The Greeks win (2)

On the question of metavariables — relaxed italics versus Greek letters. Which do you prefer? Those who voted in the poll  (and too late, I realized I should have had added a  “really don’t care” option), preferred Greek letters by 4 to 1.

Not just for that reason, I decided a couple of weeks ago (before my brain was shut down by a cold) to go for Greek letters. And returning now to the decision, yes, that is still what I am going to do.

Or rather, I am going to do something just a bit more complicated — but I hope even better than an always-italics or an always-Greek  solution.

In the very early chapters of my logic book where everything is still very informal, arm-waving, motivational, I continue to use talk of patterns of argument like  ‘All F are G, n if F, so n is G‘ in that familiar and relaxed philosophy-classroom way which is surely good enough for very introductory purposes. Though I soon point out it is of course arbitrary what we use for placeholders, so long as patterns of recurrence stay the same.

I also then point out quite quickly that it is a bit murky how such informal notation is used (are we representing patterns in the surface form of everyday arguments or patterns in some supposed underlying logical form or what?). We don’t have to worry about this matter much for very introductory purposes (just as we skim over issues about sentences vs propositions, for example).

However, after the half-dozen intro chapters, we very quickly go formal in IFL, saying that we are going to be dealing with everyday arguments by a two-step process: we regiment these everyday arguments into a nice suitable formal language, and then develop tools for assessing arguments in these formal languages. So we quickly find ourselves talking about formal languages and wanting to talk e.g. about patterns of argument in these formal languages — and now I adopt the convention that placeholders/metavariables added to English to help us talk about wffs and other expressions of our formal languages will be Greek letters. And we have a perfectly precise story about what these variables run over (everything is cleanly superficial and syntactic).

So, in short, italic letters used in a loose but good-enough way for relaxed pre-formal use (as in our philosophy lectures when sketching the form of an argument, say); Greek letters are used when we really are talking about formal languages. Neat and perspicuous. No? (Well the proof is in the pudding, but having done some rewriting along this plan, I think it works well!)