26 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] |
| 12756 | Substance is a force for acting and being acted upon [Leibniz] |
| 21227 | The Cogito demands a bridge to the world, and ends in isolating the ego [Velarde-Mayol] |
| 21215 | The representation may not be a likeness [Velarde-Mayol] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 12755 | Final causes can help with explanations in physics [Leibniz] |
| 12760 | Something rather like souls (though not intelligent) could be found everywhere [Leibniz] |
| 12759 | There are atoms of substance, but no atoms of bulk or extension [Leibniz] |
| 12718 | Secondary matter is active and complete; primary matter is passive and incomplete [Leibniz] |
| 11854 | If there is some trace of God in things, that would explain their natural force [Leibniz] |
| 21219 | Find the essence by varying an object, to see what remains invariable [Velarde-Mayol] |
| 12758 | It is plausible to think substances contain the same immanent force seen in our free will [Leibniz] |
| 19408 | To say that nature or the one universal substance is God is a pernicious doctrine [Leibniz] |