mathematics

J. C. C. McKinsey

J. C. C. McKinsey 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 J. C. C. McKinsey rather than just read about it. In short: John Charles Chenoweth McKinsey (30 April 1908 – 26 October 1953), usually cited as J. C.

Key takeaways

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

Reference excerpt

John Charles Chenoweth McKinsey (30 April 1908 – 26 October 1953), usually cited as J. C. C. McKinsey, was an American mathematician known for his work on game theory and mathematical logic, particularly, modal logic.

Biography McKinsey received B.S. and M.S. degrees from New York University and a Ph.D. degree in 1936 from the University of California, Berkeley. He was a Blumenthal Research Fellow at New York University from 1936 to 1937 and a Guggenheim Fellow from 1942 to 1943. He also taught at Montana State College, and in Nevada, then Oklahoma, and in 1947 he went "to a research group at Douglas Aircraft Corporation" that later became the RAND Corporation. McKinsey worked at RAND until he was fired in 1951. The FBI considered him a security risk because he was a homosexual, in spite of the fact that he was an open homosexual who had been in a committed relationship for years. He complained to his superior "How can anyone threaten me with disclosure when everybody already knows?" From 1951 he taught at Stanford University, where he was later appointed a Full Professor in the Department of Philosophy, where he worked with Patrick Suppes on the axiomatic foundations of classical mechanics. He committed suicide at his home in Palo Alto in 1953.

Selected works

Book McKinsey, J.C.C. (2003). Introduction to the Theory of Games. New York: Dover Publications. ISBN 978-0-486-42811-6. (originally publ. McGraw-Hill, 1952)

Papers McKinsey, J. C. C. (1934). "A reduction in number of the postulates for C. S. Lewis' system of strict implication". Bull. Amer. Math. Soc. 40 (6): 425–427. doi:10.1090/s0002-9904-1934-05881-6. MR 1562873. S2CID 120247475. McKinsey, J. C. C. (1935). "On the independence of undefined ideas". Bull. Amer. Math. Soc. 41 (4): 291–297. doi:10.1090/s0002-9904-1935-06074-4. MR 1563075. McKinsey, J. C. C. (1936). "Reducible Boolean functions". Bull. Amer. Math. Soc. 42 (4): 263–267. doi:10.1090/s0002-9904-1936-06285-3. MR 1563282. McKinsey, J. C. C. (1936). "On Boolean functions of many variables". Trans. Amer. Math. Soc. 40 (3): 343–362. doi:10.1090/s0002-9947-1936-1501878-6. MR 1501878. McKinsey, J. C. C. (1941). "A solution of the decision problem for the Lewis systems S2 and S4, with an application to topology." The Journal of Symbolic Logic. 6 (4), 117–124. doi:10.2307/2267105 "A New Definition of Truth". Synthese. 7: 428–433. 1948. McKinsey, J. C. C. (1952). "Some notions and problems of game theory". Bull. Amer. Math. Soc. 58 (6): 591–611. doi:10.1090/s0002-9904-1952-09648-8. MR 0052748. McKinsey, J.; Sugar, A.; Suppes, Patrick (1953). "Axiomatic foundations of classical particle mechanics". Journal of Rational Mechanics and Analysis. 2 (2): 253–72. doi:10.1512/iumj.1953.2.52012. "Philosophy and the axiomatic foundations of physics". Proceedings of the 11th International Congress of Philosophy. 6: 49–53. 1953.

With Alfred Tarski McKinsey, J. C. C., Tarski, Alfred (1944). "The algebra of topology." Annals of mathematics, 141–191. https://doi.org/10.2307/1969080. McKinsey, J. C., Tarski, Alfred (1946). "On closed elements in closure algebras." Annals of mathematics, 122–162. https://doi.org/10.2307/1969038. McKinsey, J. C. C.; Tarski, Alfred (1948). "Some theorem about the sentential calculi of Lewis and Heyting". Journal of Symbolic Logic. 13 (1): 1–15. doi:10.2307/2268135. JSTOR 2268135. S2CID 38559151.

References

Worked examples

Example 1 — a first encounter with J. C. C. McKinsey

Start with the simplest possible case. Write down what J. C. C. McKinsey 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 J. C. C. McKinsey 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 J. C. C. McKinsey 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 J. C. C. McKinsey

In research: J. C. C. McKinsey 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 J. C. C. McKinsey 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: J. C. C. McKinsey is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1908 births, 1953 deaths, 1953 suicides, so understanding it makes those chapters shorter.
In everyday life: Look for J. C. C. McKinsey 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 J. C. C. McKinsey in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what J. C. C. McKinsey 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 J. C. C. McKinsey out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is J. C. C. McKinsey in simple terms?

John Charles Chenoweth McKinsey (30 April 1908 – 26 October 1953), usually cited as J. C.

Why does J. C. C. McKinsey 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 J. C. C. McKinsey?

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 J. C. C. McKinsey.