35 ideas
| 8820 | Rules of reasoning precede the concept of truth, and they are what characterize it [Pollock] |
| 8819 | We need the concept of truth for defeasible reasoning [Pollock] |
| 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] |
| 8822 | Statements about necessities need not be necessarily true [Pollock] |
| 8818 | Defeasible reasoning requires us to be able to think about our thoughts [Pollock] |
| 7630 | Ryle's dichotomy between knowing how and knowing that is too simplistic [Maund] |
| 7632 | Perception is sensation-then-concept, or direct-concepts, or sensation-saturated-in-concepts [Maund] |
| 7635 | Sense-data have an epistemological purpose (foundations) and a metaphysical purpose (explanation) [Maund] |
| 7638 | One thesis says we are not aware of qualia, but only of objects and their qualities [Maund] |
| 7642 | The Myth of the Given claims that thought is rationally supported by non-conceptual experiences [Maund] |
| 7640 | Mountains are adverbial modifications of the earth, but still have object-characteristics [Maund] |
| 7641 | Adverbialism tries to avoid sense-data and preserve direct realism [Maund] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 8811 | What we want to know is - when is it all right to believe something? [Pollock] |
| 8817 | Logical entailments are not always reasons for beliefs, because they may be irrelevant [Pollock] |
| 8814 | Epistemic norms are internalised procedural rules for reasoning [Pollock] |
| 8823 | Reasons are always for beliefs, but a perceptual state is a reason without itself being a belief [Pollock] |
| 8813 | If we have to appeal explicitly to epistemic norms, that will produce an infinite regress [Pollock] |
| 8812 | Norm Externalism says norms must be internal, but their selection is partly external [Pollock] |
| 8816 | Externalists tend to take a third-person point of view of epistemology [Pollock] |
| 8815 | Belief externalism is false, because external considerations cannot be internalized for actual use [Pollock] |
| 7637 | Thought content is either satisfaction conditions, or exercise of concepts [Maund, by PG] |