22 ideas
14799 | Metaphysics rests on observations, but ones so common we hardly notice them [Peirce] |
6118 | Philosophy is logical analysis, followed by synthesis [Russell] |
6116 | A logical language would show up the fallacy of inferring reality from ordinary language [Russell] |
6117 | Philosophy should be built on science, to reduce error [Russell] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
6110 | Subject-predicate logic (and substance-attribute metaphysics) arise from Aryan languages [Russell] |
6107 | It is logic, not metaphysics, that is fundamental to philosophy [Russell] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
6115 | Vagueness, and simples being beyond experience, are obstacles to a logical language [Russell] |
6109 | Some axioms may only become accepted when they lead to obvious conclusions [Russell] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
10968 | Russell gave up logical atomism because of negative, general and belief propositions [Russell, by Read] |
6113 | To mean facts we assert them; to mean simples we name them [Russell] |
6114 | 'Simples' are not experienced, but are inferred at the limits of analysis [Russell] |
21722 | Better to construct from what is known, than to infer what is unknown [Russell] |
6111 | As propositions can be put in subject-predicate form, we wrongly infer that facts have substance-quality form [Russell] |
6112 | Meaning takes many different forms, depending on different logical types [Russell] |