28 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] |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| 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] |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| 6109 | Some axioms may only become accepted when they lead to obvious conclusions [Russell] |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| 6108 | Maths can be deduced from logical axioms and the logic of relations [Russell] |
| 10580 | Mathematics is both necessary and a priori because it really consists of logical truths [Yablo] |
| 10579 | Putting numbers in quantifiable position (rather than many quantifiers) makes expression easier [Yablo] |
| 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] |
| 10577 | Concrete objects have few essential properties, but properties of abstractions are mostly essential [Yablo] |
| 10578 | We are thought to know concreta a posteriori, and many abstracta a priori [Yablo] |
| 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] |