29 ideas
| 22462 | We should speak the truth, but also preserve and pursue it [Foot] |
| 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] |
| 15561 | The events that suit semantics may not be the events that suit causation [Lewis] |
| 15565 | Events have inbuilt essences, as necessary conditions for their occurrence [Lewis] |
| 15566 | Events are classes, and so there is a mereology of their parts [Lewis] |
| 15567 | Some events involve no change; they must, because causal histories involve unchanges [Lewis] |
| 15564 | An event is a property of a unique space-time region [Lewis] |
| 15563 | Properties are very abundant (unlike universals), and are used for semantics and higher-order variables [Lewis] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 22458 | Consequentialists can hurt the innocent in order to prevent further wickedness [Foot] |
| 22460 | Why might we think that a state of affairs can be morally good or bad? [Foot] |
| 22461 | Good outcomes are not external guides to morality, but a part of virtuous actions [Foot] |
| 22464 | The idea of a good state of affairs has no role in the thought of Aristotle, Rawls or Scanlon [Foot] |
| 22463 | Morality is seen as tacit legislation by the community [Foot] |
| 22459 | For consequentialism, it is irrational to follow a rule which in this instance ends badly [Foot] |
| 15562 | Causation is a general relation derived from instances of causal dependence [Lewis] |