Philosopher's Tool

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42723/1/10670_2004_Article_263273.pd

Innocent Statements and Their Metaphysically Loaded Counterparts

here is an old puzzle about ontology, one that has been puzzling enough to cast a shadow of doubt over the legitimacy of ontology as a philosophical project. The puzzle concerns in particular ontological questions about natural numbers, properties, and propositions, but also some other things as well. It arises as follows: ontological questions about numbers, properties, or propositions are questions about whether reality contains such entities, whether they are part of the stuff that the world is made of. The ontological questions about numbers, properties, or propositions thus seem to be substantive metaphysical questions about what is part of reality. Complicated as these questions may be, they can nonetheless be stated simply in ordinary English with the words ‘Are there numbers/properties/propositions?’ However, it seems that such a question can be answered quite immediately in the affirmative. It seems that there are trivial arguments that have the conclusion that there are numbers/properties