Category Archives: Math. Thought and Its Objects

Why does the principle of mathematical induction hold for the natural numbers? Well, arguably, “induction falls out of an explanation of the meaning of the term ‘natural number’”. How so? Well, the thought can of course be developed along Frege’s … Continue reading →

Here, as promised, are some comments on Chapter 7 of Parsons’s book. They are quite lengthy, and since in writing them I found myself going back to revise/improve some of my discussions of earlier sections, I’m just posting a single … Continue reading →

There’s now a version of my posts on the first five chapters of Parsons book: so the newly added pages are on Chapter 5 of his book, on “Intuition”. I found these sections unconvincing (when I didn’t find them baffling) … Continue reading →

Well, “blogging at a snail’s pace” is all well and good, but my posts about Parsons have recently ground to a complete halt. Sorry about that. Pressure of other things. But I’m back on the case, now with the pressure … Continue reading →

Suppose we accept that “it is not necessary to attribute to the agent perception or intuition of a set as a single object” in order to ground arithmetical beliefs. Still, we might wonder whether some such intuition of sets-as-objects might … Continue reading →

So where have we got to in talking about Parsons’s book? Chapter 6, you’ll recall, is titled “Numbers as objects”. So our questions are: what are the natural numbers, how are they “given” to us, are they objects available to … Continue reading →

Chapter 6 of Parsons’s book is titled ‘Numbers as objects’. So: what are the natural numbers, how are they “given” to us, are they objects available to intuition in the kinds of ways suggested in the previous chapter? Sec. 31 … Continue reading →

Luca Incurvati has just pointed out to me that John Burgess has a review of Parsons forthcoming in Philosophia Mathematica, and an electronic pre-print is available here (if your library has a subscription). Burgess is very polite, but reading between … Continue reading →

Qn: “You do seem increasingly out of sympathy with Parsons’s book. So why are you spending all this effort blogging about it?” Ans: “Well, as I think I said at the outset, I have promised to write a review (indeed, … Continue reading →

I’ve been trying to make good sense of the rest of Parsons’s chapter on intuition, and have to confess failure. We might reasonably have hoped that we’d get here a really clear definitive version of the position on intuition that … Continue reading →