42 ideas
| 9978 | Analytic philosophy focuses too much on forms of expression, instead of what is actually said [Tait] |
| 7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
| 9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
| 9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
| 9986 | The null set was doubted, because numbering seemed to require 'units' [Tait] |
| 9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
| 9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
| 9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
| 9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
| 9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
| 9984 | We can have a series with identical members [Tait] |
| 9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
| 18151 | Could we replace sets by the open sentences that define them? [Chihara, by Bostock] |
| 9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
| 8758 | We could talk of open sentences, instead of sets [Chihara, by Shapiro] |
| 9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| 9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
| 9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
| 10856 | A truly infinite quantity does not need to be a variable [Bolzano] |
| 9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| 9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
| 10265 | Chihara's system is a variant of type theory, from which he can translate sentences [Chihara, by Shapiro] |
| 8759 | We can replace type theory with open sentences and a constructibility quantifier [Chihara, by Shapiro] |
| 10264 | Introduce a constructibility quantifiers (Cx)Φ - 'it is possible to construct an x such that Φ' [Chihara, by Shapiro] |
| 17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
| 9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
| 9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
| 9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
| 9981 | Abstraction is 'logical' if the sense and truth of the abstraction depend on the concrete [Tait] |
| 9982 | Cantor and Dedekind use abstraction to fix grammar and objects, not to carry out proofs [Tait] |
| 9985 | Abstraction may concern the individuation of the set itself, not its elements [Tait] |
| 9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
| 9972 | Why should abstraction from two equipollent sets lead to the same set of 'pure units'? [Tait] |
| 9980 | If abstraction produces power sets, their identity should imply identity of the originals [Tait] |
| 9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
| 22276 | Bolzano saw propositions as objective entities, existing independently of us [Bolzano, by Potter] |
| 17264 | Propositions are abstract structures of concepts, ready for judgement or assertion [Bolzano, by Correia/Schnieder] |
| 12232 | A 'proposition' is the sense of a linguistic expression, and can be true or false [Bolzano] |
| 12233 | The ground of a pure conceptual truth is only in other conceptual truths [Bolzano] |
| 9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |