mathematics

Warren Goldfarb

Warren Goldfarb 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 Warren Goldfarb rather than just read about it. In short: Warren David Goldfarb (born 1949) is an American logician and philosopher who is Walter Beverly Pearson Professor of Modern Mathematics and Mathematical Logic, emeritus, at Harvard University. He specializes in the history of analytic philosophy and in logic, most notably the classical decision problem.

Key takeaways

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

Reference excerpt

Warren David Goldfarb (born 1949) is an American logician and philosopher who is Walter Beverly Pearson Professor of Modern Mathematics and Mathematical Logic, emeritus, at Harvard University. He specializes in the history of analytic philosophy and in logic, most notably the classical decision problem.

Education and career He received his A.B. and philosophy Ph.D. from Harvard University under the supervision of Burton Dreben, and has been a member of the Harvard faculty since 1975. He received tenure in 1982, the only philosopher to be promoted to tenure at Harvard between 1962 and 1999. Prof. Goldfarb is also one of the founders of the Harvard Gay & Lesbian Caucus and was one of the first openly gay Harvard faculty members.

Philosophical work Goldfarb was an editor of volumes III–V of Kurt Gödel's Collected Works. He has also published articles on important analytic philosophers, including Frege, Russell, Wittgenstein's early and later work, Carnap and Quine.

Selected publications

Books The Decision Problem: Solvable Classes of Quantificational Formulas, Addison-Wesley, 1979. ISBN 0-201-02540-X (with Burton Dreben). Deductive Logic, Hackett, 2003.

Articles "Logic in the Twenties: the Nature of the Quantifier," The Journal of Symbolic Logic (1979) "I want you to bring me a slab: Remarks on the opening sections of the Philosophical Investigations," Synthese (1983) "Kripke on Wittgenstein on Rules," The Journal of Philosophy (1985) "Poincare Against the Logicists," in History and Philosophy of Modern Mathematics (University of Minnesota Press, 1987) "Wittgenstein on Understanding," Midwest Studies in Philosophy (1992) "Frege's Conception of Logic," in Future Pasts: The Analytic Tradition in the 20th Century, Juliet Floyd and Sanford Shieh, editors (Oxford University Press, 2001) “Rule-Following Revisited," in Wittgenstein and the Philosophy of Mind, Jonathan Ellis and Daniel Guevara, editors (Oxford University Press, 2012). "The Undecidability of the Second-Order Unification Problem" (PDF). Theoretical Computer Science. 13: 225–230. 1981. doi:10.1016/0304-3975(81)90040-2.

References

External links Goldfarb's web page at Harvard University

Worked examples

Example 1 — a first encounter with Warren Goldfarb

Start with the simplest possible case. Write down what Warren Goldfarb 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 Warren Goldfarb 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 Warren Goldfarb 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 Warren Goldfarb

In research: Warren Goldfarb 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 Warren Goldfarb 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: Warren Goldfarb is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1949 births, 20th-century American LGBTQ people, 21st-century American LGBTQ people, so understanding it makes those chapters shorter.
In everyday life: Look for Warren Goldfarb 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 Warren Goldfarb in 20 minutes

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

Frequently asked questions

What is Warren Goldfarb in simple terms?

Why does Warren Goldfarb 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 Warren Goldfarb?

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 Warren Goldfarb.