It is so sad, if not disturbing, when people with a poor understanding of mathematics and statistics try to impress the laypersons with their erroneous use of these tools. Dr Craig is one of such individuals. For a quick example of his misunderstanding I start by reviewing a short instance of one of his errors and then deal with his misunderstanding of the laws of probability as is documented in this video.
In a different debate, with a Muslim scholar, who was quoting psalms 5:4-7 that says, Jehovah, who according to Dr Craig is the same as Jesus, hates wicked people and thus cannot be the "most loving" god according to Craig's definition:
הכִּ֚י | לֹ֘א אֵ֤ל חָפֵ֖ץ רֶ֥שַׁע | אָ֑תָּה לֹ֖א יְגֻֽרְךָ֣ רָֽע
ולֹֽא־יִתְיַצְּב֣וּ הֽ֖וֹלְלִים לְנֶ֣גֶד עֵינֶ֑יךָ שָֹ֜נֵ֗אתָ כָּל־פֹּ֥עֲלֵי אָֽוֶן:
דֹּֽבְרֵ֪י כָ֫זָ֥ב אִישׁ־דָּמִ֥ים וּ֜מִרְמָ֗ה יְתָ֘עֵ֥ב | יְהֹוָֽה:
5. For You are not a God Who desires wickedness; evil does not abide with You.
6. Confused people shall not stand before Your eyes; You hate all evil doers.
7. You destroy speakers of lies; the Lord abhors a man of blood and deceit.
Dr Craig responds by saying that " Notice that, love and hate, paradoxically, are not contradictories. Indeed we will often speak of someone having love-hate relationship with someone else! These are not contrdictories, because you can love a person and yet hate certain aspects of his personality's, his actions, what he does, what he stands for, and so forth, ...", and then in his rebuttal Craig continues with this same line of argument and says: "As I explained, love and hates are not contradictoreis, and he [Dr. Ali] says: 'in what language?' Well, its simply a point of logic! The opposite of black is not white, or a contradictory of black is not white. The contradictory of black is not-black. The contradictory of P is not any p. So it is not the contradictory of love to say hate, indeed we often speak of having love-hate relationships with certain individuals, don't we? The opposite or the contradictory of love is not-love. and bible never says God does not love evil-doers!"
Of course, any high-school kid with an elementary knowledge of Algebra can see immediately the flaws in this sophistry. In fact, if one represents love, not-love and hate in a Cartesian space, it would be immediately obvious that hate is far more stronger than not-love which is represented by the value zero in the continuum from hate in the negative set to love in the positive set. The point is so obvious that needs not any further elaboration and lets now turn our attention to his misunderstanding of probability-based inferences.
In his debate with professor Ehrman, Doctor Craig states : "When we talk about the probability of some event or hypothesis A, that probability is always relative to a body of background information B. So we speak of the probability of A on B, or of A with respect to B.[ Pr (A/B).]"
The students of probability should immediately realize that how nonsensical it would be to find a high probability for resurrection, Let's assume that we adopt the standard 95% confidence band and are able to reject the null hypothesis of no-resurrection. This would mean in each one hundred deaths there are 95 cases of resurrection! Very interesting! Of course, Dr. Craig may now want to change his alternative hypothesis. I will deal with any change that he might propose when he does that for the time being let's continue with the rest of his argument. He then says:
"So in order to figure out the probability of the resurrection, let B stand for our background knowledge of the world apart from any evidence for the resurrection. Let E stand for the specific evidence for Jesus’ resurrection: the empty tomb, the post-mortem appearances, and so on. Finally, let R stand for Jesus’ resurrection. Now what we want to figure out is the probability of Jesus’ resurrection given our background knowledge of the world and the specific evidence in this case.
Calculating the Probability of the Resurrection
B = Background knowledge
E = Specific evidence (empty tomb, post-mortem appearances, etc.)
R = Resurrection of Jesus
Pr (R/B & E) = ?
Now probability theorists have developed a very complex formula for calculating probabilities like this, and I’m going to walk you through it one step at a time, so that you’ll be able to get it.
The first factor that we need to consider is the probability of the resurrection on the background knowledge alone:
Pr (R/B) is called the intrinsic probability of the resurrection. It tells how probable the resurrection is given our general knowledge of the world.
Next we multiply that by the probability of the evidence given our background knowledge and the resurrection."
Now of course, the value of this intrinsic probability is very close to zero, because according to the Christian belief R is representing only one event, i.e., the resurrection of Christ, while B is set of all possible background knowledge, which could be a very large number (if not infinity), because it includes the knowledge of all the people who understand that in the bio-physical world the phenomena of empty tomb, and post mortem appearance, etc, can each be explained by numerous possible scenarios, including one suggested by Professor Ehrman. Thus, we have already a numerator of the new probability, that is multiplied by zero, and the outcome would be zero. Dr Craig continues
Pr (E/B&R) is called the explanatory power of the resurrection hypothesis. It tells how probable the resurrection makes the evidence of the empty tomb and so forth. These two factors form the numerator of this ratio.
Unfortunately, for Dr. Craig, the value of this second argument in the numerator is also close to zero. Since there is only one empty tomb, and again virtually an infinite number of possible scenarios. Dr, Craig now explains the denominator of his probability of resurrection and says:
Now below the line, in the denominator, just reproduce the numerator. Just move everything above the line down below the line:
Finally, we add to that the product of two more factors: the intrinsic probability that Jesus did not rise from the dead times the explanatory power of the hypothesis of no resurrection:
Students of probability, understand that this denominator is in fact the union set of the null and the alternative hypotheses, in other words, it is the set of all possible events, which is of course, very close to infinity. Thus, the result is the ratio of (zero/infinity) which is unambiguously equal to zero.
It should be quite obvious that, this whole exercise, is extremely silly. Because, to construct a probabilistic model, we need to specify a probability law on a suitably defined sample space. Although, there are no hard rules to guide this first step, other than the requirement that the probability law conform to the three axioms which are:
I. (Nonnegativity) P(A) ≥ 0, for every event A.
II. (Additivity) If A and B are two disjoint events, then the probability of their union satisfies P(A ∪ B) = P(A) + P(B). More generally, if the sample space has an infinite number of elements and A1, A2,... is a sequence of disjoint events, then the probability of their union satisfies P(A1 ∪ A2 ∪···) = P(A1) + P(A2) + ··· .
III. (Normalization) The probability of the entire sample space Ω is equal to 1, that is, P(Ω) = 1.
We can assume that these conditions are satisfied, However, the problem is that our sample includes only one observation (which is highly dubious), and our degrees of freedom is just zero!
No comments:
Post a Comment