32 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] |
| 10170 | While true-in-a-model seems relative, true-in-all-models seems not to be [Reck/Price] |
| 10166 | ZFC set theory has only 'pure' sets, without 'urelements' [Reck/Price] |
| 15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
| 10175 | Three types of variable in second-order logic, for objects, functions, and predicates/sets [Reck/Price] |
| 15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
| 15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
| 10165 | 'Analysis' is the theory of the real numbers [Reck/Price] |
| 15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
| 15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
| 10174 | Mereological arithmetic needs infinite objects, and function definitions [Reck/Price] |
| 10164 | Peano Arithmetic can have three second-order axioms, plus '1' and 'successor' [Reck/Price] |
| 10172 | Set-theory gives a unified and an explicit basis for mathematics [Reck/Price] |
| 10167 | Structuralism emerged from abstract algebra, axioms, and set theory and its structures [Reck/Price] |
| 10169 | Relativist Structuralism just stipulates one successful model as its arithmetic [Reck/Price] |
| 10179 | There are 'particular' structures, and 'universal' structures (what the former have in common) [Reck/Price] |
| 10181 | Pattern Structuralism studies what isomorphic arithmetic models have in common [Reck/Price] |
| 10182 | There are Formalist, Relativist, Universalist and Pattern structuralism [Reck/Price] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 10176 | Universalist Structuralism is based on generalised if-then claims, not one particular model [Reck/Price] |
| 10177 | Universalist Structuralism eliminates the base element, as a variable, which is then quantified out [Reck/Price] |
| 10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
| 10173 | A nominalist might avoid abstract objects by just appealing to mereological sums [Reck/Price] |
| 22357 | The 'experimenter's regress' says success needs reliability, which is only tested by success [Reiss/Sprenger] |
| 15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
| 22365 | The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger] |