34 ideas
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] |
15561 | The events that suit semantics may not be the events that suit causation [Lewis] |
15565 | Events have inbuilt essences, as necessary conditions for their occurrence [Lewis] |
15566 | Events are classes, and so there is a mereology of their parts [Lewis] |
15567 | Some events involve no change; they must, because causal histories involve unchanges [Lewis] |
15564 | An event is a property of a unique space-time region [Lewis] |
15563 | Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
4608 | Minds are hard-wired, or trial-and-error, or experimental, or full self-aware [Dennett, by Heil] |
4880 | Sentience comes in grades from robotic to super-human; we only draw a line for moral reasons [Dennett] |
4873 | What is it like to notice an uncomfortable position when you are asleep? [Dennett] |
4881 | Being a person must involve having second-order beliefs and desires (about beliefs and desires) [Dennett] |
4875 | We descend from robots, and our intentionality is composed of billions of crude intentional systems [Dennett] |
4879 | There is no more anger in adrenaline than silliness in a bottle of whiskey [Dennett] |
4876 | Maybe there is a minimum brain speed for supporting a mind [Dennett] |
4878 | The materials for a mind only matter because of speed, and a need for transducers and effectors [Dennett] |
4874 | The predecessor and rival of the language of thought hypothesis is the picture theory of ideas [Dennett] |
4882 | Concepts are things we (unlike dogs) can think about, because we have language [Dennett] |
4872 | Most people see an abortion differently if the foetus lacks a brain [Dennett] |
15562 | Causation is a general relation derived from instances of causal dependence [Lewis] |
4877 | Maybe plants are very slow (and sentient) animals, overlooked because we are faster? [Dennett] |