Logic Matters 2008-08-19

Parsons's Mathematical Thought: Sec. 15, Mathematical modality

Chapter 3 of Mathematical Thought and Its Objects is called "Modality and structuralism". Before turning to discuss modal structuralism in Secs. 16 and 17, Parsons discusses what kind modality it might involve. Setting aside epistemic modalities as not to the present purpose, he considers (i) physical (or natural) necessity, (ii) metaphysical necessity (truth in all possible worlds), (iii) mathematical necessity, (iv) logical necessity (meant in a narrow sense that can be explicated model-theoretically).Parsons argues that we don't want to spell out a modal structuralism in terms of (i) natural modalities: "it demands too much to ask that the structures considered in mathematics be physically possible; indeed, in the case of higher set theory, there is every reason to believe that they are not physically possible." I'll buy that.Second, Parsons argues that logical possibility -- in the sense explicated via the ...

read more    1 hit

more posts from Logic Matters