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What Mathematical Certainty?

Fifth in a series on the search for meaning in a world that doesn't want to bother with it.

by Everett Wilson
February 2, 2005

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As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
—Albert Einstein
I found Einstein's comment among the exercises in With Good Reason, a textbook on informal fallacies by S. Morris Engel. In the exercise, Engel directed the reader to analyze the language of the statement. Two questions came to my mind. Was Einstein kidding? Was he making a defensible assertion?
Without the context of the statement, I do not know. Even with the context, I probably wouldn't know, seeing it was Einstein who said it - but I would tend to believe it because it was Einstein. If I believe him when he says that energy equals mass multiplied by the square of the speed of light, though I have no idea what that means or why it should be so, I can easily believe him when he says that mathematics has an uncertain reference to reality.
 
My belief proves nothing. Neither would the opposite conclusion that Einstein was talking nonsense. We know from other instances that he was not above paradox — a fancy way to kid around — as when he said that God does not play dice with the universe. While it is unlikely he had the biblical God in mind, we are not sure what or who else he had in mind. This lack of definition doesn't keep it from being one of his more popular quotations. We assume he meant something, even if we don't get it ourselves.
 
In the statement about mathematical certainty, however, he used "reality" as a standard of comparison. While we may or not know who God is, the concept of reality is available to all. We all live in the real world, right? Reality, to be real, only has to be. It doesn't owe anything to anybody. Mathematical descriptions apply to realities, but mathematical certainties apply only to themselves. Whether he was kidding or not, Einstein still brought into question the phrase — to a mathematical certainty — as it applies to the world beyond mathematics.
 
Mathematics is one of many ways we have to describe reality, not to explain it. Description is not explanation. "Two plus two" is a description. So is "Energy equals mass multiplied by the square of the speed of light."
  • In the search for meaning, the absolute theist declares: "Mathematics will never be able to explain reality, only to describe it, because mathematics is not ultimate reality."
     
  • In the same search, the absolute secularist declares: "Mathematics hasn't yet explained reality. But it still might; and in collaboration with the hard sciences, I think it will."

Theist and secularist agree with each other that bigotry needs exposing and fact needs establishing, but the work of both proceeds on faith. Both the scientist and the metaphysician say at the beginning, "I will treat this statement as true and see if it leads anywhere but to a dead end." Neither should criticize the other for this commonsense approach to knowledge. 
 
If there are any who declare that faith is not a method of knowing, they can declare it only by faith! Faith is the road to certainty, but ultimate certainty is grounded in ultimate reality. Faith in less than ultimate reality leads to less than ultimate certainty.
 
If there are no mathematical certainties in the cosmos, only provisional descriptions of its varied phenomena, we must look beyond the cosmos for the ultimate and find it there, if it is to be found. 

All Installments of this Series:
1. The Possible Possibility, 10/2/2004
2. The Legitimately Weird, 10/16/2004
3. Nature and Supernature, 11/29/2004
4. Designer Jeans, Designer God, 1/6/2005
5. What Mathematical Certainty?, 2/2/2005
6. Credible, Not Verifiable, 2/28/2005
7. The God of Ultimate Meaning, 2/28/2005
8. Dialogue with a Postmodern Nephew, 5/11/2005 
9. Why the Bible?, 5/21/2005
10. Why Jesus?, 6/4/2005

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Real Things first appeared in serialized form on the Partial Observer in 2001. It is now available in print for the first time.

Over thirty years after a senseless crash redefined his life, Greg Thompson and his family finally learn why.

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