What The Tortoise Said To Achilles - Discussion

Discussion

Several philosophers have tried to resolve the Carroll paradox. Bertrand Russell discussed the paradox briefly in ยง 38 of The Principles of Mathematics (1903), distinguishing between implication (associated with the form "if p, then q"), which he held to be a relation between unasserted propositions, and inference (associated with the form "p, therefore q"), which he held to be a relation between asserted propositions; having made this distinction, Russell could deny that the Tortoise's attempt to treat inferring Z from A and B is equivalent to, or dependent on, agreeing to the hypothetical "If A and B are true, then Z is true."

The Wittgensteinian philosopher Peter Winch discussed the paradox in The Idea of a Social Science and its Relation to Philosophy (1958), where he argued that the paradox showed that "the actual process of drawing an inference, which is after all at the heart of logic, is something which cannot be represented as a logical formula ... Learning to infer is not just a matter of being taught about explicit logical relations between propositions; it is learning to do something" (p. 57). Winch goes on to suggest that the moral of the dialogue is a particular case of a general lesson, to the effect that the proper application of rules governing a form of human activity cannot itself be summed up with a set of further rules, and so that "a form of human activity can never be summed up in a set of explicit precepts" (p. 53).

Read more about this topic:  What The Tortoise Said To Achilles

Famous quotes containing the word discussion:

    There are answers which, in turning away wrath, only send it to the other end of the room, and to have a discussion coolly waived when you feel that justice is all on your own side is even more exasperating in marriage than in philosophy.
    George Eliot [Mary Ann (or Marian)

    If we had had more time for discussion we should probably have made a great many more mistakes.
    Leon Trotsky (1879–1940)

    If the abstract rights of man will bear discussion and explanation, those of women, by a parity of reasoning, will not shrink from the same test: though a different opinion prevails in this country.
    Mary Wollstonecraft (1759–1797)