30 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] |
16659 | Relations do not add anything to reality, though they are real aspects of the world [Olivi] |
16673 | Quantity just adds union and location to the extension of parts [Olivi] |
8822 | Statements about necessities need not be necessarily true [Pollock] |
8818 | Defeasible reasoning requires us to be able to think about our thoughts [Pollock] |
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] |
16663 | Things are limited by the species to certain modes of being [Olivi] |