Combining Texts

All the ideas for 'fragments/reports', 'First-Order Logic' and 'Beyond internal Foundations to external Virtues'

expand these ideas     |    start again     |     specify just one area for these texts

20 ideas

2. Reason / A. Nature of Reason / 6. Coherence
8877 We can't attain a coherent system by lopping off any beliefs that won't fit [Sosa]
5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic
10282 Logic is the study of sound argument, or of certain artificial languages (or applying the latter to the former) [Hodges,W]
5. Theory of Logic / I. Semantics of Logic / 1. Semantics of Logic
10283 A formula needs an 'interpretation' of its constants, and a 'valuation' of its variables [Hodges,W]
10284 There are three different standard presentations of semantics [Hodges,W]
10285 I |= φ means that the formula φ is true in the interpretation I [Hodges,W]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10288 Down Löwenheim-Skolem: if a countable language has a consistent theory, that has a countable model [Hodges,W]
10289 Up Löwenheim-Skolem: if infinite models, then arbitrarily large models [Hodges,W]
5. Theory of Logic / K. Features of Logics / 6. Compactness
10287 If a first-order theory entails a sentence, there is a finite subset of the theory which entails it [Hodges,W]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
10286 A 'set' is a mathematically well-behaved class [Hodges,W]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / c. Against mathematical empiricism
8884 The phenomenal concept of an eleven-dot pattern does not include the concept of eleven [Sosa]
11. Knowledge Aims / A. Knowledge / 1. Knowledge
8878 It is acceptable to say a supermarket door 'knows' someone is approaching [Sosa]
12. Knowledge Sources / C. Rationalism / 1. Rationalism
8880 In reducing arithmetic to self-evident logic, logicism is in sympathy with rationalism [Sosa]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
8881 Most of our knowledge has insufficient sensory support [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / c. Empirical foundations
8882 Perception may involve thin indexical concepts, or thicker perceptual concepts [Sosa]
8883 Do beliefs only become foundationally justified if we fully attend to features of our experience? [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / d. Rational foundations
8885 Some features of a thought are known directly, but others must be inferred [Sosa]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / e. Pro-foundations
8876 Much propositional knowledge cannot be formulated, as in recognising a face [Sosa]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / c. Coherentism critique
8879 Fully comprehensive beliefs may not be knowledge [Sosa]
26. Natural Theory / A. Speculations on Nature / 5. Infinite in Nature
1748 Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius]
27. Natural Reality / G. Biology / 3. Evolution
5989 Archelaus said life began in a primeval slime [Archelaus, by Schofield]