tag:blogger.com,1999:blog-15005476.post653149212142064195..comments2023-10-10T08:02:18.073-04:00Comments on Rationally Speaking: Is chance in the map or the territory?Unknownnoreply@blogger.comBlogger41125tag:blogger.com,1999:blog-15005476.post-8183074918098759982011-10-12T11:20:30.051-04:002011-10-12T11:20:30.051-04:00If I understand the many worlds interpretation ful...If I understand the many worlds interpretation fully, it doesn't provide any mechanism for predicting in which world-branch we are - i.e. from our point of view randomness is maintained, in spite of a deterministic ensemble of worlds. <br />Even that divine calculator would either be "in" our quantum world and resort to probabilities (derived from a frequentist interpretation of previous observations?) or outside it and forced to consider all world branches as an ensemble, unable to posit chains of discrete (or what we would call discrete) events and reduced to descriptive statistics...<br />Also remember that, while quantum randomness (if it exists) is usually effectively unimportant for classic "real-life" systems, it can have direct impacts in the macroscopic world - mutations are a good example. Add to that the fact that chaos theory is studied as a possible direct link between quantum effects and macroscopic effects (since it provides well-characterized mechanisms to amplify fluctuations in stead of damping them).Anonymoushttps://www.blogger.com/profile/09275188884660131076noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-3897348038153188622011-09-20T14:26:28.493-04:002011-09-20T14:26:28.493-04:00Kevin, I think, makes a good comment: "...the...Kevin, I think, makes a good comment: "...the metaphysical view of a deterministic world, insofar as it was motivated by the perceived determinism of classical physics, is generally regarded as a kind of modern myth..." <br /><br />I was about to post something in a similar vein: for determinism, you need to make predictions based upon the principles of physics. But our physical laws are themselves based upon assumptions (e.g. Euclid's axioms).<br /><br />Godel's theorem shows that ANY logical system is inconsistent or incomplete in the sense that there are undecideable propositions. So, if we had perfect knowledge of the position and tragectory of each particle, our system for evaluating the result may not be consistent or comprehensive. Moreover, the laws were built upon a frequentist's argument. Will they be the same tomorrow? I can only say that light will move away from me at 186,000 mi/sec because it has in the past. Some speculate that even the constants may change.Tom D.https://www.blogger.com/profile/16005219519644708237noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-29680191210724903742011-09-20T01:09:14.930-04:002011-09-20T01:09:14.930-04:00I want to thank Ian for his post. Just a couple of...I want to thank Ian for his post. Just a couple of thoughts on this provocative discussion:<br /><br />1. Ian's post doesn't mention what is arguably the most common objection to frequentism among probability theorists who do reject it as a general interpretation of the probability concept -- namely, that the ratios that define the frequencies can only be specified relative to some reference class, and if you vary the reference class you'll vary the frequencies. But frequency interpretations of the probability calculus don't specify an algorithm or decision procedure for picking a unique reference class. The result is that for a given question, like "How likely is that a 44 year old man will live to 80?", frequency approaches don't yield a unique answer, they yield different answers depending on the reference class you pick (relative to males, relative to males who earn more that 40,000 dollars a year, relative to white males, relative to smokers, relative to non-smokers, etc.) <br /><br />I suppose you could spin this objection into a version of Ian's where we're talking about different reference classes related to types of coin tosses and how much information we have have about the initial conditions and forces acting on the coin, the mass distribution within the coin, etc. <br /><br />2. My understanding is that the strongest arguments for some kind of objective chance in quantum mechanics have to do with the fact that so-called "ignorance" interpretations of the quantum probabilities (the natural attitude of someone assuming a classical worldview) are actually incompatible with the standard quantum formalism. (Michael Redhead's book Incompleteness, Nonlocality and Realism gives one version of the argument, I think; it has to with how the algebra of statistical mixtures differs from the algebra of "pure" quantum states). <br /><br />I once asked a professor of mine whether Bohm's deterministic interpretation undermined these sorts of algebraic arguments against ignorance interpretations of the probabilities. He wasn't sure, and I've never really followed it up so I can't say. <br /><br />3. I think the prevailing view among philosophers of physics these days is that even the strict truth of classical physical theories wouldn't guarantee predictability, much less metaphysical determinism. John Earman is the expert on this, see his book A Primer on Determinism. Newtonian mechanics, for example, is only deterministic if certain mathematical conditions are satisfied, and the theorems that establish the existence and uniqueness of solutions (the mathematical correlate of deterministic evolution) are only valid over finite time scales. There are also results from computability theory showing how certain types of classical dynamical systems can have non-computable solutions, which is a much stronger form of unpredictability than chaotic indeterminacy (even Laplace's demon couldn't predict the behaviors of these kinds of systems). <br /><br />For these reasons, the metaphysical view of a deterministic world, insofar as it was motivated by the perceived determinism of classical physics, is generally regarded as a kind of modern myth by contemporary philosophers of physics. Even if Newton's or Maxwell's laws were strictly true in our world, neither metaphysical determinism nor epistemological predictability would follow. This is a result that few outside of the philosophy of physics seem to appreciate, I wish it were more widely known, since it bears on so many philosophical discussions.Kevinhttps://www.blogger.com/profile/14510869204237618255noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-37845874592756315122011-09-16T21:16:32.824-04:002011-09-16T21:16:32.824-04:00I don't see how what the frequency-results (or...I don't see how what the frequency-results (or Bayesian or whatever) would be IF you repeated this thing many times has any relevance whatever to what the result will be if you do it only once. Eg. the Monty Hall case: it's both theoretically and empirically clear that you will win more often if you switch your choice; but if you play the game only ONCE, why does it matter whether you switch or not? Seems to me it doesn't matter at all.Phiwillihttps://www.blogger.com/profile/05434702023421961210noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-62681123943936564122011-09-16T16:00:51.031-04:002011-09-16T16:00:51.031-04:00Ian, you write that, "unpredictability, rando...Ian, you write that, "unpredictability, randomness, chaos . . . is a map-level phenomenon, not a territory-level phenomenon". How do you know that? If we do indeed have "epistemic limits" that are forever insuperable, then on what basis can you make your claim? <br /><br />If we don't know then we don't know. Wouldn't it be similar to the fabled "black box" into which no one can ever look (or get any information from the inside)? It would be just as absurd to claim that the box contains a chicken than to say it doesn't. In either case, you do not know and never will, so why speculate? It seems to me that you are saying in effect, "yes, I agree we are ignorant of "x"(the unmappable territory), but let me tell you right now -- I know it contains a chicken!"Tom D.https://www.blogger.com/profile/16005219519644708237noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-10258048607695884022011-09-16T15:15:19.000-04:002011-09-16T15:15:19.000-04:00Ian cites my words: ""As for repeating &...Ian cites my words: ""As for repeating "the same" phenomenon, I think this is a case of angels dancing on a pinhead. I do not know of ANY measurement, however precise, that has absolutely no variability."<br /><br />And then comments upon them:<br />"Indeed, but it seems to me that this misses the point a little bit, which is not about measurement accuracy per se but about the randomness that is supposed to be in the experiment itself."<br /><br />In fact, for some specific sets of phenomena, e.g. those covered by quantum theory, we have a theory stating that there is randomness in the objective process itself, irrespective of random variability in measurements, instruments and the like. In fact, what we have with QM is not exactly a THEORY (we cannot exactly explain how and why the weird things apparently going on at subatomic level can occur at all; we only have a set of equations that work, in fact work wonderfully well. In a sense, we are in this regard in the same predicament in which Newton (and Newtonians) were before the arrival of Einstein's General Relativity: gravitation theory worked wonderfully well (with some minor quirks like the orbit of Mercury) but they did not have a clue about what gravitation was, or how it could act at a distance. <br />In other cases, we do not have such a theory. We simply observe phenomena that appear to vary randomly. The variability may be "in the mapping" or "in the territory", to follow Ian's jargon, but in most cases we are unable to tell: measurements are too rough, and theory too poor, to tell which is the right answer. Some disciplines have attempted to develop a theory; for instance Economics models economic behavior as a mixture of perfectly rational behavior plus random error caused by unnamed and unidentified individual causes. But even within Economics such theory (neoclassical economics) has been hotly disputed, with different schools proposing various possible alternatives. Just as QM and GR have not been reconciled in Physics, micro and macroeconomics are still not fully integrated, and both are poorly corroborated by experimental or observational evidence (behavioral and experimental economics are novelties not yet digested by mainstream economics).<br /><br />Excellent discussion, Ian.Hector M.https://www.blogger.com/profile/10008738285159771679noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-37681697184234450642011-09-16T13:06:47.262-04:002011-09-16T13:06:47.262-04:00We can split physical behaviors into three groups:...We can split physical behaviors into three groups: <br /><br />1) those where purely deterministic models are highly accurate (i.e. flightpath of a cannonball)<br />2) those where purely deterministic models are not accurate (i.e. quantum behavior) <br />3) those where we don't yet have strong deterministic models (i.e. human social behavior)<br /><br />Ian argues that behaviors in category (3) will likely move into category (1), because historically this has occurred many times. Ian grants that the existence of category (2) casts some doubt on this hypothesis, but argues that it's limited because category (1) is larger than category (2).<br /><br />However, behaviors that remain in category (3) are presumably harder to model effectively than those in category (1) or (2). Given that these behaviors haven't yet been modeled effectively, they probably require models that are relatively complex. Since models that required objective randomness are inherently more complex than models that are purely deterministic, it seems likely that behaviors in category (3) will end up in category (2) more often than has historically been the trend.<br /><br />To be clear, I'm not suggesting that human behavior is governed by quantum mechanics itself. Rather, I'm suggesting that human behavior may be governed by some as-yet-undiscovered mechanism that can't be accurately modeled purely deterministically.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15005476.post-49811444851672148812011-09-16T10:19:18.821-04:002011-09-16T10:19:18.821-04:00"Why refuse to call this a probability?"...<em>"Why refuse to call this a probability?"</em><br />Of course, it's a probability. We simply can't apply the frequentist's interpretation to the election case. <br /><br />Random = Unknown. A random toss means we don't know what the result will be. In the magician example, the magician knows what it will be. However, I can <em>predict</em> that it'll be a tail with a probability of 0.5 (a fair coin). Just being picky. :)<br /><br />Good post.jrhshttps://www.blogger.com/profile/01074853182840350306noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-12331985366119114122011-09-16T09:00:50.229-04:002011-09-16T09:00:50.229-04:00@Tom:
"But doesn't the micro generalize u...@Tom:<br />"But doesn't the micro generalize up to the macro ala a "Schrodinger's Cat" mechanism? <br /><br />That is, I can open a casino with a mechanical coin flipper that flips a "head" when the tenth decimal of some quantum experiment is even and flips a "tail" when the decimal is odd. I can invite the Laplacian Calculator to play, give it a free cocktail, and watch while it loses its transitors."<br /><br />I like the image! =)<br /><br />Yes, I have no argument with this. If you wish, you can set things up so that quantum indeterminacy has macroscopic effects; the point I was trying to make is that these situations are very unusual unless you deliberately set them up that way, and so quantum indeterminacy has little bearing on the vast majority of the classic problems of probability.<br /><br />@DJD:<br />"I'm curious...What type of knowledge is capable of determining if something is either mappable or un-mappable. Empirical generated knowledge? Logical Tautological) knowledge? Inferential? What method can be used to differentiate one from the other?"<br /><br />Well, "mappable" stands for "predictable in principle" and "un-mappable" for "objectively random." So it's obvious how to show that something is predictable - just predict it. As for showing that something is objectively random, I don't think there's any way to prove that without stepping outside of physics. But as I have said before, I don't even think "objectively random" is a meaningful term, any more than "objectively delicious."ianpollockhttps://www.blogger.com/profile/15579140807988796286noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-66523244928416148982011-09-16T08:33:55.667-04:002011-09-16T08:33:55.667-04:00@jrhs: "What is the probability that Obama wi...@jrhs: "What is the probability that Obama will be re-elected in 2012? The probability cannot be interpreted in a frequentist's way because the election simply can’t be repeated under the same conditions."<br /><br />Yes, I'm aware that frequentism dismisses this kind of question as the proper meat of probability because it's a one-off. However: (a) every event is a one-off to a greater or lesser degree, which begs the question of where to draw the line; (b) there are facts of the matter which bear on the question of whether Obama is less or more likely to win, which a rational person should take into account if they need to plan for either eventuality. It turns out that there are ways of reasoning about that likelihood numerically, the correctness of which can be demonstrated (or not) in a given predictor's track record. Why refuse to call this a probability?<br /><br />@Nick Barrowman:<br />"I think what you're saying is that randomness is an aspect of the tools we're using (perhaps unavoidably), not the phenomena we're trying to understand. Is that right?<br /><br />Yes, that's right, though I might add after "tools" something about our limited metaphysical position (as creatures within physics as opposed to outside of it, looking in).<br /><br />The quick version: essentially every instance of apparent randomness that we have dealt with historically has turned out to be explained or at least explainABLE as a result of our epistemic limits alone, not as a result of some sort of strange exception to causal physical laws. So I am betting against any theories/interpretations that make randomness fundamental to physics.ianpollockhttps://www.blogger.com/profile/15579140807988796286noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-18100424461520182992011-09-15T18:55:31.750-04:002011-09-15T18:55:31.750-04:00"Maybe you have a long term frequency of 50% ...<em>"Maybe you have a long term frequency of 50% for heads, but if for example I know the magician's trick about starting positions for coin flips, my probability for this toss is going to deviate from the observed 50% frequency, whereas yours may not.”</em><br /><br />The observed 50% frequency? A long term frequency of 50% can’t be observed since it’s a limit. <br /><br />If the magician or a machine can <em>repeatedly</em> flip the coin with the same starting position, and we can obtain the limit probability. So a frequentist’s interpretation of the probability is still possible. <br /><br />What is the probability that Obama will be re-elected in 2012? The probability cannot be interpreted in a frequentist's way because the election simply can’t be repeated under the same conditions.jrhshttps://www.blogger.com/profile/01074853182840350306noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-38505917144017491192011-09-15T18:46:36.380-04:002011-09-15T18:46:36.380-04:00Nick
>"But please don’t tell me that un-ma...Nick<br />>"But please don’t tell me that un-mappability itself is out there in the territory"<br /><br />How do you know that it's not "out there"...if you don't know what method is use to differentiate between mappable and un-mappable?DJDhttps://www.blogger.com/profile/01634608128841501265noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-38856779067361278392011-09-15T17:52:05.748-04:002011-09-15T17:52:05.748-04:00Ian, the piece I quoted was:
>>The problem ...Ian, the piece I quoted was:<br /><br />>>The problem is that unpredictability, randomness, chaos — whatever you want to call it, however unavoidable it is — is a map-level phenomenon, not a territory-level phenomenon.<br /><br />So sure, you can tell me that there are some things that exist, but are un-mappable even in principle. But please don’t tell me that un-mappability itself is out there in the territory — that’s just flat out insane! You’re turning your own ignorance into ontology!<< <br /><br />I think what you're saying is that randomness is an aspect of the tools we're using (perhaps unavoidably), not the phenomena we're trying to understand. Is that right?Nick Barrowmanhttps://www.blogger.com/profile/11224940659269649220noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-45843033740109583582011-09-15T13:31:29.611-04:002011-09-15T13:31:29.611-04:00Perhaps I am not understanding this and someone ca...Perhaps I am not understanding this and someone can enlighten me. <br /><br />There was talk here of Macro systems being (almost?) always deterministic dismissing rare quantum experiments involving the tenth decimal place. <br /><br />But doesn't the micro generalize up to the macro ala a "Schrodinger's Cat" mechanism? <br /><br />That is, I can open a casino with a mechanical coin flipper that flips a "head" when the tenth decimal of some quantum experiment is even and flips a "tail" when the decimal is odd. I can invite the Laplacian Calculator to play, give it a free cocktail, and watch while it loses its transitors.Tom D.https://www.blogger.com/profile/16005219519644708237noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-5041016004670243792011-09-15T09:16:42.891-04:002011-09-15T09:16:42.891-04:00@Hector:
"You can only arrive to those value...@Hector:<br /><br />"You can only arrive to those values by theory corroborated by experience, or by experience alone (you may anticipate them from theory alone, but you'd better also seek empirical corroboration)."<br /><br />I entirely agree, but this just goes to show that the ignorance prior mentioned above should only be applied when you're, well, ignorant. In the case of head diameters, you're not entirely ignorant, and you may indeed guess that such a phenomenon follows a gaussian distribution centered around 200 mm or so, then go out and start measuring heads.<br /><br />"As for repeating "the same" phenomenon, I think this is a case of angels dancing on a pinhead. I do not know of ANY measurement, however precise, that has absolutely no variability."<br /><br />Indeed, but it seems to me that this misses the point a little bit, which is not about measurement accuracy per se but about the randomness that is supposed to be in the experiment itself. The point is that in these "random experiments" you seem to have two desiderata working at cross purposes. On the one hand, you want the different instances of the phenomenon to be sufficiently similar that you are actually talking (in a colloquial sense) about one phenomenon, not many (e.g., in the case of the coin flip, it's better not to do a coin <i>drop</i> as well, since perhaps that has a different dynamic). On the other hand, in order to have variability at all, the different instances of the phenomenon must be sufficiently distinct from each other to give a fairly broad distribution rather than to give one event, repeated over and over.<br /><br />Just to make this clear, the problem is that (to stick with the coin toss case) it's actually <i>undesirable</i> to systematize the experiment (by, say, making a mechanical coin flipper) - holding onto ignorance is <i>incentivized</i>. And yet going in the opposite direction, by introducing extra variability you risk broadening the experiment to the point that its different trials are not even <i>about</i> the same thing.<br /><br />"The time has come, I modestly surmise (following in fact an idea of John Dewey), to turn the tables. Science should judge whether a philosophical question makes any (substantive) sense."<br /><br />Are we still talking about free will here? Anyway, I'd say it's important not so much to turn the tables, but to have the judgments go both ways. There are many cases where philosophers ignore scientific results to their detriment, and there are many cases where scientists fail to notice the philosophical assumptions of their work. One thinks both of the naive things that neuroscientists say, and the naive things that philosophers of mind say.<br /><br />As for diplomacy, I'll pile on too - you're a pleasure to talk to.<br /><br />@Nick Barrowman:<br />"I'm a little concerned that Rationally Speaking is being colonized with Yudkowsky-speak."<br /><br />That's a fair criticism. I hummed and hawed about using the map/territory metaphor for epistemology & ontology for a long time, but finally decided that it was too useful to resist. But perhaps there is another, better metaphor that we could use in its place?ianpollockhttps://www.blogger.com/profile/15579140807988796286noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-89726801263849130032011-09-15T07:39:05.685-04:002011-09-15T07:39:05.685-04:00DJD,
I was quoting Ian. I'm afraid I don'...DJD,<br /><br />I was quoting Ian. I'm afraid I don't know the answers to your questions.Nick Barrowmanhttps://www.blogger.com/profile/11224940659269649220noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-31565879593556324042011-09-15T00:03:48.879-04:002011-09-15T00:03:48.879-04:00The comment that you quote from Feller is consiste...The comment that you quote from Feller is consistent with the view that probability is a mathematical term, and can only be applied to the world within the context of an appropriate mathematical model. Maybe Feller was a frequentist, but that isn't obvious from your quote.<br /><br />I would expect many mathematicians, self included, to take the mathematical model approach. So I agree with you that probability is not an objective property of the universe - it is something that exists only in mathematical models.<br /><br />The coin toss case fits within a well understood model (ignoring possible quibbles about the fairness of the coin). People following the mathematical model approach would normally assume that standard model for the coin toss case.<br /><br />One could model belief and uncertainty, which allows your subjective account of probability to also be considered. And, for some purposes, that's a reasonable thing to do.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-15005476.post-69972264092380181052011-09-14T22:30:05.595-04:002011-09-14T22:30:05.595-04:00Nick
I'm curious...What type of knowledge is c...Nick<br />I'm curious...What type of knowledge is capable of determining if something is either mappable or un-mappable. Empirical generated knowledge? Logical Tautological) knowledge? Inferential? What method can be used to differentiate one from the other?DJDhttps://www.blogger.com/profile/01634608128841501265noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-37059764624403386892011-09-14T19:19:11.050-04:002011-09-14T19:19:11.050-04:00Hector M
See....You did it again...with grace and ...Hector M<br />See....You did it again...with grace and diplomacy.DJDhttps://www.blogger.com/profile/01634608128841501265noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-69146094311528294412011-09-14T18:42:25.538-04:002011-09-14T18:42:25.538-04:00I'm a little concerned that Rationally Speakin...I'm a little concerned that Rationally Speaking is being colonized with Yudkowsky-speak. For example, I wonder if there is a more straightforward way of expressing the following:<br /><br />>>The problem is that unpredictability, randomness, chaos — whatever you want to call it, however unavoidable it is — is a map-level phenomenon, not a territory-level phenomenon.<br /><br />So sure, you can tell me that there are some things that exist, but are un-mappable even in principle. But please don’t tell me that un-mappability itself is out there in the territory — that’s just flat out insane! You’re turning your own ignorance into ontology!<<Nick Barrowmanhttps://www.blogger.com/profile/11224940659269649220noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-91378110961441936312011-09-14T17:47:02.719-04:002011-09-14T17:47:02.719-04:00DJD, I'm surprised you find that I express my ...DJD, I'm surprised you find that I express my criticisms diplomatically. I thought I was being not exactly diplomatic, but extraordinarily crash, provocatorial and politically incorrect. But it's all in the eye of the beholder, as our amiable Ian would put it.Hector M.https://www.blogger.com/profile/10008738285159771679noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-83420723761003255882011-09-14T17:08:05.633-04:002011-09-14T17:08:05.633-04:00Hector M.
Beautifully stated. I wish I had the abi...Hector M.<br />Beautifully stated. I wish I had the ability to express my criticisms as diplomatically as you.DJDhttps://www.blogger.com/profile/01634608128841501265noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-60057997387860169342011-09-14T15:06:03.145-04:002011-09-14T15:06:03.145-04:00Ian, it is a pity I chose the coin example to deve...Ian, it is a pity I chose the coin example to develop my argument. Since the chances in the coin case are fifty-fifty, this allows for the "entropy" and "ignorance" arguments to be introduced. But suppose the prior is something different from that particular case. For instance, in the case of a biological variable (such as the length of monkey tails or the diameter of human heads) the probability of a given size (or the probability of sizes lower than a given size) will probably be Gauss-normal. It could be expressed a priori in terms of z-scores (in units of standard deviation above or below the mean) or could be anticipated in absolute values once we know (from frequency distributions) the mean and SD of the relevant variable. Thus my particular prior could be 2.68% or suchlike. In other cases, theory or experience dictate that the distribution is not normal, but for instance log-normal (as with many income effects), and the values are even less intuitive. You can only arrive to those values by theory corroborated by experience, or by experience alone (you may anticipate them from theory alone, but you'd better also seek empirical corroboration).<br /><br />As for repeating "the same" phenomenon, I think this is a case of angels dancing on a pinhead. A do not know of ANY measurement, however precise, that has absolutely no variability. Try to measure the angles of a triangle with the most precise measuring rod you can get, with nanometers of precision if you can, and you'll never get "exactly" 180° in all occasions: you'll always get an "error distribution", albeit of a very diminutive scale. Even at magnitudes well above QM. Whether a "totally precise" measurement can be done is a rather otiose question (what is the "precise value" of the transcendental number pi?). Whether there would be any variability among measurements made with such a perfect measuring rod is another question I think otiose (just because such a rod does not exist). I am frankly not worried much by the map-territory distinction if it is carried to these extremes.<br /><br />If one renounces this folly of exactness, then measures are always random variables.<br /><br />Besides, think of what we mean by a "map" as distinct from a "territory". In the end, our perceptive and cognitive apparatus is also part of physical reality, and the interaction of our retinas with incoming light in the presence of light-reflecting objects is another physical phenomenon. The territory, in other terms, includes the map (and the mapper). And the mapper is, like the rest of us, a biological entity fumbling its way around with imperfect sensing organs.<br /><br />Once upon a time scientists were subjected to the judgment of philosophers, who were supposed to issue verdicts on the validity or otherwise of scientific statements. Not only on their logical coherence, which is alright, but on their substantive validity. <br />The time has come, I modestly surmise (following in fact an idea of John Dewey), to turn the tables. Science should judge whether a philosophical question makes any (substantive) sense. And science (like ancient philosophers thought about philosophy) needs no external justification; its proof, like that of the proverbial pudding, is in practice: it just works. It has evolved techniques and procedures that do work, at least in the imperfect and perfectible way any natural process works. And it has worked wonderfully for centuries now. <br />It would be nice if philosophical musings start from that stark fact (science does usually work), and subject themselves to the verdict of science as for the substantive worth of their speculations.Hector M.https://www.blogger.com/profile/10008738285159771679noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-72289951219968756452011-09-14T09:32:49.068-04:002011-09-14T09:32:49.068-04:00@contrarianmoderate: I'm not assuming my concl...@contrarianmoderate: I'm not assuming my conclusion per se, although it looks that way because the argument has a slightly unusual logical structure. First I talk about frequentism GIVEN that determinism is true (which is what you read there), then I question whether & to what extent determinism is true.<br /><br />@DJD: I admit there is a certain tactical aspect to my expressed opinion on free will, but I think it's well founded. Contracausal free will is incompatible with determism, indeed, but it's also internally contradictory and metaphysically conceited. And yet people DO make meaningful choices. So yes, I'm okay with making the argument "free will exists but can't be contracausal," rather than flatly stating "you have no free will" and then accepting the misunderstandings as people take me to mean "you're an automaton that can't make choices."<br /><br />Okay, my cat has now jumped onto the computer 30 times (I counted) and it's time for work, so I think I better reply to the other comments later. Cheers!ianpollockhttps://www.blogger.com/profile/15579140807988796286noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-51866671420020338952011-09-14T09:32:30.594-04:002011-09-14T09:32:30.594-04:00Don't get me wrong, I'm perfectly okay wit...Don't get me wrong, I'm perfectly okay with using frequencies in lots of situations, I just deny the <i>identity</i> with probabilities. Maybe you have a long term frequency of 50% for heads, but if for example I know the magician's trick about starting positions for coin flips, my probability <i>for this toss</i> is going to deviate from the observed 50% frequency, whereas yours may not.<br /><br />"For instance, a physical theory of the probable trajectories of flat cylindrical bodies, like coins, may predict that they are likely to fall on each side 50% of the time."<br /><br />Right, that would mean that such a theory was an essentially <b>ignorant</b> theory of coin flipping - i.e., it doesn't improve on the ignorance prior. There may be good reasons for that ignorance - indeed there are by hypothesis (bla bla small diffs in initial conditions). But it would be wrong to take that theory as evidence that the "true" probability is "really" about 50%. The theory is just telling you that it doesn't have any resolving power to help you predict coin flips, so you might as well stick with your ignorance prior.<br /><br />"I may assign a high likelihood to an event (such as that tomorrow will be rainy), but no actual outcome (raining or sunny) may legitimately refute my statement: rain may have been extremely likely even if tomorrow turns out to be sunny after all: what one ACTUALLY means with a meteorological forecast is that over a great many days like today, in MOST cases (i.e. with high frequency) the next day was rainy."<br /><br />Certainly; this is usually referred to in the context of "calibration." However, a single contrary outcome may not outright <i>refute</i> a probability assignment, but it will certainly give evidence that it was a bad one. To see this, take an extreme case: if I say "a million to one in favour of rain tomorrow" and it doesn't rain, my assessment is <i>effectively</i> falsified, even though I *could* just be very unlucky.<br /><br />"It may be comforting to learn that a particular piece of scientific knowledge does not imply the demise of some of our cherished beliefs, but that has nothing to do with the validity of such piece of scientific knowledge."<br /><br />While agreeing with you, I tend to see this in different terms. If science or philosophy apparently undermines a cherished belief or intuition, I tend to first look at whether our naive ideas about what was Philosophically Absolutely Necessary for said belief/intuition are correct, rather than rushing to "disprove" the belief/intuition.ianpollockhttps://www.blogger.com/profile/15579140807988796286noreply@blogger.com