27 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] |
| 5806 | Belief is the power of metarepresentation [Dretske] |
| 5801 | A mouse hearing a piano played does not believe it, because it lacks concepts and understanding [Dretske] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 5802 | Representations are in the head, but their content is not, as stories don't exist in their books [Dretske] |
| 5809 | Some activities are performed better without consciousness of them [Dretske] |
| 5808 | Qualia are just the properties objects are represented as having [Dretske] |
| 5807 | Introspection is the same as the experience one is introspecting [Dretske] |
| 5803 | In a representational theory of mind, introspection is displaced perception [Dretske] |
| 5805 | Introspection does not involve looking inwards [Dretske] |
| 5804 | A representational theory of the mind is an externalist theory of the mind [Dretske] |
| 5800 | All mental facts are representation, which consists of informational functions [Dretske] |
| 23812 | Force is what turns man into a thing, and ultimately into a corpse [Weil] |
| 23813 | Only people who understand force, and don't respect it, are capable of justice [Weil] |