A small matter. But an intro logic book needs to have a policy on whether mentioned formulae get enclosed in quotation marks. IFL1 took a sternly conservative line on this, leading to somewhat unsightly rashes of quotation marks. I originally was going to carry this over to IFL2; but I have belatedly decided on a much more relaxed policy, which will be followed in future draft chapters (a policy more in keeping, indeed, with usual mathematical practice, which is a major plus). I was uncomfortable about the amount of quotational clutter in IFL1, and I was spurred on in part by some blunt remarks about not fussing over quotation in §9.1.2 of David Makinson’s Sets, Logic and Maths for Computing.
Having made the decision, I was interested to check back to see what other intro textbooks said about quotation, use and mention. There were some real surprises. For example:
- My namesake Nick Smith, in his (in many ways excellent) Logic: The Laws of Truth, doesn’t use quotation marks round formulae. Fair enough — but he never discusses this decision: in fact in his long book, he rather oddly doesn’t talk about quotation conventions, use and mention at all.
- Likewise, Barker-Plummer, Barwise and Etchemendy in Language, Proof and Logic also do not use quotation marks around formulae — and the only sort of quotes they actually mention in the book are scare quotes.
- Greg Restall’s Logic an Introduction doesn’t use quotes either, and again doesn’t discuss the issue. He perhaps has the excuse of writing a short book, but …
- Just the same goes for Virginia Klenk’s much longer, and quite popular, book Understanding Symbolic Logic. No quotation marks round formulae, and again no discussion of quotation conventions. The reader is just presented with lopsided sentences like this: The correct symbolisation for “Nixon is not president” would be ∼N. I can’t find any account of why the English sentence gets quotation marks and the formal one doesn’t!
- Looking back at an older book which also eschews the use of quotation marks, Neil Tennant’s exceptional Natural Logic, I was surprised to find that he too — a serious philosopher of logic — again doesn’t explicitly discuss quotation, use and mention at all.
- Just the same goes too, I think, for Jan von Plato’s much more recent Elements of Logical Reasoning.
I do find this sort of silence really quite strange, however. Ok, we can exaggerate the dangers of outright use/mention confusion: but equally, you would expect introductory texts to have something to say, at least a short Quinean sermon to the troops on the topic!
Here then are three intro logic texts that do use quotation marks round inline formulae (a lot!) and do say something about the policy:
- Paul Teller’s A Modern Formal Logic Primer uses quotes but initially only gives a line of explanation on p. 5. It isn’t until p. 159 of the second volume that we get a fuller (and not wonderfully crisp) explanation of the books policy.
- Warren Goldfarb is brisker and (as you would expect) very clear in §12, ‘Use and Mention’, of his Deductive Logic. He unusually uses double quotes round non-displayed, inline, formulae. (You might have predicted that this would lead to rather messy-looking pages, but such is the text design of the book that it manages not to.)
- For our last example, let’s take Bergmann, Moor and Nelson’s weighty The Logic Book. In my third edition copy, they have a clear page-and-a-bit on object language and metalanguage, use and mention. And they adopt a consistent policy of using quotation marks round inline formulae. To my eyes this makes for some messy pages (though to be sure, aesthetics isn’t everything!).
So on the one hand, books in the first group say nothing about use/mention, and don’t use quotes; and books in the second group both say something about use/mention and adopt a policy of always using explicit quotes when we are mentioning formulae.
But there’s obviously another possible line. Give the Quinean sermon, saying something about use/mention; say something about the official convention of using quotation marks on Sundays when we feel the need to be fully explicit that what we are doing is mentioning formulae; but then avoid ugly rashes of quotes by adopting a more relaxed weekday policy, and allowing ourselves to drop explicit quotation marks in practice when it is clear what is going on.
For example, suppose we follow Barker-Plummer, Barwise and Etchemendy in using a characteristic font for formal expressions — e.g. using sans serif for all formal expressions, as against ordinary roman font for our English metalanguage. Then an English sentence that embeds expressions in sans serif font can, by default, be taken as mentioning those expressions (this is, in effect, BBE’s policy — though I think unannounced, and not quite consistently applied ): it is then overkill to use quotation marks as well. (It is perhaps not an accident that the three books I mentioned that do use quotation marks to set off mentioned formulae do not have a special font convention for formal expressions, so there is more need for some way of setting off mentioned inline expressions from the surrounding text.)
In IFL1 I was guilty of overkill — using sans serif font for expressions in formal languages, and putting these sans serif expressions in quotes when embedded in English text (where they must be being mentioned, not used). In IFL2, I again use sans serif font for expressions in formal languages. But after talking about object language and metalanguage, use and mention, I propose a default convention that such expressions occurring inline, embedded in metalinguistic text, are mentioned. Quotes are kept for use when a explicit reminder that expressions are being referred to is helpful. The resulting text looks cleaner and in line with the usual practice in more advanced mathematical logic. What’s not to like?