There are various skeptical problems which cast into doubt everything we think we know about the world. Maybe there is a bug in the human nervous system which makes all of us completely oblivious to some obvious fact. We have no proof to the effect that the laws of physics will be the same tomorrow as they are today. Maybe the physical world doesn’t really exist.
We prove a fact by pointing out other facts which imply the fact we want to prove. But suppose we think that every fact needs to be proven. It would follow that we need either an infinite series of proofs stretching out behind any belief, or we need a circularity somewhere in our chain of reasoning. Or, we can leave some facts unproven, and prove all of the rest of our beliefs from those unproven facts.
We think that 2+2=4. But how do we know that 2+2=4? There are formal theories of arithmetic which can prove that 2+2=4. But these theories cannot prove their own correctness. To prove their correctness we must use other, stronger formal theories. Those theories in turn cannot prove their own correctness; to prove that we must use other, even stronger theories.
But the stronger a theory is, the less we understand how it works, and so the less we trust it. It seems like the only way that we could prove the correctness of basic arithmetic would be to invent an infinite series of progressively less trustworthy theories, with each proving the correctness of the previous one; and it’s pretty clear that that won’t help.
We can’t supply a perfect proof, a proof which removes even the faintest shadow of a doubt, for anything at all. It follows that everything is in doubt.
What do we do about this? We could refrain from believing anything; but not only is this option unappealing, I am not sure that it is humanly possible. Believing is a function of the mind, like breathing is a function of the body. People sometimes say that they don’t believe anything; but I’m not sure that it’s ever been true. So let us eschew this option.
If everything is in doubt, this means that no additional knowledge, no additional arguments, no additional insights can remove this doubt. In order to have total certainty about anything, we would ultimately have to know everything. Otherwise there would always be the possibility of new information falsifying our beliefs. But we cannot know everything.
This seems to necessitate a “leap of faith” in order to believe anything. We must believe without proof, based on an inner feeling of confidence. We must cut the skeptical Gordian knot by an act of faith.
Not all leaps of faith are created equal. Some are modest, and some are bold.
On the extreme of modesty is the leap of faith needed to believe that, when I look at my hand, there is really a hand there.
On the extreme of boldness is the leap of faith needed to believe that I am an alien from the sixth dimension who incarnated on Earth in order to reduce the stress in the Earth’s energy field and thereby prevent a natural catastrophe from wiping out the human race.
It seems, then, that we are faced with the task of determining where to leap. We must believe something; believing anything requires some degree of faith; and so we must figure out where to place our faith, without sufficient information to be sure that we are choosing the right answer.
Note, however, that to prove that one should have faith would be a contradiction in terms. If one had a proof that one should have faith, then one would not be talking about faith at all; one would be talking about proof. So I don’t argue that we should believe without proof; I just say that we should.
My position on truth is as follows. Perfect proof does not exist. We need to assume some things. So, let us just assume that basically everything we think is right, and only question a belief when we encounter specific evidence that there is something wrong with it.