Combining Philosophers

All the ideas for Kretzmann/Stump, Philolaus and Alex Orenstein

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23 ideas

4. Formal Logic / B. Propositional Logic PL / 1. Propositional Logic
8472 Sentential logic is consistent (no contradictions) and complete (entirely provable) [Orenstein]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
8476 Axiomatization simply picks from among the true sentences a few to play a special role [Orenstein]
4. Formal Logic / D. Modal Logic ML / 4. Alethic Modal Logic
8480 S4: 'poss that poss that p' implies 'poss that p'; S5: 'poss that nec that p' implies 'nec that p' [Orenstein]
4. Formal Logic / F. Set Theory ST / 1. Set Theory
8474 Unlike elementary logic, set theory is not complete [Orenstein]
4. Formal Logic / G. Formal Mereology / 1. Mereology
8465 Mereology has been exploited by some nominalists to achieve the effects of set theory [Orenstein]
5. Theory of Logic / G. Quantification / 1. Quantification
8452 Traditionally, universal sentences had existential import, but were later treated as conditional claims [Orenstein]
5. Theory of Logic / G. Quantification / 4. Substitutional Quantification
8475 The substitution view of quantification says a sentence is true when there is a substitution instance [Orenstein]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / b. Types of number
8454 The whole numbers are 'natural'; 'rational' numbers include fractions; the 'reals' include root-2 etc. [Orenstein]
6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
8473 The logicists held that is-a-member-of is a logical constant, making set theory part of logic [Orenstein]
7. Existence / E. Categories / 3. Proposed Categories
8458 Just individuals in Nominalism; add sets for Extensionalism; add properties, concepts etc for Intensionalism [Orenstein]
9. Objects / B. Unity of Objects / 1. Unifying an Object / a. Intrinsic unification
472 No things would be clear to us as entity or relationships unless there existed Number and its essence [Philolaus]
14. Science / A. Basis of Science / 2. Demonstration
22110 Demonstration provides depth of understanding and explanation (rather than foundations) [Kretzmann/Stump]
14. Science / B. Scientific Theories / 1. Scientific Theory
8457 The Principle of Conservatism says we should violate the minimum number of background beliefs [Orenstein]
19. Language / A. Nature of Meaning / 10. Denial of Meanings
8477 People presume meanings exist because they confuse meaning and reference [Orenstein]
19. Language / C. Assigning Meanings / 3. Predicates
8471 Three ways for 'Socrates is human' to be true are nominalist, platonist, or Montague's way [Orenstein]
19. Language / D. Propositions / 4. Mental Propositions
8484 If two people believe the same proposition, this implies the existence of propositions [Orenstein]
20. Action / B. Preliminaries of Action / 2. Willed Action / d. Weakness of will
22511 Some reasonings are stronger than we are [Philolaus]
26. Natural Theory / A. Speculations on Nature / 4. Mathematical Nature
473 There is no falsehood in harmony and number, only in irrational things [Philolaus]
1519 Harmony must pre-exist the cosmos, to bring the dissimilar sources together [Philolaus]
1518 Everything must involve numbers, or it couldn't be thought about or known [Philolaus]
26. Natural Theory / A. Speculations on Nature / 6. Early Matter Theories / d. The unlimited
469 Existing things, and hence the Cosmos, are a mixture of the Limited and the Unlimited [Philolaus]
26. Natural Theory / D. Laws of Nature / 6. Laws as Numerical
476 Self-created numbers make the universe stable [Philolaus]
27. Natural Reality / E. Cosmology / 1. Cosmology
1787 Philolaus was the first person to say the earth moves in a circle [Philolaus, by Diog. Laertius]