24 ideas
21489 | Super-ordinate disciplines give laws or principles; subordinate disciplines give concrete cases [Peirce, by Atkin] |
7807 | The laws of thought are true, but they are not the axioms of logic [Bolzano, by George/Van Evra] |
19095 | Pragmatic 'truth' is a term to cover the many varied aims of enquiry [Peirce, by Misak] |
19097 | Peirce did not think a belief was true if it was useful [Peirce, by Misak] |
21494 | If truth is the end of enquiry, what if it never ends, or ends prematurely? [Atkin on Peirce] |
21493 | Pure mathematics deals only with hypotheses, of which the reality does not matter [Peirce] |
19102 | Bivalence is a regulative assumption of enquiry - not a law of logic [Peirce, by Misak] |
9618 | Bolzano wanted to reduce all of geometry to arithmetic [Bolzano, by Brown,JR] |
9830 | Bolzano began the elimination of intuition, by proving something which seemed obvious [Bolzano, by Dummett] |
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] |
10352 | The real is the idea in which the community ultimately settles down [Peirce] |
13498 | Peirce and others began the mapping out of relations [Peirce, by Hart,WD] |
21491 | Peirce's later realism about possibilities and generalities went beyond logical positivism [Peirce, by Atkin] |
16376 | The possible can only be general, and the force of actuality is needed to produce a particular [Peirce] |
19107 | Inquiry is not standing on bedrock facts, but standing in hope on a shifting bog [Peirce] |
9185 | Bolzano wanted to avoid Kantian intuitions, and prove everything that could be proved [Bolzano, by Dummett] |
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] |