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Ideas for 'fragments/reports', 'works' and 'What is Logic?'

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10 ideas

5. Theory of Logic / A. Overview of Logic / 4. Pure Logic
13845 The various logics are abstractions made from terms like 'if...then' in English [Hacking]
     Full Idea: I don't believe English is by nature classical or intuitionistic etc. These are abstractions made by logicians. Logicians attend to numerous different objects that might be served by 'If...then', like material conditional, strict or relevant implication.
     From: Ian Hacking (What is Logic? [1979], §15)
     A reaction: The idea that they are 'abstractions' is close to my heart. Abstractions from what? Surely 'if...then' has a standard character when employed in normal conversation?
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13840 First-order logic is the strongest complete compact theory with Löwenheim-Skolem [Hacking]
     Full Idea: First-order logic is the strongest complete compact theory with a Löwenheim-Skolem theorem.
     From: Ian Hacking (What is Logic? [1979], §13)
13844 A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]
     Full Idea: Henkin proved that there is no first-order treatment of branching quantifiers, which do not seem to involve any idea that is fundamentally different from ordinary quantification.
     From: Ian Hacking (What is Logic? [1979], §13)
     A reaction: See Hacking for an example of branching quantifiers. Hacking is impressed by this as a real limitation of the first-order logic which he generally favours.
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
13842 Second-order completeness seems to need intensional entities and possible worlds [Hacking]
     Full Idea: Second-order logic has no chance of a completeness theorem unless one ventures into intensional entities and possible worlds.
     From: Ian Hacking (What is Logic? [1979], §13)
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
13837 With a pure notion of truth and consequence, the meanings of connectives are fixed syntactically [Hacking]
     Full Idea: My doctrine is that the peculiarity of the logical constants resides precisely in that given a certain pure notion of truth and consequence, all the desirable semantic properties of the constants are determined by their syntactic properties.
     From: Ian Hacking (What is Logic? [1979], §09)
     A reaction: He opposes this to Peacocke 1976, who claims that the logical connectives are essentially semantic in character, concerned with the preservation of truth.
5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic
13839 Perhaps variables could be dispensed with, by arrows joining places in the scope of quantifiers [Hacking]
     Full Idea: For some purposes the variables of first-order logic can be regarded as prepositions and place-holders that could in principle be dispensed with, say by a system of arrows indicating what places fall in the scope of which quantifier.
     From: Ian Hacking (What is Logic? [1979], §11)
     A reaction: I tend to think of variables as either pronouns, or as definite descriptions, or as temporary names, but not as prepositions. Must address this new idea...
5. Theory of Logic / F. Referring in Logic / 1. Naming / b. Names as descriptive
21878 Names have a subjective aspect, especially the role of our own name [Derrida]
     Full Idea: We can give a subjective account of names, by considering our own name.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
21889 'I' is the perfect name, because it denotes without description [Derrida]
     Full Idea: 'I' is the perfect name, because it denotes without description.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
5. Theory of Logic / F. Referring in Logic / 1. Naming / c. Names as referential
21879 Even Kripke can't explain names; the word is the thing, and the thing is the word [Derrida]
     Full Idea: Even Kripke can't explain names, because the word is the thing, and also the thing is the word.
     From: Jacques Derrida (works [1990]), quoted by Barry Stocker - Derrida on Deconstruction
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
     Full Idea: A Löwenheim-Skolem theorem holds for anything which, on my delineation, is a logic.
     From: Ian Hacking (What is Logic? [1979], §13)
     A reaction: I take this to be an unusually conservative view. Shapiro is the chap who can give you an alternative view of these things, or Boolos.