|[Life & work] | [On-line introductions]|
|LIFE & WORK|
Born in London in 1925, Michael Anthony Eardley Dummett attended Sandroyd School in Wiltshire and Winchester College, after which he served in the armed forces from 1943 to 1947. On his return after the war, he went up to read P.P.E. at Christ Church, Oxford, graduating in 1950, when he won a Fellowship at All Souls College, Oxford. He also taught philosophy part-time at Birmingham University for a year (1950-51), and in 1962 was appointed Reader in the Philosophy of Mathematics at Oxford. In 1979 he was elected Wykeham Professor of Logic at Oxford, and he held the chair until his retirement in 1992. Over the years he has held visiting positions at Universities around the world. He and his wife Ann have also involved themselves in social causes, especially the fight against racism and the issue of immigration, on both of which he has written. He has also found time to publish a number of works on the Tarot.
Dummett has made significant contributions to many areas of philosophy, especially the philosophy of language, philosophical logic, and metaphysics, but his first important work was Frege: Philosophy of Language (1973). He has continued to work and write on Frege throughout his career, and is one of the most important and influential Fregean scholars in the world; we owe it to Dummett, in fact, that Frege's work is available to English-speaking philosophy in the way that it now is.
Language is at the heart of Dummett's philosophical work. Indeed, he claims that philosophy before Frege was flawed by its insistence on the primacy of epistemology instead of grounding itself in the study of language. This is a controversial view on many counts, not least because Frege himself seems not to have noticed that he was concerned with language (he thought of himself as dealing with logic and thought).
For Dummett, the debate between realists and anti-realists is in fact a debate about semantics — about how language gets its meaning. The realist holds that all meaningful statements are either true or false (this is the principle of bivalence), and that this is independent of us. Thus, a realist about the past will hold that "Ethelred the Unready had indigestion on his twenty-first birthday" is either true or false, even though there.s no way to tell which. The anti-realist, however, holds that the truth of a statement is a matter of the evidence for or against it — the conditions under which the statement would be assertible or deniable. Because we can't offer any evidence for or against the statement about Ethelred, it's neither true nor false. This denial of the principle of bivalence links Dummett's views on language and truth to his account of mathematics.
Dummett is largely responsible for the continuing interest in a certain anti-realist account of mathematics: intuitionism. This was first put forward by the Dutch mathematician L.E.J. Brouwer (1881.1966), and holds that mathematical objects are not real and independent of us, as Platonist realists hold, but constructed by mathematicians. Thus a mathematical statement is simply the report by a mathematician of what she's constructed, and is true or false just in case there's either a proof or disproof of it. In cases where no such proof or disproof exists, the statement has no truth value — is neither true nor false.
In fact Dummett didn't accept Brouwer's version of intuitionism, as it relied upon the private objects and operations in the minds of mathematicians. Rather, he took over the basic approach, but argued that what counts for the truth of a mathematical statement is that there be a proof of it; it then becomes the mathematician's job to construct such a proof.
This disagreement between realists and anti-realists has direct and practical implications for mathematics and logic. For example, given a proof that the truth of some statement p implies the truth of another statement q, and a proof that the falsity of p also implies the truth of q, the realist can conclude that q is true even if she has no proof or disproof of p, because the principle of bivalence tells us that p must be either true or false, and both possibilities imply q. The anti-realist, however, rejects the principle, so has more work to do; she has to prove either that p is true or that it's false.
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