50 ideas
18450 | Philosophy has its own mode of death, by separating soul from body [Porphyry] |
6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
21492 | Realism is basic to the scientific method [Peirce] |
6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
18451 | The presence of the incorporeal is only known by certain kinds of disposition [Porphyry] |
18459 | Diversity arises from the power of unity [Porphyry] |
6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
18452 | Memory is not conserved images, but reproduction of previous thought [Porphyry] |
6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
18453 | Intelligence is aware of itself, so the intelligence is both the thinker and the thought [Porphyry] |
18462 | The soul is everywhere and nowhere in the body, and must be its cause [Porphyry] |
18463 | Successful introspection reveals the substrate along with the object of thought [Porphyry] |
18458 | The soul is bound to matter by the force of its own disposition [Porphyry] |
18464 | Justice is each person fulfilling his function [Porphyry] |
18448 | We should avoid the pleasures of love, or at least, should not enact our dreams [Porphyry] |
18444 | Civil virtues make us behave benevolently, and thereby unite citizens [Porphyry] |
18445 | Civil virtues control the passions, and make us conform to our nature [Porphyry] |
18446 | Purificatory virtues detach the soul completely from the passions [Porphyry] |
18447 | There are practical, purificatory, contemplative, and exemplary virtues [Porphyry] |
18456 | Unified real existence is neither great nor small, though greatness and smallness participate in it [Porphyry] |
6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
18454 | Time is the circular movement of the soul [Porphyry] |
18455 | Some think time is seen at rest, as well as in movement [Porphyry] |
6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
18460 | God is nowhere, and hence everywhere [Porphyry] |
6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |
18461 | Everything existing proceeds from divinity, and is within divinity [Porphyry] |
18449 | Nature binds or detaches body to soul, but soul itself joins and detaches soul from body [Porphyry] |
18457 | Individual souls are all connected, though distinct, and without dividing universal Soul [Porphyry] |