45 ideas
4697 | There has been a distinct 'Social Turn' in recent philosophy, like the earlier 'Linguistic Turn' [O'Grady] |
4731 | Good reasoning will avoid contradiction, enhance coherence, not ignore evidence, and maximise evidence [O'Grady] |
4735 | Just as maps must simplify their subject matter, so thought has to be reductionist about reality [O'Grady] |
4703 | The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality' [O'Grady] |
4701 | To say a relative truth is inexpressible in other frameworks is 'weak', while saying it is false is 'strong' [O'Grady] |
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] |
4705 | Logical relativism appears if we allow more than one legitimate logical system [O'Grady] |
4700 | A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady] |
4704 | Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady] |
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] |
4711 | Anti-realists say our theories (such as wave-particle duality) give reality incompatible properties [O'Grady] |
4698 | What counts as a fact partly depends on the availability of human concepts to describe them [O'Grady] |
4715 | We may say that objects have intrinsic identity conditions, but still allow multiple accounts of them [O'Grady] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
4720 | Sense-data are only safe from scepticism if they are primitive and unconceptualised [O'Grady] |
4722 | Modern epistemology centres on debates about foundations, and about external justification [O'Grady] |
4724 | Internalists say the reasons for belief must be available to the subject, and externalists deny this [O'Grady] |
4723 | Coherence involves support from explanation and evidence, and also probability and confirmation [O'Grady] |
4709 | Ontological relativists are anti-realists, who deny that our theories carve nature at the joints [O'Grady] |
4725 | Contextualism says that knowledge is relative to its context; 'empty' depends on your interests [O'Grady] |
4732 | One may understand a realm of ideas, but be unable to judge their rationality or truth [O'Grady] |
4710 | Verificationism was attacked by the deniers of the analytic-synthetic distinction, needed for 'facts' [O'Grady] |
4717 | If we abandon the analytic-synthetic distinction, scepticism about meaning may be inevitable [O'Grady] |
4706 | Early Quine says all beliefs could be otherwise, but later he said we would assume mistranslation [O'Grady] |
4734 | Cryptographers can recognise that something is a language, without translating it [O'Grady] |
16713 | Philosophers are the forefathers of heretics [Tertullian] |
4727 | The chief problem for fideists is other fideists who hold contrary ideas [O'Grady] |
6610 | I believe because it is absurd [Tertullian] |