47 ideas
3123 | Science is in the business of carving nature at the joints [Segal] |
3125 | Psychology studies the way rationality links desires and beliefs to causality [Segal] |
18996 | A statement S is 'partly true' if it has some wholly true parts [Yablo] |
19006 | An 'enthymeme' is an argument with an indispensable unstated assumption [Yablo] |
18999 | y is only a proper part of x if there is a z which 'makes up the difference' between them [Yablo] |
8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
19001 | 'Pegasus doesn't exist' is false without Pegasus, yet the absence of Pegasus is its truthmaker [Yablo] |
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] |
19002 | A nominalist can assert statements about mathematical objects, as being partly true [Yablo] |
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] |
18998 | Parthood lacks the restriction of kind which most relations have [Yablo] |
3105 | Is 'Hesperus = Phosphorus' metaphysically necessary, but not logically or epistemologically necessary? [Segal] |
3106 | If claims of metaphysical necessity are based on conceivability, we should be cautious [Segal] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
19004 | Gettier says you don't know if you are confused about how it is true [Yablo] |
19007 | A theory need not be true to be good; it should just be true about its physical aspects [Yablo] |
18993 | If sentences point to different evidence, they must have different subject-matter [Yablo] |
19003 | Most people say nonblack nonravens do confirm 'all ravens are black', but only a tiny bit [Yablo] |
3113 | The success and virtue of an explanation do not guarantee its truth [Segal] |
3112 | Folk psychology is ridiculously dualist in its assumptions [Segal] |
3108 | If 'water' has narrow content, it refers to both H2O and XYZ [Segal] |
3110 | Humans are made of H2O, so 'twins' aren't actually feasible [Segal] |
3124 | Externalists can't assume old words refer to modern natural kinds [Segal] |
3104 | Must we relate to some diamonds to understand them? [Segal] |
3109 | If content is external, so are beliefs and desires [Segal] |
3103 | Maybe content involves relations to a language community [Segal] |
3116 | Maybe experts fix content, not ordinary users [Segal] |
3111 | Externalism can't explain concepts that have no reference [Segal] |
3117 | Concepts can survive a big change in extension [Segal] |
3121 | If content is narrow, my perfect twin shares my concepts [Segal] |
3118 | If thoughts ARE causal, we can't explain how they cause things [Segal] |
3119 | Even 'mass' cannot be defined in causal terms [Segal] |
18992 | Sentence-meaning is the truth-conditions - plus factors responsible for them [Yablo] |
18994 | The content of an assertion can be quite different from compositional content [Yablo] |
18997 | Truth-conditions as subject-matter has problems of relevance, short cut, and reversal [Yablo] |
19005 | Not-A is too strong to just erase an improper assertion, because it actually reverses A [Yablo] |