Category Archives: Math. Thought and Its Objects

Chapter 5 of Parsons’s book is called “Intuition”. And I guess I should declare an interest (or rather, lack of interest!) here. I’ve never really understood talk about intuition: and I’m certainly not helped when Parsons writes “I shall be … Continue reading →

These sections make up the short Chapter 4 of Parsons’s book (they are a slightly expanded version of a 1995 paper in a festschrifft for Ruth Barcan Marcus). The issue is whether there are special problems giving a broadly structuralist … Continue reading →

The previous two sections critically discussed a modal version of eliminative structuralism (though to my mind, the objections raised weren’t particularly telling). Parsons now moves on characterize his own preferred “noneliminative structuralism”, and responds to some potential obections. I wish … Continue reading →

In Sec. 16, “Modalism”, Parsons considers the stratgegy of rescuing eliminativist structuralism from the vacuity problem by going modal. To recap, we’re considering the schematic idea that an ordinary arithmetical statement is elliptical for something along the lines of For … Continue reading →

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 … Continue reading →

We’re considering the schematic idea that an ordinary arithmetical statement is elliptical for something generalizing over structures, along the lines of For any N, 0, S, if Ω(N, 0, S) then A(N, 0, S), where Ω(N, 0, S) lays down … Continue reading →