29 ideas
14001 | People who use science to make philosophical points don't realise how philosophical science is [Markosian] |
13991 | Presentism has the problem that if Socrates ceases to exist, so do propositions about him [Markosian] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
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] |
14002 | Possible worlds must be abstract, because two qualitatively identical worlds are just one world [Markosian] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
14000 | 'Grabby' truth conditions first select their object, unlike 'searchy' truth conditions [Markosian] |
23053 | The great interest of the human race is cordial unity and unlimited mutual aid [Owen] |
13990 | Presentism is the view that only present objects exist [Markosian] |
13992 | Presentism says if objects don't exist now, we can't have attitudes to them or relations with them [Markosian] |
13994 | Presentism seems to entail that we cannot talk about other times [Markosian] |
13995 | Serious Presentism says things must exist to have relations and properties; Unrestricted version denies this [Markosian] |
13996 | Maybe Presentists can refer to the haecceity of a thing, after the thing itself disappears [Markosian] |
13997 | Maybe Presentists can paraphrase singular propositions about the past [Markosian] |
13993 | Special Relativity denies the absolute present which Presentism needs [Markosian] |
13998 | Objects in the past, like Socrates, are more like imaginary objects than like remote spatial objects [Markosian] |
13999 | People are mistaken when they think 'Socrates was a philosopher' says something [Markosian] |