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...the puzzle.
The Cautious man accepts all the steps in a proof; grant that it is imaginatively obscure how he might come to revise that assessment; grant that there is every reason to believe that whenever the proof is reproduced in a satisfying way, it will lead to the same outcome; but dispute that there is anything in all that which justifies him in claiming to have apprehended any essential connection between basis, process and outcome—in claiming, indeed, of any statement in the vicinity that it ‘cannot but’ be true. (Wright’s formulation of the problem from Wittgenstein on the Foundations of Mathematics, p.455)
Is the Cautious man (henceforth CM) coherent in his attitudes?
The point of the story is that if the answer to the above stated question is ‘yes’, then modal discourse is not a fact stating discourse. For, if there were modal facts that determine CM’s attitudes then he would be incoherent in his attitudes.
Peacocke takes a route of showing that his account of metaphysics and epistemology of necessity can meet the challenge posed by the CM without postulating obscure faculties that have access to necessity or retreating to emprico-conventional epistemology of a priori truths.
I want to point to a different strategy that one could deploy in dealing with the CM problem. The idea is to point to an unexamined assumption upon which the CM example relies. If we can successfully challenge that assumption, we can say not that CM is incoherent but rather that the example is incoherent and rests on a false assumption.
In order to understand and evaluate whether CM is coherent in his attitudes it may be helpful to compare him with an ordinary cognizer who is cautious. Typically caution is called for when a thinker has a reason to think that she may be in error (for example, one may think that she doesn’t have enough evidence or that her evidence is...
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