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10180
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Mathematicians do not study objects, but relations between objects [Poincaré]
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Full Idea:
Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter.
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From:
Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6
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A reaction:
This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well.
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13857
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Truth-functional possibilities include the irrelevant, which is a mistake [Edgington]
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Full Idea:
How likely is a fair die landing on an even number to land six? My approach is, assume an even number, so three possibilities, one a six, so 'one third'; the truth-functional approach is it's true if it is not-even or six, so 'two-thirds'.
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From:
Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 3)
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A reaction:
The point is that in the truth-functional approach, if the die lands not-even, then the conditional comes out as true, when she says it should be irrelevant. She seems to be right about this.
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13853
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It is a mistake to think that conditionals are statements about how the world is [Edgington]
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Full Idea:
The mistake philosophers have made, in trying to understand the conditional, is to assume that its function is to make a statement about how the world is (or how other possible worlds are related to it), true or false, as the case may be.
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From:
Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 1)
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A reaction:
'If pigs could fly we would never catch them' may not be about the world, but 'if you press this switch the light comes on' seems to be. Actually even the first one is about the world. I've an inkling that Edgington is wrong about this. Powers!
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13854
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Conditionals express what would be the outcome, given some supposition [Edgington]
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Full Idea:
It is often necessary to suppose (or assume) that some epistemic possibility is true, and to consider what else would be the case, or would be likely to be the case, given this supposition. The conditional expresses the outcome of such thought processes.
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From:
Dorothy Edgington (Do Conditionals Have Truth Conditions? [1986], 1)
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A reaction:
This is the basic Edgington view. It seems to involve an active thought process, and imagination, rather than being the static semantic relations offered by possible worlds analyses. True conditionals state relationships in the world.
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