| 14280 | The probability of two events is the first probability times the second probability assuming the first [Bayes] |
| Full Idea: The probability that two events will both happen is the probability of the first [multiplied by] the probability of the second on the supposition that the first happens. | |
| From: Thomas Bayes (Essay on a Problem in the Doctrine of Chances [1763]), quoted by Dorothy Edgington - Conditionals (Stanf) 3.1 |
| 22656 | Trying to assess probabilities by mere calculation is absurd and impossible [James] |
| Full Idea: The absurd abstraction of an intellect verbally formulating all its evidence and carefully estimating the probability thereof solely by the size of a vulgar fraction, is as ideally inept as it is practically impossible. | |
| From: William James (The Sentiment of Rationality [1882], p.40) | |
| A reaction: James probably didn't know about Bayes, but this is directed at the Bayesian approach. My view is that full rational assessment of coherence is a much better bet than a Bayesian calculation. Factors must be weighted. |
| 19143 | Ramsey gave axioms for an uncertain agent to decide their preferences [Ramsey, by Davidson] |
| Full Idea: Ramsey gave an axiomatic treatment of preference in the face of uncertainty, when applied to a particular agent. | |
| From: report of Frank P. Ramsey (Truth and Probability [1926]) by Donald Davidson - Truth and Predication 2 | |
| A reaction: This is evidently the beginnings of Bayesian decision theory. |
| 19155 | Instead of gambling, Jeffrey made the objects of Bayesian preference to be propositions [Jeffrey, by Davidson] |
| Full Idea: Jeffrey produced a version of Bayesianism that made no direct use of gambling (as Ramsey had), but treats the objects of preference ...as propositions. | |
| From: report of Richard Jeffrey (The Logic of Decision [1965]) by Donald Davidson - Truth and Predication 3 | |
| A reaction: I'm guessing that Jeffreys launched modern Bayesian theory with this idea. It suggest that one can consider degrees of truth, rather than mere winning or losing. |
| 2751 | Probabilities can only be assessed relative to some evidence [Dancy,J] |
| Full Idea: In Probability Calculus probability is only assessed relative to some evidence. | |
| From: Jonathan Dancy (Intro to Contemporary Epistemology [1985], 4.1) |
| 2798 | Probability of H, given evidence E, is prob(H) x prob(E given H) / prob(E) [Horwich] |
| Full Idea: Bayesianism says ideally rational people should have degrees of belief (not all-or-nothing beliefs), corresponding with probability theory. Probability of H, given evidence E, is prob(H) X prob(E given H) / prob(E). | |
| From: Paul Horwich (Bayesianism [1992], p.41) |
| 2799 | Bayes' theorem explains why very surprising predictions have a higher value as evidence [Horwich] |
| Full Idea: Bayesianism can explain the fact that in science surprising predictions have greater evidential value, as the equation produces a higher degree of confirmation. | |
| From: Paul Horwich (Bayesianism [1992], p.42) |
| 16801 | A hypothesis is confirmed if an unlikely prediction comes true [Lipton] |
| Full Idea: In English, Bayes's Theorem says that there is a high confirmation when your hypothesis entails an unlikely prediction that turns out to be correct - a very plausible claim. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Descr') | |
| A reaction: Presumably the simple point is that a likely prediction could have been caused by many things, but an unlikely prediction will probably only be caused by that thing. |
| 16802 | Bayes seems to rule out prior evidence, since that has a probability of one [Lipton] |
| Full Idea: Old evidence seems to provide some confirmation, but Bayesianism does not allow for this, since old evidence will have a prior probability of one, and so have no effect on the posterior probability of the hypothesis. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Descr') |
| 16803 | Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton] |
| Full Idea: Since the Bayesian account says a hypothesis is confirmed by any of its logical consequences …it seems to inherit the over-permissiveness of the hypothetico-deductive model. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 01 'Descr') | |
| A reaction: This sounds like Hempel's Raven Paradox, where the probability of some logical consequences seems impossible to assess. |
| 16837 | Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton] |
| Full Idea: In p(H|E) = p(E|H)p(H)/p(E), the left side is the 'posterior' probability of H given E, p(E|H) is the 'likelihood' of E given H, and the others are the 'priors' of H and E. Moving from right to left is known as 'conditionalization'. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 07 'The Bayesian') |
| 16839 | Explanation may be an important part of implementing Bayes's Theorem [Lipton] |
| Full Idea: Explanatory considerations may play an important role in the actual mechanisms by which inquirers 'realize' Bayesian reasoning. | |
| From: Peter Lipton (Inference to the Best Explanation (2nd) [2004], 07 'The Bayesian') | |
| A reaction: Lipton's strategy for making peace between IBE and Bayesians. Explanations give likeliness. The background question for Bayesians always seems to be how the initial probabilities are assigned. Pure logic won't do that job. |
| 6372 | Since every tautology has a probability of 1, should we believe all tautologies? [Pollock/Cruz] |
| Full Idea: It follows from the probability calculus that every tautology has probability 1; it then follows in Bayesian epistemology that we are justified in believing every tautology. | |
| From: J Pollock / J Cruz (Contemporary theories of Knowledge (2nd) [1999], §4.3.1.5) | |
| A reaction: If I say 'a bachelor is a small ant' you wouldn't believe it, but if I said 'I define a bachelor as a small ant' you would have to believe it. 'Bachelors are unmarried' men is a description of English usage, so is not really a simple tautology. |
| 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. |
| 14990 | Bayes produces weird results if the prior probabilities are bizarre [Sider] |
| Full Idea: In the Bayesian approach, bizarre prior probability distributions will result in bizarre responses to evidence. | |
| From: Theodore Sider (Writing the Book of the World [2011], 03.3) | |
| A reaction: This is exactly what you find when people with weird beliefs encounter ridiculous evidence for things. It doesn't invalidate the formula, but just says rubbish in rubbish out. |
| 6798 | Bayesianism claims to find rationality and truth in induction, and show how science works [Bird] |
| Full Idea: Keen supporters of Bayesianism say it can show how induction is rational and can lead to truth, and it can reveal the underlying structure of actual scientific reasoning. | |
| From: Alexander Bird (Philosophy of Science [1998], Ch.6) | |
| A reaction: See Idea 2798 for Bayes' Theorem. I find it intuitively implausible that our feeling for probabilities could be reduced to precise numbers, given the subjective nature of the numbers we put into the equation. |
| 22178 | If the rules only concern changes of belief, and not the starting point, absurd views can look ratiional [Okasha] |
| Full Idea: If the only objective constraints concern how we should change our credences, but what our initial credences should be is entirely subjective, then individuals with very bizarre opinions about the world will count as perfectly rational. | |
| From: Samir Okasha (Philosophy of Science: Very Short Intro (2nd ed) [2016], 2) | |
| A reaction: The important rationality has to be the assessement of a diverse batch of evidence, for which there can never be any rules or mathematics. |
| 17943 | Probability supports Bayesianism better as degrees of belief than as ratios of frequencies [Colyvan] |
| Full Idea: Those who see probabilities as ratios of frequencies can't use Bayes's Theorem if there is no objective prior probability. Those who accept prior probabilities tend to opt for a subjectivist account, where probabilities are degrees of belief. | |
| From: Mark Colyvan (Introduction to the Philosophy of Mathematics [2012], 9.1.8) | |
| A reaction: [compressed] |
| 22365 | The Bayesian approach is explicitly subjective about probabilities [Reiss/Sprenger] |
| Full Idea: The Bayesian approach is outspokenly subjective: probability is used for quantifying a scientist's subjective degree of belief in a particular hypothesis. ...It just provides sound rules for learning from experience. | |
| From: Reiss,J/Spreger,J (Scientific Objectivity [2014], 4.2) |