30 ideas
| 12463 | Unlike correspondence, truthmaking can be one truth to many truthmakers, or vice versa [Jacobs] |
| 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] |
| 14375 | If structures result from intrinsic natures of properties, the 'relations' between them can drop out [Jacobs] |
| 14378 | Science aims at identifying the structure and nature of the powers that exist [Jacobs] |
| 12467 | Powers come from concrete particulars, not from the laws of nature [Jacobs] |
| 14377 | Possibilities are manifestations of some power, and impossibilies rest on no powers [Jacobs] |
| 14376 | States of affairs are only possible if some substance could initiate a causal chain to get there [Jacobs] |
| 14379 | Counterfactuals invite us to consider the powers picked out by the antecedent [Jacobs] |
| 14372 | Possible worlds are just not suitable truthmakers for modality [Jacobs] |
| 12466 | All modality is in the properties and relations of the actual world [Jacobs] |
| 14371 | We can base counterfactuals on powers, not possible worlds, and hence define necessity [Jacobs] |
| 12465 | Concrete worlds, unlike fictions, at least offer evidence of how the actual world could be [Jacobs] |
| 12464 | If some book described a possibe life for you, that isn't what makes such a life possible [Jacobs] |
| 12469 | Possible worlds semantics gives little insight into modality [Jacobs] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |