Two new Cambridge Elements on Phil. Maths

Just briefly to note that there are two new short contributions in the Cambridge Elements series in the Philosophy of Mathematics, both free to download for another week. The Euclidean Programme by Alex Paseau and Wesley Wrigley critically examines the traditional idea that mathematical knowledge is obtained by deduction from self-evident axioms or first principles. How much of that idea can be rescued?

And Number Concepts by Richard Samuels and Eric Snyder takes an interdisciplinary approach to reviewing and critically assessing work on number concepts in developmental psychology and cognitive science. (And after all, shouldn’t philosophers of arithmetic be interested in the concepts deployed by folk arithmeticians?)

So far, contributions in this series have been, it seems to me, a rather mixed bunch. So naive induction is little guide, in this case, as to how worthwhile these new efforts will prove to be. But let’s live in hope. When I’ve had a chance to take a proper look, I’ll let you know what I think. But I thought I would post a quick note straight away, while these two Elements are still freely downloadable, and you can judge them for yourself.

4 thoughts on “Two new Cambridge Elements on Phil. Maths”

  1. Peter, have you looked at Rich Thomason’s _Symbolic Logic_ text? It was originally published back in 1970, but is updated and online ~2007. Chapters 5 – 8 and 10 -12 are largely metatheory. It requires students to prove dozens of metatheorems and, I think, is an excellent way into mathematical logic. Here’s a link to the Michigan website I think he requires a password to get the file, but he’ll just send it to you. Otherwise I can send you a pdf copy.

    1. I have had a copy for ever, probably from shortly after it was published! And indeed, I think I first learnt Fitch-style ND from it.

      I did think, back in the day, that despite its virtues it does makes some things unnecessarily hard going as an introductory book. Is the revised version significantly different?

  2. Downloadable, yes, but not (by me) from those links. Both returned “Page not found”.

    However, for both, by deleting everything after “elements/” in the URL, going to that page, then searching for the title, I was able to reach a page that had a “Save PDF” link (which worked).

    I came here because of your tweet, BTW, so your presence on Twitter still has some value (at least from my POV).

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