Combining Texts

Ideas for 'Function and Concept', 'What is Logic?' and 'The Problem of Empty Names'

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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]

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 / E. Structures of Logic / 5. Functions in Logic

8490	First-level functions have objects as arguments; second-level functions take functions as arguments [Frege]

5. Theory of Logic / E. Structures of Logic / 6. Relations in Logic

8492	Relations are functions with two arguments [Frege]

5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names

18946

Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]

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]