43 ideas
22002 | Wolff's version of Leibniz dominated mid-18th C German thought [Pinkard] |
22021 | Romantics explored beautiful subjectivity, and the re-enchantment of nature [Pinkard] |
22010 | The combination of Kant and the French Revolution was an excited focus for German philosophy [Pinkard] |
22036 | In Hegel's time naturalism was called 'Spinozism' [Pinkard] |
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] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
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] |
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] |
16665 | There are entities, and then positive 'modes', modifying aspects outside the thing's essence [Suárez] |
16666 | A mode determines the state and character of a quantity, without adding to it [Suárez] |
16667 | Substances are incomplete unless they have modes [Suárez, by Pasnau] |
17007 | Forms must rule over faculties and accidents, and are the source of action and unity [Suárez] |
16780 | Partial forms of leaf and fruit are united in the whole form of the tree [Suárez] |
16758 | The best support for substantial forms is the co-ordinated unity of a natural being [Suárez] |
16743 | We can get at the essential nature of 'quantity' by knowing bulk and extension [Suárez] |
13074 | Only natural kinds and their members have real essences [Suárez, by Cover/O'Leary-Hawthorne] |
16742 | We only know essences through non-essential features, esp. those closest to the essence [Suárez] |
22143 | Identity does not exclude possible or imagined difference [Suárez, by Boulter] |
22144 | Real Essential distinction: A and B are of different natural kinds [Suárez, by Boulter] |
22146 | Minor Real distinction: B needs A, but A doesn't need B [Suárez, by Boulter] |
22145 | Major Real distinction: A and B have independent existences [Suárez, by Boulter] |
22147 | Conceptual/Mental distinction: one thing can be conceived of in two different ways [Suárez, by Boulter] |
22148 | Modal distinction: A isn't B or its property, but still needs B [Suárez, by Boulter] |
22149 | Scholastics assess possibility by what has actually happened in reality [Suárez, by Boulter] |
22048 | Idealism is the link between reason and freedom [Pinkard] |
7563 | The old 'influx' view of causation says it is a flow of accidental properties from A to B [Suárez, by Jolley] |
16682 | Other things could occupy the same location as an angel [Suárez] |