34 ideas
| 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] |
| 23708 | Humeans see properties as having no more essential features and relations than their distinctness [Friend/Kimpton-Nye, by PG] |
| 23709 | Dispositions are what individuate properties, and they constitute their essence [Friend/Kimpton-Nye] |
| 23707 | Powers are properties which necessitate dispositions [Friend/Kimpton-Nye] |
| 23714 | Dispositional essentialism (unlike the grounding view) says only fundamental properties are powers [Friend/Kimpton-Nye] |
| 23711 | A power is a property which consists entirely of dispositions [Friend/Kimpton-Nye] |
| 23712 | Powers are qualitative properties which fully ground dispositions [Friend/Kimpton-Nye] |
| 23698 | Dispositions have directed behaviour which occurs if triggered [Friend/Kimpton-Nye] |
| 23699 | 'Masked' dispositions fail to react because something intervenes [Friend/Kimpton-Nye] |
| 23700 | A disposition is 'altered' when the stimulus reverses the disposition [Friend/Kimpton-Nye] |
| 23701 | A disposition is 'mimicked' if a different cause produces that effect from that stimulus [Friend/Kimpton-Nye] |
| 23702 | A 'trick' can look like a stimulus for a disposition which will happen without it [Friend/Kimpton-Nye] |
| 23703 | Some dispositions manifest themselves without a stimulus [Friend/Kimpton-Nye] |
| 23704 | We could analyse dispositions as 'possibilities', with no mention of a stimulus [Friend/Kimpton-Nye] |
| 23710 | Dispositionalism says modality is in the powers of this world, not outsourced to possible worlds [Friend/Kimpton-Nye] |
| 18969 | How do you distinguish three beliefs from four beliefs or two beliefs? [Quine] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 18967 | A 'proposition' is said to be the timeless cognitive part of the meaning of a sentence [Quine] |
| 18968 | The problem with propositions is their individuation. When do two sentences express one proposition? [Quine] |
| 23706 | Hume's Dictum says no connections are necessary - so mass and spacetime warping could separate [Friend/Kimpton-Nye] |
| 18970 | The concept of a 'point' makes no sense without the idea of absolute position [Quine] |