Combining Texts

Ideas for 'Being and Time', 'The Principles of Mathematics' and 'Philosophy of Mathematics'

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15 ideas

5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic

18108

First-order logic is not decidable: there is no test of whether any formula is valid [Bostock]

18109

The completeness of first-order logic implies its compactness [Bostock]

5. Theory of Logic / B. Logical Consequence / 8. Material Implication

14106

Implication cannot be defined [Russell]

14108

It would be circular to use 'if' and 'then' to define material implication [Russell]

5. Theory of Logic / C. Ontology of Logic / 1. Ontology of Logic

14167

The only classes are things, predicates and relations [Russell]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives

14105

There seem to be eight or nine logical constants [Russell]

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not

18722

Negations are not just reversals of truth-value, since that can happen without negation [Wittgenstein on Russell]

5. Theory of Logic / E. Structures of Logic / 3. Constants in Logic

14104

Constants are absolutely definite and unambiguous [Russell]

5. Theory of Logic / E. Structures of Logic / 4. Variables in Logic

14114

Variables don't stand alone, but exist as parts of propositional functions [Russell]

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

14137

'Any' is better than 'all' where infinite classes are concerned [Russell]

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

18123

Substitutional quantification is just standard if all objects in the domain have a name [Bostock]

5. Theory of Logic / H. Proof Systems / 4. Natural Deduction

18120

The Deduction Theorem is what licenses a system of natural deduction [Bostock]

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / a. Achilles paradox

14149

The Achilles Paradox concerns the one-one correlation of infinite classes [Russell]

5. Theory of Logic / L. Paradox / 4. Paradoxes in Logic / c. Berry's paradox

18125

Berry's Paradox considers the meaning of 'The least number not named by this name' [Bostock]

5. Theory of Logic / L. Paradox / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox

15895

Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine]