I asked three different questions on twitter recently. Pity not to pass on what I learnt in a slightly more long-lasting form! In ascending order of likely interest:
- How do you pronounce “wff” in the classroom? Approximately woof seemed the majority view. Which is how I’ve always pronounced it. Some, oddly to my mind, prefer wiff. Some, apparently, spell it out w-f-f. Joel Hamkins wondered why we should use “wff” at all – why not just “formula”? Which is a very good question. The habit of a lifetime makes me a bit resistant to change, however!
- What’s a neat example of a written sentence with different meanings in different languages? — (approximate homophones are familiar, but I wanted a nice example that worked on the page). Thomas Brouwer offered the lovely “David Hume was slim”. Falsely saying in English that the bon viveur was svelte of figure, truly saying in Dutch that he was smart!
- “How many books has J.K. Rowling sold?”, “How many books has J.K. Rowling written?”. We need the distinction between tokens and types to properly construe the likely questions here. And we all know that Peirce was responsible for the nowstandard terminology for this distinction. But surely the distinction is an old one: who first made it (whatever the terminology)? Surely the stoics or other Greek writers talking about words, sentences, lekta, etc. would have somewhere made a type/token distinction? Or what about the medieval writers on logic? My learned twitter friends had no specific pointers to give. Which was a real surprise. What were we missing?
11 thoughts on “Three tweets wiser”
Curry used “wef” instead of “wff”, stating as his reason for this terminological choice that “‘wef’ has the advantage of being pronounceable” (Foundations of Mathematical Logic, p. 54, footnote 2).
I would have thought that a type/token distinction would have naturally arisen in discussions of sameness and difference. “Plato there has the same iPhone as Alcibiades” “You mean he stole it?”. “No, no the same model.” “But, it’s white…” Not sure where the relevant text is…
There is the distinction between Original and Copy figuring frequently in Plato, with echoes of still more ancient voices. Aristotle on Categories gives an example where a word for both a live animal and its true-to-life image must be shorn of ambiguity before fit to appear in a court of logic. Aristotle on Interpretation distinguishes objects from their copies, images, likenesses in the mind.
Yes, those distinctions are made — but arguably different distinctions from type/token (and the lack of discussion of the distinctions between the distinctions, if such lack there be, is itself interesting!).
Going back to Aristotle:
“Words spoken are symbols or signs (symbola) of affections or impressions (pathemata) of the soul (psyche); written words are the signs of words spoken. As writing, so also is speech not the same for all races of men. But the mental affections themselves, of which these words are primarily signs (semeia), are the same for the whole of mankind, as are also the objects (pragmata) of which those affections are representations or likenesses, images, copies (homoiomata).” (Aristotle, De Interp. i. 16a4).
From a Peircean semiotic perspective we can distinguish an object domain and a semiotic plane, so we can have three types of type/token relations: (1) within the object domain, (2) between objects and signs, (3) within the semiotic plane. We could subtilize but this much is enough for a start.
Type/token relations of type (1) are very common in mathematics and go back to the origins of mathematical thought. These days computer science is rife with them. I have seen a lot of confusion about this in Peircean circles as it’s not always grasped that type/token relations are not always all about signs. It can help to speak of types and instances or instantiations instead.
Aristotle covers type/token relations of types (2) and (3) in De Interp., the latter since he recognizes signs of signs in the clause, “written words are the signs of words spoken”.
I don’t understand what 2 is supposed to be about. By “a written sentence with different meanings in different sentences” did you mean in different languages? If you didn’t, then using different languages seems cheating to me. But also, if you didn’t mean in different languages, what would give the same sentence different meanings? A context of some sort, I suppose. But what sort?
For 3, we can use the distinction between tokens and types to construe the likely questions, but do we need it? Or might the problem also be solved in some other way? I just looks like two different meanings of “books” to me, understandable without knowing anything about tokens and types.
I did indeed mean in different languages. I wanted homographs rather than homophones, to put it more carefully!
As to the “books” — well, to be sure, two different but related meanings (referring to the works, to the copies). But you’d have expected to find discussion of this kind of homonym in the ancients (compare Aristotle on “healthy”, which we use with different but related meanings). Odd if true that the ancients didn’t discuss somewhere this other sort of case of different but related meanings and give an account of it.
I’m guessing the pronunciation wiff, at least in the U.S., is probably influenced by the Wff’n Proof Game, punning in turn on Whiffenpoof.
I played with wff ‘n proof back in high school. Pronounced it *woof*.
And here’s a semi-response to #2:
It doesn’t help much with the question of semiogenesis, which is no doubt lost to the mists of history, but Peirce being Peirce naturally distinguished three modes of signs in this respect: Tone, Token, Type. Here’s a link to a sample of excerpts I collected:
☞ Tone, Token, Type