Wikipedia defines fallibilism as follows:
Fallibilism is the philosophical principle that human beings could be wrong about their beliefs, expectations, or their understanding of the world.
Now, on its face, this seems self-evident. Who would deny that human beings could be wrong about their beliefs? Like many philosophical principles, it is when the application of the principle has unsettling results that people begin to retreat from it, afraid of the cost of accepting the principle.
For example, let's take the law of identity, which is a cornerstone of logic and rational thought. The law of identity can be expressed as "A is A" (Note: This is distinct from "A = A" for reasons I won't go into here) or as "A thing is itself." What this amounts to is the claim that all things possess an identity that distinguishes them from other things, and within a given context, they are always that thing. For example, one cannot, within the same context, treat a tree as a tree in one instance and as a car in another without being blatantly irrational. So long as the context holds constant, the tree must be regarded as itself, as a tree.
Now suppose I suggested that, like all other beliefs, the belief that a thing is itself is not an absolute truth. Many individuals who feel a strong emotional attachment to a logical or rational approach to life would take exception to that notion. I believe they do this out of a belief that, if they accepted the proposition that even basic logical principles were not absolute, reason and logic must be thrown out as possible ways of understanding the world, and the chaos of total nihilism awaits them.
Before I get ahead of myself, I want to explain why I think fallibilism is rational and why appealing to my reason still makes sense.
When an individual engages in an act of reasoning and draws a conclusion, at least two things happen. Firstly, the individual grasps the conclusion in a rational manner and is capable of using that conclusion. Secondly, and this is what I think is overlooked, the individual experiences an emotion or sensation of confidence. Along with understanding the conclusion is an emotion that signifies that this conclusion is worth relying on.
As I pointed out earlier, scarcely anyone would deny that everybody is capable of making mistakes. All of us can recall a time in our lives where we engaged in logical thinking, drew a conclusion, and later discovered that the conclusion was wrong. And it's not always because we did not have access to the necessary information; sometimes we simply reason poorly and engage in fallacies, and sometimes we fail to account for information that we have.
This means that an individual can experience the emotional feeling of confidence that accompanies reaching a conclusion while simultaneously being completely wrong. Or to put it another way; there is nothing about feeling confident about a conclusion that has any metaphysical significance on the truth value of that conclusion.
The only rational conclusion to draw from this is that all acts of reasoning and all feelings of certainty are non-absolute. They never reflect the Truth with a capital T. They merely reflect the belief that, based on the experiences of the individual, is most likely to lead to the satisfaction of that individual. (For more information, see my series on pragmatism)
(To the pragmatists reading this; I am aware that I have been sloppy with my use of the word truth in the above. Assume that I am referring to the truth as correspondence theorists mean it.)
Pragmatism seems, to me, to be the natural solution to the problem, so I'll let the series on pragmatism introduce those concepts. In short, we don't need the absolute truth; we simply need beliefs that function well for living good lives.
On a final note, I want to counter a common counter-argument to fallibilism that I myself have been guilty of making in the past. The counter-argument goes something like this:
But if you say "There is no absolute truth," isn't that an absolute truth? Aha, gotcha!
The problem with this counter-argument is that it assumes that I am trying to provide absolute truth to begin with. "There is no absolute truth" is not an absolute truth; it is merely a useful belief. Since I am not denying the existence of useful beliefs, I am not in contradiction. Even my belief that there are useful beliefs is merely a useful belief, not an absolute truth. Counter-argument rebutted.