Combining Texts

All the ideas for 'Stipulation, Meaning and Apriority', 'An Enquiry' and 'Higher-Order Logic'

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20 ideas

2. Reason / D. Definition / 13. Against Definition
9331 How do we determine which of the sentences containing a term comprise its definition? [Horwich]
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]
12. Knowledge Sources / A. A Priori Knowledge / 1. Nature of the A Priori
9333 A priori belief is not necessarily a priori justification, or a priori knowledge [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 6. A Priori from Reason
9342 Understanding needs a priori commitment [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 8. A Priori as Analytic
9332 Meaning is generated by a priori commitment to truth, not the other way around [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 9. A Priori from Concepts
9341 Meanings and concepts cannot give a priori knowledge, because they may be unacceptable [Horwich]
9334 If we stipulate the meaning of 'number' to make Hume's Principle true, we first need Hume's Principle [Horwich]
12. Knowledge Sources / A. A Priori Knowledge / 10. A Priori as Subjective
9339 A priori knowledge (e.g. classical logic) may derive from the innate structure of our minds [Horwich]
13. Knowledge Criteria / C. External Justification / 7. Testimony
23549 We treat testimony with a natural trade off of belief and caution [Reid, by Fricker,M]