50 ideas
2463 | A standard naturalist view is realist, externalist, and computationalist, and believes in rationality [Fodor] |
2435 | Psychology has to include the idea that mental processes are typically truth-preserving [Fodor] |
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] |
2442 | Inferences are surely part of the causal structure of the world [Fodor] |
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] |
2462 | Control of belief is possible if you know truth conditions and what causes beliefs [Fodor] |
2461 | An experiment is a deliberate version of what informal thinking does all the time [Fodor] |
2454 | We can deliberately cause ourselves to have true thoughts - hence the value of experiments [Fodor] |
2455 | Interrogation and experiment submit us to having beliefs caused [Fodor] |
2460 | Participation in an experiment requires agreement about what the outcome will mean [Fodor] |
18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
2458 | Theories are links in the causal chain between the environment and our beliefs [Fodor] |
2443 | I say psychology is intentional, semantics is informational, and thinking is computation [Fodor] |
2453 | We are probably the only creatures that can think about our own thoughts [Fodor] |
2446 | Cartesians consider interaction to be a miracle [Fodor] |
2445 | Semantics v syntax is the interaction problem all over again [Fodor] |
2464 | Type physicalism equates mental kinds with physical kinds [Fodor] |
2447 | Hume has no theory of the co-ordination of the mind [Fodor] |
2440 | Propositional attitudes are propositions presented in a certain way [Fodor] |
2450 | Rationality has mental properties - autonomy, productivity, experiment [Fodor] |
2437 | XYZ (Twin Earth 'water') is an impossibility [Fodor] |
2441 | Truth conditions require a broad concept of content [Fodor] |
3114 | Concepts aren't linked to stuff; they are what is caused by stuff [Fodor] |
2452 | Knowing the cause of a thought is almost knowing its content [Fodor] |
2432 | Is content basically information, fixed externally? [Fodor] |
2438 | In the information view, concepts are potentials for making distinctions [Fodor] |
2439 | Semantic externalism says the concept 'elm' needs no further beliefs or inferences [Fodor] |
2457 | If meaning is information, that establishes the causal link between the state of the world and our beliefs [Fodor] |
2451 | To know the content of a thought is to know what would make it true [Fodor] |
2433 | For holists no two thoughts are ever quite the same, which destroys faith in meaning [Fodor] |
2436 | It is claimed that reference doesn't fix sense (Jocasta), and sense doesn't fix reference (Twin Earth) [Fodor] |
2434 | Broad semantics holds that the basic semantic properties are truth and denotation [Fodor] |
2459 | Externalist semantics are necessary to connect the contents of beliefs with how the world is [Fodor] |