103 ideas
12644 | Who cares what 'philosophy' is? Most pre-1950 thought doesn't now count as philosophy [Fodor] |
12633 | Definitions often give necessary but not sufficient conditions for an extension [Fodor] |
224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
232 | Opposites are as unlike as possible [Plato] |
8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
18194 | 'Forcing' can produce new models of ZFC from old models [Maddy] |
18195 | A Large Cardinal Axiom would assert ever-increasing stages in the hierarchy [Maddy] |
18191 | Axiom of Infinity: completed infinite collections can be treated mathematically [Maddy] |
18193 | The Axiom of Foundation says every set exists at a level in the set hierarchy [Maddy] |
18169 | Axiom of Reducibility: propositional functions are extensionally predicative [Maddy] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
12664 | A truth-table, not inferential role, defines 'and' [Fodor] |
12648 | Names in thought afford a primitive way to bring John before the mind [Fodor] |
12650 | 'Paderewski' has two names in mentalese, for his pianist file and his politician file [Fodor] |
12656 | P-and-Q gets its truth from the truth of P and truth of Q, but consistency isn't like that [Fodor] |
13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on Plato] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18172 | Infinity has degrees, and large cardinals are the heart of set theory [Maddy] |
18175 | For any cardinal there is always a larger one (so there is no set of all sets) [Maddy] |
18196 | An 'inaccessible' cardinal cannot be reached by union sets or power sets [Maddy] |
18187 | Theorems about limits could only be proved once the real numbers were understood [Maddy] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
18164 | Frege solves the Caesar problem by explicitly defining each number [Maddy] |
18184 | Making set theory foundational to mathematics leads to very fruitful axioms [Maddy] |
18185 | Unified set theory gives a final court of appeal for mathematics [Maddy] |
18183 | Set theory brings mathematics into one arena, where interrelations become clearer [Maddy] |
18186 | Identifying geometric points with real numbers revealed the power of set theory [Maddy] |
18188 | The line of rationals has gaps, but set theory provided an ordered continuum [Maddy] |
18163 | Mathematics rests on the logic of proofs, and on the set theoretic axioms [Maddy] |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
227 | You must always mean the same thing when you utter the same name [Plato] |
223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
211 | If admirable things have Forms, maybe everything else does as well [Plato] |
220 | The concept of a master includes the concept of a slave [Plato] |
16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
15851 | Parts must belong to a created thing with a distinct form [Plato] |
15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
12653 | There's statistical, logical, nomological, conceptual and metaphysical possibility [Fodor] |
12651 | Some beliefs are only inferred when needed, like 'Shakespeare had not telephone' [Fodor] |
12628 | Knowing that must come before knowing how [Fodor] |
12625 | Pragmatism is the worst idea ever [Fodor] |
12636 | Mental states have causal powers [Fodor] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
12661 | The different types of resemblance don't resemble one another [Fodor] |
12632 | In the Representational view, concepts play the key linking role [Fodor] |
12624 | Only the labels of nodes have semantic content in connectionism, and they play no role [Fodor] |
12641 | Connectionism gives no account of how constituents make complex concepts [Fodor] |
12640 | Associative thinking avoids syntax, but can't preserve sense, reference or truth [Fodor] |
12643 | Ambiguities in English are the classic reason for claiming that we don't think in English [Fodor] |
12649 | We think in file names [Fodor] |
12647 | Mental representations name things in the world, but also files in our memory [Fodor] |
12655 | Frame Problem: how to eliminate most beliefs as irrelevant, without searching them? [Fodor] |
12630 | If concept content is reference, then my Twin and I are referring to the same stuff [Fodor] |
12658 | Nobody knows how concepts are acquired [Fodor] |
12662 | We have an innate capacity to form a concept, once we have grasped the stereotype [Fodor] |
12635 | Having a concept isn't a pragmatic matter, but being able to think about the concept [Fodor] |
12652 | Concepts have two sides; they are files that face thought, and also face subject-matter [Fodor] |
12626 | Cartesians put concept individuation before concept possession [Fodor] |
12637 | Frege's puzzles suggest to many that concepts have sense as well as reference [Fodor] |
12638 | If concepts have sense, we can't see the connection to their causal powers [Fodor] |
12639 | Belief in 'senses' may explain intentionality, but not mental processes [Fodor] |
12654 | You can't think 'brown dog' without thinking 'brown' and 'dog' [Fodor] |
12659 | Maybe stereotypes are a stage in concept acquisition (rather than a by-product) [Fodor] |
12660 | One stereotype might be a paradigm for two difference concepts [Fodor] |
12629 | For the referential view of thought, the content of a concept is just its reference [Fodor] |
12631 | Compositionality requires that concepts be atomic [Fodor] |
12657 | Abstractionism claims that instances provide criteria for what is shared [Fodor] |
12634 | 'Inferential-role semantics' says meaning is determined by role in inference [Fodor] |
12642 | Co-referring terms differ if they have different causal powers [Fodor] |
12663 | We refer to individuals and to properties, and we use singular terms and predicates [Fodor] |
12645 | Semantics (esp. referential semantics) allows inferences from utterances to the world [Fodor] |
12646 | Semantics relates to the world, so it is never just psychological [Fodor] |
12627 | Before you can plan action, you must decide on the truth of your estimate of success [Fodor] |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
225 | The unlimited has no shape and is endless [Plato] |
233 | Some things do not partake of the One [Plato] |
2062 | The only movement possible for the One is in space or in alteration [Plato] |
231 | Everything partakes of the One in some way [Plato] |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |