34 ideas
| 22353 | One view says objectivity is making a successful claim which captures the facts [Reiss/Sprenger] |
| 22356 | An absolute scientific picture of reality must not involve sense experience, which is perspectival [Reiss/Sprenger] |
| 22359 | Topic and application involve values, but can evidence and theory choice avoid them? [Reiss/Sprenger] |
| 22360 | The Value-Free Ideal in science avoids contextual values, but embraces epistemic values [Reiss/Sprenger] |
| 22362 | Value-free science needs impartial evaluation, theories asserting facts, and right motivation [Reiss/Sprenger] |
| 22364 | Thermometers depend on the substance used, and none of them are perfect [Reiss/Sprenger] |
| 14025 | The weaker version of Truthmaker: 'truth supervenes on being' [Crisp,TM] |
| 14023 | The Truthmaker thesis spells trouble for presentists [Crisp,TM] |
| 14024 | Truthmaker has problems with generalisation, non-existence claims, and property instantiations [Crisp,TM] |
| 13520 | A 'tautology' must include connectives [Wolf,RS] |
| 13524 | Deduction Theorem: T∪{P}|-Q, then T|-(P→Q), which justifies Conditional Proof [Wolf,RS] |
| 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] |
| 13523 | Existential Generalization (or 'proof by example'): if we can say P(t), then we can say something is P [Wolf,RS] |
| 13529 | Empty Set: ∃x∀y ¬(y∈x). The unique empty set exists [Wolf,RS] |
| 13526 | Comprehension Axiom: if a collection is clearly specified, it is a set [Wolf,RS] |
| 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] |
| 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] |
| 13537 | An 'isomorphism' is a bijection that preserves all structural components [Wolf,RS] |
| 13539 | The LST Theorem is a serious limitation of first-order logic [Wolf,RS] |
| 13538 | If a theory is complete, only a more powerful language can strengthen it [Wolf,RS] |
| 13525 | Most deductive logic (unlike ordinary reasoning) is 'monotonic' - we don't retract after new givens [Wolf,RS] |
| 13530 | An ordinal is an equivalence class of well-orderings, or a transitive set whose members are transitive [Wolf,RS] |
| 13518 | Modern mathematics has unified all of its objects within set theory [Wolf,RS] |
| 14021 | Worm Perdurantism has a fusion of all the parts; Stage Perdurantism has one part at a time [Crisp,TM] |
| 22357 | The 'experimenter's regress' says success needs reliability, which is only tested by success [Reiss/Sprenger] |
| 22365 | The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger] |
| 14020 | 'Eternalism' is the thesis that reality includes past, present and future entities [Crisp,TM] |
| 14026 | Presentists can talk of 'times', with no more commitment than modalists have to possible worlds [Crisp,TM] |
| 14022 | The only three theories are Presentism, Dynamic (A-series) Eternalism and Static (B-series) Eternalism [Crisp,TM] |