45 ideas
| 1848 | We are coerced into assent to a truth by reason's violence [Aquinas] |
| 1858 | The mind is compelled by necessary truths, but not by contingent truths [Aquinas] |
| 1852 | For the mind Good is one truth among many, and Truth is one good among many [Aquinas] |
| 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] |
| 20298 | The traditional a priori is justified without experience; post-Quine it became unrevisable by experience [Rey] |
| 1860 | Knowledge may be based on senses, but we needn't sense all our knowledge [Aquinas] |
| 1855 | If we saw something as totally and utterly good, we would be compelled to will it [Aquinas] |
| 1856 | Nothing can be willed except what is good, but good is very varied, and so choices are unpredictable [Aquinas] |
| 1862 | However habituated you are, given time to ponder you can go against a habit [Aquinas] |
| 1849 | Since will is a reasoning power, it can entertain opposites, so it is not compelled to embrace one of them [Aquinas] |
| 1861 | The will is not compelled to move, even if pleasant things are set before it [Aquinas] |
| 1853 | Because the will moves by examining alternatives, it doesn't compel itself to will [Aquinas] |
| 1854 | We must admit that when the will is not willing something, the first movement to will must come from outside the will [Aquinas] |
| 20300 | Externalist synonymy is there being a correct link to the same external phenomena [Rey] |
| 20294 | 'Married' does not 'contain' its symmetry, nor 'bigger than' its transitivity [Rey] |
| 20293 | Analytic judgements can't be explained by contradiction, since that is what is assumed [Rey] |
| 20297 | Analytic statements are undeniable (because of meaning), rather than unrevisable [Rey] |
| 20301 | The meaning properties of a term are those which explain how the term is typically used [Rey] |
| 20302 | An intrinsic language faculty may fix what is meaningful (as well as grammatical) [Rey] |
| 20303 | Research throws doubts on the claimed intuitions which support analyticity [Rey] |
| 20299 | If we claim direct insight to what is analytic, how do we know it is not sub-consciously empirical? [Rey] |
| 1847 | The will must aim at happiness, but can choose the means [Aquinas] |
| 1857 | We don't have to will even perfect good, because we can choose not to think of it [Aquinas] |
| 1846 | The will can only want what it thinks is good [Aquinas] |
| 1850 | Without free will not only is ethical action meaningless, but also planning, commanding, praising and blaming [Aquinas] |
| 1851 | Good applies to goals, just as truth applies to ideas in the mind [Aquinas] |
| 1859 | Even a sufficient cause doesn't compel its effect, because interference could interrupt the process [Aquinas] |