53 ideas
| 3593 | The only way to specify the corresponding fact is asserting the sentence [Williams,M] |
| 3585 | Coherence needs positive links, not just absence of conflict [Williams,M] |
| 3584 | Justification needs coherence, while truth might be ideal coherence [Williams,M] |
| 3599 | Deduction shows entailments, not what to believe [Williams,M] |
| 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] |
| 12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
| 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] |
| 12211 | It is plausible that x^2 = -1 had no solutions before complex numbers were 'introduced' [Fine,K] |
| 12209 | The indispensability argument shows that nature is non-numerical, not the denial of numbers [Fine,K] |
| 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] |
| 12214 | 'Exists' is a predicate, not a quantifier; 'electrons exist' is like 'electrons spin' [Fine,K] |
| 12212 | Just as we introduced complex numbers, so we introduced sums and temporal parts [Fine,K] |
| 12216 | Real objects are those which figure in the facts that constitute reality [Fine,K] |
| 12218 | Being real and being fundamental are separate; Thales's water might be real and divisible [Fine,K] |
| 12217 | For ontology we need, not internal or external views, but a view from outside reality [Fine,K] |
| 12213 | Ontological claims are often universal, and not a matter of existential quantification [Fine,K] |
| 3591 | We could never pin down how many beliefs we have [Williams,M] |
| 3582 | Propositions make error possible, so basic experiential knowledge is impossible [Williams,M] |
| 3592 | Phenomenalism is a form of idealism [Williams,M] |
| 3579 | Sense data avoid the danger of misrepresenting the world [Williams,M] |
| 3581 | Sense data can't give us knowledge if they are non-propositional [Williams,M] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 3564 | Is it people who are justified, or propositions? [Williams,M] |
| 3595 | What works always takes precedence over theories [Williams,M] |
| 3580 | Experience must be meaningful to act as foundations [Williams,M] |
| 3578 | Are empirical foundations judgements or experiences? [Williams,M] |
| 3576 | Foundationalists are torn between adequacy and security [Williams,M] |
| 3577 | Strong justification eliminates error, but also reduces our true beliefs [Williams,M] |
| 3589 | Why should diverse parts of our knowledge be connected? [Williams,M] |
| 3590 | Coherence theory must give a foundational status to coherence itself [Williams,M] |
| 3571 | Externalism does not require knowing that you know [Williams,M] |
| 3574 | Externalism ignores the social aspect of knowledge [Williams,M] |
| 3569 | In the causal theory of knowledge the facts must cause the belief [Williams,M] |
| 3567 | How could there be causal relations to mathematical facts? [Williams,M] |
| 3586 | Only a belief can justify a belief [Williams,M] |
| 3573 | Externalist reliability refers to a range of conventional conditions [Williams,M] |
| 3565 | Sometimes I ought to distrust sources which are actually reliable [Williams,M] |
| 3566 | We control our beliefs by virtue of how we enquire [Williams,M] |
| 3594 | Scepticism just reveals our limited ability to explain things [Williams,M] |
| 3575 | Scepticism can involve discrepancy, relativity, infinity, assumption and circularity [Williams,M] |
| 3587 | Seeing electrons in a cloud chamber requires theory [Williams,M] |
| 3588 | Foundationalists base meaning in words, coherentists base it in sentences [Williams,M] |