Combining Texts

All the ideas for 'works (fragments)', 'Higher-Order Logic' and 'Analyticity Reconsidered'

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26 ideas

2. Reason / D. Definition / 4. Real Definition
9376 A sentence may simultaneously define a term, and also assert a fact [Boghossian]
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 / I. Semantics of Logic / 2. Formal Truth
9375 Conventionalism agrees with realists that logic has truth values, but not over the source [Boghossian]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
10292 Downward Löwenheim-Skolem: if there's an infinite model, there is a countable model [Shapiro]
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]
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]
12. Knowledge Sources / A. A Priori Knowledge / 4. A Priori as Necessities
9369 'Snow is white or it isn't' is just true, not made true by stipulation [Boghossian]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
9367 The a priori is explained as analytic to avoid a dubious faculty of intuition [Boghossian]
9373 That logic is a priori because it is analytic resulted from explaining the meaning of logical constants [Boghossian]
9380 We can't hold a sentence true without evidence if we can't agree which sentence is definitive of it [Boghossian]
12. Knowledge Sources / A. A Priori Knowledge / 11. Denying the A Priori
9384 We may have strong a priori beliefs which we pragmatically drop from our best theory [Boghossian]
12. Knowledge Sources / E. Direct Knowledge / 2. Intuition
9374 If we learn geometry by intuition, how could this faculty have misled us for so long? [Boghossian]
19. Language / A. Nature of Meaning / 7. Meaning Holism / c. Meaning by Role
9378 If meaning depends on conceptual role, what properties are needed to do the job? [Boghossian]
9377 'Conceptual role semantics' says terms have meaning from sentences and/or inferences [Boghossian]
19. Language / A. Nature of Meaning / 8. Synonymy
9372 Could expressions have meaning, without two expressions possibly meaning the same? [Boghossian]
19. Language / E. Analyticity / 2. Analytic Truths
17721 There are no truths in virtue of meaning, but there is knowability in virtue of understanding [Boghossian, by Jenkins]
19. Language / E. Analyticity / 3. Analytic and Synthetic
9368 Epistemological analyticity: grasp of meaning is justification; metaphysical: truth depends on meaning [Boghossian]
22. Metaethics / C. The Good / 2. Happiness / b. Eudaimonia
5996 Critolaus redefined Aristotle's moral aim as fulfilment instead of happiness [Critolaus, by White,SA]