32 ideas
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] |
13132 | A snowball's haecceity is the property of being identical with itself [Plantinga, by Westerhoff] |
9240 | Love creates a necessity concerning what to care about [Frankfurt] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
9228 | Ranking order of desires reveals nothing, because none of them may be considered important [Frankfurt] |
9238 | Morality isn't based on reason; moral indignation is quite unlike disapproval of irrationality [Frankfurt] |
9232 | It is by caring about things that we infuse the world with importance [Frankfurt] |
9234 | If you don't care about at least one thing, you can't find reasons to care about anything [Frankfurt] |
9229 | What is worthwhile for its own sake alone may be worth very little [Frankfurt] |
9233 | Our criteria for evaluating how to live offer an answer to the problem [Frankfurt] |
9235 | Rather than loving things because we value them, I think we value things because we love them [Frankfurt] |
9236 | Love can be cool, and it may not involve liking its object [Frankfurt] |
9237 | The paradigm case of pure love is not romantic, but that between parents and infants [Frankfurt] |
9239 | I value my children for their sake, but I also value my love for them for its own sake [Frankfurt] |
9227 | We might not choose a very moral life, if the character or constitution was deficient [Frankfurt] |
9230 | People want to fulfill their desires, but also for their desires to be sustained [Frankfurt] |
9241 | Loving oneself is not a failing, but is essential to a successful life [Frankfurt] |
9300 | Boredom is serious, not just uncomfortable; it threatens our psychic survival [Frankfurt] |
9231 | Freedom needs autonomy (rather than causal independence) - embracing our own desires and choices [Frankfurt] |