29 ideas
| 23548 | Indeterminacy is in conflict with classical logic [Fine,K] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 23539 | Classical semantics has referents for names, extensions for predicates, and T or F for sentences [Fine,K] |
| 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] |
| 23540 | Conjoining two indefinites by related sentences seems to produce a contradiction [Fine,K] |
| 23546 | Standardly vagueness involves borderline cases, and a higher standpoint from which they can be seen [Fine,K] |
| 23544 | Local indeterminacy concerns a single object, and global indeterminacy covers a range [Fine,K] |
| 23542 | Identifying vagueness with ignorance is the common mistake of confusing symptoms with cause [Fine,K] |
| 23541 | Supervaluation can give no answer to 'who is the last bald man' [Fine,K] |
| 23545 | We do not have an intelligible concept of a borderline case [Fine,K] |
| 19566 | Epistemology does not just concern knowledge; all aspects of cognitive activity are involved [Kvanvig] |
| 19568 | Making sense of things, or finding a good theory, are non-truth-related cognitive successes [Kvanvig] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 19567 | The 'defeasibility' approach says true justified belief is knowledge if no undermining facts could be known [Kvanvig] |
| 19570 | Reliabilism cannot assess the justification for propositions we don't believe [Kvanvig] |
| 23547 | It seems absurd that there is no identity of any kind between two objects which involve survival [Fine,K] |
| 23543 | We identify laws with regularities because we mistakenly identify causes with their symptoms [Fine,K] |