Abstract
According to Arthur Falk,1 the theorem that I established in The Probable and the Provable2 'does turn out to be central to an understanding of the application of the mathematical theory of probability to everyday inductive reasoning and to corroboration in particular'. But he also claims that I have 'succumbed to a illusion', since in my proof the presence of three 'superfluous premisses' that 'have nothing to do with the proof. . . creates the cognitive illusion that the theorem concerns corroboration'.3 And he makes the further accusation that I have only proved one third of what I needed to prove.4 When philosophers or psychologists accuse others of succumbing to a illusion, the beam is often in their own eye. And thus it is in Falk's case. What I offered was a proof, using standard mathematical principles, that ran from six premisses
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