38 ideas
| 8893 | For any given area, there seem to be a huge number of possible coherent systems of beliefs [Bonjour] |
| 12442 | 'Mickey Mouse is a fictional mouse' is true without a truthmaker [Azzouni] |
| 12439 | Truth is dispensable, by replacing truth claims with the sentence itself [Azzouni] |
| 12437 | Truth lets us assent to sentences we can't explicitly exhibit [Azzouni] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 12446 | Names function the same way, even if there is no object [Azzouni] |
| 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] |
| 12447 | That all existents have causal powers is unknowable; the claim is simply an epistemic one [Azzouni] |
| 12445 | If fictional objects really don't exist, then they aren't abstract objects [Azzouni] |
| 12449 | Modern metaphysics often derives ontology from the logical forms of sentences [Azzouni] |
| 12440 | If objectual quantifiers ontologically commit, so does the metalanguage for its semantics [Azzouni] |
| 12438 | In the vernacular there is no unequivocal ontological commitment [Azzouni] |
| 12441 | We only get ontology from semantics if we have already smuggled it in [Azzouni] |
| 12448 | Things that don't exist don't have any properties [Azzouni] |
| 8888 | The concept of knowledge is so confused that it is best avoided [Bonjour] |
| 8887 | It is hard to give the concept of 'self-evident' a clear and defensible characterization [Bonjour] |
| 8897 | The adverbial account will still be needed when a mind apprehends its sense-data [Bonjour] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 8896 | Conscious states have built-in awareness of content, so we know if a conceptual description of it is correct [Bonjour] |
| 8891 | My incoherent beliefs about art should not undermine my very coherent beliefs about physics [Bonjour] |
| 8892 | Coherence seems to justify empirical beliefs about externals when there is no external input [Bonjour] |
| 8894 | Coherentists must give a reason why coherent justification is likely to lead to the truth [Bonjour] |
| 8889 | Reliabilists disagree over whether some further requirement is needed to produce knowledge [Bonjour] |
| 8890 | If the reliable facts producing a belief are unknown to me, my belief is not rational or responsible [Bonjour] |
| 8895 | If neither the first-level nor the second-level is itself conscious, there seems to be no consciousness present [Bonjour] |
| 12450 | The periodic table not only defines the elements, but also excludes other possible elements [Azzouni] |