28 ideas
22002 | Wolff's version of Leibniz dominated mid-18th C German thought [Pinkard] |
22021 | Romantics explored beautiful subjectivity, and the re-enchantment of nature [Pinkard] |
22010 | The combination of Kant and the French Revolution was an excited focus for German philosophy [Pinkard] |
22036 | In Hegel's time naturalism was called 'Spinozism' [Pinkard] |
2546 | Philosophy is a magnificent failure in its attempt to overstep the limits of our knowledge [McGinn] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
2544 | Thoughts have a dual aspect: as they seem to introspection, and their underlying logical reality [McGinn] |
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] |
22048 | Idealism is the link between reason and freedom [Pinkard] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
2539 | Mental modules for language, social, action, theory, space, emotion [McGinn] |
2545 | Free will is mental causation in action [McGinn] |
2543 | Brains aren't made of anything special, suggesting panpsychism [McGinn] |
2540 | Examining mind sees no brain; examining brain sees no mind [McGinn] |
2547 | There is information if there are symbols which refer, and which can combine into a truth or falsehood [McGinn] |
2542 | Causation in the material world is energy-transfer, of motion, electricity or gravity [McGinn] |