Combining Texts

All the ideas for 'talk', 'On the Nature of Acquaintance' and 'Intros to Russell's 'Essays in Analysis''

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4 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
6410 The only real proper names are 'this' and 'that'; the rest are really definite descriptions. [Russell, by Grayling]
     Full Idea: Russell argued that the only 'logically proper' names are those which denote particular entities with which one can be acquainted. The best examples are 'this' and 'that'; other apparent names turn out, when analysed, to be definite descriptions.
     From: report of Bertrand Russell (On the Nature of Acquaintance [1914]) by A.C. Grayling - Russell Ch.2
     A reaction: This view is firm countered by the causal theory of reference, proposed by Kripke and others, in which not only people like Aristotle are 'baptised' with a name, but also natural kinds such as water. It is hard to disagree with Kripke on this.
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.
14. Science / C. Induction / 3. Limits of Induction
7295 Maybe induction is only reliable IF reality is stable [Mitchell,A]
     Full Idea: Maybe we should say that IF regularities are stable, only then is induction a reliable procedure.
     From: Alistair Mitchell (talk [2006]), quoted by PG - Db (ideas)
     A reaction: This seems to me a very good proposal. In a wildly unpredictable reality, it is hard to see how anyone could learn from experience, or do any reasoning about the future. Natural stability is the axiom on which induction is built.