As Dr. Anderson summarizes the issue of induction:
“More generally, what reason do we have to believe that our conclusions about observed instances may be extended (even with probability) to include unobserved instances? The same basic question is most frequently framed in temporal terms: What reason do we have to think that we can draw reliable conclusions about future (unobserved) instances on the basis of past (observed) instances?
Hume’s conclusion was that, regrettably, we have no good reason to think that such inductive inferences are justified. The problem of induction, then, is the problem of answering Hume by giving good reasons for thinking that the ‘inductive principle’ (i.e. the principle that future unobserved instances will resemble past observed instances) is true.
The need for such an answer is immeasurable, since the majority of scientific research is based on inductive reasoning — not to mention most of our everyday inferences about what to expect in the world.”[http://www.ccir.ed.ac.uk/~jad/induction.html]
The problem for Descartes, Hume and Kant was the problem of certainty. That is, what could be known with certainty? Descartes, the rationalist, argued that his own awareness of his consciousness could be known as a certain belief. Hume, the empiricist, questioned whether or not we have direct sense data of God, the self, and cause and effect. Since we don’t have this direct awareness, Hume questioned how we could know of these things. Kant, the rational-empiricist, claimed that the mind structures our sense data based upon categories of the mind. But they were all concerned with what we can know with certainty.
So, to quote Hume, for instance, as saying we cannot ultimately justify induction, means that we have no certainty that the future will resemble the past. According to Hume, to ultimately justify my belief in induction is to prove with certainty that the rules of probability (and or induction) can be ultimately trusted, and I cannot do this. But the point that misses my critics is that theists cannot do this either.
Theists will conclude that if I cannot ultimately (and certainly) justify my belief in induction, that somehow they win their case when I say it’s improbable that miracles have occurred, for I’m basing my belief upon induction and probabilities for which I have no ultimate justification.
I don’t see how this follows. I claim that certainty is well nigh impossible to achieve for any of us. It may well be that this universe is completely and utterly chaotic, not just on the micro level, but also on the macro level. We just may not have enough evidence to the contrary to state otherwise.
There may, in the end, be no probability calculus to apply to life. But so what? In my whole life that’s what I have experienced during every waking moment of my life (assuming for the moment I haven’t been in one very long dream). I punch a key and the letter appears on the computer screen multiple times every time I get up to the computer.
But maybe my memory fails me? Maybe I’m dreaming? So?
Let’s say that I have a completely chaotic memory and/or I’m dreaming. In this particular dream of mine induction still applies, and my memory is all I have to go on—I can do nothing other.
And it appears that my memory is correct and my dream gets me through my dream world (if it really is a dream). It gets me by….
Again, neither Hume nor I said miracles are impossible. But based upon my memory and based upon my life (whether dreaming or not) miracles don’t happen as a regular occurrence in a cause and effect world run by the principles of induction and probability.
What Anderson and others are asking me to do is to forgo all of my experience—all of it—and believe instead, that miracles can and do happen.
Earlier I said that theists do not have a justification for believing in the principle of induction. They don’t, just like me, although unlike me, they claim they do. Why do they claim this? Because they claim God provides for them a basis for believing in induction. But where is their certainty when it comes to the Triune everlasting barbaric God of the Bible who sent a son to be a man and atoned for our sins, will come again and punish the unbeliever in an everlasting hell? For them to justify the principle of induction they must justify their God. And if the standard is the same one that Hume was seeking, then they must show that their God certainly exists. But they obviously cannot do this. For if this were possible, why don’t more people believe in their God?
This only thing we have is probabilities, even if what one considers to be a probability is person related. They think it’s probable that their God exists and that he does miracles, even though none of them have ever seen a man born blind who was instantaneously healed, or a dead man who arose from the grave, or an amputee whose limb was restored before their very eyes. I think, on the contrary, that it’s probably true that there have been no miracles in our world, based upon what we have all experienced—all of us—believer and unbeliever alike.
So it should no longer be a question of whether I can ultimately (and certainly) justify induction, since Christians cannot ultimately (and certainly) justify their God. The question is whether or not we should believe contrary to all of our known experiences throughout our entire lives irregardless of whether our memories are faulty, or whether nature is completely chaotic, or whether or not we’re dreaming right now. I say it isn’t reasonable to believe in miracles from what I have experienced and know. That's all I can say.