By Stephen Law & Julian Baggini
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Extra resources for 30-Second Philosophies: The 50 Most Thought-provoking Philosophies, Each Explained in Half a Minute
3-SECOND THRASH Why you can never make a mountain out of a molehill. 3-MINUTE THOUGHT What might this paradox show? That concepts such as fat and thin are vague, so it is a mistake to ever treat them as though there were factual questions to which they definitely apply? Or is it that, counter-intuitively, there is a firm boundary between fat and thin, a heap and a small pile, and that, if you step across it by one grain or 1 gram, the correct description changes? 3-SECOND BIOGRAPHY EUBULIDES Fourth century BCE 30-SECOND TEXT Julian Baggini The journey from being a thin man to being a fat man and back again begins with a single gram.
3-MINUTE THOUGHT In the 20th century two great mathematical results were proved concerning first order logic: it is complete, and it is undecidable. Kurt Gödel demonstrated that it is possible to program a computer to list all the valid inferences (completeness), and Alonzo Church demonstrated that it is impossible to program a computer to determine whether or not every inference is valid (undecidability). RELATED PHILOSOPHIES RUSSELL’S PARADOX & FREGE’S LOGICISM 3-SECOND BIOGRAPHIES ARISTOTLE 384–322 BCE GOTTLOB FREGE 1848–1925 KURT GÖDEL 1906–1978 ALONZO CHURCH 1903–1995 30-SECOND TEXT Barry Loewer To Aristotle it was logical—we are people, we are going to die, and therefore we are frightened.
If sentence 1 is true then it is not true, and if it is not true then it is true. The paradox arises because it seems to be part of the meaning of “is true” that, where S can be any sentence, one can validly infer “S” is true from S and also validly infer S from “S” is true. From 1 we can infer both that S is true and that S is not true. A paradox! The most famous response to the liar paradox came from the logician Alfred Tarski, who distinguished a language (L) from a meta-language (ML), in which one can refer to sentences of L.
30-Second Philosophies: The 50 Most Thought-provoking Philosophies, Each Explained in Half a Minute by Stephen Law & Julian Baggini