I’m rather fond of this quotation from Richard Montague. When I mention it to people, it tends to elicit either a hearty nod of agreement or a puzzlement about why anyone would ever think it. He says:
I reject the contention that an important theoretical difference exists between formal and natural languages. … Like Donald Davidson, I regard the construction of a theory of truth — or rather, of the more general notion of truth under an arbitrary interpretation — as the basic goal of serious syntax and semantics.
That is from the opening of his “English as a Formal Language.” I usually only remember the first sentence, which is what gets the reactions. The second sentence quoted surprised me a bit, but it probably should not have. Montague worked on paradoxes as well as general topics in semantics. It is, perhaps, surprising that a theory of meaning does not come in as the basic goal of serious semantics. That might be slightly further on in the article.
More substantive stuff to come later this weekend.
Words and Other Things 
3 comments
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March 20, 2009 at 10:58 am
Colin
I’m less confused by the thought expressed here that ‘formal’ and ‘natural’ are just types of languages, hence no important theoretical difference between them. What does confuse me is the claim that English *is* a formal language. Now, if I recall that’s not exactly how Montague puts the point, but his claim is something like: the formal language with its formal semantics developed in this paper *is* a fragment of English. What in the world does that mean?
March 20, 2009 at 12:29 pm
Bryan
Thanks for the great quote. Attitudes toward this claim really do seem to split analytic philosophy down the middle. I wonder what Montague might count as an “important theoretical difference”. A formal language minimally includes:
1. An alphabet (the letters and symbols);
2. A set of sentences defined over that alphabet (the well-defined sentences);
and I assume that Montague was also concerned with:
3. A deductive system for the formal language (axiom set + inference rules);
4. A semantics (assignments of truth values to sentences)
I assume that non-Montague users of English don’t usually express their language with a formal construction like 1-4, or even behave as if they were using a formal language. That’s certainly a difference. But, maybe it’s not an “important difference”. I suppose Montague thinks that English still has a structure that can still be specified by 1-4.
What I don’t get is the standard by which one could establish that some specification of 1-4 specifies the structure of English. How could one test or verify that claim? Is it by looking at how people actually speak? — That might work, but I’m suspicious that they don’t all agree about 1-4. And if it’s not that, then how do we have access to any fact of the matter?
March 20, 2009 at 3:34 pm
Shawn
This is not a proper response to the comments, which hopefully I will be able to provide later, but here is the bit Colin alludes to.
The formal language with the formal semantics is a fragment of English.