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18244
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I say the irrational is not the cut itself, but a new creation which corresponds to the cut [Dedekind]
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Full Idea:
Of my theory of irrationals you say that the irrational number is nothing else than the cut itself, whereas I prefer to create something new (different from the cut), which corresponds to the cut. We have the right to claim such a creative power.
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From:
Richard Dedekind (Letter to Weber [1888], 1888 Jan), quoted by Stewart Shapiro - Philosophy of Mathematics 5.4
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A reaction:
Clearly a cut will not locate a unique irrational number, so something more needs to be done. Shapiro remarks here that for Dedekind numbers are objects.
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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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