50 ideas
| 18730 | The history of philosophy only matters if the subject is a choice between rival theories [Wittgenstein] |
| 18704 | Philosophy tries to be rid of certain intellectual puzzles, irrelevant to daily life [Wittgenstein] |
| 18710 | Philosophers express puzzlement, but don't clearly state the puzzle [Wittgenstein] |
| 18732 | We don't need a theory of truth, because we use the word perfectly well [Wittgenstein] |
| 18714 | We already know what we want to know, and analysis gives us no new facts [Wittgenstein] |
| 18706 | Words of the same kind can be substituted in a proposition without producing nonsense [Wittgenstein] |
| 18719 | Grammar says that saying 'sound is red' is not false, but nonsense [Wittgenstein] |
| 18735 | Talking nonsense is not following the rules [Wittgenstein] |
| 18731 | There is no theory of truth, because it isn't a concept [Wittgenstein] |
| 18707 | All thought has the logical form of reality [Wittgenstein] |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| 13044 | Infinity: There is at least one limit level [Potter] |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| 18724 | In logic nothing is hidden [Wittgenstein] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 18709 | Laws of logic are like laws of chess - if you change them, it's just a different game [Wittgenstein] |
| 18736 | Contradiction is between two rules, not between rule and reality [Wittgenstein] |
| 18723 | We may correctly use 'not' without making the rule explicit [Wittgenstein] |
| 18718 | Saying 'and' has meaning is just saying it works in a sentence [Wittgenstein] |
| 18727 | A person's name doesn't mean their body; bodies don't sit down, and their existence can be denied [Wittgenstein] |
| 14235 | Saying 'they can become a set' is a tautology, because reference to 'they' implies a collection [Cargile] |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| 18738 | We don't get 'nearer' to something by adding decimals to 1.1412... (root-2) [Wittgenstein] |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| 18708 | Infinity is not a number, so doesn't say how many; it is the property of a law [Wittgenstein] |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| 18737 | There are no positive or negative facts; these are just the forms of propositions [Wittgenstein] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 18715 | Using 'green' is a commitment to future usage of 'green' [Wittgenstein] |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 18726 | For each necessity in the world there is an arbitrary rule of language [Wittgenstein] |
| 18712 | Understanding is translation, into action or into other symbols [Wittgenstein] |
| 18280 | We live in sense-data, but talk about physical objects [Wittgenstein] |
| 18729 | Part of what we mean by stating the facts is the way we tend to experience them [Wittgenstein] |
| 18734 | If you remember wrongly, then there must be some other criterion than your remembering [Wittgenstein] |
| 18721 | Explanation and understanding are the same [Wittgenstein] |
| 18720 | Explanation gives understanding by revealing the full multiplicity of the thing [Wittgenstein] |
| 18716 | A machine strikes us as being a rule of movement [Wittgenstein] |
| 18713 | If an explanation is good, the symbol is used properly in the future [Wittgenstein] |
| 18717 | Thought is an activity which we perform by the expression of it [Wittgenstein] |
| 18725 | A proposition draws a line around the facts which agree with it [Wittgenstein] |
| 18728 | The meaning of a proposition is the mode of its verification [Wittgenstein] |
| 18705 | Words function only in propositions, like levers in a machine [Wittgenstein] |
| 18711 | A proposition is any expression which can be significantly negated [Wittgenstein] |
| 18733 | Laws of nature are an aspect of the phenomena, and are just our mode of description [Wittgenstein] |