Tuesday, June 14, 2016

An Atheist Inductive Argument Scrutinized

A reader asks me to take a look at an Atheist’s probability arguments. It’s taken a few days, sorry. But here it is. First the argument as it is presented:
"Let S be the proposition that human moral experiences are a product of subjective values functions, and that those value functions are informed primarily by socialization and evolutionary history.

Let O be the proposition that human moral experiences are a product of some apprehension of objective moral values.

Let V be the observation that human moral opinions vary from person to person.

Let C be the observation that human moral opinions tend to vary more between cultures than between individuals.

P(V|O) < P(V|S) P(C|O) << P(V|S) Further, there does not appear to be any further evidence, E, such that P(E|V) > P(E|S)

Further, O is strictly less parsimonious than S.

Hence, we have strong justification for S over O."

The analysis appears to be a partial Bayesian induction, which doesn't go as far as the final calculation. It's just inductive, to the point of weighting, and it's not related to Kolmogorov algorithmic probability in any way. Its premises can be analyzed for any truth value which might inhere. As in any logical conclusions, including inductive of course, if the premises are not valid, true, and grounded in first principles, then they are false. That is the standard of Aristotlelian logic – college logic 101 – and it is the logic used here to analyze the probability claims. This is a failure of Bayes usage: besides being prone to prejudicial misuse, when used for metaphysical claims or unfalsifiable claims, it provides only highly dubious probability at best. It is incapable of objective fact generation, even using empirically derived probabilities. It is incapable of the capacity of deduction's ability to provide unquestionable truth when done properly.

A discussion of Induction via Bayesian assumptions is here, for a refresher (It's embedded in the articles):

The probability argument begins:

"Let S be the proposition that human moral experiences are a product of subjective values functions, and that those value functions are informed primarily by socialization and evolutionary history.

Let O be the proposition that human moral experiences are a product of some apprehension of objective moral values."

The term, “moral experiences” is undefined, and seems to be without any value regarding to the actual objective existence of moral principles. The term “experiences” seems to indicate subjective apprehension in both premises, not objective knowledge of anything. Science, for example, is not done on the basis of “human material experiences”; it is done on the basis of objective experimentation, performable by other experimenters as a test of replicability for validation and non-falsifiability. That’s how objectivity is produced in materialist premises.

So O has no bearing on actual existence of objective morality. Using it for such is false.
"Let V be the observation that human moral opinions vary from person to person.

Let C be the observation that human moral opinions tend to vary more between cultures than between individuals."

This “observation”, C, is beyond dubious, it is prejudiced and prejudicial for purposes of biasing the faux Bayesian analysis below; it is without any supporting data and is highly likely false purely because there are no Atheist moral principles at all which are derivable from Atheism, beyond those “moral” principles each individual Atheist creates for himself. Therefore, given the number of Atheists on the globe – and counting the communists, secularists, Hindus and Buddhists – the number of dissimilar, individually-derived “moralities” is very likely far higher than the objectively held moralities.

C is merely a prejudicial opinion, not an objective fact. It has no truth value for use in any calculation.

Now for the relative positioning of the premises.
"P(V|O) < P(V|S)"
This is a typical Bayesian Probability set up technique. It uses pure opinion, with no possible actual data to support any validity it might have. Especially given that O does not describe any useful information regarding the actual existence of objective morality.

In this case, the relative positioning of the two probabilities is purely by opinion, not by any objective factual probability calculation. In other words, it is a prejudiced personal projection made toward a presupposed objective. Were any actual facts discovered for use here, the relative positioning would likely be reversed.
"P(C|O) << P(V|S)"
This placement of relative probabilities also is based not on any fact or data or study, it is purely based on the presuppositional prejudices of the author. Given that both C and O are personal opinion, and obviously prejudicial, there is precisely no actual rational or empirical reason to believe that this is the case.
"Further, there does not appear to be any further evidence, E, such that P(E|V) > P(E|S)"

This is really interesting, given that there is no evidence provided for any of the premises, period. Denial of “further evidence” is in the form of a joke, then.
"Further, O is strictly less parsimonious than S."
It is hardly arguable that O is less parsimonious than S; this is a truth claim which has no basis whatsoever for its belief, because O has no actual meaning in the argument. In fact, if parsimony refers to simplicity vs excessive complexity, then O is far MORE parsimonious than S, given the complexity of S. So this is another failure, possibly that of Equivocation of the term, parsimony, but more likely just a blatant biasing of the argument toward the desired conclusion. It is based on no justification of any kind for the declared truth being asserted.
"Hence, we have strong justification for S over O."
No, there is absolutely nothing presented here which is anything other than opinion, which is declared to be truth for purposes of biasing “premises” in a phony “probability” calculation. That is not justification, it is propaganda. It is a poor man’s Bayesian exercise, where opinion is plugged in and declared to be factually useful for calculating a probability in the favor of the author.

Bayesian induction is a favorite of individuals who are scamming lesser knowledgeable folks. Bayesian calculations are useful only when prior premises have probabilities which are factually available as empirical determinations (I.e. NOT opinion). One example of successful usage of Bayesian Inference is the Coast Guard’s calculations regarding the probable position of a lost boater, based on prior conditions of wind, currents, tides, time at last known location, and prior routes taken by the boater. These are not opinions, they are facts which can be plugged into the Bayes equation, and the probable current location of the lost boater can then successfully calculated.

Bayesian Induction for metaphysical use is a resort of anti-intellectual scoundrels and scammers.


Phoenix said...

Excellent refutation.

And to the reader who is unfamiliar with probability theory and asked Stan for his analysis, here is a free online course on "Data Basics". It starts 20th June. I've re-enrolled because I was unable to complete it the first time.
You can join here: https://www.coursera.org/learn/probability-intro/lecture/Q0zu3/data-basics

Or visit the coursera.org site and search for any other course on statistical analysis.

JBsptfn said...

Good write-up, Stan. I notice that Atheists use Bayes from time to time to analyze the Gospels (Joe talked about Carrier doing that a few times):

I hope that you are almost done with that Weekend Fisher critique. He is saying some weird things. I posted a comment making an analogy to a radio (how the radio is the brain, and how consciousness isn't produced inside the brain like a program isn't produced inside a radio). He doesn't understand how people believe that consciousness is non-physical.

Dogbyte said...

What about using bayes theorem along with the likelihood principle based on epistemic probability, where statistical calculations are not possible if the event isn't repeatable. Alex Collins appeals to this sort of probabilities in his Teleological article in the Blackwell Companion to Natural Theology. Ive seen atheists demand a statistical calculation account for the inadequacy of chance hypotheses over design, but then turn around and use the same sort of common use of probabilities like is used in science all the time for the theory of evolution. Its a one time event, how can it be statistical? Ive learned a lot from this article Stan.

Stan said...

If an event is not repeatable, then there is no empirical, contingent knowledge, and certainly no objective, immutable knowledge regarding the event. The event is a memory, which possibly left trace evidence, but no certain knowledge.

So the probability of the event occurring in a fortuitous fashion in correlation with other events is unknown, and should be given a probability of zero: not useful in a disciplined calculation. If it is used, then, it is for prejudicial use only.

There is virtually no case where metaphysics should or could be determined by Bayesian probability calculations. They are always prejudiced by the opinion of the calculating calculator. The use of Bayes improperly is a refuge of scoundrels, and is intended to fool the ignorant with words and processes they haven't any knowledge about. In other words, it is a purposeful scam.

Dogbyte said...

But isnt the likelihood principle used all over the place to talk about the best explanation based on some evidence? What wrong with talking about probabilities, as in: more probable than not, without actually having a statistical calculation which isnt possible for a 1 time event.

if you rolled a 100 sided die to the same number 100 times, I personally would say that is highly improbably without actually calculating the chances on paper, even though you could, 1/100 x 1/100 x 1/100 ect....

My point was that its never the theist thats demanding an actual statistical calculation for some evidence being the more likely explanation of evidence (e). I understand the inability to quantify something that doesnt require prejudice or personal opinion as to how much weight e has. But surely bayes theorem can just be a logical way to denote what is being claimed when one says based on e, and its background knowledge k', one would expect h1 over h2. You dont think that has any place as a way to talk about explanations of evidence? It makes sense to me in a common use of language when saying "probably so", or "more probable than not", we dont always mean a statistical probability. Im still trying to read more about the use of these principles and maybe just not grasping the core distinctions yet.

Stan said...

What is the actual probability that there is a God?

When an Atheist claims a probability, it is just his opinion. Same goes for a Buddhist, Mormon, and Baptist. But the probabilities they give to plug into a calculation have no objective meaning, other than to force a preconception into a pretense of mathematical "proof".

Certainly Bayes has its place, as I described in the Coast Guard scenario. But that is where evidence is objective and not opinion. Opinion is not evidence, even though Atheists call it evidence when they use their own bias to force conclusions.

The differentiation is in the nature of "evidence". Evidence is found and validated, not declared out of a vacuum without cause.

Dogbyte said...

"What is the actual probability that there is a God?"

I would say its more probable than not, that there is a God. Then I might argue, based on several natural theology arguments, that they pose a cumulative case as the best explanation that is expected given everything we know about the evidence. While the arguments may be deductive, i'd put the use of bayes theorem on non statistical types of probabilities as inductive, and only meant as a way to show where the evidence strongly supports Theism over naturalism. It may not be the best use of Bayes Theorem, as in epistemology, but it may be a handy way as one might use pseudo code to plan the application, instead here it may help to plan the argument. I do see your point about the subjective aspect of using math equations, but what about logical equations, if the variables are said to be beliefs held based on logical reasoning? Cant that be objective if you examine the claims and find them lacking?

Here's Collins justification:

The core fi ne-tuning argument relies on a standard Principle of Confi rmation theory,

the so-called Likelihood Principle. This principle can be stated as follows. Let h1 and h2 be

two competing hypotheses. According to the Likelihood Principle, an observation e counts

as evidence in favor of hypothesis h1 over h2 if the observation is more probable under h1

than h2. Put symbolically, e counts in favor of h1 over h2 if P(e|h1) > P(e|h2), where P(e|h1)

and P(e|h2) represent the conditional probability of e on h1 and h2, respectively. Moreover,

the degree to which the evidence counts in favor of one hypothesis over another is pro-
portional to the degree to which e is more probable under h1 than h2: specifi cally, it is

proportional to P(e|h1)/P(e|h2).2

2. There are many reasons why the Likelihood Principle should be accepted (e.g. see Edwards 1972; Royall 1997;

Forster & Sober 2001; Sober 2002); for the purposes of this chapter, I take what I call the restricted version of

the Likelihood Principle (see further discussion) as providing a suffi cient condition for when evidence e supports

a hypothesis, h1, over another, h2. For a counterexample to the Likelihood Principle’s being a necessary condition,

see Forster (2006). For an application of the Likelihood Principle to arguments for design, see Sober (2005). (I

address Sober’s main criticism of the fi ne-tuning argument in Sections 3.2, 5.2, and 7.5.)

The Likelihood Principle can be derived from the so-called odds form of Bayes’s Theorem, which also allows

one to give a precise statement of the degree to which evidence counts in favor of one hypothesis over another. The

odds form of Bayes’s Theorem is P(h1|e)/P(h2|e) = [P(h1)/P(h2)] × [P(e|h1)/P(e|h2)]. The Likelihood Principle,

however, does not require the applicability or truth of Bayes’s Theorem and can be given independent justifi cation

by appealing to our normal epistemic practices.

Stan said...

Here's the rub:

"providing a sufficient condition for when evidence e supports a hypothesis, h1, over another, h2. "

The Atheist will reject any claim that there is any actual evidence for the existence of God. Re: Dawkins' use of Bertrand Russells' complaint: "Why did God conceal himself?" For a hard core Atheist, there is no evidence - zero, none - for the existence of God, a god, or gods. All evidence which is submitted to the Atheist will be rejected as having no actual meaning for the existence of a deity. It is the "meaning" attached to the evidence which is rejected. The Atheist can attached Materialist "meaning" to the evidence in order to satisfy his own presupposed biases. He will do this no matter how ludicrous the attached deduction might be, such as multiverse existence to explain fine tuning in our universe.

Therefore, the calculation is biased (by pure rejectionist opinion) due to the probability of h2 being assigned the value of zero. When h2=0, any other fantasy proposition will find satisfaction via the Bayes method.

That is why metaphysical use of Bayes or any probability calculation is phony from the very beginning: the quality and/or quantity of evidence is not empirically determined (not objective knowledge), it is opinion. So there is no objectivity in the equations and the calculated results merely show the results which the input bias drives them to be.

You may use the calculations to show your own bias regarding the evidence which, in your opinion, qualifies. No one else is obligated to accept either the non-empirical subjective evidence OR the probability which you give it. But for yourself, it might be meaningful in that it confirms your previously held bias. Just as the Atheist is able to confirm his own previously held biases.

According to Hacking, there are two types of probability derivations: (1) Personal Probability (belief oriented), and (2) Logical Probability (hard objective evidence oriented).
Ian Hacking; "An Introduction to Probability and Inductive Logic", Cambridge University Press;2009;p140-143.

Abelson discusses the misuse of Bayes for hypotheses which cannot be true (p=0), and other defective "priors" (prior probabilities which are not objective evidence as required, but are subjective opinion:
Robert P Abelson; "Statistics as Principled Argument"; Psychology Press Pubs; 2009; p42-45.

It is not possible to use Bayes successfully against the biased manipulations of dogmatists. However, one can argue against the irrational conclusions of the improper use of evidence, using Reductio Ad Absurdum, which is a Deductive test, not inductive.

Dogbyte said...

"Therefore, the calculation is biased (by pure rejectionist opinion) due to the probability of h2 being assigned the value of zero. When h2=0, any other fantasy proposition will find satisfaction via the Bayes method."

Is that what is being claimed in Collins FT argument? Because i thought he was just saying the evidence of fine tuning, is what you'd expect in H1 over H2 (more probable than not), given the argument that either H1 and H2 = 1, or assuming they are true. If H1 is true, you'd expect evidence of fine tuning, meaning its more probable than not if H2 = 1.

I think you are right in your description of how you can wrongly use bayes theorem for evidence, where the objective ingredient is missing. However, i'd be interested to see where you think his argument becomes subjective using the restricted version of the likelihood principle. I left off the definitions of terms if you still need them i'll post. Ive not forgotten the original post, im just trying to flesh out the difference between appropriate usage of probabilities and the different types of probabilities.

Using the restricted version of the Likelihood Principle, the core fine-tuning argument

can be stated as follows:

(1) Given the fine-tuning evidence, LPU is very, very epistemically unlikely under NSU:

that is, P(LPU|NSU & k′) << 1, where k′ represents some appropriately chosen

background information, and << represents much, much less than (thus making

P(LPU|NSU & k′) close to zero).

(2) Given the fine-tuning evidence, LPU is not unlikely under T: that is, ~P(LPU|T &

k′) << 1.

(3) T was advocated prior to the fine-tuning evidence (and has independent


(4) Therefore, by the restricted version of the Likelihood Principle, LPU strongly sup-
ports T over NSU.

Dogbyte said...

Remember now, the evidence spoken of are the constants and arbitrary values of their entailed quantities. So the question arises, why do all these separate constants and quantities seem to all be within that life permitting range? That is an objective piece of evidence, you've seen the ranges. The odds involved are mind boggling, that all of these values should all coincide given a naturalist framework. I mean, its the sheer volume of potential non life permitting likelihoods, that make the question have meaning. So in this sense, isnt it common language to say LPU is less probable, given all we know about the constants and quantities?

Dogbyte said...

btw thank you for the book info. im still wading through Forster/Sober/Edwards/Royall papers as well with regards to application of the likelihood principle.

Stan said...

Could you give me a link to the last quote, please? Neither LPU nor NSU Nor T are defined in the bit you included. However, he seems to declare that the probability of LPU is roughly zero, even with additional background information, k'.

There's not enough there to determine the criteria for deciding the probability value of LPU, and that drives the overall calculation.

I need to read the whole thought process before I can know how it was done.


Dogbyte said...

I can send you the article its quite long. I cant post the definitions once it get back to my pc where ive got a digital copy.

Stan said...

OK, thanks, I'd need to see it before commenting further.