34 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
9108 | From an impossibility anything follows [William of Ockham] |
9107 | A proposition is true if its subject and predicate stand for the same thing [William of Ockham] |
16300 | Ockham had an early axiomatic account of truth [William of Ockham, by Halbach] |
13011 | New axioms are being sought, to determine the size of the continuum [Maddy] |
13013 | The Axiom of Extensionality seems to be analytic [Maddy] |
13014 | Extensional sets are clearer, simpler, unique and expressive [Maddy] |
13021 | The Axiom of Infinity states Cantor's breakthrough that launched modern mathematics [Maddy] |
13022 | Infinite sets are essential for giving an account of the real numbers [Maddy] |
13023 | The Power Set Axiom is needed for, and supported by, accounts of the continuum [Maddy] |
13024 | Efforts to prove the Axiom of Choice have failed [Maddy] |
13025 | Modern views say the Choice set exists, even if it can't be constructed [Maddy] |
13026 | A large array of theorems depend on the Axiom of Choice [Maddy] |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
13019 | The Iterative Conception says everything appears at a stage, derived from the preceding appearances [Maddy] |
13018 | Limitation of Size is a vague intuition that over-large sets may generate paradoxes [Maddy] |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
9106 | The word 'every' only signifies when added to a term such as 'man', referring to all men [William of Ockham] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
9113 | Just as unity is not a property of a single thing, so numbers are not properties of many things [William of Ockham] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
9110 | The words 'thing' and 'to be' assert the same idea, as a noun and as a verb [William of Ockham] |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
15388 | Universals are single things, and only universal in what they signify [William of Ockham] |
9109 | If essence and existence were two things, one could exist without the other, which is impossible [William of Ockham] |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
9105 | Some concepts for propositions exist only in the mind, and in no language [William of Ockham] |