Logic: inductive force

You can see that the inference is correct. But is this argument deductively valid, or only inductively forceful? The conclusion, it seems, can be asserted on the basis of PI with perfect confidence; surely there is no need to insert a 'Probably' before the conditional conclusion as well as before its consequent. It might seem, then, that the argument is deductively valid. However, there is a slight complication that one should be aware of. We said that statements of probability are usually statements of conditional probabilities, even if the evidence upon which the claim is based is left implicit. When we say something like 'Probably, your dog has fleas', we usually mean given everything we know, it is reasonable to accept the proposition. If so, then the consequent of C in the argument above really means something like:

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