32 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] |
| 13886 | Later Frege held that definitions must fix a function's value for every possible argument [Frege, by Wright,C] |
| 9845 | We can't define a word by defining an expression containing it, as the remaining parts are a problem [Frege] |
| 10019 | Only what is logically complex can be defined; what is simple must be pointed to [Frege] |
| 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] |
| 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] |
| 9886 | Cardinals say how many, and reals give measurements compared to a unit quantity [Frege] |
| 9889 | Real numbers are ratios of quantities [Frege, by Dummett] |
| 10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
| 10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
| 10185 | Set theory is the standard background for modern mathematics [Burgess] |
| 10184 | Structuralists take the name 'R' of the reals to be a variable ranging over structures, not a structure [Burgess] |
| 10189 | There is no one relation for the real number 2, as relations differ in different models [Burgess] |
| 10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
| 10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
| 10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
| 6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
| 9887 | Formalism misunderstands applications, metatheory, and infinity [Frege, by Dummett] |
| 8751 | Only applicability raises arithmetic from a game to a science [Frege] |
| 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] |
| 9891 | The first demand of logic is of a sharp boundary [Frege] |
| 9890 | The modern account of real numbers detaches a ratio from its geometrical origins [Frege] |
| 11846 | If we abstract the difference between two houses, they don't become the same house [Frege] |
| 6112 | Meaning takes many different forms, depending on different logical types [Russell] |