44 ideas
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] |
16477 | Asserting not-p is saying p is false [Russell] |
16484 | There are four experiences that lead us to talk of 'some' things [Russell] |
16867 | Logic not only proves things, but also reveals logical relations between them [Frege] |
16486 | The physical world doesn't need logic, but the mental world does [Russell] |
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] |
2947 | Questions wouldn't lead anywhere without the law of excluded middle [Russell] |
16483 | Disjunction may also arise in practice if there is imperfect memory. [Russell] |
16480 | A disjunction expresses indecision [Russell] |
16479 | 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell] |
16481 | 'Or' expresses a mental state, not something about the world [Russell] |
16487 | Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell] |
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] |
16871 | A truth can be an axiom in one system and not in another [Frege] |
16870 | Axioms are truths which cannot be doubted, and for which no proof is needed [Frege] |
16475 | A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell] |
16869 | To create order in mathematics we need a full system, guided by patterns of inference [Frege] |
16864 | If principles are provable, they are theorems; if not, they are axioms [Frege] |
14193 | 'Substance theorists' take modal properties as primitive, without structure, just falling under a sortal [Paul,LA] |
14195 | If an object's sort determines its properties, we need to ask what determines its sort [Paul,LA] |
14196 | Substance essentialism says an object is multiple, as falling under various different sortals [Paul,LA] |
9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
14198 | Absolutely unrestricted qualitative composition would allow things with incompatible properties [Paul,LA] |
14190 | Deep essentialist objects have intrinsic properties that fix their nature; the shallow version makes it contextual [Paul,LA] |
14191 | Deep essentialists say essences constrain how things could change; modal profiles fix natures [Paul,LA] |
14192 | Essentialism must deal with charges of arbitrariness, and failure to reduce de re modality [Paul,LA] |
14197 | An object's modal properties don't determine its possibilities [Paul,LA] |
14189 | 'Modal realists' believe in many concrete worlds, 'actualists' in just this world, 'ersatzists' in abstract other worlds [Paul,LA] |
16482 | All our knowledge (if verbal) is general, because all sentences contain general words [Russell] |
4758 | Naïve realism leads to physics, but physics then shows that naïve realism is false [Russell] |
16476 | For simple words, a single experience can show that they are true [Russell] |
16485 | Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell] |
16876 | We need definitions to cram retrievable sense into a signed receptacle [Frege] |
16875 | We use signs to mark receptacles for complex senses [Frege] |
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] |
16478 | A mother cat is paralysed if equidistant between two needy kittens [Russell] |