65 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] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 2442 | Inferences are surely part of the causal structure of the world [Fodor] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 12189 | Logical necessity involves a decision about usage, and is non-realist and non-cognitive [Wright,C, by McFetridge] |
| 2462 | Control of belief is possible if you know truth conditions and what causes beliefs [Fodor] |
| 2460 | Participation in an experiment requires agreement about what the outcome will mean [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] |
| 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] |
| 7320 | Holism cannot give a coherent account of scientific methodology [Wright,C, by Miller,A] |
| 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] |