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Fragment of a discussion from User talk:Tmtoulouse
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The only way to equalize P(H0) and P(H1) is if P(observed reality | H0) = P( observed reality | H1). This means that all observed reality acts as if it can be completely explained through naturalistic mechanisms. This is Spinoza's God. The problem is that the pragmatic and epistemological weight of H0 and H1 in this case are not equal. Since observed reality in this construct acts as if there is no God, an appeal to the existence of a God is expanding the complexity of the system without gaining any explanatory power. Therefore, the principle of parsimony kicks in and we still embrace H0 as the preferred hypothesis.

Tmtoulouse (talk)05:13, 4 July 2011

Well, then it all comes down to what is the correct version of the "principle of parsimony" or "Occam's razor", which I have been debating back and forth with Röstigraben recently. A couple of points open to dispute:

  1. Is "God does not exist" really simpler than "God exists"? Atheists make that claim, but I am not convinced
  2. The principle of parsimony says to avoid unnecessary complexity. The question is, what determines whether extra complexity is "necessary" or not. You say it is only necessary if it adds explanatory power. But, it is open to someone to argue that human thought performs other purposes than just explanation, and that a complication, which may be unnecessary for explanation, may yet be necessary for other purposes
(((Zack Martin)))05:20, 4 July 2011

Uh seems pretty axiomatic to me. Lets set this up using a linear system just for simplicity sake.

Mo = X0+X1+X2

R = O - Mo

We have some model of reality, Mo is the prediction of our observations given the elements of our model (X0...XN). If we then take our observed reality (O) we can calculate the "residuals" left over that are not accounted for by our model. The "complexity" of the model is then defined as the number of elements with in the set. To determine if an extra element is worth adding to the model we need to compare the residuals of those two models.

Mo1 = X0+X1 Mo2 = X0+X1+X2

R1 = O - Mo1 R2 = O - Mo2

In order for us to say that Mo2 is "better" than Mo1 R2 must be significantly less than R1. Now what "significantly" means is something we work out in statistics and doesn't need to be defined here. The reason we do not need to worry about it here is because what you guys are postulating is something like this:

Mo1(there is no god) = X0+X1...XN Mo2(there is a god) = X0+X1....XN+1

R1= O-Mo1 R2= O-Mo2

R1=R2

You have therefor added an element to the model XN+1, but kept the residuals equal. Therefore, an sane system of knowledge would reject Mo2 in favor of Mo1.

Tmtoulouse (talk)05:34, 4 July 2011

Well, most deist/theist worldviews include an afterlife, so they actually make additional predictions. Adding a deity to the model, and the assumption that we will observe the deity post mortem, produces additional predicted observations.

The problem with your metamodel, is that you are looking at things in a static/atemporal manner, rather than a dynamic manner, not taking into account that observations (and also predicted observations) vary over time.

We can talk about objective time, in the sense of something which is a property of the external universe, and which we share with other observers. And we can talk about subjective time, which is something relative to ourselves as individuals. (Roughly speaking, subjective time is relative to the frame of reference of our own consciousness; objective time is relative to some frame of reference external to our own consciousness.) Our individual personal observations are indexed with respect to subjective time - we have no observations prior to the beginning of subjective time, nor after its end, even if objective time extends beyond those bounds.

If death is extinction, then our subjective time is a finite duration, t0 >= t >= t1.

If there is an afterlife, then our subjective time extends beyond t1, at least up to some other time t2, where t1 < t2. (Whether it extends infinitely past t1, or eventually ends, is not relevant at this point).

The no God model predicts certain observations within the bounds of t0 >= t >= t1, and no observations whatsoever for t > t1.

The God+afterlife model predicts the same observations within the bounds of t0 >= t >= t1, and further observations (e.g. experiences of God) for t1 > t >= t2.

So, we've added one or more elements to our model. What we've done to the residuals, is hard to say, because you've defined the residuals in a time-invariant manner, when the residuals really need to be defined in a time-variant one.

(((Zack Martin)))06:06, 4 July 2011

The model I have proposed isn't static at all, the elements vary in time in conjunction with observation points. I did limit the dimensionality of the equations because non-linear statistical modeling is needlessly complex when the point can be shown in a linear context.

Your use of the after life is no different than any proposed model that makes a claim about a specific point in the future that has yet to occur. I could say that we actually all live in a giant lollipop, but that the lollipop is structured so that we will never know that we live in it until the giant finishes licking it to the center core. The giant will finish licking the lollipop and reach the center core on March 26th, 2014.

When does my giant lollipop model become superior to the anti-thesis that we don't live in a lollipop? Well when we reach the point that our observational evidence can show that we do. Until then the rational thing to do is to accept the more parsimonious model and wait further observation.

This is how science works, we change our models when new data is introduced that is better explained by another model. But until that time the rational individual will rely on the simplest model with the greatest explanatory power.

If you abandon this idea and say that any model that postulates some future event should be viewed as equally likely as any other, then you are stuck in your infinite loop of gibberish and giant lollipops.

Tmtoulouse (talk)06:24, 4 July 2011

Let me put it this way: The giant lolipop theory (GLT) claims that on 26th March 2014, we will make some observation which clearly supports its claims (e.g. we will see the giant's tongue through our telescopes.) More formally, at some time tg, where tg > tnow, we will have some observation og; but predicts no observations for times t < tg. And, GLT specifies tg as 26th March 2014.

Anti-GLT theory claims that on that same date, we will see no such observations (e.g. we look out our telescopes, and no giant tongue can be seen). More formally, at tg, we will have some observation o~g, which by its nature is incompatible with having observation og.

So, both theories predict different observations at tg, og and o~g. Why should we assume anti-GLT is more likely than GLT? Because, our existing knowledge + anti-GLT is simpler than our existing knowledge + GLT. Let O = {all ot for all t0 <= t <= tnow}. In other words, O is all the observations we have had so far. Anti-GLT is more likely, because C(O + o~g) < C(O + og), where C(x) is a measure of complexity. (I would say Kolmogorov complexity, or some computable approximation thereto.) Hence, parsimony leads us to prefer anti-GLT, since anti-GLT is a simpler theory than GLT.

Now, the God+afterlife theory (GA theory) says that post mortem, I will make certain observations. Unlike GLT, it doesn't predict a precise date for its observations, but that is fine. Consider the theory "My cat will die one day". That theory predicts certain observations in the future. It doesn't specify a precise date, but it can provide a function p(t) = probability we have had those observations by time t. Obviously, all animals, my cat included, have a finite lifespan, and the longer they live, the more likely they'll die now (to simplify things a bit). So, the fact that the afterlife theory doesn't precisely specify a time for my own death is fine, since that is analogous to the case when dealing with the death of my cat. It simply claims that, whenever my death occurs, then observations of a certain sort will follow, reasonably promptly thereafter, measured in subjective terms. Depending on one's theology, maybe one believes in soul sleep, and I will be unconscious post mortem for thousands or millions of billions of years before God returns me to consciousness; but, since the theory references subjective time, that duration doesn't count.

So, GA theory says I'll have certain observations oGod at time tpm, where tpm > tdeath > tnow.

What does no-God-no-afterlife theory (NGNA theory) predict at tpm? Well, interestingly, it doesn't predict any observation at all. It predicts, not an observation, but this strange entity called observing nothing, a null set of observations. This is why, GLT and anti-GLT are symmetric, in a way which GA and NGNA aren't. So, comparing the GLT/anti-GLT pair to the GA/NGNA pair isn't really valid.

Should parsimony prefer NGNA to GA theory? Using the same logic we used for the GLT/anti-GLT case, we have to compare C(O + GA) to C(O + NGNA). Now, NGNA is essentially a null set, so we are basically comparing C(O + GA) to C(O + null), and it seems reasonable to assume that C(O + null) = C(O). So, if C(O) < C(O + GA), then NGNA wins by parsimony.

Can adding an observation make the set of observations simpler? Indeed it can. Consider a program which generates all the digits of pi, call any program meeting this description P1. Consider instead a program which generates the first n digits of pi, where n is a large but finite arbitrary number (say one on the order of Graham's number); call this program P2. Now, is the shortest P1 program shorter than the shortest P2 program? Yes; a P1 program must just encode an algorithm to calculate pi; a P2 program must also encode some large number n, and the logic to stop the generation when that many digits have been output. The Kolmogorov complexity of a finite initial substring of pi will be greater than the Kolmogorov complexity of pi itself, when that initial substring is long enough.

Furthermore, let me present the following theory, call it universe extinction theory (UET). UET claims, that at some time tend, where tend >= tnow, the universe, and everyone and everything within it, will suddenly cease to exist, and thus time will end, and nothing will exist at all, ever thereafter. Of course, UET is not a single theory, but a family of theories, for differing values of tend. At one extreme, where tend is many billions or trillions of years in the future, UET may match various theories from cosmology of the end of the universe (e.g. the Big Crunch). On the other hand, if tend is next week, or next second, or this very instant, well now we are in reverse Last Thursdayism territory - Next Thursdayism rather than Last Thursdayism.

Won't the principle of parsimony prefer UET(tnext Thursday)? Isn't it simpler to assume the universe suddenly ceases to exist next Thursday, than it exists for billions, trillions of years to come. That is an immense extra volume of spacetime we are adding to the universe, an immense subsequent series of observations - surely, that immense addition is not perfectly compressible, and even if combined with O it compresses significantly, it seems likely that C(O + a tiny bit extra) << C(O + billions of years extra). But, if the principle of parsimony leads us to prefer the hypothesis that the universe will end next Thursday, doesn't it lead us to believe in preference to that, that right now is the last moment of the universe's existence? But, clearly that is preposterous; so something must be wrong with the principle of parsimony.

Furthermore, no-afterlife theory (NA theory) is very similar to UET(tmy death), except the U (the universe) is my personal universe rather than everybody's. If UET has problems, why won't NA have similar problems?

Now, maybe my presentation of the principle of parsimony is wrong; but if so, I challenge you to explain why, and provide an alternative.

(((Zack Martin)))07:56, 4 July 2011

The principle of parsimony doesn't care the least about the amount of time in which an observation takes place. It cares about the number of elements in a model.

The predicted end of the universe or the existence of the end is not a model itself but rather a prediction of a model. To compare two models in terms of parsimony (one predicting the end next thursday, one predicting the end in 15 billion years) we need to see the elements that make up those models that make that prediction. The prediction itself whether next thursday or 15 billion years is a single prediction, a single point of data. The relative time between now and that prediction is not a factor in the models complexity.

Also keep in mind parsimony includes the "all things being equal" more complex models are better than simplier models when the residuals of the complex model are some significant value less than the simpler model.

I don't really see much to reply to here. A lot of it has nothing to do with what we are talking about, and the rest seems to be a misstatement of how parsimony as applied to model building is actually used.

Tmtoulouse (talk)08:11, 4 July 2011

Define model, element in a model. Can you give a precise definition to these terms? I have some idea what you are talking about, but it would be clearer if you could define these terms more precisely.

Consider the following claim: "The universe will cease to exist on Friday 8th July 2011". How many "elements" are in that "model"? Considering the opposite claim: "The universe will continue to exist after Friday 8th July 2011". How many elements in the model of that claim? Is one of these statements more parsimonious than the other, or are they equal in complexity?

The relative time between now and that prediction is not a factor in the models complexity. So, its not the complexity of the universe that would exist were the model true, or the complexity of the observations we would expect to have were the model true, but the complexity of the model itself? This goes back to part of my point - we have multiple competing formulations of the principle of parsimony. Why choose to follow your formulation rather than some other one?

more complex models are better than simplier models when the residuals of the complex model are some significant value less than the simpler model. - comparing my two claims, i.e. the universe will suddenly end on this Friday, v.s. it will continue to exist after that date, how do their residuals differ?

(((Zack Martin)))08:35, 4 July 2011

A model is a set of causative or predictive rules/statements used to simulate some observed phenomenon.

An element of a model is a specific causative or predictive rule/statement with in the model's set.

A prediction is a specific predicted data point generated from the model to be compared with actual observation.

"The universe will cease to exist on Friday 8th July 2011" and "The universe will continue to exist after Friday 8th July 2011" are predictions not models.

A model would be something like: Since Gargurtle the giant turtle who exists outside of space and time and eats universes is coming for us next and will reach us on Friday 8th July 2011.

The elements of the model are: {All existing scientific theories}+the existence of Gargurtle

The prediction is: "The universe will cease to exist on Friday 8th July 2011"

The Gargurtle model adds an element to our model that adds zero explanatory power except for a single future prediction.

Until Friday 8th July 2011 the Gargurtle model has less epistemological value than the standard model.

Tmtoulouse (talk)18:19, 4 July 2011

Why should I adopt your "model theoretic" approach to the principle of parsimony? Why not another approach instead?

(((Zack Martin)))08:16, 5 July 2011

You don't have to do accept anything. The premise of this discussion is whether or not science as an epistemological framework has anything to say about the god hypothesis.

If you want to reject science and all that science tells us about reality that is your call. What you don't get to do is have your cake and eat it to, by claiming that you can accept science but reject what it would say about your made up god.

The approach to parsimony I have presented isn't "mine" its how science works. You can see it Bayesian model selection, or in something as basic as a statistical significance scale (hint why does the difference score increase for the same p-value as our degrees of freedom increase?).

Now this principle can be used for model-free approaches, but the same basic idea that predictive power has to scale up with degrees of freedom to maintain significance applies.

Tmtoulouse (talk)15:33, 5 July 2011

I have no problem with approaches which are genuinely part of science, as in required by and implied by science. But I can question whether the approach you've proposed is the only one which works with science. You claim science uses your interpretation of the principle of parsimony rather than some other - have evidence for that claim? You suggest that science only works with your interpretation of the principle of parsimony, and won't work with competing interpretations - have evidence for that claim?

I don't think science actually does use your principle of parsimony. Consider the theory of gravitation. Say we have Einstein's general relativity (hereafter GR), and we have some new theory, super-GR (maybe one of the GR alternatives listed by WP). Now, super-GR produces almost identical results to GR, except in very rare/extreme circumstances. Due to the rareity/extremity of those circumstances where super-GR behaves differently from GR, it is unlikely we will be able to distinguish super-GR from GR experimentally or observationally in the medium term. But, while Einstein's field equations are frequently lauded for their simplicity, super-GR's field equations are far more complicated. So, quite validly, physicists use the principle of parsimony to exclude super-GR: (1) GR and super-GR are experimentally/observationally indistinguishable at present; (2) GR is simpler than super-GR; (3) hence, prefer GR to super-GR. (Of course, maybe one day the experiments/observations needed to distinguish GR/super-GR will become feasible, and the results may actually favour super-GR. So, the rejection of super-GR by the principle of parsimony is provisional.)

Now, the reason I bring up this case, is that I think it demonstrates your account of the principle of parsimony - the "model element counting" approach you are using - doesn't match how scientists actually reason. GR and super-GR have the same elements in their model (spacetime, mass/energy, etc.). But super-GR's equations are much more complex than GR's. But I don't see how your model counting approach can measure the complexity of the equations, since all you do is count model elements. So, your definition of the principle of parsimony does not match the one actually used in science.

Moving on, let me produce two theories: theory 1: "The universe will instantaneously cease to exist this Friday". theory 2: "The universe will still exist this Saturday". Theory 2 is nothing more than the denial of theory 1. And what I've given is the whole of theory 1. There is no "Gargaturtle", no agent which ends the universe. The universe just ends for no particular reason. So these two theories have identical models. Hence, you can't use the principle of parsimony, as you describe it, to distinguish these two theories.

(((Zack Martin)))20:08, 5 July 2011
 
 

Ah, so that's what's happening on the 8th. I did wonder.

ADK...I'll xerox your virus!09:24, 5 July 2011