Proof vs. Evidence

Proof vs Evidence

There is a difference between Proof and Evidence.

Is it not a mistake to seek a mathematical proof for an empirical fact?

The word ‘Empirical’ means ‘based on observation and fact, not on theory’.

The Romans had a proverb: ‘Contra factum non arguméntum’ = ‘Against a Fact there is no argument.’

We assess an alleged mathematical or logical proof by testing it against our innate understanding of rationality.

With claims, however, of empirical facts or situations, we do not 'prove' them in the way we prove a mathematical or a logical proposition:  we weigh the evidence, and make a judgment on whether to accept the evidence or not.  And while it is next to impossible to reject a valid mathematical or logical proof, experience of human beings shows that it is next to impossible to get a particular individual to accept a piece of evidence as convincing if they are previously determined not to accept it.

Yet for many things the evidence is 'beyond all reasonable doubt' and those who do not accept it are considered mentally unstable:  for there is always the possibility of 'unreasonable doubt'.  See below.

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If I am told that a triangle cannot be trisected using a straight edge and a compass alone, or that all possible quadratic equations can be solved using the Quadratic Formula, I can test this by logic. But If I am told an empirical fact, I cannot either prove or disprove it, I can only either choose to believe or to disbelieve it. If I am told that Jesus walked on the water, or that my impression of the world is actually related to what is out there, and that I am not simply dreaming on a couch on an intensive care machine (as in some excellent Sci-Fi stories) I can only either accept or reject it.

Evidence can be an observable physical fact, or it can be the word of a trustworthy witness. We send an accused man (or woman) to the electric chair on such evidence, if it is deemed worthy of acceptance.

If, e.g., a bloodstained knife is found by a corpse, and a witness states that he saw Mr Murphy strike the blow, the juror will weigh the probability that the witness is telling the truth. He might conclude, on other evidence, that the witness is lying for ulterior motives of his own. If he rejects the evidence on these grounds, he will not state, 'this cannot be proven – it is illogical', he will say, 'There is sufficient contrary evidence to give cause for rejecting the evidence of the witness.'

On the other hand, if no such ulterior motive can be shown, and if there is no contrary evidence, the juror might judge that the witness is reliable. He does not exactly choose to accept it; he feels bound by the evidence to arrive at a verdict of 'Guilty'.

Alternatively, the lawyer for the Defence might show that the wound on the corpse is not compatible with the knife found by the corpse.

Alternatively, a body taken out of a river, apparently drowned, might show, on forensic evidence, the the cause of death was strangling and not drowning (hoping you will excuse the gruesome examples.) In this case, the juror might conclude that the evidence conflicts with the assertion (that the accused either is or is not guilty). Alternatively, the accused might present a convincing alibi, such as that he was on a live TV programme during the time the murder was committed. This, perhaps, constitutes a logical disproof: There is an internal inconsistency.

Apollo Program

Let us consider the Apollo Program.

There are those who refuse to believe that the Apollo Program was genuine, & who hold that nobody ever walked on the Moon. These people have accepted an elaborately-constructed alternative explanation, & they simply reject the evidence offered that the astronauts really did go there. I put it to you that you cannot *prove* to them the empirical fact of the Moon Landing: showing them a piece of Moon rock would only elicit the response that it was picked up somewhere on Earth; showing them a return capsule, burned and battered, they would reply that it had been constructed on Earth to look like something that had dropped out of the sky. And so on. All one can do (if so motivated) is to present the evidence. For my part, I take it to be overwhelmingly in favour of the genuine Apollo program; but it hasn't been proven, I simply accept it on the weight of evidence. I do not say, "I reject the Apollo Program because you can't prove it was genuine."

Flat Earthers

Then, there are those who believe that the Earth is flat. It is harder to 'disprove' this assertion than might meet the eye: the proponents in effect construct an alternative Physics, which does seem to fit the evidence sufficiently closely to convince some people.

Atheist objection: << You would have about the same luck trying to "Logically Argue" that Santa Claus is real>>

Christian: If I were to try this, I would not try to argue from logic, but from evidence. I might produce a string of 6-year-olds who would testify they had seen him with their own eyes. The Lawyer for the Prosecution might provide a string of adult witnesses who would state that it was all an elaborate game,  and that it was they who had planted the presents themselves; and one or two who would state that they had dressed up as Santa Claus to please the children (and their parents). On the weight of evidence, a jury might be expected to conclude that the Santa Claus of the fairy tale does not, in fact, exist.

Your example, therefore, serves only to prove my original point, that there is a difference between 'logical proof' and 'weight of evidence.'

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Belief in God

Nobody can pick God up and place him on somebody else's lap. The evidence (which I won't burden you with on this page) can be either accepted or rejected; but I contend it is invalid to reject it on the basis that it cannot be proven.

Atheist: <<But It can be neither proved or disproved, thus I don't "believe" in something without evidence.>>

Christian: But we do it all the time. When I fly from Cork to London I have not examined the blueprint for the aircraft engine, or the ID of the pilot (who might be a suicide bomber) but I stake my life in the belief that these things are worth my trust. In fact, it is beyond reasonable doubt that my faith in the airline is justified, but that is not the same as proving it. Likewise, I believe that the Church's account of the Resurrection is trustworthy, and make at least a stab at staking my life on it. Is it reasonable to single out belief in God for rejecting this principle?