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Ideas for 'works', 'works' and 'Frege's Distinction of Sense and Reference'

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5 ideas

5. Theory of Logic / E. Structures of Logic / 1. Logical Form
4730 For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady]
     Full Idea: Aristotle apparently believed that the subject-predicate structure of Greek reflected the substance-accident nature of reality.
     From: report of Aristotle (works [c.330 BCE]) by Paul O'Grady - Relativism Ch.4
     A reaction: We need not assume that Aristotle is wrong. It is a chicken-and-egg. There is something obvious about subject-predicate language, if one assumes that unified objects are part of nature, and not just conventional.
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
9182 Ancient names like 'Obadiah' depend on tradition, not on where the name originated [Dummett]
     Full Idea: In the case of 'Obadiah', associated only with one act of writing a prophecy, ..it is the tradition which connects our use of the name with the man; where the actual name itself first came from has little to do with it.
     From: Michael Dummett (Frege's Distinction of Sense and Reference [1975], p.256)
     A reaction: Excellent. This seems to me a much more accurate account of reference than the notion of a baptism. In the case of 'Homer', whether someone was ever baptised thus is of no importance to us. The tradition is everything. Also Shakespeare.
5. Theory of Logic / K. Features of Logics / 8. Enumerability
10082 There are infinite sets that are not enumerable [Cantor, by Smith,P]
     Full Idea: Cantor's Theorem (1874) says there are infinite sets that are not enumerable. This is proved by his 1891 'diagonal argument'.
     From: report of George Cantor (works [1880]) by Peter Smith - Intro to Gödel's Theorems 2.3
     A reaction: [Smith summarises the diagonal argument]
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / b. Cantor's paradox
13483 Cantor's Paradox: the power set of the universe must be bigger than the universe, yet a subset of it [Cantor, by Hart,WD]
     Full Idea: The problem of Cantor's Paradox is that the power set of the universe has to be both bigger than the universe (by Cantor's theorem) and not bigger (since it is a subset of the universe).
     From: report of George Cantor (works [1880]) by William D. Hart - The Evolution of Logic 3
     A reaction: Russell eliminates the 'universe' in his theory of types. I don't see why you can't just say that the members of the set are hypothetical rather than real, and that hypothetically the universe might contain more things than it does.
5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / e. Mirimanoff's paradox
8710 The powerset of all the cardinal numbers is required to be greater than itself [Cantor, by Friend]
     Full Idea: Cantor's Paradox says that the powerset of a set has a cardinal number strictly greater than the original set, but that means that the powerset of the set of all the cardinal numbers is greater than itself.
     From: report of George Cantor (works [1880]) by Michčle Friend - Introducing the Philosophy of Mathematics
     A reaction: Friend cites this with the Burali-Forti paradox and the Russell paradox as the best examples of the problems of set theory in the early twentieth century. Did this mean that sets misdescribe reality, or that we had constructed them wrongly?