Combining Philosophers

All the ideas for Robert S. Wolf, Vincent C. Punzo and Michael Frede

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31 ideas

1. Philosophy / C. History of Philosophy / 2. Ancient Philosophy / e. Late classical philosophy
23326 In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M]
23335 In late antiquity nearly all philosophers were monotheists [Frede,M]
1. Philosophy / C. History of Philosophy / 3. Earlier European Philosophy / b. Early medieval philosophy
16137 Earlier views of Aristotle were dominated by 'Categories' [Frede,M]
2. Reason / A. Nature of Reason / 1. On Reason
23249 The early philosophers thought that reason has its own needs and desires [Frede,M]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
13520 A 'tautology' must include connectives [Wolf,RS]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
13524 Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
13522 Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS]
13521 Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
13523 Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / e. Axiom of the Empty Set IV
13529 Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13526 Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13534 In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS]
13535 First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13531 Model theory reveals the structures of mathematics [Wolf,RS]
13532 Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS]
13519 Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
13533 First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
13537 An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13539 The LST Theorem is a serious limitation of first-order logic [Wolf,RS]
5. Theory of Logic / K. Features of Logics / 4. Completeness
13538 If a theory is complete, only a more powerful language can strengthen it [Wolf,RS]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
13525 Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13530 An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13518 Modern mathematics has unified all of its objects within set theory [Wolf,RS]
9. Objects / E. Objects over Time / 9. Ship of Theseus
16157 Insurance on the original ship would hardly be paid out if the plank version was wrecked! [Frede,M]
16. Persons / F. Free Will / 2. Sources of Free Will
23334 For Christians man has free will by creation in God's image (as in Genesis) [Frede,M]
23333 The idea of free will achieved universal acceptance because of Christianity [Frede,M]
23337 The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M]
20. Action / B. Preliminaries of Action / 2. Willed Action / a. Will to Act
23336 There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M]
25. Social Practice / F. Life Issues / 5. Sexual Morality
20890 Why do sexual relationships need permanence, if other relationships don't? [Punzo]
20891 Does engaging in sexual intercourse really need no more thought than playing tennis? [Punzo]
29. Religion / A. Polytheistic Religion / 4. Dualist Religion
23313 The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M]