28 ideas
| 18365 | If truths are just identical with facts, then truths will make themselves true [David] |
| 18362 | Examples show that truth-making is just non-symmetric, not asymmetric [David] |
| 18360 | It is assumed that a proposition is necessarily true if its truth-maker exists [David] |
| 18358 | Two different propositions can have the same fact as truth-maker [David] |
| 18355 | What matters is truth-making (not truth-makers) [David] |
| 18354 | Correspondence is symmetric, while truth-making is taken to be asymmetric [David] |
| 18356 | Correspondence is an over-ambitious attempt to explain truth-making [David] |
| 18363 | Correspondence theorists see facts as the only truth-makers [David] |
| 18364 | Correspondence theory likes ideal languages, that reveal the structure of propositions [David] |
| 18357 | What makes a disjunction true is simpler than the disjunctive fact it names [David] |
| 18359 | One proposition can be made true by many different facts [David] |
| 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] |
| 18361 | A reflexive relation entails that the relation can't be asymmetric [David] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 15313 | By 'force' I mean the sources of all actions - sometimes called 'powers' by their outcomes [Breheny] |