"Proof" : What is it Exactly ? part 1
You hear that a lot in epistemic or scientific discussions : "we can't prove anything" or "proof is for mathematics". Is that true ? What would make proof impossible or restricted in this way ?
Well, let's look at the dictionary first. It tells us :
1. The evidence or argument that compels the mind to accept an assertion as true.
a. The validation of a proposition by application of specified rules, as of induction or deduction, to assumptions, axioms, and sequentially derived conclusions.
b. A statement or argument used in such a validation.
So we have two very different aspects here. The first is psychological, the second is epistemic. If we keep these in mind, we can now say that proof is eminently possible, and about pretty much anything. Which is to say, that any given individual, if conditioned sufficiently, could be theoretically compelled to accept anything, even that his body is composed of small creatures that feed him their memories and which must be taken off his body by asking them questions and registering their emotional response on a tin can machine (as in Scientology's self-auditing OT levels). So the scope of "proof", at least psychologically, is extremely vast.
On the other hand, epistemic proof is obviously more limited. For one thing, we can only prove, in this sense, that which is true. So the Scientologist's belief cannot be proven epistemically, while he may be so convinced of it as to find it ironclad. The proposition cannot be validated by the correct application of any rules, since it is wholly unscientific and has no relation with empirical reality.
Both kinds of proof are post facto - they cannot be applied before the act of knowing. Any act of knowing, be it science or otherwise, is not orderly in this manner, but chaotic and often branches out in many different directions. It is after we come to know something that we can neatly trace a path from our context of knowledge to this new proposition. Proof is therefore presentation, not discovery.
What do we need to prove something ? Well, both kinds of proof have different requirements, but they both require some way to explicitly or implicitly communicate concepts, and they both require that one value honest discussion and persuasion. Without these prerequisites, there will be either no possibility for substantial communication, or no desire of such.
Now, to dispel the first myth. Mathematics does not somehow fulfill some prerequisite that all other disciplines lack. Certainly people can mount arguments that convince others of a proposition in any discipline, and they can validate their knowledge in any discipline. I can use the rules of reasoning on empirical data to validate mathematical propositions, but I can do the same for, say, physics, economy, poultry raising, or bridge building. The only difference is that mathematics is used by other disciplines to express natural laws in precise and universal forms. But this perspective does not make it more or less susceptible to proof.
It is sometimes said that science (or reasoning in general) cannot prove that anything does not exist, or is not true. This is a grave and fundamental misunderstanding. Science is founded on precisely proving that things are not certain ways. This is called falsification, perhaps the most important idea in science : that a proposition is worthless unless it can be tested, and that whatever is not proven wrong, that is to say whatever is found to conform the most to our observations, must be closest to the facts. By testing extensively a hypothesis, and eliminating all the things we know are not so, we arrive at an approximate understanding of the facts. This is how science has always worked.
In fact, it is precisely when something cannot be proven wrong, even in theory, that we say it cannot be scientific at all. For example, the idea that there is a pink elephant in my garage, an elephant which cannot in any way be observed or measured, is not scientific because it is not falsifiable in any way. Such an idea is precisely the same thing as saying nothing at all, because it is the equivalent in all respects of saying that there is nothing in the garage.
Go to part 2.