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Ideas for 'What is Logic?st1=Ian Hacking', 'Particulars in Particular Clothing' and 'Logic (Encyclopedia I)'

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11 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]
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 / D. Assumptions for Logic / 2. Excluded Middle
21595 Excluded middle is the maxim of definite understanding, but just produces contradictions [Hegel]
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 / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13843 If it is a logic, the Löwenheim-Skolem theorem holds for it [Hacking]
5. Theory of Logic / L. Paradox / 3. Antinomies
15628 The idea that contradiction is essential to rational understanding is a key modern idea [Hegel]
15629 Tenderness for the world solves the antinomies; contradiction is in our reason, not in the essence of the world [Hegel]
15630 Antinomies are not just in four objects, but in all objects, all representations, all objects and all ideas [Hegel]