43 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] |
| 22355 | In the realist view, the real external world explains how it (and perceptions of it) are possible [Williams,B] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 4243 | Our ability to react to an alien culture shows that ethical thought extends beyond cultural boundaries [Williams,B] |
| 4244 | It is very confused to deduce a nonrelativist morality of universal toleration from relativism [Williams,B] |
| 4114 | Philosophers try to produce ethical theories because they falsely assume that ethics can be simple [Williams,B] |
| 4128 | Intuitionism has been demolished by critics, and no longer looks interesting [Williams,B] |
| 4132 | The category of person is a weak basis for ethics, because it is not fixed but comes in degrees [Williams,B] |
| 4134 | The weakness of prescriptivism is shown by "I simply don't like staying at good hotels" [Williams,B] |
| 4135 | Some ethical ideas, such as 'treachery' and 'promise', seem to express a union of facts and values [Williams,B] |
| 4120 | It is an error of consequentialism to think we just aim at certain states of affairs; we also want to act [Williams,B] |
| 4252 | Promise keeping increases reliability, by making deliberation focus on something which would be overlooked [Williams,B] |
| 4116 | A weakness of contractual theories is the position of a person of superior ability and power [Williams,B] |
| 4112 | A crucial feature of moral thought is second-order desire - the desire to have certain desires [Williams,B] |
| 4113 | 'Deon' in Greek means what one must do; there was no word meaning 'duty' [Williams,B] |
| 4110 | Obligation and duty look backwards (because of a promise or job), although the acts are in the future [Williams,B] |
| 4249 | "Ought implies can" is a famous formula in connection with moral obligation [Williams,B] |
| 4248 | Not all moral deliberations lead to obligations; some merely reveal what 'may' be done [Williams,B] |
| 4250 | The concept of a 'duty to myself' is fraudulent [Williams,B] |
| 4121 | Why should I think of myself as both the legislator and the citizen who follows the laws? [Williams,B] |
| 4122 | If the self becomes completely impartial, it no longer has enough identity to worry about its interests [Williams,B] |
| 4124 | Utilitarian benevolence involves no particular attachments, and is immune to the inverse square law [Williams,B] |
| 4245 | Ethical conviction must be to some extent passive, and can't just depend on the will and decisions [Williams,B] |
| 4246 | Taking responsibility won't cure ethical uncertainty by; we are uncertain what to decide [Williams,B] |
| 4247 | It is a mark of our having ethical values that we aim to reproduce them in our children [Williams,B] |
| 4131 | Most women see an early miscarriage and a late stillbirth as being very different in character [Williams,B] |
| 4133 | Speciesism isn't like racism, because the former implies a viewpoint which belongs to no one [Williams,B] |
| 17371 | Some kinds are very explanatory, but others less so, and some not at all [Devitt] |
| 17373 | Species pluralism says there are several good accounts of what a species is [Devitt] |
| 17372 | The higher categories are not natural kinds, so the Linnaean hierarchy should be given up [Devitt] |