On 1/29/2017 1:00 PM, Jon Awbrey wrote:
The distinction between nominal thinking and real thinking is distinct from the distinction between extensional thinking and intensional thinking, as one can see from the fact that extreme nominalists do not admit sets as entities.
Quine was as extreme as you can get without destroying mathematics. He never accepted possible worlds by his best buddy Rudolf C, he was highly critical about the versions by Kripke and others, and he was always trying to find ways to paraphrase mathematical theories in order to avoid intensions. JA
Peirce admitted both extensions and intensions of concepts, as integrated in his theory of information.
Yes. But Quine did not admit concepts in his ontology. Remember the title of his magnum opus: _Word and Reality_. He would admit words (sounds or marks on paper) as part of his reality, but not concepts as "meanings" of words. Quine's dictum: "To be is to be the value of a quantified variable." He would allow variables to refer to words, but not to abstract entities. For him, the word 'set' is just a placeholder. It could be explained in terms of a "disposition to behavior" by the people who use it. In their 1947 article, Goodman and Quine adopted mereology, in which a collection is "constructed" from the things it contains. Quine allowed quantified variables to refer to the constructions. He would also allow "axiom schemata" that generate an open-ended number of axioms. They don't imply the existence of a principle, rule, function, relation, law, or habit as the intension. But Quine's "dispositions to behavior" sound a lot like habits. John
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