32 ideas
3656 | The greatest good for a state is true philosophers [Descartes] |
13201 | ∈ says the whole set is in the other; ⊆ says the members of the subset are in the other [Enderton] |
13204 | The 'ordered pair' <x,y> is defined to be {{x}, {x,y}} [Enderton] |
13206 | A 'linear or total ordering' must be transitive and satisfy trichotomy [Enderton] |
13200 | Note that {Φ} =/= Φ, because Φ ∈ {Φ} but Φ ∉ Φ [Enderton] |
13199 | The empty set may look pointless, but many sets can be constructed from it [Enderton] |
13203 | The singleton is defined using the pairing axiom (as {x,x}) [Enderton] |
13202 | Fraenkel added Replacement, to give a theory of ordinal numbers [Enderton] |
13205 | We can only define functions if Choice tells us which items are involved [Enderton] |
16744 | All powers can be explained by obvious features like size, shape and motion of matter [Descartes] |
5016 | Five universals: genus, species, difference, property, accident [Descartes] |
5015 | A universal is a single idea applied to individual things that are similar to one another [Descartes] |
16630 | If we perceive an attribute, we infer the existence of some substance [Descartes] |
5013 | A substance needs nothing else in order to exist [Descartes] |
16633 | A substance has one principal property which is its nature and essence [Descartes] |
3658 | Total doubt can't include your existence while doubting [Descartes] |
5005 | I think, therefore I am, because for a thinking thing to not exist is a contradiction [Descartes] |
5006 | 'Thought' is all our conscious awareness, including feeling as well as understanding [Descartes] |
5012 | 'Nothing comes from nothing' is an eternal truth found within the mind [Descartes] |
5004 | We can know basic Principles without further knowledge, but not the other way round [Descartes] |
5014 | We can understand thinking occuring without imagination or sensation [Descartes] |
5017 | In thinking we shut ourselves off from other substances, showing our identity and separateness [Descartes] |
5010 | Our free will is so self-evident to us that it must be a basic innate idea [Descartes] |
5011 | There are two ultimate classes of existence: thinking substance and extended substance [Descartes] |
5018 | Even if tightly united, mind and body are different, as God could separate them [Descartes] |
23221 | The brain, and all the mental events within it, consists entirely of sensitive and rational matter [Cavendish] |
5007 | Most errors of judgement result from an inaccurate perception of the facts [Descartes] |
5009 | We do not praise the acts of an efficient automaton, as their acts are necessary [Descartes] |
5008 | The greatest perfection of man is to act by free will, and thus merit praise or blame [Descartes] |
15987 | Physics only needs geometry or abstract mathematics, which can explain and demonstrate everything [Descartes] |
12730 | We will not try to understand natural or divine ends, or final causes [Descartes] |
16601 | Matter is not hard, heavy or coloured, but merely extended in space [Descartes] |