Warren Christian Apologetics Center
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Articles - Miscellanea

A Few Thoughts On Probability

When I was training gospel preachers, I would at times tell them the following: The affirmation of a probability is the admission of the possibility of the contradictory. What does that precisely mean? It means that when a person asserts that something is only probable, he is already saying at the same time what is being asserted may not be correct at all. In other words, if I say that I will probably attend a ball game tonight, it is also the case that I may not attend that ball game. The contradictory (I may not attend) is possible just as the affirmation (I will probably attend) is possible and stated as a probability. The chances of the occurrence of my attending or not attending do not cancel this truth: When I say that something is probably the case, I am also saying that it is possible that it may not be the case at all.

A second fundamental point needs to be stated just here: Nothing ever probably occurs in the real world external to the human mind. Probability is not a characteristic or an attribute of the world in which we live. I am afraid that in the discussion of probability this truth is sometimes not realized.

Whatever happens—happens. Whatever does not happen—does not happen. When it happens or does not happen, probability is nowhere to be found in the event.

In the third place, consider that probability is a human calculation that takes place in the mind regarding the likelihood or the non-likelihood of something’s occurrence whether considering it from the viewpoint of the past, present, or future. Given what we currently understand, we might say,

(1)       President George Washington probably liked strawberries (past).
(2)       My health is probably already improving since I changed my diet (present).
(3)       My wife will probably drive to town tomorrow (future).

In the fourth place, given “The Law of Excluded Middle” (see Logic An Introduction by Lionel Ruby, pp. 265-67), when I declare a probability, either what I assert is correct or its contradictory is correct. That is, given the illustrations already stated: (1) President George Washington either did or did not like strawberries, and (2) my health is either already improving or it is not since I changed my diet, and (3) my wife either will or will not drive to town tomorrow. As stated probabilities, there is the lack of claim for knowledge regarding which alternative will result, but one of the “either-or” possibilities will occur.

Fifth, when I state a proposition as a probability, I am saying that given my understanding of existing evidence, I am claiming that the evidence (all relevant truth regarding the issue) seems to support what I am explicitly asserting. When I say that President George Washington probably liked strawberries, I am saying that as a claim, I am aware of certain relevant truths and that, though not conclusive, the truth that I know supports the assertion that he did like strawberries. But the implication still remains that when I explicitly say that he probably liked strawberries, it is also possible that he did not like them at all.

Sixth, when I claim that something is probably the case, my claim though I think it is supported by certain known information, is a guarded one. I am not willing to make the definite claim that President George Washington liked strawberries. I do not make this claim because I am not certain that it is true. In graduate school, brother Warren taught us that knowledge is justified true belief. That is quite a descriptive. If I say that I know that the Bible exists, if I can claim knowledge of its existence it is because of (1) the nature of the book itself as an object (2) the nature of my mind (subject) by which I am able to comprehend its existence, and by (3) the relationship that exists between the object and subject—I am intellectually able to perceive the object and evaluate the impression that the object forms in my mind.

The same process holds for the relationship that obtains between the knower (subject) and the known (object) even when the relationship is not one based on perceiving the physical but rather in conceiving the metaphysical. I can know myself as both object and subject in personal reflective analysis of myself. I can both consider my body and more fundamentally reflect upon my mind.

For knowledge to be “justified true belief” it must be justified by at least the three conditions just named, and it must be “true” or an accurate assessment of those three things, and it is a belief in that it is conviction based on my faith or trust in the conclusion reached with regard to my comprehension of subject (self), object (the other), and the relationship that obtains between myself and that object.

Seventh, there is a difference between (1) something’s happening by chance, and between (2) something’s probably happening. That is, it is clear that some things happened that were not planned or purposed or designed to happen. We call them chance occurrences. The Bible makes it clear that these are a part of reality as experienced by all of us humans (Ecclesiastes 9:11; Luke 10:31-32). Jesus believed in chance occurrences, but he never once described truth as “probability truth” or as something probably true. To the Lord saving truth was not a matter of mere possibility, nor even of probability, but of certitude (John 8:31-32; cf. 1 Timothy 2:4).

Many things happen by chance in that they were simply not specifically planned by the one who experiences the chance occurrence. If I find on the ground a dollar, I consider myself lucky because good luck is nothing more than fortunate chance. If I see the dollar but am unable to procure it because a dog sees it, too, and grabs it and runs off with it before I can reach it, I consider myself somewhat unlucky because I experienced unfortunate chance.

Eighth, coincidence is chance occurrence between two events or conditions or states of affair. Would it be possible for God to exist and not be the creator of our world? In other words, theoretically speaking, could reality be such that while God does exist and the world does exist that there is no connection between God and the world? Is it possible for God’s existence (if it is there) to be coincidental with the existence of our physical universe? Or does the nature of God and the nature of the world necessitate the relationship of cause and effect? Those reading this article likely realize what the Bible teaches regarding such questions.

Ninth, regarding the human intellect and its relationship to itself and to everything else, I can say that either “I know” or “I do not know.” Ignorance is the absence of knowledge. Ignorance is not knowing. Knowledge is the negation of not knowing. That is, knowledge is not-not knowing. When I do not not-know, I know. When I know, I am not ignorant.

Tenth, regarding events in time, the seemingly improbable do occur. Statistically, what would be the chances of my own conception’s taking place? What were the chances that my parents would be conceived? What were the chances that my parents would meet, that they would fall in love, marry, and beget me? Of all the possibilities of sperm-egg fertilization, how was it possible for the two to meet that resulted in me? And yet, here I am! When one considers all the factors involved in a single person’s conception, each person is from the statistical point of view, an improbability.

Furthermore, there is absolutely no way to statistically calculate the effect that divine providence has on natural law. In the days of miracles, such acts defied human calculation that they would occur. What effect, after all, would a statistically calculated prediction have on the appearance of any given miracle? Just so now when considering divine providence in its effect on natural law, it is impossible to calculate in terms of mathematical statistics when providentially affected events in time will occur.

Eleventh, probability is an exercise of the mind in its ignorance regarding which the probability is held. It is the formation of a calculation based on the intellectual condition of not knowing.

Twelfth, let us look at why something is not known by me.

(1)       It may be something that cannot be known.
(2)       It  may be something that is knowable, but I have not as yet come to know it.

For example, the Bible teaches that some truth has never been revealed by God which is only knowable by his divine revelation (Deuteronomy 29:29). On the other hand, some things are knowable by nature even without resorting to divine revelation. Divine revelation assures us of this truth (Psalm 19:1-4; Romans 1:18-23; Acts 14:17; 17:22-31).

Finally, let us consider the existence of God and its relationship to probability as asserted by some. Ontologically there is no “question” as to whether or not God is there. The only “question” is in regard to our knowledge or ignorance of that existence. Now, regarding the relationship of my mind to the existence of God, I face three intellectual choices:

(1)       We can know that God exists (the evidence for his existence is available and conclusive).
(2)       We can know that God does not exist (the evidence for his non-existence is available and   conclusive).
(3)       We cannot know whether God exists or not because the evidence that is available is non-conclusive.

Now, what I have just stated is not new material. But what I want to make clear in this brief essay is that those who claim that God probably exists are in the third classification. When a man says that he knows that God exists, he is rightly considered a biblical theist. When a man says that he knows that God does not exist, he is considered an atheist. When a man says that no one can know whether or not God exists for sure, but that God probably exists, he is taking an agnostic view with regard to the knowledge of God. He is saying that we cannot definitely know. And, furthermore, when he positions his assertion on the basis that the claim is more likely or even much, much, much more likely to be truth than for its contradictory to be true, he is still claiming that we cannot know for sure that God exists!

We were taught years ago that with regard to theistic agnosticism, there are two broad categories: those who while being agnostic evaluate the evidence to mean that it is more likely than not that God exists (and so lean toward theism). And there are those who while being agnostic evaluate the evidence to mean that it is more likely than not that God does not exist (and so lean toward atheism). We learned that Blaise Pascal was a theistic agnostic who tended to accept the existence of God, and that Bertrand Russell was a theistic agnostic who tended to accept the non-existence of God. But both men were unsure as to God’s existence.

Now, when members of the Lord’s church claim that God probably exists, they align themselves with other agnostics that tend toward theism! But, let us be clear: this is not a part of Biblical theism. And it is not a part of an epistemology presupposed by the Bible and assumed by all of the teaching of Jesus Christ. And it certainly is contradictory to the explicit declarations of the New Testament that saving truth can and must be known (John 8:31-32; 1 Timothy 2:4).

We cannot know saving truth if we cannot know any truth. And we cannot know saving truth if we do not know that that truth is saving truth because it is God’s truth! And we cannot know it is God’s truth if we cannot know that God exists.

As we were taught, if God exists, he does so necessarily. He can’t simply happen to exist. If he exists necessarily, then his non-existence is impossible. So, if I can rightly conclude that his non-existence is impossible, then his existence should not be a mere “probability” in my mind. If God’s existence is necessary, then calculating his existence as a probability results in a weaker claim than the fact (of his necessary existence) warrants! Regarding the existence of God, to state, as one’s final conclusion in the matter, that “God probably exists” is to make an unconditionally irrelevant remark.