3 ideas
| 13416 | Mathematics must be based on axioms, which are true because they are axioms, not vice versa [Tait, by Parsons,C] |
| Full Idea: The axiomatic conception of mathematics is the only viable one. ...But they are true because they are axioms, in contrast to the view advanced by Frege (to Hilbert) that to be a candidate for axiomhood a statement must be true. | |
| From: report of William W. Tait (Intro to 'Provenance of Pure Reason' [2005], p.4) by Charles Parsons - Review of Tait 'Provenance of Pure Reason' §2 | |
| A reaction: This looks like the classic twentieth century shift in the attitude to axioms. The Greek idea is that they must be self-evident truths, but the Tait-style view is that they are just the first steps in establishing a logical structure. I prefer the Greeks. |
| 19708 | Rational internal belief is conviction that a proposition enhances a belief system [Foley, by Vahid] |
| Full Idea: In Foley's subjective internalist account it is egocentrically rational for an agent to believe a proposition only if he would think on deep reflection that believing it is conducive to having an accurate and comprehensive belief system. | |
| From: report of Richard Foley (The Theory of Epistemic Rationality [1987], 2.1 B) by Hamid Vahid - Externalism/Internalism | |
| A reaction: I like this idea, because it indicates the link between internalism and coherence about justification. I don't think you can be an externalist coherence theorist for justification. [Reminder: Paul Thagard is the best writer on coherence]. |
| 18284 | Particulars can be verified or falsified, but general statements can only be falsified (conclusively) [Popper] |
| Full Idea: Whereas particular reality statements are in principle completely verifiable or falsifiable, things are different for general reality statements: they can indeed be conclusively falsified, they can acquire a negative truth value, but not a positive one. | |
| From: Karl Popper (Two Problems of Epistemology [1932], p.256), quoted by J. Alberto Coffa - The Semantic Tradition from Kant to Carnap 18 'Laws' | |
| A reaction: This sounds like a logician's approach to science, but I prefer to look at coherence, where very little is actually conclusive, and one tinkers with the theory instead. |