Abstract
All reasoners described in the most widespread models of a rational reasoner exhibit logical omniscience, which is impossible for finite reasoners (real reasoners). The most common strategy for dealing with the problem of logical omniscience is to interpret the models using a notion of beliefs different from explicit beliefs. For example, the models could be interpreted as describing the beliefs that the reasoner would hold if the reasoner were able reason indefinitely (stable beliefs). Then the models would describe maximum rationality, which a finite reasoner can only approach in the limit of a reasoning sequence. This strategy has important consequences for epistemology. If a finite reasoner can only approach maximum rationality in the limit of a reasoning sequence, then the efficiency of reasoning is epistemically (and not only pragmatically) relevant. In this paper, I present an argument to this conclusion and discuss its consequences, as, for example, the vindication of the principle ‘no rationality through brute-force’. Keywords: finite reasoning, logical omniscience, efficient reasoning, asymptotic analysis, computational complexity.
Highlights
Rationality is often studied as if it were independent from the limitations of the cognitive structures that implement it
P3: If p1 and p2, the computational complexity of patterns of inference is relevant to epistemology
The claim in p1 is that if a finite reasoner with a polynomial pattern of inference had increasingly more cognitive resources, it would tend to reach infinitely farther in a reasoning sequence9
Summary
Rationality is often studied as if it were independent from the limitations of the cognitive structures that implement it. P1: If a finite reasoner with a polynomial pattern of inference had increasingly more cognitive resources, it would tend to reach infinitely farther in a reasoning sequence (in comparison to if it had an exponential pattern of inference).
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