mathematics

Richard Montague

Richard Montague is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Richard Montague rather than just read about it. In short: Richard Merritt Montague (September 20, 1930 – March 7, 1971) was an American mathematician and philosopher who made contributions to mathematical logic and the philosophy of language. He is known for proposing Montague grammar to formalize the semantics of natural language.

Key takeaways

Richard Montague belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Richard Montague to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Richard Montague from memory before moving on to harder problems.

Reference excerpt

Richard Merritt Montague (September 20, 1930 – March 7, 1971) was an American mathematician and philosopher who made contributions to mathematical logic and the philosophy of language. He is known for proposing Montague grammar to formalize the semantics of natural language. As a student of Alfred Tarski, he also contributed early developments to axiomatic set theory (ZFC). For the latter half of his life, he was a professor at the University of California, Los Angeles until his early death, believed to be a homicide, at age 40.

Career At the University of California, Berkeley, Montague earned a BA in philosophy in 1950, an MA in mathematics in 1953, and a PhD in Philosophy in 1957, the latter under the direction of the mathematician and logician Alfred Tarski. Montague spent his entire career teaching in the UCLA Department of Philosophy, where he supervised the dissertations of Nino Cocchiarella and Hans Kamp. Montague wrote on the foundations of logic and set theory, as would befit a student of Tarski. His PhD dissertation, titled Contributions to the Axiomatic Foundations of Set Theory, contained the first proof that all possible axiomatizations of the standard axiomatic set theory ZFC must contain infinitely many axioms. In other words, ZFC cannot be finitely axiomatized. He pioneered a logical approach to natural language semantics that became known as Montague grammar. This approach to language has been especially influential among certain computational linguists—perhaps more so than among more traditional philosophers of language. In particular, Montague's influence lives on in grammar approaches like categorial grammar (such as Unification Categorial Grammar, Left-Associative Grammar, or Combinatory Categorial Grammar), which attempt a derivation of syntactic and semantic representation in tandem and the semantics of quantifiers, scope and discourse (Hans Kamp, a student of Montague's, co-developed Discourse Representation Theory). Montague was an accomplished organist and a successful real estate investor. He died violently in his own home; the crime is unsolved to this day. Anita Feferman and Solomon Feferman argue that he usually went to bars "cruising" and bringing people home with him. On the day that he was murdered, he brought home several people "for some kind of soirée", but they strangled him.

In popular culture Three novels have been inspired by the life and death of Richard M. Montague:

The Mad Man by American science fiction author Samuel R. Delany (1994) Less Than Meets the Eye by American philosopher David Berlinski (1994) The Semantics of Murder by Irish writer Aifric Campbell (2008)

See also American philosophy List of American philosophers List of unsolved murders (1900–1979)

Notes

References Feferman, Anita, and Solomon Feferman, 2004. Alfred Tarski: Life and Logic. Cambridge Univ. Press. Donald Kalish, and Montague, Richard, 1964. Logic: Techniques of Formal Reasoning. Harcourt, Brace, and Jovanovich. Donald Kalish, and Montague, Richard, and Mar, Gary, 1980. Logic: Techniques of Formal Reasoning (second edition). Oxford University Press. Montague, Richard, 1974. Formal philosophy : selected papers of Richard Montague / ed. and with an introd. by Richmond H. Thomason. New Haven: Yale Univ. Press. (1979 printing: ISBN 0-300-01527-5) Partee, Barbara H., 2006, "Richard Montague (1930 - 1971)" in Brown, Keith, ed., Encyclopedia of Language and Linguistics, Vol. 8, 2nd ed. Oxford: Elsevier: 255–57. Includes a bibliography of the secondary literature on Montague and his eponymous grammar.

External links Richard Montague at the Mathematics Genealogy Project "Montague, Richard (1930–1971) ." Encyclopedia of Philosophy, Encyclopedia.com. Montague Semantics at Stanford Encyclopedia of Philosophy RICHARD MONTAGUE 1930-1971 memorial page by Ivano Caponigro published on the fiftieth anniversary of his death That’s Just Semantics! (or, the Proper Treatment of Richard Montague in Literary Fiction) (Archived by Wayback Machine).

Worked examples

Example 1 — a first encounter with Richard Montague

Start with the simplest possible case. Write down what Richard Montague claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Richard Montague before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Richard Montague ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Richard Montague

In research: Richard Montague appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Richard Montague in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Richard Montague is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1930 births, 1971 deaths, 20th-century American LGBTQ people, so understanding it makes those chapters shorter.
In everyday life: Look for Richard Montague outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Richard Montague in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Richard Montague means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Richard Montague out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Richard Montague in simple terms?

Why does Richard Montague matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Richard Montague?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Richard Montague.