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All the ideas for 'Dthat', 'talk' and 'Intros to Russell's 'Essays in Analysis''

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5 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?

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox

21554	Sets always exceed terms, so all the sets must exceed all the sets [Lackey]
	Full Idea: Cantor proved that the number of sets in a collection of terms is larger than the number of terms. Hence Cantor's Paradox says the number of sets in the collection of all sets must be larger than the number of sets in the collection of all sets.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: The sets must count as terms in the next iteration, but that is a normal application of the Power Set axiom.

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox

21553	It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey]
	Full Idea: The ordinal series is well-ordered and thus has an ordinal number, and a series of ordinals to a given ordinal exceeds that ordinal by 1. So the series of all ordinals has an ordinal number that exceeds its own ordinal number by 1.
	From: Douglas Lackey (Intros to Russell's 'Essays in Analysis' [1973], p.127)
	A reaction: Formulated by Burali-Forti in 1897.

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.

19. Language / B. Reference / 3. Direct Reference / b. Causal reference

14080	Are causal descriptions part of the causal theory of reference, or are they just metasemantic? [Kaplan, by Schaffer,J]
	Full Idea: Kaplan notes that the causal theory of reference can be understood in two quite different ways, as part of the semantics (involving descriptions of causal processes), or as metasemantics, explaining why a term has the referent it does.
	From: report of David Kaplan (Dthat [1970]) by Jonathan Schaffer - Deflationary Metaontology of Thomasson 1
	A reaction: [Kaplan 'Afterthought' 1989] The theory tends to be labelled as 'direct' rather than as 'causal' these days, but causal chains are still at the heart of the story (even if more diffused socially). Nice question. Kaplan takes the meta- version as orthodox.