28 ideas
22353 | One view says objectivity is making a successful claim which captures the facts [Reiss/Sprenger] |
22356 | An absolute scientific picture of reality must not involve sense experience, which is perspectival [Reiss/Sprenger] |
22359 | Topic and application involve values, but can evidence and theory choice avoid them? [Reiss/Sprenger] |
22360 | The Value-Free Ideal in science avoids contextual values, but embraces epistemic values [Reiss/Sprenger] |
22362 | Value-free science needs impartial evaluation, theories asserting facts, and right motivation [Reiss/Sprenger] |
22364 | Thermometers depend on the substance used, and none of them are perfect [Reiss/Sprenger] |
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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
21500 | We rely on memory for empirical beliefs because they mutually support one another [Lewis,CI] |
21501 | If we doubt memories we cannot assess our doubt, or what is being doubted [Lewis,CI] |
6556 | If anything is to be probable, then something must be certain [Lewis,CI] |
21498 | Congruents assertions increase the probability of each individual assertion in the set [Lewis,CI] |
22357 | The 'experimenter's regress' says success needs reliability, which is only tested by success [Reiss/Sprenger] |
22365 | The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger] |
5828 | Extension is the class of things, intension is the correct definition of the thing, and intension determines extension [Lewis,CI] |