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

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21 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

9020	My logical grammar has sentences by predication, then negation, conjunction, and existential quantification [Quine]

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

9028	Maybe logical truth reflects reality, but in different ways in different languages [Quine]

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

10014

Quine rejects second-order logic, saying that predicates refer to multiple objects [Quine, by Hodes]

10828

Quantifying over predicates is treating them as names of entities [Quine]

13842

Second-order completeness seems to need intensional entities and possible worlds [Hacking]

5. Theory of Logic / B. Logical Consequence / 5. Modus Ponens

8078	Modus ponens is one of five inference rules identified by the Stoics [Chrysippus, by Devlin]

5. Theory of Logic / D. Assumptions for Logic / 2. Excluded Middle

6023	Every proposition is either true or false [Chrysippus, by Cicero]

9024	Excluded middle has three different definitions [Quine]

5. Theory of Logic / D. Assumptions for Logic / 4. Identity in Logic

10012

Quantification theory can still be proved complete if we add identity [Quine]

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 / F. Referring in Logic / 1. Naming / f. Names eliminated

9016	Names are not essential, because naming can be turned into predication [Quine]

5. Theory of Logic / G. Quantification / 1. Quantification

9015	Universal quantification is widespread, but it is definable in terms of existential quantification [Quine]

5. Theory of Logic / G. Quantification / 4. Substitutional Quantification

9025	You can't base quantification on substituting names for variables, if the irrationals cannot all be named [Quine]

9026	Some quantifications could be false substitutionally and true objectually, because of nameless objects [Quine]

5. Theory of Logic / G. Quantification / 5. Second-Order Quantification

10705

Putting a predicate letter in a quantifier is to make it the name of an entity [Quine]

5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth

9027	A sentence is logically true if all sentences with that grammatical structure are true [Quine]

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]