21 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] |
| 14330 | To be realists about dispositions, we can only discuss them through their categorical basis [Armstrong] |
| 6498 | Armstrong suggests secondary qualities are blurred primary qualities [Armstrong, by Robinson,H] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 5690 | A mental state without belief refutes self-intimation; a belief with no state refutes infallibility [Armstrong, by Shoemaker] |
| 5493 | If pains are defined causally, and research shows that the causal role is physical, then pains are physical [Armstrong, by Lycan] |
| 4600 | Armstrong and Lewis see functionalism as an identity of the function and its realiser [Armstrong, by Heil] |
| 23053 | The great interest of the human race is cordial unity and unlimited mutual aid [Owen] |