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Ideas for 'What is Logic?st1=Ian Hacking', 'Lectures on Aesthetics' and 'Plural Quantification'

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13 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]

10638

A pure logic is wholly general, purely formal, and directly known [Linnebo]

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]

13844

A limitation of first-order logic is that it cannot handle branching quantifiers [Hacking]

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]

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]

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]

5. Theory of Logic / G. Quantification / 6. Plural Quantification

10640

Instead of complex objects like tables, plurally quantify over mereological atoms tablewise [Linnebo]

10636

Plural plurals are unnatural and need a first-level ontology [Linnebo]

10639

Plural quantification may allow a monadic second-order theory with first-order ontology [Linnebo]

10635

Second-order quantification and plural quantification are different [Linnebo]

10641

Traditionally we eliminate plurals by quantifying over sets [Linnebo]

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]