[Corpora-List] ad-hoc generalization and meaning

[John F. Sowa]

Rob,

Montague's system is first and foremost a very rigid system
of logic, and his grammar is best viewed as an English-like
"syntactic sugar" for his logic.

 > Do I need to map from one set of rules to another? Can't I
 > just interpret the syntactic rules directly as some kind of
 > logic? These are formal systems, after all, just combinations
 > of symbols. It might not be the logic we are used to, but
 > doesn't any combination of symbols define a "logic" of its own?

To start with the last question, the short answer is "No!"

The longer answer is that logic is intimately connected with
the distinction between what is true and what is false about
the domain of discourse -- usually some aspect of the real world,
but possibly some abstract or imaginary world.

In versions with more than two truth values, you can generalize
logic to handle an unknown truth value in the middle or to modal
versions with distinctions of what is necessarily or possibly
true or false.

But an arbitrary string of symbols with no criteria of what
would be true or false is definitely not a logic and most
definitely not Montague's particular version of logic.

To answer your first question, if you have a more generalized
way of handling grammar that would permit more kinds of
sentences to be admitted as acceptable than Montague would
admit, you would have to specify how those additional sentences
could be mapped to some formula in his logic.

  1. Unless you did that, those additional sentences would have
     no semantic interpretation.

  2. And if you did that, all you would accomplish is to define
     those new sentences as synonymous ways of expressing the
     same semantics as other English-like sentences that were
     already in Montague's very tiny subset of English.

In other words, the exercise you propose, even if carried
to completion, would be a useless definition of synonyms.

 > To cut to the chase a little, in going from an idea of syntax
 > based on fixed grammatical patterns to an idea of syntax based
 > on ad-hoc generalizations, haven't we brought syntax into much
 > closer correspondence with the idea of meaning associated with
 > Wittgenstein's "games", as described in your own article:

Not unless you are prepared to specify the details of a completely
new Wittgensteinian theory of logic as a supplement to that tiny
subset of logic supported by Montague.  But that is another very
difficult task to accomplish.

 > In short, can't we now have, perhaps, the close correspondence
 > between syntax and semantics hypothesized in a Montague grammar,
 > but also have the power and flexibility of an ad-hoc semantic
 > system of the kind of Wittgenstein's games?

You can't get something for nothing.  Just providing a more
robust syntax that assigns parse trees to more sentences won't
do anything to give you a new system of semantics.

John



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