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No longer take comments. Post's 'labels' are unreliable for linking or searching. Use the INDEX OF POSTS instead. A fairly accurate, but incomplete INDEX of Posts & good overview and understanding of this blog READ SOME REASONS TO REJECT ORTHODOX JUDAISM my April 2014 post or click link above. Born into an Orthodox Jewish family (1950's) and went to Orthodox Yeshiva from kindergarten thru High School plus some Beis Medrash.Became an agnostic in my 20's and an atheist later on. My blog will discuss the arguments for god and Orthodox Judaism and will provide counter arguments. I no longer take comments. My blog uses academic sources, the Torah, Talmud and commentators to justify my assertions. The posts get updated. IF YOU GET A MESSAGE THAT THE POST IS MISSING - LOOK FOR IT IN THE INDEX or search or the date is found in the address.

Sunday, January 20, 2019

Fine Tuning Argument (Part III) - Using Probability or Chance

This is a follow up to the Fine Tuning Argument  Proof of God from Fine Tuning (Part II) Using Probability or Chance, but I think this can be a stand alone.

Compared to Part II,  I  am going to make the premises even more favorable to the Theist and show his desired conclusion still does not follow. To do this I will prove two interesting probability results - called PR1 and PR2. See later.

Premise -   The probability or chance of a Life Permitting Universe  given supernatural,  is greater than the probability of a  Life Permitting Universe  given solely nature (no supernatural, no god(s)).

Conclusion: Given our life permitting universe, the  probability of “only nature” is less than the probability of supernatural. We should invoke the existence of a god fine tuner to explain why our Universe is such that it  permits life.

The Premise  seems very difficult to support and I wholly reject it. For example determining the  probability or chance of a Life Permitting Universe, given supernatural seems impossible. But but for the sake of argument I will accept the Premise. Nevertheless, we will see the argument fails.

First A Short Digression On Probability, Plus PR1 and PR2

Assume no divisions by zero.

For event A, we denote it’s probability as P(A)

For two events A and B, the Probability of A given B is denoted by P(A/B) and equals P(A and B)/P(B). 

Also, P(B/A)= P(A and B)/P(A)

Notice that in general  P(B/A) does not equal P(A/B).

Rather P(B/A)= P(A/B)*P(B)/P(A).

Thus  if  P(A/B) is very low, it does not follow P(B/A) is very low. If the ratio P(B)/P(A) is very high, then  P(B/A) may not be low and in fact can be quite high.  

Also, P(~B/A)= 1-P(B/A). The symbol ‘~’ means negation or not.

Proving PR1 

PR1  is stated as follows

If P(A/~B) > P(A/B) then P(~B/A) > P(B/A)*P(~B)/P(B)

Proof:  Multiply the left and right side of the inequality by P(~B) then use definitions of conditional probabilities as given above.

P(~B)* P(A/~B)  >  P(~B)* P(A/B)

P(~B and A) > P(~B)*P(A/B)*P(B)/P(B) , I multiplied by unity.

So P(~B/A) * P(A) > P(~B)*P(B/A)*P(A)/P(B) I used definition of conditional probability to restate P(A/B)*P(B) as P(B/A)*P(A)

Divide by P(A) to complete the proof.

Deriving PR2

PR2 Relates P(~B/A)/ P(B/A) to the value chosen for  P(~B)/P(B). 

From PR1, notice P(~B/A)/ P(B/A) > P(~B)/P(B).  Let X = P(~B)/P(B). If X is greater than or equal to unity  we know   P(~B/A) >  P(B/A) . If X is less than unity then we can not draw conclusions. For example if X is say .2, then P(~B/A) is greater than .17 and P(B/A) is less than 0.83. Or if say X = .8, then P(~B/A) > .44 and P(B/A) is less than .56. These results follow from  P(~B/A) +  P(B/A) = 1 and solving the inequality. If X is less than unity then  P(B/A) < 1/(1+X) and P(~B/A) > X/(1+X)

Here is a table

X          P(~B/A)      P(B/A)
----       ------------     -----------
.01         >.01            <.99
.20         >.17            <.83
.50         >.33            <.67
.80         >.44            <.56
.99         >.4975        <.5025

If X is less than unity, we can not determine if P(~B/A)> P(B/A) or if P(~B/A) < P(B/A). We only have lower bounds and upper bounds for P(~B/A), (and also for P(B/A)), and their ranges overlap. We are stuck.

Clarification of the Fine Tuning Argument in terms of Probability

With the basic probability theory understood, we can state the Premise as follows

Let A be the event Life Permitting Universe

Let B be the event Only Nature

Then the Premise is  P(Life Permitting Universe/Supernatural) > P(Life Permitting Universe/Only Nature).   The Premise  seems very difficult to support and I wholly reject it. For example determining the  probability or chance of a Life Permitting Universe, given supernatural seems impossible. But but for the sake of argument I will accept the Premise. Nevertheless, we will see the argument fails.

The conclusion can be stated as  P(Supernatural /Life Permitting Universe) > P(Nature Only  /Life Permitting Universe). That is the conclusion a religious person would like to reach.  

Hopefully, I got the math right and now we can begin to apply it.

Let A be the event Life Permitting Universe

Let B be the event Only Nature

Using the premise and PR1 we have

P(Supernatural/Life Permitting Universe)> P( Only Nature/Life Permitting Universe)*P(Supernatural)/P(Only nature)

Now use PR2. If we assume P(Supernatural)/P(Only nature) > 1  i.e X >1,  then the Fine Tuning Argument would work. But if  we made that assumption there would be no need to bother with the Fine Tune argument at all, since the assumption would  state  P(Supernatural) > P(Only nature). {ETA - What I mean is Theologians would have no need for the Fine Tune argument if it was assumed P(Supernatural) > P(Only nature). However, Theologians could attempt  to use a Fine Tuning argument to increase the odds of Supernatural vs (Only nature).} 

Furthermore, I would reject P(Supernatural) > P(Only nature) for lack of support. If we assume X=1, that would give equal probability  for 'Supernatural' and 'Only Nature'  and then the Fine Tuning argument would work. However I do not think it is reasonable to give equal probability for supernatural and 'Only Nature' since we have plenty of observations of 'Only Nature' compared to Supernatural. It seems more reasonable to choose X<1, (arguably much less than unity), and if  X is less than unity the fine tuning argument is inconclusive as shown by PR2.

Continued Part IV

Wednesday, January 16, 2019

Fine Tuning Argument (Part II) - Using Probability or Chance

Updated 1/24/2019

This is a follow up to the Fine Tuning Argument  Proof of God from Fine Tuning (Part I), but I think this can be a stand alone.

Here is one popular version

Premise -   The probability or chance of a Life Permitting Universe, given solely nature (no supernatural, no god(s)), is very very low.

Conclusion: Given our life permitting universe, the  probability of “only nature” is very very low. Thus given  our life permitting universe the probability of supernatural intervention is high. We should invoke the existence of a god fine tuner to explain why our Universe is such that it  permits life.

The Premise  seems very difficult to support, but for the sake of argument I will accept the Premise. Nevertheless, we will see the argument fails.

A Short Digression On Probability

For event A, we denote it’s probability as P(A)

For two events A and B, the Probability of A given B is denoted by P(A/B) and equals P(A and B)/P(B). 

Also, P(B/A)= P(A and B)/P(A)

Notice that in general  P(B/A) does not equal P(A/B).

Rather P(B/A)= P(A/B)*P(B)/P(A).

Thus  if  P(A/B) is very low, it does not follow P(B/A) is very low. If the ratio P(B)/P(A) is very high, then  P(B/A) may not be low and in fact can be quite high.  We will see the importance of this ratio.

Also, P(~B/A)= 1-P(B/A). The symbol ‘~’ means negation or not.

{ETA 1/24/2019   P(A) = P (B)*P(A/B) + P(~B)*P(A/~B) }

Clarification of the Fine Tuning Argument in terms of Probability

With the basic probability theory understood, we can state the Premise as follows

Let A be the event Life Permitting Universe

Let B be the event Only Nature

Then the Premise  is P(A/B) is very low. Meaning P(Life Permitting Universe/Only Nature) is very low.  For the sake of argument I am accepting this premise. 

The conclusion can be stated as P(B/A) is very low. Meaning P(Only Nature/Life Permitting Universe) is very low. Thus P(~B/A) is very high. Meaning  P(Supernatural//Life Permitting Universe) is high. That is the conclusion a religious person would like to reach. 

Repudiation of the Argument 

Using probability theory, the conclusion P(Only Nature/Life Permitting Universe) is very low, does not follow from the Premise unless the ratio  P(Only Nature)/P(Life Permitting Universe) is not high.  I could argue the ratio is high. There are very few Life Permitting Universes according to the Fine Tuning advocates. That would mean P(Life Permitting Universe) is low. That tends to make the ratio P(Only Nature)/P(Life Permitting Universe) towards the higher side. 

{ETA 1/24/2019 Fine Tuning advocates may argue if the the product of P(Supernatural)*P( Life Permitting Universe/Supernatural) is not low,  then P(Life Permitting Universe) is not low. 

[This follows from P(A) = P (B)*P(A/B) + P(~B)*P(A/~B) under the assumption P(Only Nature)* P(Life Permitting Universe/Only Nature) is very low]. 

I do not know how they can justify P(Supernatural)*P( Life Permitting Universe/Supernatural) is not low. For example, how do they know the probabilities of the sort of Universes Supernatural can create and with what probabilities ? If so, why assume P( Life Permitting Universe/Supernatural) is not low ? P(Supernatural) is also undefined or even arguably low. I am aware of no data providing P(Supernatural) is anything other than being low. }

I would argue P(Only Nature) is also on the high side since we have natural explanations for many things, and very little if any evidence for supernatural things. That would also make the ratio towards the high side. So the ratio, P(Only Nature)/P(Life Permitting Universe) can be argued to be high. It follows  we cannot conclude P(Only Nature / Life Permitting Universe) is low even though P(Life Permitting Universe / Only Nature) is very low.  Given our Life Permitting Universe we can not use probability to support the notion we need something more than ‘only nature’; that we need G-d. 

An objection can be raised that I cannot really support that the ratio P(Only Nature)/P(Life Permitting Universe) is towards the higher side, or at least high enough to offset the low probability of P(Life Permitting Universe/Only Nature). Then I will argue neither can they support that the ratio is not high. Since they are using the argument to prove something, the burden of proof falls more on them than me and they need to provide good support for their lower chosen ratio.  

Conclusion 

Every version of Fine Tuning argument or Design argument (that I am aware of), that uses probability to argue against “nature only” (i.e. to invoke supernatural)  suffers from weak premises, misuses of probability and statistical inference, questionable assumed ‘priors’, begging the question and perhaps other problems. Let the buyer beware.

P.S. I wrote a continuation of this sort of Fine Tune probability  argument - see Fine Tuning Argument (Part III) - Using Probability or Chance