10 ideas
| 17596 | Coherence problems have positive and negative restraints; solutions maximise constraint satisfaction [Thagard] |
| Full Idea: A coherence problem is a set of elements connected by positive and negative restraints, and a solution consists of partitioning the elements into two sets (accepted and rejected) in a way that maximises satisfaction of the constraints. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.42) | |
| A reaction: I'm enthusiastic about this, as it begins to clarify the central activity of epistemology, which is the quest for best explanations. |
| 17597 | Coherence is explanatory, deductive, conceptual, analogical, perceptual, and deliberative [Thagard] |
| Full Idea: I propose that there are six main kinds of coherence: explanatory, deductive, conceptual, analogical, perceptual, and deliberative. ...Epistemic coherence is a combination of the first five kinds, and ethics adds the sixth. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.43) | |
| A reaction: Wonderful. Someone is getting to grips with the concept of coherence, instead of just whingeing about how vague it is. |
| 17598 | Explanatory coherence needs symmetry,explanation,analogy,data priority, contradiction,competition,acceptance [Thagard] |
| Full Idea: Informally, a theory of explanatory coherence has the principles of symmetry, explanation, analogy, data priority, contradiction, competition and acceptance. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.44) | |
| A reaction: [Thagard give a concise summary of his theory here] Again Thagard makes a wonderful contribution in an area where most thinkers are pessimistic about making any progress. His principles are very plausible. |
| 17602 | Verisimilitude comes from including more phenomena, and revealing what underlies [Thagard] |
| Full Idea: A scientific theory is progressively approximating the truth if it increases its explanatory coherence by broadening to more phenomena and deepening by investigating layers of mechanisms. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.46) |
| 15943 | Limitation of Size is not self-evident, and seems too strong [Lavine on Neumann] |
| Full Idea: Von Neumann's Limitation of Size axiom is not self-evident, and he himself admitted that it seemed too strong. | |
| From: comment on John von Neumann (An Axiomatization of Set Theory [1925]) by Shaughan Lavine - Understanding the Infinite VII.1 |
| 13672 | All the axioms for mathematics presuppose set theory [Neumann] |
| Full Idea: There is no axiom system for mathematics, geometry, and so forth that does not presuppose set theory. | |
| From: John von Neumann (An Axiomatization of Set Theory [1925]), quoted by Stewart Shapiro - Foundations without Foundationalism 8.2 | |
| A reaction: Von Neumann was doubting whether set theory could have axioms, and hence the whole project is doomed, and we face relativism about such things. His ally was Skolem in this. |
| 17601 | Neither a priori rationalism nor sense data empiricism account for scientific knowledge [Thagard] |
| Full Idea: Both rationalists (who start with a priori truths and make deductions) and empiricists (starting with indubitable sense data and what follows) would guarantee truth, but neither even begins to account for scientific knowledge. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.46) | |
| A reaction: Thagard's answer, and mine, is inference to the best explanation, but goes beyond both the a priori truths and the perceptions. |
| 17600 | Bayesian inference is forced to rely on approximations [Thagard] |
| Full Idea: It is well known that the general problem with Bayesian inference is that it is computationally intractable, so the algorithms used for computing posterior probabilities have to be approximations. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.45) | |
| A reaction: Thagard makes this sound devastating, but then concedes that all theories have to rely on approximations, so I haven't quite grasped this idea. He gives references. |
| 17599 | The best theory has the highest subjective (Bayesian) probability? [Thagard] |
| Full Idea: On the Bayesian view, the best theory is the one with the highest subjective probability, given the evidence as calculated by Bayes's theorem. | |
| From: Paul Thagard (Coherence: The Price is Right [2012], p.45) |
| 12709 | Motion is not absolute, but consists in relation [Leibniz] |
| Full Idea: In reality motion is not something absolute, but consists in relation. | |
| From: Gottfried Leibniz (On Motion [1677], A6.4.1968), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3 | |
| A reaction: It is often thought that motion being relative was invented by Einstein, but Leibniz wholeheartedly embraced 'Galilean relativity', and refused to even consider any absolute concept of motion. Acceleration is a bit trickier than velocity. |