26 ideas
| 5035 | The two basics of reasoning are contradiction and sufficient reason [Leibniz] |
| 17311 | Real definitions don't just single out a thing; they must also explain its essence [Koslicki] |
| 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] |
| 17312 | It is more explanatory if you show how a number is constructed from basic entities and relations [Koslicki] |
| 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] |
| 17314 | The relata of grounding are propositions or facts, but for dependence it is objects and their features [Koslicki] |
| 17313 | Modern views want essences just to individuate things across worlds and times [Koslicki] |
| 17309 | For Fine, essences are propositions true because of identity, so they are just real definitions [Koslicki] |
| 17315 | We need a less propositional view of essence, and so must distinguish it clearly from real definitions [Koslicki] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 17317 | A good explanation captures the real-world dependence among the phenomena [Koslicki] |
| 5038 | Assume that mind and body follow their own laws, but God has harmonised them [Leibniz] |
| 17316 | We can abstract to a dependent entity by blocking out features of its bearer [Koslicki] |
| 5037 | God doesn't decide that Adam will sin, but that sinful Adam's existence is to be preferred [Leibniz] |