Combining Texts

All the ideas for 'Letters to Edward Stillingfleet', 'Coherence Theory of Truth and Knowledge' and 'Higher-Order Logic'

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23 ideas

3. Truth / D. Coherence Truth / 1. Coherence Truth
19081 Coherence with a set of propositions suggests we can know the proposition corresponds [Davidson, by Donnellan]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / j. Axiom of Choice IX
10301 The axiom of choice is controversial, but it could be replaced [Shapiro]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
10588 First-order logic is Complete, and Compact, with the Löwenheim-Skolem Theorems [Shapiro]
5. Theory of Logic / A. Overview of Logic / 7. Second-Order Logic
10298 Some say that second-order logic is mathematics, not logic [Shapiro]
10299 If the aim of logic is to codify inferences, second-order logic is useless [Shapiro]
5. Theory of Logic / B. Logical Consequence / 1. Logical Consequence
10300 Logical consequence can be defined in terms of the logical terminology [Shapiro]
5. Theory of Logic / G. Quantification / 5. Second-Order Quantification
10290 Second-order variables also range over properties, sets, relations or functions [Shapiro]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10590 Up Löwenheim-Skolem: if natural numbers satisfy wffs, then an infinite domain satisfies them [Shapiro]
10296 The Löwenheim-Skolem Theorems fail for second-order languages with standard semantics [Shapiro]
10297 The Löwenheim-Skolem theorem seems to be a defect of first-order logic [Shapiro]
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
6. Mathematics / B. Foundations for Mathematics / 4. Axioms for Number / e. Peano arithmetic 2nd-order
10294 Second-order logic has the expressive power for mathematics, but an unworkable model theory [Shapiro]
8. Modes of Existence / B. Properties / 11. Properties as Sets
10591 Logicians use 'property' and 'set' interchangeably, with little hanging on it [Shapiro]
9. Objects / D. Essence of Objects / 3. Individual Essences
15990 Every individual thing which exists has an essence, which is its internal constitution [Locke]
11. Knowledge Aims / A. Knowledge / 4. Belief / b. Elements of beliefs
8806 The concepts of belief and truth are linked, since beliefs are meant to fit reality [Davidson]
11. Knowledge Aims / B. Certain Knowledge / 1. Certainty
15994 If it is knowledge, it is certain; if it isn't certain, it isn't knowledge [Locke]
12. Knowledge Sources / D. Empiricism / 1. Empiricism
8252 Davidson believes experience is non-conceptual, and outside the space of reasons [Davidson, by McDowell]
12. Knowledge Sources / D. Empiricism / 5. Empiricism Critique
8255 Davidson says the world influences us causally; I say it influences us rationally [McDowell on Davidson]
13. Knowledge Criteria / A. Justification Problems / 3. Internal or External / a. Pro-internalism
8804 Reasons for beliefs are not the same as evidence [Davidson]
13. Knowledge Criteria / B. Internal Justification / 4. Foundationalism / f. Foundationalism critique
8802 Sensations lack the content to be logical; they cause beliefs, but they cannot justify them [Davidson]
13. Knowledge Criteria / B. Internal Justification / 5. Coherentism / a. Coherence as justification
8801 Coherent justification says only beliefs can be reasons for holding other beliefs [Davidson]
13. Knowledge Criteria / D. Scepticism / 6. Scepticism Critique
8805 Skepticism is false because our utterances agree, because they are caused by the same objects [Davidson]
19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity
18703 Davidson's Cogito: 'I think, therefore I am generally right' [Davidson, by Button]