36 ideas
24032 | Clever scholars can obscure things which are obvious even to peasants [Descartes] |
24033 | Most scholastic disputes concern words, where agreeing on meanings would settle them [Descartes] |
24024 | The secret of the method is to recognise which thing in a series is the simplest [Descartes] |
24018 | One truth leads us to another [Descartes] |
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] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
24035 | Unity is something shared by many things, so in that respect they are equals [Descartes] |
24036 | I can only see the proportion of two to three if there is a common measure - their unity [Descartes] |
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] |
24029 | Among the simples are the graspable negations, such as rest and instants [Descartes] |
18528 | The single imagined 'interval' between things only exists in the intellect [Auriol] |
24030 | 3+4=7 is necessary because we cannot conceive of seven without including three and four [Descartes] |
24019 | If we accept mere probabilities as true we undermine our existing knowledge [Descartes] |
24020 | We all see intuitively that we exist, where intuition is attentive, clear and distinct rational understanding [Descartes] |
24031 | When Socrates doubts, he know he doubts, and that truth is possible [Descartes] |
24025 | Clear and distinct truths must be known all at once (unlike deductions) [Descartes] |
24022 | Our souls possess divine seeds of knowledge, which can bear spontaneous fruit [Descartes] |
24034 | If someone had only seen the basic colours, they could deduce the others from resemblance [Descartes] |
24021 | The method starts with clear intuitions, followed by a process of deduction [Descartes] |
24027 | Nerves and movement originate in the brain, where imagination moves them [Descartes] |
24026 | Our four knowledge faculties are intelligence, imagination, the senses, and memory [Descartes] |
24028 | The force by which we know things is spiritual, and quite distinct from the body [Descartes] |
24023 | All the sciences searching for order and measure are related to mathematics [Descartes] |
16589 | Prime matter lacks essence, but is only potentially and indeterminately a physical thing [Auriol] |
16651 | God can do anything non-contradictory, as making straightness with no line, or lightness with no parts [Auriol] |