57 ideas
| 21955 | My dogmatic slumber was first interrupted by David Hume [Kant] |
| 22026 | Philosophy is homesickness - the urge to be at home everywhere [Novalis] |
| 16931 | Metaphysics is generating a priori knowledge by intuition and concepts, leading to the synthetic [Kant] |
| 15413 | With four tense operators, all complex tenses reduce to fourteen basic cases [Burgess] |
| 15415 | The temporal Barcan formulas fix what exists, which seems absurd [Burgess] |
| 15430 | Is classical logic a part of intuitionist logic, or vice versa? [Burgess] |
| 15431 | It is still unsettled whether standard intuitionist logic is complete [Burgess] |
| 15429 | Relevance logic's → is perhaps expressible by 'if A, then B, for that reason' [Burgess] |
| 15404 | Technical people see logic as any formal system that can be studied, not a study of argument validity [Burgess] |
| 15405 | Classical logic neglects the non-mathematical, such as temporality or modality [Burgess] |
| 15427 | The Cut Rule expresses the classical idea that entailment is transitive [Burgess] |
| 15421 | Classical logic neglects counterfactuals, temporality and modality, because maths doesn't use them [Burgess] |
| 15403 | Philosophical logic is a branch of logic, and is now centred in computer science [Burgess] |
| 15407 | Formalising arguments favours lots of connectives; proving things favours having very few [Burgess] |
| 15424 | Asserting a disjunction from one disjunct seems odd, but can be sensible, and needed in maths [Burgess] |
| 15409 | All occurrences of variables in atomic formulas are free [Burgess] |
| 15414 | The denotation of a definite description is flexible, rather than rigid [Burgess] |
| 15406 | 'Induction' and 'recursion' on complexity prove by connecting a formula to its atomic components [Burgess] |
| 15425 | The sequent calculus makes it possible to have proof without transitivity of entailment [Burgess] |
| 15426 | We can build one expanding sequence, instead of a chain of deductions [Burgess] |
| 15408 | 'Tautologies' are valid formulas of classical sentential logic - or substitution instances in other logics [Burgess] |
| 15418 | Validity (for truth) and demonstrability (for proof) have correlates in satisfiability and consistency [Burgess] |
| 15412 | Models leave out meaning, and just focus on truth values [Burgess] |
| 15411 | We only need to study mathematical models, since all other models are isomorphic to these [Burgess] |
| 15416 | We aim to get the technical notion of truth in all models matching intuitive truth in all instances [Burgess] |
| 15428 | The Liar seems like a truth-value 'gap', but dialethists see it as a 'glut' [Burgess] |
| 16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
| 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] |
| 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] |
| 15420 | De re modality seems to apply to objects a concept intended for sentences [Burgess] |
| 15419 | General consensus is S5 for logical modality of validity, and S4 for proof [Burgess] |
| 15417 | Logical necessity has two sides - validity and demonstrability - which coincide in classical logic [Burgess] |
| 15422 | Three conditionals theories: Materialism (material conditional), Idealism (true=assertable), Nihilism (no truth) [Burgess] |
| 15423 | It is doubtful whether the negation of a conditional has any clear meaning [Burgess] |
| 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] |
| 19591 | Desire for perfection is an illness, if it turns against what is imperfect [Novalis] |
| 16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause [Kant] |
| 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] |