Poke: let’s attack the problem a different way. You seem to want to cast doubt on the difference along the dimension of certainty between induction and deduction. (“the difference you cite between deductive and inductive arguments (that the former is certain and the latter not), is the conclusion of the problem of induction; you can’t use it to argue for the problem of induction”)
Either deduction and induction are different along the dimension of certainty, or they’re not. So there are four possibilities. induction = certain, deduction = certain (IC, DC); InC, DnC; IC, DnC; and InC, DC.
Surely, you don’t agree that induction gives us certain knowledge. The “imagination-based” story: the fact that the coin came up heads the last three million times gives us very high probability for the proposition that the coin is loaded, but not certain. But you’ve rejected the “imagination-based” story. I’m fine with that. Because there are real stories. Countless real stories. Every time one scientist repeats another scientist’s experiment and gets a different result, it’s a demonstration of the fact that inductive knowledge isn’t certain: the first scientist validly drew a conclusion from induction as a result of his/her experiments (do you disagree with that??), and the second scientist showed that the conclusion was wrong or at least incomplete. Ergo, induction doesn’t give us certain knowledge.
That eliminates two possibilities, leaving us with InC, DnC and InC, DC. The following is a deductive argument. “1. A. 2. A-->B. 3. B.” Assume 1 and 2 are true. Do you think we thereby have certain knowledge that B? If so, you seem to be committed to DC, and thereby to a difference between induction and deduction on the domain of certainty.
Poke: let’s attack the problem a different way. You seem to want to cast doubt on the difference along the dimension of certainty between induction and deduction. (“the difference you cite between deductive and inductive arguments (that the former is certain and the latter not), is the conclusion of the problem of induction; you can’t use it to argue for the problem of induction”)
Either deduction and induction are different along the dimension of certainty, or they’re not. So there are four possibilities. induction = certain, deduction = certain (IC, DC); InC, DnC; IC, DnC; and InC, DC.
Surely, you don’t agree that induction gives us certain knowledge. The “imagination-based” story: the fact that the coin came up heads the last three million times gives us very high probability for the proposition that the coin is loaded, but not certain. But you’ve rejected the “imagination-based” story. I’m fine with that. Because there are real stories. Countless real stories. Every time one scientist repeats another scientist’s experiment and gets a different result, it’s a demonstration of the fact that inductive knowledge isn’t certain: the first scientist validly drew a conclusion from induction as a result of his/her experiments (do you disagree with that??), and the second scientist showed that the conclusion was wrong or at least incomplete. Ergo, induction doesn’t give us certain knowledge.
That eliminates two possibilities, leaving us with InC, DnC and InC, DC. The following is a deductive argument. “1. A. 2. A-->B. 3. B.” Assume 1 and 2 are true. Do you think we thereby have certain knowledge that B? If so, you seem to be committed to DC, and thereby to a difference between induction and deduction on the domain of certainty.
(Heavens… the things I do rather than sleep.)