# How do you like your metavariables?

Ok, logic people: it’s time to vote on a Grave Matter of Great Pedagogic Import!

So here I am, revising my intro logic book — which, recall, is intended for first year philosophers. I try to get things fairly precise, at least when we get down to formal business after the initial informal faffing around, but I  also aim to keep things unscary.

I’m still a bit torn about what to use as metalinguistic variables.

In the first edition of my book, I use a sans serif font for wffs in the formal languages, as in: $\mathsf{(P \lor Q)}$,  $\mathsf{\forall x(Fx \to Gx)}$.

Then I use serif italic for metavariables, e.g. as in ‘A’, ‘Fn’.  Though on the board in class, some years I’d actually use Greek letters for metavariables.

• Pro using italics: Familiar italic type  makes the book look rather less mathematical, rather less daunting (most philosophers are neither classicists nor mathematicians — so initially $\varphi(\xi)$ is about as friendly as ‘squiggle squoggle’).
• Pro using Greek: It’s the convention in more advanced texts so you might as well get used to it straight away. And for lecturers writing on the board, and for students taking notes, keeping track in your handwriting of ‘ordinary letters’ (for formal languages) vs Greek letters (metalinguistic) is much easier than trying to mark the distinction between e.g. upright and sloping letters.

In writing the first edition, friendliness-on-the-printed-page was the winning consideration. I still lean in that direction. But I’m interested to know what you think. So here is a poll (vote thinking of the interests of likely readers of an intro text!).

Greek letters for metavariables for beginning logic, or italic letters?

View Results

By all means add further thoughts in the comments below, as obviously this is a Very Serious Issue.

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### 8 Responses to How do you like your metavariables?

1. The “it’s how it is in future books” and “this is how the lecturer will write it on the board” arguments are VERY strong in my opinion.

2. David Auerbach says:

As you know, I’m with the Greek contingent. (very minor btw: ‘α’ and ‘β’ turn out to be easier for students than ‘φ’).
A compromise position would be what I think of as a very scripty Roman font, all curves and curlicues. Those at least are easier to draw on the board and students’ homework than serifs.

• David Auerbach says:

Oh, I should add, in the interests of full disclosure, that students at NCSU are a) familiar with fraternities (the Greeks) and b) often STEM majors who have seen Greek letters spattered here and there in their texts.

3. As a first-year student presently taking a philosophical logic course, but *also* as a software developer of 15 years experience who does a fair amount of algebraic math, I lean toward italic latin characters. For two reasons:

1. It’s what I’m already used to, from years of computer-centric maths.
2. It’s easier for me to code the examples from your book, if I don’t have to convert them first, into computer-centric terms.

4. There are alternatives other than the two advertised. Personally, I favour a pragmatic one, along the following ‘mixed’ lines:

In propositional logic: Use sample sentence letters p, q, r,… also as metavariables ranging over all sentence letters; use Greek alpha, beta etc as metavariables ranging over all formulae.

In first-order logic: use sample individual variables, individual constants, and predicate and relation letters also as metavariables, each ranging over all of its respective class of signs, and compose them to form metavariables ranging over all atomic formulae. Again, use Greek alpha, beta etc as metavariables ranging over all formulae.

Benefits; Keeps notation and funny symbols to a minimum, and focuses attention on essential ideas rather than on fussy book-keeping.

Costs: Some may fear that this dual role for certain letters, as signs of the object language and as metavariables ranging over all signs of the category they come from, will leave students confused about the distinction between object and metalanguage. My experience is that this is not the case at all. Students easily see that a single sign can have two different but related roles, just as a single actor can have two different parts in a play, or Teresa May can sometimes speak for the government and sometimes for herself alone. Instead of asking “Is this letter a sign of the object language or of the metalanguage?”, they learn to ask “Is this sign, in the remark I am reading, playing an object-language role or a meta-language role?”

5. Philip Papayannopoylos says:

Although Greek myself (and with a physics background), I still get intimidated (or, at least, alarmed), when I see Greek letters coming on the next page. Italics are indeed way friendlier, and when I read the IFL book (twice, cover to cover) in the past, it didn’t feel like a scary/mathematics book at all. So I voted for italics here, no matter what it is to come in the more advanced books.
Besides, not all philosophy students will have to go to an advanced text after IFL, and those who will, they will anyways be more mathematically inclined and/or psychologically prepared for scary symbols.

6. Daryl Sidle says:

For a student trying to copy the font distinction between italic and non italic into notes is well nigh impossible. Greek letters are much easier to take from the board into a notebook.

7. Would it be completely mad to use unsubscripted x, A, and so on for the meta-variables and subscripted ones ($x_1, x_2, p_1, p_2, A_1, B_1$) within the formal language? It might not be, given that when you set up a formal language, you probably would specify subscripted letters so as to be sure that you would not run out of variables, sentence letters, predicate letters and so on.