16 ideas
18261 | A simplification which is complete constitutes a definition [Kant] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
22275 | Logic gives us the necessary rules which show us how we ought to think [Kant] |
10001 | An adjective contributes semantically to a noun phrase [Hofweber] |
10007 | Quantifiers for domains and for inference come apart if there are no entities [Hofweber] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
9998 | What is the relation of number words as singular-terms, adjectives/determiners, and symbols? [Hofweber] |
10002 | '2 + 2 = 4' can be read as either singular or plural [Hofweber] |
10003 | Why is arithmetic hard to learn, but then becomes easy? [Hofweber] |
10008 | Arithmetic is not about a domain of entities, as the quantifiers are purely inferential [Hofweber] |
10005 | Arithmetic doesn’t simply depend on objects, since it is true of fictional objects [Hofweber] |
10000 | We might eliminate adjectival numbers by analysing them into blocks of quantifiers [Hofweber] |
10006 | First-order logic captures the inferential relations of numbers, but not the semantics [Hofweber] |
18260 | If we knew what we know, we would be astonished [Kant] |
10004 | Our minds are at their best when reasoning about objects [Hofweber] |