January 07, 2014

What a Proof Is: Probable Proofs

"Present your case, says the Lord; bring forward your arguments, says the King of Jacob." (Is 41:21)
We're still considering the idea of a "proof". A proof establishes something as true. A proof leads us to belief or conviction.

One strange (at first) consequence of that definition is that a "proof" need not be certain. It need only be probable--or, rather, probable enough.

4. Some things we accept as true by abduction, or "inference to the best explanation". My car is clean now, and it was dirty last night. It must have rained. I investigate and find that no one I know came by and washed it, everyone else has a clean car too, etc.; after elimating other explanations (or finding them very unlikely), I accept the most reasonable conclusion that it rained. I did not see it rain, but I believe that it did.

5. Some things we accept as true because of anecdotal evidence. I know that in 1492 Christopher Columbus sailed the ocean blue. This is not empirically verifiable – he is not out there doing it right now, where I can observe him. Rather, I have heaps of documentary evidence that he did, and I have no legitimate documentation that claims otherwise. Again, I did not see him do it, but I believe that he did.

6. Some things we accept as true by induction. I have tried a Big Mac and didn't like it. All McDonald's stores make the Big Mac in a consistent manner. Therefore, I don't like any Big Mac. I haven't tasted every single Big Mac, or even one from every store in the chain, but I believe that I don't like them.

Note that accepting a truth does not require absolute certainty. Some truths are probable - like those reached by anecdote or induction. Is it even remotely possible that Columbus didn't sail in 1492, and there has been a vast conspiracy to fool everyone? (Or a vast conspiracy to fool me -- but you wouldn't all do that, now would you?) Well, yes. It isn't technically impossible, just staggeringly improbable. But for most purposes, we find that that's good enough.

proof. Oxford Dictionary of Philosophy. Oxford University Press. http://www.oxfordreference.com/view/10.1093/acref/9780199541430.001.0001/acref-9780199541430-e-2542?rskey=wQw6Cu&result=2545 (accessed: November 24, 2013).


Anna said...

And proof still makes it objective, even when it is proof established by probable evidence?

Anonymous said...

Thanks Anna -- sorry it took a bit to get your comment moderated.

A proof about some object -- something outside the speaker -- is always objective. We're talking about something out there, outside of the person's subjective experience. The main reason I defined "objective" and "subjective" so carefully is to later distinguish between someone's personal experience and opinion (subjective matters) and things outside the person (objective matters).

Is a probable proof still a good proof? It certainly is. Courts operate on probable proofs. Most people do in passing every day judgements. Most times we use the word "proof", outside of mathematics, we don't mean "absolute certainty". We mean something like "so likely, everything else seems silly by comparison".

Anna said...

Well, it seems so obvious from this side. But when spinning your wheels in a discussion, probable proof is very simply just... dismissed for nothing more than the lack of desire to see the truth.
I suppose the take away here is that a challenge such as "you can't prove that" is often attempting a "gotcha" because the empirical evidence just isn't there. That being assumed, the answer is legitimately "I don't have to prove it." Empirically, at least.

Anonymous said...

The person saying "you can't prove that" may mean "you can't provide a deductive argument" or "you can't test that in a lab". That's why I've started with these terms: I've found myself having to circle back them when such a complaint comes up.

I'm going to answer a little more fully in the next post! Thanks for the great thoughts.

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