25 ideas
| 17325 | Truth-maker theory can't cope with non-causal dependence [Liggins] |
| 17318 | Truthmakers for existence is fine; otherwise maybe restrict it to synthetic truths? [Liggins] |
| 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] |
| 17320 | Either p is true or not-p is true, so something is true, so something exists [Liggins] |
| 17326 | The dependence of {Socrates} on Socrates involves a set and a philosopher, not facts [Liggins] |
| 17327 | Non-causal dependence is at present only dimly understood [Liggins] |
| 17322 | Necessities supervene on everything, but don't depend on everything [Liggins] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 17324 | 'Because' can signal an inference rather than an explanation [Liggins] |
| 17321 | Value, constitution and realisation are non-causal dependences that explain [Liggins] |
| 17323 | If explanations track dependence, then 'determinative' explanations seem to exist [Liggins] |
| 23222 | A soul with physical extension is more likely than an immaterial soul that moves bodies [Elizabeth] |