29 ideas
3340 | Von Neumann defines each number as the set of all smaller numbers [Neumann, by Blackburn] |
15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
3355 | Von Neumann wanted mathematical functions to replace sets [Neumann, by Benardete,JA] |
13489 | Von Neumann treated cardinals as a special sort of ordinal [Neumann, by Hart,WD] |
22716 | Von Neumann defined ordinals as the set of all smaller ordinals [Neumann, by Poundstone] |
12336 | A von Neumann ordinal is a transitive set with transitive elements [Neumann, by Badiou] |
18179 | For Von Neumann the successor of n is n U {n} (rather than {n}) [Neumann, by Maddy] |
18180 | Von Neumann numbers are preferred, because they continue into the transfinite [Maddy on Neumann] |
15925 | Each Von Neumann ordinal number is the set of its predecessors [Neumann, by Lavine] |
13672 | All the axioms for mathematics presuppose set theory [Neumann] |
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] |
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] |
1513 | The Egyptians were the first to say the soul is immortal and reincarnated [Herodotus] |