65 ideas
| 5750 | Consistency is modal, saying propositions are consistent if they could be true together [Melia] |
| 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] |
| 21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
| 5737 | Predicate logic has connectives, quantifiers, variables, predicates, equality, names and brackets [Melia] |
| 5744 | First-order predicate calculus is extensional logic, but quantified modal logic is intensional (hence dubious) [Melia] |
| 17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
| 2442 | Inferences are surely part of the causal structure of the world [Fodor] |
| 5740 | Second-order logic needs second-order variables and quantification into predicate position [Melia] |
| 5741 | If every model that makes premises true also makes conclusion true, the argument is valid [Melia] |
| 17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
| 10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
| 19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
| 10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
| 17888 | The undecidable sentence can be decided at a 'higher' level in the system [Gödel] |
| 10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
| 3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
| 10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
| 9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
| 11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
| 10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
| 10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
| 10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
| 10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
| 8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, by Shapiro] |
| 5736 | No sort of plain language or levels of logic can express modal facts properly [Melia] |
| 5735 | Maybe names and predicates can capture any fact [Melia] |
| 5746 | The Identity of Indiscernibles is contentious for qualities, and trivial for non-qualities [Melia] |
| 5738 | We may be sure that P is necessary, but is it necessarily necessary? [Melia] |
| 5732 | 'De re' modality is about things themselves, 'de dicto' modality is about propositions [Melia] |
| 5739 | Sometimes we want to specify in what ways a thing is possible [Melia] |
| 5734 | Possible worlds make it possible to define necessity and counterfactuals without new primitives [Melia] |
| 5742 | In possible worlds semantics the modal operators are treated as quantifiers [Melia] |
| 5743 | If possible worlds semantics is not realist about possible worlds, logic becomes merely formal [Melia] |
| 5749 | Possible worlds could be real as mathematics, propositions, properties, or like books [Melia] |
| 5751 | The truth of propositions at possible worlds are implied by the world, just as in books [Melia] |
| 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] |
| 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] |
| 3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
| 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] |
| 5748 | We accept unverifiable propositions because of simplicity, utility, explanation and plausibility [Melia] |
| 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] |