I’ll be brief. I’m going to skip the fifteenth piece, ‘Application of Categories to Biology and Cognition’ by Andrée Ehresmann: this reader made absolutely nothing of it. The next piece by David Spivak on ‘Categories as mathematical models’ (downloadable here) is pretty empty of serious content, the notion of ‘model’ in play being hopelessly vague. This is followed by Hans Halvorson and Dimitris Tsementzis on ‘Categories of scientific theories’ (downloadable here) which proceeds at such a stratospheric level of abstraction as to cast no light at all on the sort of issues in the philosophy of science that back in the day used to interest me. The final paper is by our editor, Elaine Landry, ‘Structural realism and category mistakes’ is disappointing in a different way. Landry has written thought-provoking pieces about category theory elsewhere (e.g. here and here): but this present piece has the flavour of a narrower-interest journal article replying to particular target papers rather than the sort of more general-interest essay appropriate for this sort of collection.
Heavens! Haven’t I been curmudgeonly? But I confess I started pretty sceptical about claims about the wider significance of category theory (once we go beyond the world of pure mathematics/logic — and perhaps functional programming): and on the evidence of this book, I remain as sceptical. And happy enough to be so: there is some lovely maths in e.g. the Elephant as far as I understand it, and lovely maths is good enough for me!
If you want to read more judicious(?) responses to Categories for the Working Philosopher, you could try Neil Barton’s review or the review by Chris Kapulkin and Nicholas Teh. Obviously, those reviewers are nicer and more generous than I am! But life is short …
The Kapulkin and Teh review promotes a principle of extensionality that seems designed to take the word “extensionality” away from set theory. They even have it that the set-theoretic axiom of extensionality violates extensionality because it means “one is required to ‘look inside’ the sets to examine whether or not they are equal”. If their definition prevails, are we supposed to think sets are defined intensionally in set theory? Or is the idea that we won’t have any word for it?
A better name for their principle might be “the principle of opacity”.
In any case, I don’t think I’ve seen that particular line of attack before.
I think probably a lot of us appreciate getting your honest perspective on things, curmudgeonly or not.