31 ideas
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
16901 | The equivalent algebra model of geometry loses some essential spatial meaning [Burge] |
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] |
16902 | Peano arithmetic requires grasping 0 as a primitive number [Burge] |
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] |
5791 | Reduction is either by elimination, or by explanation [Searle] |
5799 | Eliminative reduction needs a gap between appearance and reality, as in sunsets [Searle] |
5790 | A property is 'emergent' if it is caused by elements of a system, when the elements lack the property [Searle] |
16892 | Is apriority predicated mainly of truths and proofs, or of human cognition? [Burge] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
5792 | Explanation of how we unify our mental stimuli into a single experience is the 'binding problem' [Searle] |
5786 | A system is either conscious or it isn't, though the intensity varies a lot [Searle] |
5794 | Consciousness has a first-person ontology, which only exists from a subjective viewpoint [Searle] |
5795 | There isn't one consciousness (information-processing) which can be investigated, and another (phenomenal) which can't [Searle] |
5788 | The use of 'qualia' seems to imply that consciousness and qualia are separate [Searle] |
5789 | I now think syntax is not in the physics, but in the eye of the beholder [Searle] |
5798 | Consciousness has a first-person ontology, so it cannot be reduced without omitting something [Searle] |
5787 | There is non-event causation between mind and brain, as between a table and its solidity [Searle] |
5797 | The pattern of molecules in the sea is much more complex than the complexity of brain neurons [Searle] |
5796 | If tree rings contain information about age, then age contains information about rings [Searle] |