The sun has risen more than a million times in recorded history, and yet, logically speaking, there is no apparent justification for us to assume it will rise tomorrow, as common sense would dictate. This is the predicament of the lack of justification for inductive logic. We can, however, consider this from a different perspective: If induction is truly unjustified, then either we have enjoyed an incredible streak of dumb luck up until now (just witness the general past success of inductive inferences) or something else explains our good fortune. (1) Induction has justification after all—we just haven’t found it, (2) We’ve enjoyed an incredible streak of dumb luck but have no reason to expect it to last, or (3) Some force or being has been ensuring that our unjustified inferences tend to pay off. Let us begin with the view that induction does have justification.
The idea that induction is not justified, and as such does not exist, simply because we have not yet found a method of justification strikes me as rather arrogant. The existence of a thing is not dependent upon man's ability to discover it. The problem here, of course, is that it is all well and good to say that, but the fact is that induction does not always work, e.g. black swans. It does however work most of the time. But if we appeal to the apparent past efficacy of inference then we do no more than to justify induction with itself, and this path of circular justification is one which must be avoided as shown by Salmon in his examples with counter-inference rules as justifying themselves and creating the paradox of giving the opposite likelihood of something happening as an inference rule would given that both are self justifying and given the same starting set of information. This paradox leads us away from those attempts at justifying induction but, again, to rule out the possibility of something simply because we lack the ability to account for it seems the hight of folly and arrogance.
Given that, perhaps it is true, we have merely enjoyed an incredible streak of dumb luck; we have flipped the coin a million times and it has nearly every time landed heads. But this is a highly unsatisfying answer. If true then we simply drift in a sea of chaos on an island of apparent order, viewing the world as a model for the rest of existence when in fact the only thing we can say about the universe is that we are damn lucky to even be here to see it. But if this is true then all knowledge we have about the world falls apart. We cannot say that we have not been created from nothing five minutes ago and merely have the
That leaves us with the idea that there is some force which has been ensuring our unjustified inferences pay off. This strikes me as even less likely than the idea that it has been all mere chance. That there could first be some force out there both powerful enough to know what our inductive inferences have been (though not all apparently, see again: black swans) and additionally willing to make sure that some of those inferences come to be seems highly outlandish. Although this view can be reconciled quite well with Berkeley's view of the world existing only insofar as it is perceived and that there must be a God to perceive things when there is no person. Then we have both an explanation for why we appear to live in a physical world, despite the lack of proof for said world actually existing, and why inductive logic works on a regular basis. The interesting aspect of this idea, that there is a force working to make our inferences come true, is that said force cannot be a force which enacts actual inductive logic, it must be a force which merely makes the world conform to our inferences. This again seems a bit more than absurd. If there were this force with the power to make all these things happen, then why would it not simply make inductive logic justified? Or perhaps we can say that the force would come from us, that we through sheer force of will can cause our inferences to come to be, but again with the arrogance.
Given all of these three options it seems that one of them must be true, that is to say, we can think of no other possibility. I suppose one could argue that there is some other possibility and that our inability to conceive of it does not rule it out, but we lean in that case away from philosophy and logic and more towards esoterica and mysticism. So it seems that we have here a good argument, one of these three must be true.