Combining Texts

All the ideas for 'A World of States of Affairs', 'works' and 'Maths as a Science of Patterns'

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19 ideas

2. Reason / A. Nature of Reason / 1. On Reason
17892 For clear questions posed by reason, reason can also find clear answers [Gödel]
3. Truth / C. Correspondence Truth / 1. Correspondence Truth
4742 Correspondence may be one-many or many one, as when either p or q make 'p or q' true [Armstrong]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / e. Axioms of PL
6299 Axioms are often affirmed simply because they produce results which have been accepted [Resnik]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
9188 Gödel proved that first-order logic is complete, and second-order logic incomplete [Gödel, by Dummett]
5. Theory of Logic / I. Semantics of Logic / 2. Formal Truth
10620 Originally truth was viewed with total suspicion, and only demonstrability was accepted [Gödel]
5. Theory of Logic / K. Features of Logics / 5. Incompleteness
17883 Gödel's Theorems did not refute the claim that all good mathematical questions have answers [Gödel, by Koellner]
6. Mathematics / A. Nature of Mathematics / 1. Mathematics
6304 Mathematical realism says that maths exists, is largely true, and is independent of proofs [Resnik]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / g. Incompleteness of Arithmetic
17885 Gödel eventually hoped for a generalised completeness theorem leaving nothing undecidable [Gödel, by Koellner]
10614 The real reason for Incompleteness in arithmetic is inability to define truth in a language [Gödel]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
6300 Mathematical constants and quantifiers only exist as locations within structures or patterns [Resnik]
6303 Sets are positions in patterns [Resnik]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
6302 Structuralism must explain why a triangle is a whole, and not a random set of points [Resnik]
6295 There are too many mathematical objects for them all to be mental or physical [Resnik]
6296 Maths is pattern recognition and representation, and its truth and proofs are based on these [Resnik]
6301 Congruence is the strongest relationship of patterns, equivalence comes next, and mutual occurrence is the weakest [Resnik]
7. Existence / D. Theories of Reality / 7. Fictionalism
9497 Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong]
8. Modes of Existence / B. Properties / 1. Nature of Properties
15550 Properties are contingently existing beings with multiple locations in space and time [Armstrong, by Lewis]
10. Modality / C. Sources of Modality / 1. Sources of Necessity
4743 The truth-maker for a truth must necessitate that truth [Armstrong]
26. Natural Theory / C. Causation / 9. General Causation / d. Causal necessity
4798 In recent writings, Armstrong makes a direct identification of necessitation with causation [Armstrong, by Psillos]