I've often seen fallibilism discussed with reference to the Münchhausen trilemma and the problem of scientific induction. There is a simpler and more encompassing model of fallibilism that I might call "mechanistic fallibility."
According to mechanistic fallibility, the human brain is a machine made of neurons and so forth, and all machines are at least slightly fallible due to a variety of hardware defects, software defects, and environmental interference. Therefore the human brain is fallible. Therefore, the conclusions of a human brain cannot be trusted with perfect certainty. This holds even if the brain in question is your own, and even on a priori propositions.
The argument also holds up even if we allow the possibility that the human brain is not a machine or that the mind is somehow independent of it. Because, as long as this is merely one possibility and not an absolute certainty, the chance the brain is a machine is still nonzero. Thus the chance that the brain is a machine and the machine has just made an error is also always nonzero.
In practice we observe that humans do often make mistakes on a priori propositions; arithmetic errors, for example, are such mistakes. We make errors because of inattention, the inherent randomness of neuron operation, micro-strokes, and so on. Computers sometimes make arithmetic errors too, for a variety of hardware and software reasons. So, it is not rational to perfectly trust the conclusions of computers or humans, including yourself, on any proposition.
This holds no matter how thoroughly the human or computer checks their work. There could always be a mechanistic failure anywhere in the error-checking process - in all stages of checking, or just the last and most critical stage.
What philosopher is best associated with this type of mechanistic fallibilism?
Is any philosopher strongly associated with it? I would now accept as an answer a philosopher who emphasized the importance of accidental mistakes in calculation, with the conclusion that we cannot be certain of anything, even if they did not use a direct comparison to machines.