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] |
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] |
12708 | The soul is not a substance but a substantial form, the first active faculty [Leibniz] |
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] |