11 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) |
| 9987 | An aggregate in which order does not matter I call a 'set' [Bolzano] |
| Full Idea: An aggregate whose basic conception renders the arrangement of its members a matter of indifference, and whose permutation therefore produces no essential difference, I call a 'set'. | |
| From: Bernard Bolzano (Paradoxes of the Infinite [1846], §4), quoted by William W. Tait - Frege versus Cantor and Dedekind IX | |
| A reaction: The idea of 'sets' was emerging before Cantor formalised it, and clarified it by thinking about infinite sets. Nowadays we also have 'ordered' sets, which rather contradicts Bolzano, and we also expect the cardinality to be determinate. |
| 10856 | A truly infinite quantity does not need to be a variable [Bolzano] |
| Full Idea: A truly infinite quantity (for example, the length of a straight line, unbounded in either direction) does not by any means need to be a variable. | |
| From: Bernard Bolzano (Paradoxes of the Infinite [1846]), quoted by Brian Clegg - Infinity: Quest to Think the Unthinkable §10 | |
| A reaction: This is an important idea, followed up by Cantor, which relegated to the sidelines the view of infinity as simply something that could increase without limit. Personally I like the old view, but there is something mathematically stable about infinity. |
| 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) |
| 1748 | Archelaus was the first person to say that the universe is boundless [Archelaus, by Diog. Laertius] |
| Full Idea: Archelaus was the first person to say that the universe is boundless. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Diogenes Laertius - Lives of Eminent Philosophers 02.Ar.3 |
| 5989 | Archelaus said life began in a primeval slime [Archelaus, by Schofield] |
| Full Idea: Archelaus wrote that life on Earth began in a primeval slime. | |
| From: report of Archelaus (fragments/reports [c.450 BCE]) by Malcolm Schofield - Archelaus | |
| A reaction: This sounds like a fairly clearcut assertion of the production of life by evolution. Darwin's contribution was to propose the mechanism for achieving it. We should honour the name of Archelaus for this idea. |