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All the ideas for 'Realistic Rationalism', 'What are Sets and What are they For?' and 'Logical Consequence'

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27 ideas

1. Philosophy / D. Nature of Philosophy / 3. Philosophy Defined
2510 Traditionally philosophy is an a priori enquiry into general truths about reality [Katz]
2516 Most of philosophy begins where science leaves off [Katz]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / b. Empty (Null) Set
14239 The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley]
14240 The empty set is something, not nothing! [Oliver/Smiley]
14241 We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley]
14242 Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley]
4. Formal Logic / F. Set Theory ST / 3. Types of Set / c. Unit (Singleton) Sets
14243 The unit set may be needed to express intersections that leave a single member [Oliver/Smiley]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
18755 Validity is explained as truth in all models, because that relies on the logical terms [McGee]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18751 Natural language includes connectives like 'because' which are not truth-functional [McGee]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
18761 Second-order variables need to range over more than collections of first-order objects [McGee]
5. Theory of Logic / G. Quantification / 6. Plural Quantification
14234 If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley]
14237 We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
18753 An ontologically secure semantics for predicate calculus relies on sets [McGee]
5. Theory of Logic / I. Semantics of Logic / 3. Logical Truth
14245 Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley]
18754 Logically valid sentences are analytic truths which are just true because of their logical words [McGee]
5. Theory of Logic / K. Features of Logics / 3. Soundness
18757 Soundness theorems are uninformative, because they rely on soundness in their proofs [McGee]
6. Mathematics / A. Nature of Mathematics / 4. Using Numbers / g. Applying mathematics
14246 If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley]
6. Mathematics / B. Foundations for Mathematics / 3. Axioms for Geometry
18760 The culmination of Euclidean geometry was axioms that made all models isomorphic [McGee]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
14247 Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley]
6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism
2521 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz]
12. Knowledge Sources / A. A Priori Knowledge / 5. A Priori Synthetic
2513 We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
2522 Experience cannot teach us why maths and logic are necessary [Katz]
19. Language / A. Nature of Meaning / 1. Meaning
2517 Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz]
19. Language / B. Reference / 4. Descriptive Reference / a. Sense and reference
2519 It is generally accepted that sense is defined as the determiner of reference [Katz]
19. Language / C. Assigning Meanings / 5. Fregean Semantics
2520 Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz]
19. Language / D. Propositions / 2. Abstract Propositions / a. Propositions as sense
2518 Sentences are abstract types (like musical scores), not individual tokens [Katz]
19. Language / F. Communication / 2. Assertion
18762 A maxim claims that if we are allowed to assert a sentence, that means it must be true [McGee]