6862
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Fuzzy logic uses a continuum of truth, but it implies contradictions [Williamson]
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Full Idea:
Fuzzy logic is based on a continuum of degrees of truth, but it is committed to the idea that it is half-true that one identical twin is tall and the other twin is not, even though they are the same height.
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From:
Timothy Williamson (Interview with Baggini and Stangroom [2001], p.154)
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A reaction:
Maybe to be shocked by a contradiction is missing the point of fuzzy logic? Half full is the same as half empty. The logic does not say the twins are different, because it is half-true that they are both tall, and half-true that they both aren't.
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6861
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What sort of logic is needed for vague concepts, and what sort of concept of truth? [Williamson]
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Full Idea:
The problem of vagueness is the problem of what logic is correct for vague concepts, and correspondingly what notions of truth and falsity are applicable to vague statements (does one need a continuum of degrees of truth, for example?).
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From:
Timothy Williamson (Interview with Baggini and Stangroom [2001], p.153)
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A reaction:
This certainly makes vagueness sound like one of the most interesting problems in all of philosophy, though also one of the most difficult. Williamson's solution is that we may be vague, but the world isn't.
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6860
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How can one discriminate yellow from red, but not the colours in between? [Williamson]
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Full Idea:
If one takes a spectrum of colours from yellow to red, it might be that given a series of colour samples along that spectrum, each sample is indiscriminable by the naked eye from the next one, though samples at either end are blatantly different.
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From:
Timothy Williamson (Interview with Baggini and Stangroom [2001], p.151)
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A reaction:
This seems like a nice variant of the Sorites paradox (Idea 6008). One could demonstrate it with just three samples, where A and C seemed different from each other, but other comparisons didn't.
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9145
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We form the image of a cardinal number by a double abstraction, from the elements and from their order [Cantor]
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Full Idea:
We call 'cardinal number' the general concept which, by means of our active faculty of thought, arises when we make abstraction from an aggregate of its various elements, and of their order. From this double abstraction the number is an image in our mind.
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From:
George Cantor (Beitrage [1915], §1), quoted by Kit Fine - Cantorian Abstraction: Recon. and Defence Intro
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A reaction:
[compressed] This is the great Cantor, creator of set theory, endorsing the traditional abstractionism which Frege and his followers so despise. Fine offers a defence of it. The Frege view is platonist, because it refuses to connect numbers to the world.
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