21 ideas
7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
10631 | If 'x is heterological' iff it does not apply to itself, then 'heterological' is heterological if it isn't heterological [Hale/Wright] |
9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
10624 | The incompletability of formal arithmetic reveals that logic also cannot be completely characterized [Hale/Wright] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
10622 | The neo-Fregean is more optimistic than Frege about contextual definitions of numbers [Hale/Wright] |
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] |
17265 | Philosophical proofs in mathematics establish truths, and also show their grounds [Bolzano, by Correia/Schnieder] |
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] |
10626 | Objects just are what singular terms refer to [Hale/Wright] |
9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
10630 | Abstracted objects are not mental creations, but depend on equivalence between given entities [Hale/Wright] |
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] |
10627 | Many conceptual truths ('yellow is extended') are not analytic, as derived from logic and definitions [Hale/Wright] |