51 ideas
| 3656 | The greatest good for a state is true philosophers [Descartes] |
| 22024 | Fichte's subjectivity struggles to then give any account of objectivity [Pinkard on Fichte] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 22017 | Normativity needs the possibility of negation, in affirmation and denial [Fichte, by Pinkard] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 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] |
| 22018 | Necessary truths derive from basic assertion and negation [Fichte, by Pinkard] |
| 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] |
| 22064 | Fichte's logic is much too narrow, and doesn't deduce ethics, art, society or life [Schlegel,F on Fichte] |
| 22032 | Fichte's key claim was that the subjective-objective distinction must itself be subjective [Fichte, by Pinkard] |
| 5012 | 'Nothing comes from nothing' is an eternal truth found within the mind [Descartes] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 5004 | We can know basic Principles without further knowledge, but not the other way round [Descartes] |
| 22020 | We only see ourselves as self-conscious and rational in relation to other rationalities [Fichte] |
| 5014 | We can understand thinking occuring without imagination or sensation [Descartes] |
| 22060 | The Self is the spontaneity, self-relatedness and unity needed for knowledge [Fichte, by Siep] |
| 22066 | Novalis sought a much wider concept of the ego than Fichte's proposal [Novalis on Fichte] |
| 22016 | The self is not a 'thing', but what emerges from an assertion of normativity [Fichte, by Pinkard] |
| 22019 | Consciousness of an object always entails awareness of the self [Fichte] |
| 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] |
| 22061 | Judgement is distinguishing concepts, and seeing their relations [Fichte, by Siep] |
| 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] |
| 22023 | Fichte's idea of spontaneity implied that nothing counts unless we give it status [Fichte, by Pinkard] |
| 15987 | Physics only needs geometry or abstract mathematics, which can explain and demonstrate everything [Descartes] |
| 22065 | Fichte reduces nature to a lifeless immobility [Schlegel,F on Fichte] |
| 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] |