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Ideas for 'Logicism and Ontological Commits. of Arithmetic', 'The Principles of Mathematics' and 'On the Freedom of the Will'

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13 ideas

5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10015 Higher-order logic may be unintelligible, but it isn't set theory [Hodes]
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 / D. Assumptions for Logic / 4. Identity in Logic
10011 Identity is a level one relation with a second-order definition [Hodes]
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 / I. Semantics of Logic / 1. Semantics of Logic
10016 When an 'interpretation' creates a model based on truth, this doesn't include Fregean 'sense' [Hodes]
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 / 5. Paradoxes in Set Theory / c. Burali-Forti's paradox
15895 Russell discovered the paradox suggested by Burali-Forti's work [Russell, by Lavine]