25 ideas
| 14965 | Truth rests on Elimination ('A' is true → A) and Introduction (A → 'A' is true) [Gupta] |
| 14968 | A weakened classical language can contain its own truth predicate [Gupta] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 14964 | The Liar reappears, even if one insists on propositions instead of sentences [Gupta] |
| 14969 | Strengthened Liar: either this sentence is neither-true-nor-false, or it is not true [Gupta] |
| 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] |
| 4483 | If abstract terms are sets of tropes, 'being a unicorn' and 'being a griffin' turn out identical [Loux] |
| 4481 | Austere nominalists insist that the realist's universals lack the requisite independent identifiability [Loux] |
| 4477 | Universals come in hierarchies of generality [Loux] |
| 4482 | Austere nominalism has to take a host of things (like being red, or human) as primitive [Loux] |
| 4478 | Nominalism needs to account for abstract singular terms like 'circularity'. [Loux] |
| 4480 | Times and places are identified by objects, so cannot be used in a theory of object-identity [Loux] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |