38 ideas
6575 | Philosophy may never find foundations, and may undermine our lives in the process [Fogelin] |
6585 | Rationality is threatened by fear of inconsistency, illusions of absolutes or relativism, and doubt [Fogelin] |
6557 | Humans may never be able to attain a world view which is both rich and consistent [Fogelin] |
6568 | A game can be played, despite having inconsistent rules [Fogelin] |
6560 | The law of noncontradiction is traditionally the most basic principle of rationality [Fogelin] |
6565 | The law of noncontradiction makes the distinction between asserting something and denying it [Fogelin] |
6574 | Legal reasoning is analogical, not deductive [Fogelin] |
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] |
6582 | Conventions can only work if they are based on something non-conventional [Fogelin] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
6576 | My view is 'circumspect rationalism' - that only our intellect can comprehend the world [Fogelin] |
6589 | Knowledge is legitimate only if all relevant defeaters have been eliminated [Fogelin] |
6596 | For coherentists, circularity is acceptable if the circle is large, rich and coherent [Fogelin] |
6597 | A rule of justification might be: don't raise the level of scrutiny without a good reason [Fogelin] |
6588 | Scepticism is cartesian (sceptical scenarios), or Humean (future), or Pyrrhonian (suspend belief) [Fogelin] |
6590 | Scepticism deals in remote possibilities that are ineliminable and set the standard very high [Fogelin] |
6583 | Radical perspectivism replaces Kant's necessary scheme with many different schemes [Fogelin] |
5880 | Xenocrates held that the soul had no form or substance, but was number [Xenocrates, by Cicero] |
6555 | We are also irrational, with a unique ability to believe in bizarre self-created fictions [Fogelin] |
6605 | Critics must be causally entangled with their subject matter [Fogelin] |
6607 | The word 'beautiful', when deprived of context, is nearly contentless [Fogelin] |
6604 | Saying 'It's all a matter to taste' ignores the properties of the object discussed [Fogelin] |
6586 | Cynics are committed to morality, but disappointed or disgusted by human failings [Fogelin] |
6572 | Deterrence, prevention, rehabilitation and retribution can come into conflict in punishments [Fogelin] |
6573 | Retributivists say a crime can be 'paid for'; deterrentists still worry about potential victims [Fogelin] |