49 ideas
| 6947 | Metaphysics does not rest on facts, but on what we are inclined to believe [Peirce] |
| 6937 | Reason aims to discover the unknown by thinking about the known [Peirce] |
| 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] |
| 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] |
| 20457 | Zeno assumes collecting an infinity of things makes an infinite thing [Rovelli] |
| 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] |
| 20468 | Quantum mechanics deals with processes, rather than with things [Rovelli] |
| 20467 | Quantum mechanics describes the world entirely as events [Rovelli] |
| 21492 | Realism is basic to the scientific method [Peirce] |
| 6949 | If someone doubted reality, they would not actually feel dissatisfaction [Peirce] |
| 9388 | Every concept must have a sharp boundary; we cannot allow an indeterminate third case [Frege] |
| 6940 | The feeling of belief shows a habit which will determine our actions [Peirce] |
| 6941 | We are entirely satisfied with a firm belief, even if it is false [Peirce] |
| 6942 | We want true beliefs, but obviously we think our beliefs are true [Peirce] |
| 6943 | A mere question does not stimulate a struggle for belief; there must be a real doubt [Peirce] |
| 6598 | We need our beliefs to be determined by some external inhuman permanency [Peirce] |
| 6944 | Demonstration does not rest on first principles of reason or sensation, but on freedom from actual doubt [Peirce] |
| 6948 | Doubts should be satisfied by some external permanency upon which thinking has no effect [Peirce] |
| 6945 | Once doubt ceases, there is no point in continuing to argue [Peirce] |
| 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] |
| 20469 | There are probably no infinities, and 'infinite' names what we do not yet know [Rovelli] |
| 20461 | The basic ideas of fields and particles are merged in quantum mechanics [Rovelli] |
| 6939 | What is true of one piece of copper is true of another (unlike brass) [Peirce] |
| 20462 | Because it is quantised, a field behaves like a set of packets of energy [Rovelli] |
| 20463 | There are about fifteen particles fields, plus a few force fields [Rovelli] |
| 20464 | The world consists of quantum fields, with elementary events happening in spacetime [Rovelli] |
| 20459 | Electrons only exist when they interact, and their being is their combination of quantum leaps [Rovelli] |
| 20460 | Electrons are not waves, because their collisions are at a point, and not spread out [Rovelli] |
| 20466 | Quantum Theory describes events and possible interactions - not how things are [Rovelli] |
| 20465 | Nature has three aspects: granularity, indeterminacy, and relations [Rovelli] |
| 20458 | The world is just particles plus fields; space is the gravitational field [Rovelli] |
| 20470 | Only heat distinguishes past from future [Rovelli] |
| 6938 | Natural selection might well fill an animal's mind with pleasing thoughts rather than true ones [Peirce] |
| 6946 | If death is annihilation, belief in heaven is a cheap pleasure with no disappointment [Peirce] |