The Problem of Induction

[Anonymous No.11426792]

Principles of deductive inference are justified by their conformity with accepted deductive practice. Their validity depends upon accordance with the particular deductive inferences we actually make and sanction. If a rule yields inacceptable inferences, we drop it as invalid. Justification of general rules thus derives from judgments rejecting or accepting particular deductive inferences.
This looks flagrantly circular. I have said that deductive inferences are justified by their conformity to valid general rules, and that general rules are justified by their conformity to valid inferences. But this circle is a virtuous one. The point is that rules and particular inferences alike are justified by being brought into agreement with each other. A rule is amended if it yields an inference we are unwilling to accept; an inference is rejected if it violates a rule we are unwilling to amend. The process of justification is the delicate one of making mutual adjustments between rules and accepted inferences; and in the agreement achieved lies the only justification needed for either.
All this applies equally well to induction. An inductive inference, too, is justified by conformity to general rules, and a general rule by conformity to accepted inductive inferences. Predictions are justified if they conform to valid canons of induction; and the canons are valid if they accurately codify accepted inductive practice.
A result of such analysis is that we can stop plaguing ourselves with certain spurious questions about induction. We no longer demand an explanation for guarantees that we do not have, or seek keys to knowledge that we cannot obtain. It dawns upon us that the traditional smug insistence upon a hard-and-fast line between justifying induction and describing ordinary inductive practice distorts the problem. And we owe belated apologies to Hume. For in dealing with the question how normally accepted inductive judgments are made, he was in fact dealing with the question of inductive validity.
The validity of a prediction consisted for him in its arising from habit, and thus in its exemplifying some past regularity. His answer was incomplete and perhaps not entirely correct; but it was not beside the point. The problem of induction is not a problem of demonstration but a problem of defining the difference between valid and invalid predictions.

[Anonymous No.11426822]

Hume BTFO

[Anonymous No.11426841]

>>11426792
based

[Anonymous No.11426849]

>>11426841
Gotta love Neo-Humean solutions to perceived Humean problems. Ontic Structural Realism is the best

[Anonymous No.11426870]

OP here, to go further.
If two compatible evi- dence statements confirm two hypotheses, then naturally the conjunction of the evidence statements should confirm the conjunction of the hypothese. Suppose our evidence consists of the statements EIsaying that a given thing b is black, and E2 saying that a second thing c is not black. By our present definition, EI confirms the hypothesis that everything is black, and E2 the hypothesis that everything is non-black. The conjunction of these perfectly compatible evidence statements will then confirm the self-contradictory hypothesis that everything is both black and non- black. Simple as this anomaly is, it requires drastic modification of our definition. What given evidence confirms is not what we arrive at by generalizing from separate items of it, but—roughly speaking—what we arrive at by generalizing from the total stated evidence. The central idea for an improved definition is that, within certain limitations, what is asserted to be true for the narrow universe of the evidence statements is confirmed for the whole universe of discourse. Thus if our evidence is E1 and E2 neither the hypothesis that all things are black nor the hypothesis that all things are non-black is confirmed; for neither is true for the evidence-universe consisting of b and c. Of course, much more careful formulation is needed, since some statements that are true of the evidence-universe—such as that there is only one black thing—are obviously not confirmed for the whole universe. These matters are taken care of by the studied formal definition that Hempel develops on this basis; but we cannot and need not go into further detail here.
No one supposes that the task of confirmation-theory has been completed. But the few steps I have reviewed—chosen partly for their bearing on what is to follow—show how things move along once the problem of definition displaces the problem of justification. Important and long-unnoticed questions are brought to light and answered; and we are encouraged to expect that the many remaining questions will in time yield to similar treatment.