re americans and evolution now with free ockham s razor inside sorry about the delay in responding due to conference paper deadline panic in article qsnqqinn nr senator bedfellow mit edu bobs thnext mit edu robert singleton writes in article apr dcs warwick ac uk simon dcs warwick ac uk simon clippingdale writes alarming amounts of agreement deleted i made my statement about ockums razor from my experiences in physics thanks for info in baysian statistics very interesting and i didn t know it before i follow your proof but i have one questions we have two hypotheses h and hg the latter is more complicated which by definition means p h p hg that complicated isn t in fact where p h p hg comes from it s more the other way around it s from p h p hg p hg where g is the complement of g and by axiom p anything so p hg so p h p hg in a sense hg is necessarily more complicated than h for any h and g so i may be splitting hairs but what i m trying to say is that irrespective of subjective impressions of how complicated something is p h p hg holds with equality if and only if p hg as you point out it s a very simple matter to show p x h p x hg p h x p hg x and thus h is to be preferd to hg now to say that h is as consistent with the data as hg is to say p x h p x hg can you elaborate some on this well p x a p x b means that x is as likely to be observed if a is operative as it is if b is operative this implies that observing x does not provide any useful information which might allow us to discriminate between the respective possibilities that a and b are operative the difference reduces to the difference between the unknown and unhelpful prior probabilities p a and p b p x a p x b p a x k p a and p b x k p b where k p x a p x p x b p x so a and b are equally consistent with the data in that observing x doesn t give any pointers as to which of a or b is operative in the particular case where a h and b hg however we know that their prior probabilities are ordered by p h p hg although we don t know the actual values and it s this which allows us to deploy the razor to throw out any such hg also in the real world it isn t as clear cut and dry it seems to me we can t always determine whether the equality p x h p x hg is true that s certainly true but the particular point here was whether or not a divine component actually underlies the prevalence of religion in addition to the memetic transmission component which even the religious implicitly acknowledge to be operative when they talk of spreading the word now it seems to me as i ve said that the observed variance in religious belief is well accounted for by the memetic transmission model but rather less well if one proposes a divine component in addition since i would expect the latter to conspire against wide variance and even mutual exclusion among beliefs thus my personal feeling is that p x hg isn t even equal to p x h in this case but is smaller h is memetic transmission g is divine component x is the variance among beliefs but i happily acknowledge that this is a subjective impression btw my beef with your baysian argument was not a mathematical one i checked most of your work and didn t find an error and you seem very careful so there probably isn t a math mistake i think the mistake is philosophical but just to make sure i understand you can please rephrase it in non technical terms i think this is a reasonable request i always try to look for ways of explaining physics to non physicist i m not a baysian statistician nor any type of statistician so this would be very helpful not that i m a statistician as such either but the idea is that both theism and atheism are compatible with all of the read my observations to date however theism of the type with which i am concerned also suggests that for instance prayer may be answered people may be miraculously healed both are in principle amenable to statistical verification and that god s may generally intervene in measurable ways this means that these regions of the space of possible observations which i loosely termed appearances of god s have some nonzero probability under the theistic hypothesis and zero under the atheistic since there is only so much probability available for each hypothesis to scatter around over the observation space the probability which theism expends on making appearances of god s possible must come from somewhere else i e other possible observations all else being equal this means that an observation which isn t an appearance of god s must have a slightly higher probability under atheism than under theism the bayesian stuff implies that such observations must cause my running estimate for the probability of the atheistic hypothesis to increase with a corresponding decrease in my running estimate for the probability of the theistic hypothesis sorry if that s still a bit jargonesque but it s rather difficult to put it any other way since it does depend intimately on the properties of conditional probability densities and particularly that the total area under them is always unity an analogy may or may not be helpful say that hypothesis a is the coin is fair and that b is the coin is unfair two headed i ve used a and b to avoid confusion with h heads and t tails then p h a total p t a p h b total p t b the observations are a string of heads with no tails this is compatible with both a fair coin a and a two headed coin b however the probability expended by a on making possible the appearance of tails even though they don t actually appear must come from somewhere else since the total must be unity and it comes in this case from the probability of the appearance of heads say our running estimates at time n are e n a and e n b the observation x n at time n is another head x n h the estimates are modified according to p h a e n a e n a e n a m p h and p h b e n b e n b e n b m p h now we don t know p h the actual prior probability of a head but the multiplier for e a is half that for e b this is true every time the coin is tossed and a head is observed thus whatever the initial values of the estimates after n heads we have n e n a m e a and n e n b m e b and since e k a e k b at any time k you can show that m and thus m hence the estimate for the fair coin hypothesis a must decrease at each trial and that for the two headed coin hypothesis b must increase even though both hypotheses are compatible with a string of heads the loose analogy is between unfair coin and atheism and between fair coin and theism with observations consistent with both a tail which would falsify unfair coin is analogous to an appearance of god s which would falsify atheism i am not claiming that the analogy extends to the numerical values of the various probabilities just that the principle is the same constant observation of no evidence for gods if evidence for them is at all possible under the respective theisms constantly increases the notional estimated probability that they don t exist it s important to draw a distinction between theism that could be supported or not supported by evidence and theism that can t given a theism for which evidence is in principle not possible it doesn t make sense to say lack of evidence supports the contrary view quite so but this type of theism is what i might call the g in the hg in terms of our ockham s razor discussion and i d bin it on those grounds so it depends upon your conception of this god if it s a conception like zeus who happened to come down to earth to play quite frequently then i agree with you lack of evidence for this conception of god is evidence that it does not exist but if your conception of god is one that does not make falsifiable predictions see below on falsifiable predictions then i disagree lack of evidence does not support a disbelief the hypotheses don t have to be falsifiable and indeed in my model the theism isn t falsifiable i used the phrase should obverse given any specific x theism does not make the prediction p x ht that s why i used the word should theism makes no predictions about any specific event i can only say i believe that god did such and such after such and such happens or i believe god will do such and such but for any given x i can never a priori say p x ht i can not even say this for the set of all x or some x this is what don t like about your use of probability we also have no way of assigning these probabilities i hold science to positivistic criteria if someone cannot tell me how to measure even in principle p x h then probability is not applicable to hypothesis h such is the case when h ht theistic and ha atheistic for example p x ha p x ha p ha what is p ha how do i measure it you don t have to we don t need in the above analogy to know any prior probabilities to deduce that the updating multiplier for the fair coin hypothesis is less than unity and that the corresponding multiplier for the two headed coin hypothesis is greater than unity you don t need to know the initial values of the running estimates either it s clear that after a large number of observations p fair coin approaches zero and p two headed coin approaches unity all you need to know is whether p x ha is larger than p x ht for observed x and this follows from the assumptions that there are certain events rendered possible not necessary under ht which are not possible under ha and all else is equal baysian statistics relies upon a series of observations but what if the hypothesis isn t amenable to observation and even for statements that are amenable to observation some observations are not relevant a sequence of observations must be chosen with care i m curious to know what types of observations x x you have in mind concerning theism and atheism any observations you like it really doesn t matter nor affect the reasoning provided that there are some possible observations which would count as appearances of god s examples of this might be a demonstration of the efficacy of prayer or of the veracity of revelation but any statement about p x h for general x still counts as a prediction of h if the theism in question ht says that prayer may be answered or that miracles may happen see my interpretation quoted again above of what god exists means then this is a prediction p x ht for such x it s what distinguishes it from the atheist hypothesis ha which predicts that this stuff does not happen p x ha for such x theism does not make the claim that p x ht for such x or i should say that my theism doesn t maybe i was too quick to say we had a common language you said that by the existence of god you mean the notion that the deity described by the bible and by christians does interact with the universe as claimed by those agents i agreed with this however i must be careful here i believe this i m not making any claims maybe i should have changed does to can there is an important shift of emphasis but any way since i only have a belief i cannot conclude p x ht for such x ok we ll downgrade does interact to may interact which would actually be better since does interact implies a falsifiability which we both agree is misplaced i don t think my theism makes predictions maybe i m not understanding what you mean by prediction could you explain what you mean by this word i ll explain but bear in mind that this isn t central all i require of a theism is that it not make the prediction appearances of god s will never happen as does atheism before somebody points out that quantum mechanics doesn t make this prediction either the difference is that qm and atheism do not form a partition predictions include such statements as prayer is efficacious implying if you do the stats you will find that prayer is efficacious or prayer is not efficacious or verily i say unto you this generation shall not pass till all these things be fulfilled i don t think we have any problems of misunderstanding here persistent observation of this stuff not happening consistent with ht though it may be is more consistent with ha as explained in the bayesian stats post even if ht god exists is unfalsifiable that s no problem for my argument other than that you have to let the number of observations go to infinity to falsify it asymptotically btw i do not consider an argument that requires an infinite number of observations as valid or rather that part of the argument is not valid we as existing humans can never make an infinite number of measurments and any conclusion that reilies on this i don t accept as valid that s fine i don t claim that theism is false merely that the finite number of observations available to me so far suggest that it is and that as i continue to observe the suggestion looks better and better renormalization stuff deleted in the bayesian stats post i assumed that theism was indeed unfalsifiable in a finite number of observations here s the relevant quote the important assumption is that there are some observations which are compatible with the theist hypothesis and not with the atheist hypothesis and thus would falsify atheism these are what i called appearances of god s but this need not be taken too literally any observation which requires for its explanation that one or more gods exist will count all other observations are assumed to be compatible with both hypotheses this leaves theism as unfalsifiable and atheism as falsifiable in a single observation only by such appearances of god s here is my problem with this for something to be falsifiable it must make the prediction that x should not be seen if x is seen then the hypothesis has been falsified now atheism is a word in oposition to something theism a theism aserts a belief and an atheism aserts a disbelief so there are certain atheisms that are certainly falsifiable just as there are certain theisms that are falsifable e g if my theism asserts the world is only years old and that god does not decieve then this has been falsified however the atheism that is in oposition to an unfalsifiable theism is also unfalsifiable i could be wrong on this statment contd i think you are an appearance of god s is sufficient to falsify atheism whereas in general the corresponding theism is unfalsifiable i ll think more about it until then here is a general question suppse x were unfalsifiable is not x also unfalsifiable no by way of a counterexample let x the coin is fair or more accurately so that not x makes sense the two sides of the coin are different this is unfalsifiable by tossing the coin even a string of heads is consistent with a fair coin and you have to go to an infinite number of tosses to falsify x in the limit its converse is falsifiable and is falsified when at least one head and at least one tail have appeared this is partly what s wrong with you baysian argument which requires observations x x n to be made there are simply no such observations that have a truth value in relation to the statement god exists now by use of your symmetry argument i can understand why someone would say since the statement god does not exist makes no predictions i will choose not to believe it but none the less this would be founded on a type of faith or if you don t like the word faith insert belief for which there is no falsifiable evidence instead i ll assume you meant god exists up there at the highlight but by our agreed definition of exists the statement makes predictions as i said above although it isn t falsifiable in a finite number of observations actually i mean god does not exist makes no predictions oops sorry mea culpa the truth of this statment actually depends upon which god you are refering to but i can think of some conceptions of god for which it is true but once again i m open to the posibility that i could be wrong so give me some examples of predictions of the statment god does not exist here is one that i can think of if true then there would be no healing or miricles but this can in principle never be determined one way or the other there are cases in which people seem to recover and are healed without the help of a doctor and for no known reason these situations do in fact happen they are consistent with a theistic hypothesis but in no way support such a hypothesis we agree here they are not inconsistent with an atheistic hypothesis i can t think of one prediction from god does not exist that isn t of this type but i might be missing something the rapture will not happen on october said rapture would have falsified atheism to my satisfaction had it happened although its failure to happen does not of course falsify any theisms other than those which specifically predicted it no phenomenon which requires the existence of one or more gods for its explanation will ever be observed that about sums the whole thing up bob singleton bobs thnext mit edu cheers simon simon clippingdale simon dcs warwick ac uk department of computer science tel university of warwick fax coventry cv al u k
