33 ideas
| 17729 | Examining concepts can recover information obtained through the senses [Jenkins] |
| 17740 | Instead of correspondence of proposition to fact, look at correspondence of its parts [Jenkins] |
| 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] |
| 17730 | Combining the concepts of negation and finiteness gives the concept of infinity [Jenkins] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 13007 | Archimedes defined a straight line as the shortest distance between two points [Archimedes, by Leibniz] |
| 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] |
| 17719 | Arithmetic concepts are indispensable because they accurately map the world [Jenkins] |
| 17717 | Senses produce concepts that map the world, and arithmetic is known through these concepts [Jenkins] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 17724 | It is not easy to show that Hume's Principle is analytic or definitive in the required sense [Jenkins] |
| 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] |
| 17727 | We can learn about the world by studying the grounding of our concepts [Jenkins] |
| 17720 | There's essential, modal, explanatory, conceptual, metaphysical and constitutive dependence [Jenkins, by PG] |
| 17728 | The concepts we have to use for categorising are ones which map the real world well [Jenkins] |
| 17726 | Examining accurate, justified or grounded concepts brings understanding of the world [Jenkins] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 17734 | It is not enough that intuition be reliable - we need to know why it is reliable [Jenkins] |
| 17723 | Knowledge is true belief which can be explained just by citing the proposition believed [Jenkins] |
| 17739 | The physical effect of world on brain explains the concepts we possess [Jenkins] |
| 17718 | Grounded concepts are trustworthy maps of the world [Jenkins] |
| 17731 | Verificationism is better if it says meaningfulness needs concepts grounded in the senses [Jenkins] |
| 17732 | Success semantics explains representation in terms of success in action [Jenkins] |
| 17725 | 'Analytic' can be conceptual, or by meaning, or predicate inclusion, or definition... [Jenkins] |