Combining Texts

All the ideas for 'Review of Parsons (1983)', 'A Tour through Mathematical Logic' and 'Truthmakers'

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

40 ideas

3. Truth / A. Truth Problems / 2. Defining Truth
18486 We might define truth as arising from the truth-maker relation [MacBride]
3. Truth / B. Truthmakers / 1. For Truthmakers
18484 Phenomenalists, behaviourists and presentists can't supply credible truth-makers [MacBride]
3. Truth / B. Truthmakers / 2. Truthmaker Relation
18466 If truthmaking is classical entailment, then anything whatsoever makes a necessary truth [MacBride]
3. Truth / B. Truthmakers / 3. Truthmaker Maximalism
18473 'Maximalism' says every truth has an actual truthmaker [MacBride]
18481 Maximalism follows Russell, and optimalism (no negative or universal truthmakers) follows Wittgenstein [MacBride]
3. Truth / B. Truthmakers / 5. What Makes Truths / a. What makes truths
18483 The main idea of truth-making is that what a proposition is about is what matters [MacBride]
3. Truth / B. Truthmakers / 6. Making Negative Truths
18479 There are different types of truthmakers for different types of negative truth [MacBride]
18477 There aren't enough positive states out there to support all the negative truths [MacBride]
3. Truth / B. Truthmakers / 8. Making General Truths
18482 Optimalists say that negative and universal are true 'by default' from the positive truths [MacBride]
3. Truth / B. Truthmakers / 12. Rejecting Truthmakers
18474 Does 'this sentence has no truth-maker' have a truth-maker? Reductio suggests it can't have [MacBride]
18485 Even idealists could accept truthmakers, as mind-dependent [MacBride]
18490 Maybe 'makes true' is not an active verb, but just a formal connective like 'because'? [MacBride]
18493 Truthmaker talk of 'something' making sentences true, which presupposes objectual quantification [MacBride]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / b. Terminology of PL
13520 A 'tautology' must include connectives [Wolf,RS]
4. Formal Logic / B. Propositional Logic PL / 2. Tools of Propositional Logic / c. Derivation rules of PL
13524 Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / d. Universal quantifier ∀
13522 Universal Generalization: If we prove P(x) with no special assumptions, we can conclude ∀xP(x) [Wolf,RS]
13521 Universal Specification: ∀xP(x) implies P(t). True for all? Then true for an instance [Wolf,RS]
4. Formal Logic / C. Predicate Calculus PC / 2. Tools of Predicate Calculus / e. Existential quantifier ∃
13523 Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / e. Axiom of the Empty Set IV
13529 Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS]
4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / n. Axiom of Comprehension
13526 Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS]
5. Theory of Logic / A. Overview of Logic / 5. First-Order Logic
13534 In first-order logic syntactic and semantic consequence (|- and |=) nicely coincide [Wolf,RS]
13535 First-order logic is weakly complete (valid sentences are provable); we can't prove every sentence or its negation [Wolf,RS]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives
18489 Connectives link sentences without linking their meanings [MacBride]
5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / c. not
18476 'A is F' may not be positive ('is dead'), and 'A is not-F' may not be negative ('is not blind') [MacBride]
5. Theory of Logic / J. Model Theory in Logic / 1. Logical Models
13531 Model theory reveals the structures of mathematics [Wolf,RS]
13532 Model theory 'structures' have a 'universe', some 'relations', some 'functions', and some 'constants' [Wolf,RS]
13519 Model theory uses sets to show that mathematical deduction fits mathematical truth [Wolf,RS]
13533 First-order model theory rests on completeness, compactness, and the Löwenheim-Skolem-Tarski theorem [Wolf,RS]
5. Theory of Logic / J. Model Theory in Logic / 2. Isomorphisms
13537 An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS]
5. Theory of Logic / J. Model Theory in Logic / 3. Löwenheim-Skolem Theorems
13539 The LST Theorem is a serious limitation of first-order logic [Wolf,RS]
5. Theory of Logic / K. Features of Logics / 4. Completeness
13538 If a theory is complete, only a more powerful language can strengthen it [Wolf,RS]
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
13525 Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS]
6. Mathematics / A. Nature of Mathematics / 3. Nature of Numbers / e. Ordinal numbers
13530 An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS]
6. Mathematics / B. Foundations for Mathematics / 6. Mathematics as Set Theory / a. Mathematics is set theory
13518 Modern mathematics has unified all of its objects within set theory [Wolf,RS]
6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics
18198 Mathematics is part of science; transfinite mathematics I take as mostly uninterpreted [Quine]
7. Existence / A. Nature of Existence / 6. Criterion for Existence
18480 Maybe it only exists if it is a truthmaker (rather than the value of a variable)? [MacBride]
7. Existence / C. Structure of Existence / 1. Grounding / a. Nature of grounding
18471 Different types of 'grounding' seem to have no more than a family resemblance relation [MacBride]
18472 Which has priority - 'grounding' or 'truth-making'? [MacBride]
7. Existence / C. Structure of Existence / 6. Fundamentals / d. Logical atoms
18475 Russell allows some complex facts, but Wittgenstein only allows atomic facts [MacBride]
10. Modality / A. Necessity / 6. Logical Necessity
18478 Wittgenstein's plan to show there is only logical necessity failed, because of colours [MacBride]