48 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] |
16877 | A 'constructive' (as opposed to 'analytic') definition creates a new sign [Frege] |
11219 | Frege suggested that mathematics should only accept stipulative definitions [Frege, by Gupta] |
16878 | We must be clear about every premise and every law used in a proof [Frege] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
16863 | Does some mathematical reasoning (such as mathematical induction) not belong to logic? [Frege] |
16862 | The closest subject to logic is mathematics, which does little apart from drawing inferences [Frege] |
16865 | 'Theorems' are both proved, and used in proofs [Frege] |
16866 | Tracing inference backwards closes in on a small set of axioms and postulates [Frege] |
16868 | The essence of mathematics is the kernel of primitive truths on which it rests [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
16930 | Geometry is not analytic, because a line's being 'straight' is a quality [Kant] |
16919 | Geometry rests on our intuition of space [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] |
16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
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] |
11833 | The substance, once the predicates are removed, remains unknown to us [Kant] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
3016 | Even the gods cannot strive against necessity [Pittacus, by Diog. Laertius] |
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] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause [Kant] |
16879 | A sign won't gain sense just from being used in sentences with familiar components [Frege] |
16873 | Thoughts are not subjective or psychological, because some thoughts are the same for us all [Frege] |
16872 | A thought is the sense expressed by a sentence, and is what we prove [Frege] |
16874 | The parts of a thought map onto the parts of a sentence [Frege] |
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] |