47 ideas
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
22355 | In the realist view, the real external world explains how it (and perceptions of it) are possible [Williams,B] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
4244 | It is very confused to deduce a nonrelativist morality of universal toleration from relativism [Williams,B] |
4243 | Our ability to react to an alien culture shows that ethical thought extends beyond cultural boundaries [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] |
21093 | Friendship without community spirit misses out on the main part of virtue [Hume] |
4113 | 'Deon' in Greek means what one must do; there was no word meaning 'duty' [Williams,B] |
4250 | The concept of a 'duty to myself' is fraudulent [Williams,B] |
4110 | Obligation and duty look backwards (because of a promise or job), although the acts are in the future [Williams,B] |
4248 | Not all moral deliberations lead to obligations; some merely reveal what 'may' be done [Williams,B] |
4249 | "Ought implies can" is a famous formula in connection with moral obligation [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] |
21091 | It would be absurd if even a free constitution did not impose restraints, for the public good [Hume] |
21092 | Nobility either share in the power of the whole, or they compose the power of the whole [Hume] |
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] |