10152
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Set theory and logic are fairy tales, but still worth studying [Tarski]
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Full Idea:
People have asked me, 'How can you, a nominalist, do work in set theory and in logic, which are theories about things you do not believe in?' ...I believe that there is a value even in fairy tales and the study of fairy tales.
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From:
Alfred Tarski (talk [1965]), quoted by Feferman / Feferman - Alfred Tarski: life and logic
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A reaction:
This is obviously an oversimplification. I don't think for a moment that Tarski literally believed that the study of fairy tales had as much value as the study of logic. Why do we have this particular logic, and not some other?
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10579
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Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
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Full Idea:
Saying 'the number of Fs is 5', instead of using five quantifiers, puts the numeral in quantifiable position, which brings expressive advantages. 'There are more sheep in the field than cows' is an infinite disjunction, expressible in finite compass.
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From:
Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
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A reaction:
See Hofweber with similar thoughts. This idea I take to be a key one in explaining many metaphysical confusions. The human mind just has a strong tendency to objectify properties, relations, qualities, categories etc. - for expression and for reasoning.
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8249
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Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra]
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Full Idea:
Lesniewski distinguished the part-whole relationship from class membership. Membership is not transitive: if s is an element of t, and t of u, then s is not an element of u, whereas a part of a part is a part of the whole.
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From:
report of Stanislaw Lesniewski (works [1916]) by George / Van Evra - The Rise of Modern Logic 7
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A reaction:
If I am a member of a sports club, and my club is a member of the league, I am not thereby a member of the league (so clubs are classes, not wholes). This distinction is clearly fairly crucial in ontology.
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