The metaphysics of logic?

A collection of essays on The Metaphysics of Logic, edited by Penelope Rush, was published as a very expensive haddock — no, no, you idiot spell-checker, hardback — in 2014. Even with my large discount as a CUP author, I balked at the price. But it is now newly available as a paperback, and (I confess, without looking too closely) I picked up a copy the other day.

I can’t honestly recommend that you do the same.

At my not-so-tender years, I’m just not very willing to spend my limited time reading papers that are badly written or  unclear where they are going. So I didn’t get very far with the first two pieces in the collection, by Penelope Rush herself and by Jody Azzouni.

The next paper by Stewart Shapiro is predictably three steps up in terms of clarity, focus, and lightness of touch. He is writing about ‘Pluralism, relativism and objectivity’. But if you have read his interesting 2014 book Varieties of Logic then you won’t find much new here.

There follows a typically thought-provoking paper by the late Solomon Feferman on his so-called conceptual structuralism. But it is available on his website here: Logic, mathematics and conceptual structuralism.

Penelope Maddy follows with ‘A second philosophy of logic’, again written with her characteristic clarity. But as with Shapiro’s paper, if you have been keeping up with this  author’s recent work, there will be no surprises. Maddy herself says that the paper “reworks and condenses the presentation” of Part III of her earlier book Second Philosophy. So while the paper here might serve some as a useful introduction to her thinking, it doesn’t really add anything new.

The next paper is at least new, but I’m not sure what other virtues it has. Curtis Franks is out to defend the idea that ‘logic, in the vigor and profundity that it displays nowadays, does and ought to command our interest precisely because of its disregard for norms of correctness’. So he aims to ‘lead the reader around a bit until his or her taste for a correct logic sours’. (Note the ‘a’.) Well, the therapy didn’t work on this reader (though there some interesting but hardly original remarks on the relationship of classical and intuitionist logic). But you can try for yourself here: Logical nihilism.

There follows a piece by Mark Steiner on ‘Wittgenstein and the covert Platonism of mathematical logic’. Wittgenstein seems to make both radical criticisms of classical ideas and to want to leave everything as it is. Steiner explores how to reconcile these tendencies.  Just how much you get out of this will depend on how much residual interest you have in Wittgenstein on the philosophy of the mathematics-he-really-seems-not-to-have-known-much-about.

And that’s all the papers in the first part of the collection, ‘The Main Positions’. These are  all papers by old hands, Rush apart, who have already contributed books on logic and foundations of mathematics. It would have been much more interesting to hear new takes on old positions from younger philosophers.

The next part of the book consists on four random papers cobbled together under the catch-all ‘History and Authors’. The only interesting one is Sandra Lapointe writing about Bolzano’s Logical Realism.

Finally we have three papers on ‘Specific issues’ (now the editor is really struggling to find an organising principle for her heap of contributions). Graham Priest has a short and thin piece on Revising Logic. Jc Beall, Michael Hughes, and Ross Vandegrift contribute another short paper, on Glutty theories and the logic of antinomies (how is this relevant to the volume? — ‘We shall argue that [the logic] LA reflects a fairly distinctive set of metaphysical and philosophical commitments, whereas LP, like any formal logic, is compatible with a broad set of metaphysical and philosophical commitments’). Finally, Tuomas Tahko writes on The Metaphysical Interpretation of Logical Truth: you’ll only like this paper if you think there is anything to be said for slogans like ‘A belief, or an assertion, is true if and only if its content is isomorphic with reality.’ Which I don’t.

So a pretty disappointing collection, one way or another. Save your pennies for some good haddock.

8 thoughts on “The metaphysics of logic?”

    1. Paul Thom, Logic and its Objects, A medieval Aristotelian view (about Kilwardby — a new name to me!); and Gyula Klima, The Problem of Universals and the Subject Matter of Logic.

  1. One thing I’ve learned from your reviews is to be wary of collections. Almost all of your reviews of collections have been negative. Perhaps it’s even all: I don’t recall any exceptions.

    Since I still buy far too many books, I welcome anything that helps me resist a purchase, and seeing that a book is a collection now makes me wonder if buying it might be like buying a greatest hits album from a band that hasn’t had enough hits.

    1. I think I’ve been rather negative about many collections, yes, but in two different sorts of ways. Sometimes I’ve been plain negative: some collections just seem to be ill-conceived (e.g. a heap of papers from a conference, with not enough focus and with rather little quality control, and with Big Names often just recycling their familiar themes). Other times I’ve been, so to speak, regretfully negative: some collections can be more focused, with many serious papers that are worth engaging with, though in the end I was disappointeed and just didn’t get as much out of the collection as I’d hoped for.

      But it isn’t all bad news. Recent useful collections which I haven’t mentioned here include Patterson’s New Essays on Tarski and Philosophy, Ebert and Rossberg’s Abstractionism, Caret and Hjortland’s Foundations of Logical Consequence.

      1. Unfortunately (fortunately?), there’s another deterrent:

        New Essays on Tarski — £90, £85.50 on Kindle.

        Foundations of Logical Consequence — £64, £60.80 on Kindle.

        Abstractionism is at least less extreme: £50 RRP, but £34.77 on Amazon UK.

        1. You might well think that those prices explain why many people don’t feel too guilty about using the PDF depository of which we do not speak. I could not possibly comment.

  2. Peter, what are your thoughts on the book “Logic for Computer Science: Foundations of Automatic Theorem Proving” by Jean Gallier. It covers Gentzen’s sequent calculus, proves rigorously even the seemingly trivial lemmas and proves many theorems constructively by algorithm, making it unique among many logic books, so I wonder what your opinion is.

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