30 ideas
1489 | Modern philosophy tends to be a theory-constructing extension of science, but there is also problem-solving [Nagel] |
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] |
10888 | Sets can be defined by 'enumeration', or by 'abstraction' (based on a property) [Zalabardo] |
10889 | The 'Cartesian Product' of two sets relates them by pairing every element with every element [Zalabardo] |
10890 | A 'partial ordering' is reflexive, antisymmetric and transitive [Zalabardo] |
10886 | Determinacy: an object is either in a set, or it isn't [Zalabardo] |
10887 | Specification: Determinate totals of objects always make a set [Zalabardo] |
10897 | A first-order 'sentence' is a formula with no free variables [Zalabardo] |
10893 | Γ |= φ for sentences if φ is true when all of Γ is true [Zalabardo] |
10899 | Γ |= φ if φ is true when all of Γ is true, for all structures and interpretations [Zalabardo] |
10896 | Propositional logic just needs ¬, and one of ∧, ∨ and → [Zalabardo] |
10898 | The semantics shows how truth values depend on instantiations of properties and relations [Zalabardo] |
10902 | We can do semantics by looking at given propositions, or by building new ones [Zalabardo] |
10892 | We make a truth assignment to T and F, which may be true and false, but merely differ from one another [Zalabardo] |
10895 | 'Logically true' (|= φ) is true for every truth-assignment [Zalabardo] |
10900 | Logically true sentences are true in all structures [Zalabardo] |
10894 | A sentence-set is 'satisfiable' if at least one truth-assignment makes them all true [Zalabardo] |
10901 | Some formulas are 'satisfiable' if there is a structure and interpretation that makes them true [Zalabardo] |
10903 | A structure models a sentence if it is true in the model, and a set of sentences if they are all true in the model [Zalabardo] |
10891 | If a set is defined by induction, then proof by induction can be applied to it [Zalabardo] |
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] |