Roro, et al:

I am reading a short paper on his theories. It seems quite complicated. Can you tell me if it's worth the effort?

Montague said: "There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of languages within a single natural and mathematically precise theory."

I wonder if he is just wishing that natural language were as analyzable as logic.
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Hello, rvw. Yes, indeed, it's quite complicated. It's a whole system of logical language. I learned it stepwise, from traditional propositional logic, predicate logic, two-sorted logic, modal logic, tense logic, type theory, categorial grammar, intensional logic (they all are simple systems of formal language, so it's not difficult at all to acquire them). Montague grammar is a combination of these. Once you've learned basics and got a perspective, then you would understand these formal methods are considerably flexible methods. If you have a concrete (semantic) question, it will be useful. I don't know ... perhaps useful only for special linguistic (semantic) purpose.

So if you don't have special linguistic questions now, I'd advise you strongly not to try to acquire it.
(Unfortunately I had.)

rvw, I understand your question very well: Montague died at an early age, so.. what did he envisaged in the future development...? what kind of expansion of his framework in order to analyze natural languages?

But I think you should take his word conversely: his intention was not to analyze natural language itself, but to expand logical language to analyze a (fundamental) fragment of natural language.

Did I answer to your question...? Are there another questions...? Thank you for your question!


Perhaps each of our 'languages' is best suited for its use. Roughly in increasing order of unambiguity and systematization:

legal prose
philosophical prose
scientific prose
computer languages

Each is appealing in its way. In poetry, Robert Frost could say:

Two roads diverged in a wood,
and I took the one less traveled by,
and that has made all the difference.

In mathematics, one can write the formula for the Fourier Series of a square wave.

Sometimes in prose we pose arguments and need to call in the expertise of logic. And there are surely other overlapping areas.

But by and large a language evolves to communicate what its users want and need to communicate. Would it not be a mistake to give up prose for predicate logic or some such?

I would appreciate your thoughts.

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Dear rvw, your point of view toward languages is beautiful. I need some time to answer to your question.
So for the meantime I'd like to give you a translation of my favorite tanka:

Today, too, I can sleep
after my efforts to stay
on my best behaviour,
not having infected
others with my loneliness.

I'll answer to your question, from my point of view. Roro
Hello, rvw, sorry for my slow reply ... I got frightened to answer to your huge question ... I'm not qualified yet! ... so please bear in mind this is only some of my personal, shortsighted ideas.

Can I rephrase your question as: why do we need this formal language? We can pose arguments, communicate, express, discuss without it. (This way of presenting the question is not beautiful, but...)

This is actually one of frequent asked questions, and I can understand the feeling of embarrassment of questioners. It's very easy ... they say ... to understand the meaning of some expressions. Why on earth do we need completely another formal language to understand our everyday-used natural language?

I think we DO need some elaborated tool to analyze the meaning, because the meaning itself is very, very vague, unidentifiable thing. It's flexible and fragile, so we need some keen tool to analyze its structure.

(Just like ... we cannot cut a tomato with another tomato. If we want to know the inner structure of it, we need some keen tool.)

There's another reason. D.R.Dowty once wrote:
... the goal of formalization in linguistic research is to enable subsequent researchers to see the defects of an analyses as clearly as its merites; only then can further progress be made efficiently.

I have experienced when I read some paper written in formal approach I can understand the author's point, very clearly. It was a kind of surprise for me. This is, too, one of reasons why I use formal methods.
Hello, rvw. I'd like to add just a few words.
I remember reading in Gamut1991 roughly such an exciting passage:

G.W. Leibniz (1646-1716) had proposed a program for logic and developed ideas of a universal language, in which thought could be represented directly, without any of the ambiguities. Frege's predicate logic is a more powerful language system, and Montague Grammar is a much more productive paradigm which can give a semantics for natural language. (This is a very rough paraphrase ... I cannot find the exact place in Gamut now...)

And I think ... a truth-conditional semantics which is based on a model is similar to an axiomatic corollary in mathematics. ( I haven't got any conformation, maybe there's inaccuracy in my BLOCKED EXPRESSION

Here's another translation of tanka:

Ever since I placed
a yellow birdcage beside
the open window,
I keep imagining that
some bird will come and live there.
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Dear Roro,

As you said in a previous post, this is a "huge question." I think the answer will come from many fields: linguistics, philosophy, psychology, physiology, neuro-science....

Our language and our thinking are inherently and necessarily vague. If I ask for a hammer, I will be happy to get just about any hammer, not just a particular one. If I see an object in the distance at twilight, my brain goes through its library of known objects and may or may not settle on one without additional sensory input.

I looked up "vagueness" in the on-line Stanford Encyclopedia of Philosophy. Vagueness is a subject unto itself. The article also has a link to a bibliography on vagueness. At the head of that bibliography is a quote from Wittgenstein:

It is clear that every sentence in our language ’is in order as it is’. That is to say, we are not striving after an ideal, as if our ordinary vague sentences had not yet got a quite unexceptionable sense, and a perfect language awaited construction by us. - On the other hand it seems clear that where there is sense there must be perfect order. -- So there must be perfect order even in the vaguest sentence.

For remember that in general we don't use language according to strict rules - it hasn't been taught us by means of strict rules, either. We, in our discussions on the other hand, constantly compare language with a calculus proceeding according to exact rules.

I gather that a great deal of research on language is currently being carried out. Montague Grammar and every other discipline will likely make helpful contributions. I look forward to learning more.
Thank you for the delightful tankas.

Here is one of my favorite quotations -- from William Butler Yeats:

Though I am old with wandering
Through hollow lands and hilly lands,
I will find out where she has gone,
And kiss her lips and take her hands;
And walk among long dappled grass,
And pluck till time and times are done
The silver apples of the moon,
The golden apples of the sun.

(Hard to express in a predicate calculus!)
... thank you ... !
If you are interested in this matter, I will be very glad to help you.
Above all, it's useful for me, before everything. ... thank you again ...
(Hard to express in a predicate calculus!)

How true it is. I wanted to say the same thing, but I couldn't find an appropriate word. Your favorite quotations are fabulous ...! J.Brodsky once wrote ... :

That's what's interesting about poets: after them you don't feel like talking. That is, don't feel as if you can.
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