30 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] |
8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
18648 | Freedom to live according to our own conception of the good is the ultimate value [Nozick, by Kymlicka] |
20585 | If an experience machine gives you any experience you want, should you hook up for life? [Nozick] |
18643 | A minimal state should protect, but a state forcing us to do more is unjustified [Nozick] |
18642 | Individual rights are so strong that the state and its officials must be very limited in power [Nozick] |
18644 | States can't enforce mutual aid on citizens, or interfere for their own good [Nozick] |
22661 | My Anarchy, State and Utopia neglected our formal social ties and concerns [Nozick on Nozick] |
19745 | The nature of people is decided by the government and politics of their society [Rousseau] |
18641 | If people hold things legitimately, just distribution is simply the result of free exchanges [Nozick, by Kymlicka] |
20539 | Property is legitimate by initial acquisition, voluntary transfer, or rectification of injustice [Nozick, by Swift] |
18645 | Nozick assumes initial holdings include property rights, but we can challenge that [Kymlicka on Nozick] |
20521 | Can I come to own the sea, by mixing my private tomato juice with it? [Nozick] |
18646 | How did the private property get started? If violence was involved, we can redistribute it [Kymlicka on Nozick] |
18647 | If property is only initially acquired by denying the rights of others, Nozick can't get started [Kymlicka on Nozick] |
21737 | Unowned things may be permanently acquired, if it doesn't worsen the position of other people [Nozick] |
21738 | Maybe land was originally collectively owned, rather than unowned? [Cohen,GA on Nozick] |