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All the ideas for 'Abstract Objects: a Case Study', 'talk' and 'works'

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7 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

10152	Set theory and logic are fairy tales, but still worth studying [Tarski]
	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.
	From: Alfred Tarski (talk [1965]), quoted by Feferman / Feferman - Alfred Tarski: life and logic
	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?

6. Mathematics / C. Sources of Mathematics / 6. Logicism / c. Neo-logicism

10580	Mathematics is both necessary and a priori because it really consists of logical truths [Yablo]
	Full Idea: Mathematics seems necessary because the real contents of mathematical statements are logical truths, which are necessary, and it seems a priori because logical truths really are a priori.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 10)
	A reaction: Yablo says his logicism has a Kantian strain, because numbers and sets 'inscribed on our spectacles', but he takes a different view (in the present Idea) from Kant about where the necessity resides. Personally I am tempted by an a posteriori necessity.

6. Mathematics / C. Sources of Mathematics / 9. Fictional Mathematics

10579	Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo]
	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.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 08)
	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.

7. Existence / C. Structure of Existence / 7. Abstract/Concrete / a. Abstract/concrete

10577	Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo]
	Full Idea: Objects like me have a few essential properties, and numerous accidental ones. Abstract objects are a different story. The intrinsic properties of the empty set are mostly essential. The relations of numbers are also mostly essential.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 01)

10578	We are thought to know concreta a posteriori, and many abstracta a priori [Yablo]
	Full Idea: Our knowledge of concreta is a posteriori, but our knowledge of numbers, at least, has often been considered a priori.
	From: Stephen Yablo (Abstract Objects: a Case Study [2002], 02)

8. Modes of Existence / E. Nominalism / 1. Nominalism / a. Nominalism

10151	I am a deeply convinced nominalist [Tarski]
	Full Idea: I am a nominalist. This is a very deep conviction of mine. ...I am a tortured nominalist.
	From: Alfred Tarski (talk [1965]), quoted by Feferman / Feferman - Alfred Tarski: life and logic Int I
	A reaction: I too am of the nominalist persuasion, but I don't feel justified in such a strong commitment.

9. Objects / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects

8249	Class membership is not transitive, unlike being part of a part of the whole [Lesniewski, by George/Van Evra]
	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.
	From: report of Stanislaw Lesniewski (works [1916]) by George / Van Evra - The Rise of Modern Logic 7
	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.