58 ideas
| 21955 | My dogmatic slumber was first interrupted by David Hume [Kant] |
| 16931 | Metaphysics is generating a priori knowledge by intuition and concepts, leading to the synthetic [Kant] |
| 13252 | Some truths have true negations [Beall/Restall] |
| 13247 | A truthmaker is an object which entails a sentence [Beall/Restall] |
| 13249 | (∀x)(A v B) |- (∀x)A v (∃x)B) is valid in classical logic but invalid intuitionistically [Beall/Restall] |
| 13243 | Excluded middle must be true for some situation, not for all situations [Beall/Restall] |
| 13245 | Relevant consequence says invalidity is the conclusion not being 'in' the premises [Beall/Restall] |
| 13246 | Relevant logic does not abandon classical logic [Beall/Restall] |
| 13254 | A doesn't imply A - that would be circular [Beall/Restall] |
| 13255 | Relevant logic may reject transitivity [Beall/Restall] |
| 13242 | It's 'relevantly' valid if all those situations make it true [Beall/Restall] |
| 13250 | Free logic terms aren't existential; classical is non-empty, with referring names [Beall/Restall] |
| 17824 | The master science is physical objects divided into sets [Maddy] |
| 13235 | Logic studies consequence; logical truths are consequences of everything, or nothing [Beall/Restall] |
| 13238 | Syllogisms are only logic when they use variables, and not concrete terms [Beall/Restall] |
| 13234 | The view of logic as knowing a body of truths looks out-of-date [Beall/Restall] |
| 13232 | Logic studies arguments, not formal languages; this involves interpretations [Beall/Restall] |
| 13241 | The model theory of classical predicate logic is mathematics [Beall/Restall] |
| 13253 | There are several different consequence relations [Beall/Restall] |
| 13240 | A sentence follows from others if they always model it [Beall/Restall] |
| 13236 | Logical truth is much more important if mathematics rests on it, as logicism claims [Beall/Restall] |
| 13237 | Preface Paradox affirms and denies the conjunction of propositions in the book [Beall/Restall] |
| 16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
| 16919 | Geometry rests on our intuition of space [Kant] |
| 16930 | Geometry is not analytic, because a line's being 'straight' is a quality [Kant] |
| 16920 | Numbers are formed by addition of units in time [Kant] |
| 16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
| 17825 | Set theory (unlike the Peano postulates) can explain why multiplication is commutative [Maddy] |
| 17826 | Standardly, numbers are said to be sets, which is neat ontology and epistemology [Maddy] |
| 17828 | Numbers are properties of sets, just as lengths are properties of physical objects [Maddy] |
| 17827 | Sets exist where their elements are, but numbers are more like universals [Maddy] |
| 17830 | Number theory doesn't 'reduce' to set theory, because sets have number properties [Maddy] |
| 17823 | If mathematical objects exist, how can we know them, and which objects are they? [Maddy] |
| 16910 | Mathematics can only start from an a priori intuition which is not empirical but pure [Kant] |
| 16917 | All necessary mathematical judgements are based on intuitions of space and time [Kant] |
| 16928 | Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant] |
| 17829 | Number words are unusual as adjectives; we don't say 'is five', and numbers always come first [Maddy] |
| 11833 | The substance, once the predicates are removed, remains unknown to us [Kant] |
| 13244 | Relevant necessity is always true for some situation (not all situations) [Beall/Restall] |
| 21957 | 'Transcendental' concerns how we know, rather than what we know [Kant] |
| 16923 | I admit there are bodies outside us [Kant] |
| 21441 | 'Transcendental' is not beyond experience, but a prerequisite of experience [Kant] |
| 16916 | A priori synthetic knowledge is only of appearances, not of things in themselves [Kant] |
| 16915 | A priori intuitions can only concern the objects of our senses [Kant] |
| 16914 | A priori intuition of objects is only possible by containing the form of my sensibility [Kant] |
| 21447 | I can make no sense of the red experience being similar to the quality in the object [Kant] |
| 16924 | I count the primary features of things (as well as the secondary ones) as mere appearances [Kant] |
| 16913 | I can't intuit a present thing in itself, because the properties can't enter my representations [Kant] |
| 16925 | Appearance gives truth, as long as it is only used within experience [Kant] |
| 16911 | Intuition is a representation that depends on the presence of the object [Kant] |
| 13239 | Judgement is always predicating a property of a subject [Beall/Restall] |
| 16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause [Kant] |
| 13248 | We can rest truth-conditions on situations, rather than on possible worlds [Beall/Restall] |
| 13233 | Propositions commit to content, and not to any way of spelling it out [Beall/Restall] |
| 16926 | Analytic judgements say clearly what was in the concept of the subject [Kant] |
| 16927 | Analytic judgement rests on contradiction, since the predicate cannot be denied of the subject [Kant] |
| 16922 | Space must have three dimensions, because only three lines can meet at right angles [Kant] |
| 16921 | If all empirical sensation of bodies is removed, space and time are still left [Kant] |