Combining Philosophers

All the ideas for Benjamin Constant, Anon (Par) and Jos L. Zalabardo

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25 ideas

4. Formal Logic / F. Set Theory ST / 1. Set Theory
10888 Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo]
4. Formal Logic / F. Set Theory ST / 2. Mechanics of Set Theory / b. Terminology of ST
10889 The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo]
10890 A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets
10886 Determinacy: an object is either in a set, or it isn't [Zalabardo]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / l. Axiom of Specification
10887 Specification: Determinate totals of objects always make a set [Zalabardo]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10897 A first-order 'sentence' is a formula with no free variables [Zalabardo]
5. Theory of Logic / B. Logical Consequence / 4. Semantic Consequence |=
10893 Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo]
10899 Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / b. Basic connectives
10896 Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10898 The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo]
10902 We can do semantics by looking at given propositions, or by building new ones [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10892 We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
10895 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo]
10900 Logically true sentences are true in all structures [Zalabardo]
5. Theory of Logic / I. Semantics of Logic / 4. Satisfaction
10901 Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo]
10894 A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
10903 A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / f. Mathematical induction
10891 If a set is defined by induction, then proof by induction can be applied to it [Zalabardo]
10. Modality / B. Possibility / 1. Possibility
22142 In future, only logical limits can be placed on divine omnipotence [Anon (Par), by Boulter]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
16716 It is heresy to require self-evident foundational principles in order to be certain [Anon (Par)]
24. Political Theory / D. Ideologies / 6. Liberalism / b. Liberal individualism
22595 Liberty is the triumph of the individual, over both despotic government and enslaving majorities [Constant]
24. Political Theory / D. Ideologies / 6. Liberalism / c. Liberal equality
22597 Minority rights are everyone's rights, because we all have turns in the minority [Constant]
25. Social Practice / E. Policies / 5. Education / d. Study of history
1866 It is heresy to teach that history repeats every 36,000 years [Anon (Par)]
28. God / A. Divine Nature / 3. Divine Perfections
1865 It is heresy to teach that natural impossibilities cannot even be achieved by God [Anon (Par)]
28. God / B. Proving God / 2. Proofs of Reason / b. Ontological Proof critique
1864 It is heresy to teach that we can know God by his essence in this mortal life [Anon (Par)]