Combining Texts

All the ideas for 'The philosophical basis of intuitionist logic', 'Apology of Socrates' and 'Higher-Order Logic'

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

18 ideas

4. Formal Logic / E. Nonclassical Logics / 2. Intuitionist Logic
18073 Dummett says classical logic rests on meaning as truth, while intuitionist logic rests on assertability [Dummett, by Kitcher]
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 / 1. Quantification
19057 Classical quantification is an infinite conjunction or disjunction - but you may not know all the instances [Dummett]
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]
19. Language / A. Nature of Meaning / 4. Meaning as Truth-Conditions
19055 Stating a sentence's truth-conditions is just paraphrasing the sentence [Dummett]
19056 If a sentence is effectively undecidable, we can never know its truth conditions [Dummett]
19. Language / A. Nature of Meaning / 6. Meaning as Use
19054 Meaning as use puts use beyond criticism, and needs a holistic view of language [Dummett]
25. Social Practice / E. Policies / 5. Education / b. Education principles
5833 Education is the greatest of human goods [Xenophon]