31 ideas
18543 | Do aesthetic reasons count as reasons, if they are rejectable without contradiction? [Scruton] |
18542 | Defining truth presupposes that there can be a true definition [Scruton] |
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] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
19440 | How do you know you have conceived a thing deeply enough to assess its possibility? [Vaidya] |
18546 | The pleasure taken in beauty also aims at understanding and valuing [Scruton] |
18550 | Art gives us imaginary worlds which we can view impartially [Scruton] |
18544 | Maybe 'beauty' is too loaded, and we should talk of fittingness or harmony [Scruton] |
18553 | Beauty shows us what we should want in order to achieve human fulfilment [Scruton] |
18556 | Beauty is rationally founded, inviting meaning, comparison and self-reflection [Scruton] |
18548 | Natural beauty reassures us that the world is where we belong [Scruton] |
18551 | Croce says art makes inarticulate intuitions conscious; rival views say the audience is the main concern [Scruton] |
18541 | Beauty (unlike truth and goodness) is questionable as an ultimate value [Scruton] |
18554 | Prostitution is wrong because it hardens the soul, since soul and body are one [Scruton] |