“Objective Public Proof”?

“Objective Public Proof”? March 13, 2024

 

Euclid in pastel colors
A public domain illustration of Euclid’s proof of the Pythagorean theorem from Wikimedia Commons. Nothing remotely like this exists in the social sciences (e.g., psychology, sociology, and anthropology) or in historiography. And such reasoning is quite rare even in the physical and natural sciences.

I occasionally use the expression objective public proof.  I’ve recently been asked what I mean by it.

Let me take the phrase apart just a bit.

“Proof,” as the word is typically used and as I am using it here, is a fact or a piece of information that demonstrates the existence of something or, more broadly, the truth of a proposition.

In mathematics, which (along with formal logic) probably illustrates the notion of “proof” most clearly, a proof is a deductive argument for a mathematical statement that logically guarantees the truth of that statement.

What, though, is a “deductive argument”?  The classic deductive syllogism takes a form like this:

All A are B.

X is an A.

Therefore, X is B.

To put some simple and obvious flesh on those bones, here’s a venerable example:

All men are mortal.

Socrates is a man.

Therefore, Socrates is mortal.

In such reasoning, if the premises are true, the conclusion is absolutely, certainly, inarguably true as well.  However, the premises may not be true:

All elephants have trunks.

My cat is an elephant.

Therefore, my cat has a trunk.

The second premise in the syllogism above is not true.  (Not, at least, in my personal experience with cats.). Thus, although the syllogism is, technically, logically valid—which is to say that it has the proper form—it is not sound and its conclusion is not true.  And, of course, the error can occur in the first premise:

All humans are French.

Tom Hanks is human.

Therefore, Tom Hanks is French.

Clearly, not even deductive arguments provide absolute certainty in every case.  If one or both of the premises of a standard deductive syllogism can be doubted, the conclusion is correspondingly weakened or even rendered false.

We sometimes refer to isolated facts as “proofs,” but it seems to me that, in such cases, those individual facts represent a premise in an implicit deductive syllogism.  They don’t stand alone.  For example, the isolated fact that the shower towel is completely dry leads to the conclusion that Max didn’t take a shower by virtue of its place in this very simple bit of reasoning:

If the shower towel is dry, nobody has taken a shower.

The shower towel is dry.

Therefore, nobody has taken a shower.

And, clearly, the term nobody includes (or excludes) even Max.

But absolutely certain deductive arguments aren’t available for most subjects.

Questions like the nature of the Big Bang, the causes of the Great Depression, the probability of Frankie and Johnny having a successful marriage, whether or not humans possess free will, and so forth cannot be reduced to simple deductive syllogisms.  Many such questions have been debated for years, indeed for centuries.  Many have advocates on both (or all) sides.  The Anglo-American common law recognizes this by calling for decisions in civil cases to be made “on the preponderance of the evidence” or even, in criminal cases, when a conclusion seems to be “beyond a reasonable doubt” (but not, plainly, beyond any possibility of doubt).

Nevertheless, a person can be persuaded of the truth of a proposition, and even convinced that he or she has personal “proof” for it, but be unable to convince others.  (Hence, my use of the words public and objective, as opposed to private and subjective.)

If, for example, someone says that Sarah wasn’t at the party last week, you might respond that you know she was, because you saw her there and even talked with her.  You have proof.  However, the other person may have reason to believe that you’re wrong and to disbelieve your testimony.  If he feels really strongly about it, he may even say that you’re lying or that you were hallucinating.  He is not compelled to believe your testimony, however certain you may be of what you experienced.

This gets at what I mean by the phrase objective public proof.

Anybody who understands a valid geometric proof must accept its conclusion.  Anybody who understands a sound and valid demonstrative syllogism must accept the proposition that it affirms.  If all men really are mortal and Socrates really is a man, then it follows inevitably and inescapably that Socrates is mortal.  The person faced with such a proof is compelled to accept it.

A person faced with your testimony that Sally was really at the party last week is not compelled to accept it.  You may have subjective certainty, but he does not have either your subjective certainty or, in a sense, any certainty at all.

Oliver Cowdery may have been subjectively certain that he saw an angel displaying the gold plates of the Book of Mormon and heard the voice of God certifying the translation of them to be correct, and it may well be completely reasonable—I think it is completely reasonable—for others to believe his testimony.  But, by virtue of the very definition of subjectivity, his subjective certainty cannot, as such, be transferred to others.  And some may still choose, for whatever reasons, to doubt or deny his claim.

So, when I refer to objective public proof, I mean something of the nature of

If P, then Q.

P

Therefore Q.

No reasonable person with even rudimentary understanding of English and of basic biology can deny the conclusion in this next specimen of thinking:

If John has a pulse, John is alive.

John has a pulse.

Therefore, John is alive.

That is a matter of objective reasoning that is publicly available.  Even on the matter of whether or not John has a pulse, others can test it.  Not so, necessarily, with the next one:

If John has been seen since his purported death, he’s still alive.

John has been seen since his purported death.

Therefore, John is still alive.

I do not claim, and have never claimed, that I can “prove” my religious beliefs true.  I do not claim “objective public proof.”

I do claim, however, that I and others can provide—and have provided—evidence for theism in general, for Christian theism more particularly, and, yes, most particularly for the specifically Latter-day Saint form of Christian theism.

By evidence, I mean something that justifies greater confidence in a proposition.  But evidence and proof are not identical concepts.

Is the evidence for theism to which I’ve referred “coercive,” in the sense that any person faced with such evidence has no alternative to accept it once she understands it and is compelled to by it to agree with my conclusion from it?

No.

Outside of mathematics and symbolic logic and the most simple questions—e.g., “Does the Mississippi flow from north to south?”  “Are deer mammals?”  “Do butterflies live in Antarctica?”—there are few questions in the sciences, and none in history or philosophy or the social sciences, that can be answered with absolute, undoubtable certainty.

The same is certainly true in courtrooms.  That, again, is why standards like “beyond reasonable doubt” and “preponderance of the evidence” exist.

Can there be “proof” for a proposition that, in the end, turns out to be false?  No.  There can be seeming proofs for such propositions. In the end, though, they are not proofs.  There can, for example, be no proof that triangles have 185 degrees, or that, for a right triangle bounded by sides a and b and the hypotenuse c, the following equation is false:

This, incidentally, is what is behind my answer to a question years ago about whether there can be “proof” against the claims of the Restoration.  I’m still often beaten up online by people who didn’t understand my response, which was along the following lines:  No, there cannot be proof against the claims of the Restoration on the assumption that the claims of the Restoration are true.  But there can be, and is, seeming evidence against it

Can there be seeming evidence for a proposition that, in the end, turns out to be false?  Yes.  Clearly.

The earth seems to be flat.  The stars and the planets seem to revolve around us.  Spoons in glasses of water seem to be broken.  Railroad tracks seem to converge in the distance.

There are many reasons on which someone may doubt.  Some may be good, and some may not.  Consider, again, the syllogism

If John has a pulse, John is alive.

John has a pulse.

Therefore, John is alive.

Does John really have a pulse?  Should I trust the person who took John’s pulse?  Maybe he doesn’t know how to take a pulse.  Maybe he stands to gain from our thinking that John is still alive.  Maybe he is too emotionally involved to be trusted.  Maybe I’m self-interested and have something to gain from John’s death.  Maybe John has been so badly interested that the claim of a pulse simply isn’t believable.

Consider, again, the syllogism above regarding John’s being seen alive after his alleged death.  It may be no big deal (other than for John and his closest friends and family, of course) if John turns out to be still alive.  Maybe somebody had simply heard a rumor of his death — perhaps confusing John Jones with Jon Jonas — and then finds out that, actually, John was just in that last department meeting, looking perfectly healthy.

But how about changing the name of the supposedly dead person?

If Jesus has been seen since his purported death, he’s still alive.

Jesus has been seen since his purported death.

Therefore, Jesus is still alive.

A lot more hangs on this proposition, and there will be those who fervently believe it and others who fervently deny it.

And this points, again, to the fact — which I may or may not discuss at some future point — of the subjectivity of personal conviction.  There is not, at least now and available to us, objective public proof that Jesus is still alive.  And people have different personal standards of what constitutes evidence, sufficient evidence, persuasive evidence, and what they will regard as subjective personal “proof.”

What I’ve written above represents merely a few rambling and fairly hasty notes in answer to the question mentioned above.  I would welcome (constructive) comments on them, or questions about them, or objections to them, or requests for their clarification.

 

 

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