39 ideas
1798 | He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius] |
1800 | Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [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] |
12756 | Substance is a force for acting and being acted upon [Leibniz] |
6595 | If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin] |
6593 | The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin] |
6592 | Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin] |
1801 | Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius] |
1803 | Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius] |
1809 | Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius] |
1805 | Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius] |
1808 | Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius] |
1804 | Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius] |
1806 | Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius] |
1802 | Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius] |
1807 | Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius] |
1810 | Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius] |
12755 | Final causes can help with explanations in physics [Leibniz] |
12760 | Something rather like souls (though not intelligent) could be found everywhere [Leibniz] |
12759 | There are atoms of substance, but no atoms of bulk or extension [Leibniz] |
12718 | Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz] |
3062 | There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius] |
11854 | If there is some trace of God in things, that would explain their natural force [Leibniz] |
3063 | Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius] |
12758 | It is plausible to think substances contain the same immanent force seen in our free will [Leibniz] |
19408 | To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz] |