Guy walks up to you in the street and says, “If f is some continuous function on the closed interval a to b, and if you take the definite integral of that function from a to x, then the first derivative of that definite integral is the function f(x).”
You say, “Sounds spooky to me. How do you know it’s true?”
“It just is, buddy. I don’t know why it’s true, but it is.”
And he’s right. Not just that his statement is true, which it is, but that he doesn’t have to provide you with an explanation why it’s true. That is, his ignorance of the why does not in any way change the truth of the statement.
Now whether this guy, lacking any convincing tale or other corroborative evidence, succeeds in transmitting this truth is another question. But it just doesn’t matter how he came by his truth: whether he proved it from first principles, whether he heard it as a rumor, whether it was revealed to him in a dream, whether he actually thought it was false but was pretending it was true as a little joke, or whether he just insists it is true.
You might be tempted to accept this because you know the example (the readers of this blog are nothing if not mathematically literate); which is to say, you know how to prove the proposition from first principles. But that would be a mistake. The majority of folks who hear propositions like the above will only be able to judge them on the veracity of the deliverer and will not be able to gauge it in any other way.
Think about it. People are asked to believe that (say) neutrinos have mass, and given the source of the pronouncements on this weighty subject, they accept it. Of course, given the lives of most people, this information, like most highly technical and scientific information, is of no use and will not cause anybody to act differently than if they hadn’t believed the proposition.
The weakest argument in favor of something is, as all know, the argument from authority: though despite what you might have heard, it is not a formal fallacy (and most things you believe are probably based on it!). And anyway, even if it were, if any authority were to say, “X is true because I say so”, the statement is no proof of X’s falsity. X can be true even if every argument you know which asserts it is fallacious.
Occasionally we get lucky and are able, from first principles, to formally prove a proposition asserted by an authority false. In the public arena, this is a daily and even trivial occurrence (listen to NPR for dozens of examples of easily disproved propositions). But this is not so in more advanced fields.
You have to work hard, and maybe for years (and maybe never), to identify formal fallacies in the work of many philosophers, and even when you do, you haven’t proven the contentions of these folks false. Proving anything false still requires formal proof. This proof must begin with a list of axioms all agree upon, and lead through successive propositions using rules of argument also believed by all.
In absence of this disproof, it is always the case that the contentions of anybody might be true, even if all that it is offered is an argument from authority (or revelation).
So if somebody on authority contends that an infinite number of turtles supports the earth, you can disbelieve it, but in order to argue its falsity you’re going to need proof. Sneering isn’t proof. Neither is laughter or haughtiness or insults. Nor are other counter-arguments from authority, i.e. “Most philosophers now believe it is aardvarks and not turtles shouldering the burden.”
That one is easy to disprove (an observation will do it). But other contentions are not. And some might even be true, even if you don’t want them to be.