31 ideas
| 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] |
| 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] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 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] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 6112 | Meaning takes many different forms, depending on different logical types [Russell] |
| 16713 | Philosophers are the forefathers of heretics [Tertullian] |
| 6610 | I believe because it is absurd [Tertullian] |