Combining Texts

All the ideas for 'Frege's Theory of Numbers', 'What Metaphors Mean' and 'The Thesis that Mathematics is Logic'

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5 ideas

5. Theory of Logic / C. Ontology of Logic / 3. If-Thenism
Putnam coined the term 'if-thenism' [Putnam, by Musgrave]
     Full Idea: Putnam coined the term 'if-thenism'.
     From: report of Hilary Putnam (The Thesis that Mathematics is Logic [1967]) by Alan Musgrave - Logicism Revisited §5 n
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / c. Counting procedure
Parsons says counting is tagging as first, second, third..., and converting the last to a cardinal [Parsons,C, by Heck]
     Full Idea: In Parsons's demonstrative model of counting, '1' means the first, and counting says 'the first, the second, the third', where one is supposed to 'tag' each object exactly once, and report how many by converting the last ordinal into a cardinal.
     From: report of Charles Parsons (Frege's Theory of Numbers [1965]) by Richard G. Heck - Cardinality, Counting and Equinumerosity 3
     A reaction: This sounds good. Counting seems to rely on that fact that numbers can be both ordinals and cardinals. You don't 'convert' at the end, though, because all the way you mean 'this cardinality in this order'.
19. Language / F. Communication / 6. Interpreting Language / d. Metaphor
We accept a metaphor when we see the sentence is false [Davidson]
     Full Idea: It is only when a sentence is taken to be false that we accept it as a metaphor.
     From: Donald Davidson (What Metaphors Mean [1978], p.40)
     A reaction: This strikes me as a very nice and true generalisation, even though Davidson mentions "no man is an island" as a counterexample. We thirst for meaning, and switch to a second meaning when the first one looks peculiar.
Understanding a metaphor is a creative act, with no rules [Davidson]
     Full Idea: Understanding a metaphor is as much a creative endeavour as making a metaphor, and as little guided by rules.
     From: Donald Davidson (What Metaphors Mean [1978], p.29)
     A reaction: This is good news for literature studies courses. Davidson's point is that the metaphor itself only gives you a literal meaning, so it doesn't tell you how to interpret it. It seems an attractive proposal.
Metaphors just mean what their words literally mean [Davidson]
     Full Idea: Metaphors mean what the words, in their most literal interpretation, mean, and nothing more.
     From: Donald Davidson (What Metaphors Mean [1978], p.30)
     A reaction: This pronouncement must be the result of Davidson anguishing over the truth conditions for metaphors, which are usually either taken to have a 'metaphorical meaning', or to be abbreviated similes. He solved his problem at a stroke! Plausible.