42 ideas
| 2352 | The job of the philosopher is to distinguish facts about the world from conventions [Putnam] |
| 2345 | Semantic notions do not occur in Tarski's definitions, but assessing their correctness involves translation [Putnam] |
| 2347 | Asserting the truth of an indexical statement is not the same as uttering the statement [Putnam] |
| 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] |
| 2349 | Realists believe truth is correspondence, independent of humans, is bivalent, and is unique [Putnam] |
| 2351 | Aristotle says an object (e.g. a lamp) has identity if its parts stay together when it is moved [Putnam] |
| 2331 | Functionalism says robots and people are the same at one level of abstraction [Putnam] |
| 2071 | If concepts have external meaning, computational states won't explain psychology [Putnam] |
| 2332 | Functionalism can't explain reference and truth, which are needed for logic [Putnam] |
| 2348 | Is there just one computational state for each specific belief? [Putnam] |
| 2344 | If we are going to eliminate folk psychology, we must also eliminate folk logic [Putnam] |
| 2074 | Can we give a scientific, computational account of folk psychology? [Putnam] |
| 2343 | Reference may be different while mental representation is the same [Putnam] |
| 2346 | Meaning and translation (which are needed to define truth) both presuppose the notion of reference [Putnam] |
| 2354 | "Meaning is use" is not a definition of meaning [Putnam] |
| 2336 | Holism seems to make fixed definition more or less impossible [Putnam] |
| 2334 | Meaning holism tried to show that you can't get fixed meanings built out of observation terms [Putnam] |
| 2335 | Understanding a sentence involves background knowledge and can't be done in isolation [Putnam] |
| 2340 | We should separate how the reference of 'gold' is fixed from its conceptual content [Putnam] |
| 2341 | Like names, natural kind terms have their meaning fixed by extension and reference [Putnam] |
| 2339 | Aristotle implies that we have the complete concepts of a language in our heads, but we don't [Putnam] |
| 2338 | Reference (say to 'elms') is a social phenomenon which we can leave to experts [Putnam] |
| 6017 | Nomos is king [Pindar] |
| 2342 | "Water" is a natural kind term, but "H2O" is a description [Putnam] |