74 ideas
19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
23770 | Reductive analysis makes a concept clearer, by giving an alternative simpler set [Williams,NE] |
1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
23769 | Promoting an ontology by its implied good metaphysic is an 'argument-by-display' [Williams,NE] |
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] |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
18168 | 'Propositional functions' are propositions with a variable as subject or predicate [Maddy] |
18190 | Completed infinities resulted from giving foundations to calculus [Maddy] |
18171 | Cantor and Dedekind brought completed infinities into mathematics [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] |
18207 | Maybe applications of continuum mathematics are all idealisations [Maddy] |
18204 | Scientists posit as few entities as possible, but set theorist posit as many as possible [Maddy] |
18167 | We can get arithmetic directly from HP; Law V was used to get HP from the definition of number [Maddy] |
23783 | Change exists, it is causal, and it needs an explanation [Williams,NE] |
23784 | Processes don't begin or end; they just change direction unexpectedly [Williams,NE] |
23790 | Processes are either strings of short unchanging states, or continuous and unreducible events [Williams,NE] |
23786 | The status quo is part of what exists, and so needs metaphysical explanation [Williams,NE] |
23768 | A metaphysic is a set of wider explanations derived from a basic ontology [Williams,NE] |
23773 | Humeans say properties are passive, possibility is vast, laws are descriptions, causation is weak [Williams,NE] |
23779 | We shouldn't posit the existence of anything we have a word for [Williams,NE] |
18205 | The theoretical indispensability of atoms did not at first convince scientists that they were real [Maddy] |
23775 | Powers are 'multi-track' if they can produce a variety of manifestations [Williams,NE] |
23780 | Every possible state of affairs is written into its originating powers [Williams,NE] |
23789 | Naming powers is unwise, because that it usually done by a single manifestation [Williams,NE] |
23771 | Fundamental physics describes everything in terms of powers [Williams,NE] |
23776 | Rather than pure powers or pure categoricals, I favour basics which are both at once [Williams,NE] |
23777 | Powers are more complicated than properties which are always on display [Williams,NE] |
23774 | There are basic powers, which underlie dispositions, potentialities, capacities etc [Williams,NE] |
23791 | Dispositions are just useful descriptions, which are explained by underlying powers [Williams,NE] |
23772 | If objects are property bundles, the properties need combining powers [Williams,NE] |
13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
23788 | Four-Dimensional is Perdurantism (temporal parts), plus Eternalism [Williams,NE] |
5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
18206 | Science idealises the earth's surface, the oceans, continuities, and liquids [Maddy] |
23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
23785 | Causation needs to explain stasis, as well as change [Williams,NE] |
23782 | Causation is the exercise of powers [Williams,NE] |
23787 | If causes and effects overlap, that makes changes impossible [Williams,NE] |
23778 | Powers contain lawlike features, pointing to possible future states [Williams,NE] |
22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |