72 ideas
19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
21955 | My dogmatic slumber was first interrupted by David Hume [Kant] |
16931 | Metaphysics is generating a priori knowledge by intuition and concepts, leading to the synthetic [Kant] |
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] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
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] |
16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
16930 | Geometry is not analytic, because a line's being 'straight' is a quality [Kant] |
16919 | Geometry rests on our intuition of space [Kant] |
16920 | Numbers are formed by addition of units in time [Kant] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
16910 | Mathematics can only start from an a priori intuition which is not empirical but pure [Kant] |
16917 | All necessary mathematical judgements are based on intuitions of space and time [Kant] |
16928 | Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant] |
11833 | The substance, once the predicates are removed, remains unknown to us [Kant] |
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] |
5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
21957 | 'Transcendental' concerns how we know, rather than what we know [Kant] |
16923 | I admit there are bodies outside us [Kant] |
21441 | 'Transcendental' is not beyond experience, but a prerequisite of experience [Kant] |
11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
16916 | A priori synthetic knowledge is only of appearances, not of things in themselves [Kant] |
16915 | A priori intuitions can only concern the objects of our senses [Kant] |
16914 | A priori intuition of objects is only possible by containing the form of my sensibility [Kant] |
21447 | I can make no sense of the red experience being similar to the quality in the object [Kant] |
16924 | I count the primary features of things (as well as the secondary ones) as mere appearances [Kant] |
16913 | I can't intuit a present thing in itself, because the properties can't enter my representations [Kant] |
23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
16925 | Appearance gives truth, as long as it is only used within experience [Kant] |
16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
16911 | Intuition is a representation that depends on the presence of the object [Kant] |
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] |
23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause [Kant] |
16926 | Analytic judgements say clearly what was in the concept of the subject [Kant] |
16927 | Analytic judgement rests on contradiction, since the predicate cannot be denied of the subject [Kant] |
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] |
16922 | Space must have three dimensions, because only three lines can meet at right angles [Kant] |
16921 | If all empirical sensation of bodies is removed, space and time are still left [Kant] |
22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |