Thursday, May 07, 2009

The problem of induction

One of the stock objections to sense knowledge which Scripturalists like to raise is the problem of induction. Can we infer the future from the past? Can we predict the future in light of the past? Does the future resemble the past?

The objection goes back to Hume: can enumerative induction justify a universal inference? On the face of it, the answer is no, since the breadth of the inference is underdetermined by the breadth of the evidence.

To take a stock example, if I observe 999 black ravens in a row, that doesn’t mean the 1000th raven I observe will be black.

What are we to make of this objection? I’ll make three brief points:

1.While enumerative induction illustrates the limitations of sense knowledge, it doesn’t begin to demonstrate the impossibility of sense knowledge.

If I observe 999 black ravens, then I’ve learned something: observation has taught me that at least 999 ravens are black.

That doesn’t tell me that all ravens are black, or even that most ravens are black. But it does tell me that some ravels are black. I know something, as a result of observation, that I wouldn’t know absent such observation.

2.I’m typing this sentence on a computer keyboard. I believe that if I depress a particular key, it will probably produce a particular letter. Likewise, I believe that if I depress certain keys in a certain order, it will probably produce a particular sequence of letters.

Why is that? Well, it’s partly a result of experience. In my experience, when I depress a particular key, it produces a particular letter.

But there’s more to it than bare experience. My computer keyboard was designed to function in a particular way. It was designed so that, if I depress a particular key, it will produce a particular letter. It was designed so that, if I depress certain keys in a certain order, it will produce a particular sequence of letters.

My experience of using the keyboard is essentially confirmatory. Before I use the keyboard for the first time, I don’t know if the keyboard suffers from a design flaw. Using it is a way of testing it. Does it do what it was designed to do?

It is, of course, possible for the keyboard to malfunction. It’s possible that in a random number of cases, a keystroke won’t yield the corresponding letter.

However, even in the case of malfunction, that presupposes an underlying design. Proper function.

Unless my keyboard suffers from a design flaw, it’s basically reliable. Indeed, highly reliable.

It’s not totally reliable. It can wear out. Or need to be repaired.

But it’s sufficiently reliable that I can make plans for the future based on my keyboard. I can plan to write something tomorrow, using my keyboard. And most of the time, my confidence is well-placed.

This is analogous to sensory perception or memory. The senses sometimes deceive us. Memories sometimes fail us. But our memories and perceptions are sufficiently reliable that we can use them to plan for the future.

Sometimes our plans fall through. But that’s quite different from a dream world which is so mutable and unpredictable that you can’t make any successful plans.

To a great extent, it’s possible to successfully plan for the future on the basis of induction. For induction, like using my computer keyboard for the first time, need not be the ultimate source of our belief in natural patterns. Rather, it’s confirmatory. Observation is a way to recognize natural patterns. To recognize design.

3.Hume was a secularist. So he doesn’t have anything else to go by beyond induction itself. But in a Christian worldview, the future generally resembles the past because it was designed that way. The reason for causal correlations is that God designed nature such that certain prior events correspond to certain posterior events. If I depress a particular key, that triggers a corresponding outcome.

For a Christian, enumerative induction is grounded in the principle of divine design. God’s plan for the world. Inferences about the future aren’t limited to past samples. They also derive from our belief in a God whomade the world to function in a fairly predictable way. Hence, the past is a generally reliable guide to the future.

This doesn’t even require a particular theory of causation. It doesn’t matter whether or not a particular action actually causes a particular effect. It’s sufficient that God has designed the natural world in such a way that these correlations generally obtain.

There are, of course, exceptions to the rule. Miracles.

But that doesn’t prevent us from successfully planning for the future most of the time. It’s not like a dream world where there’s no connection between what went before and what happens afterwards.

And even miracles are purposeful events. These are not random anomalies.

Christians don’t draw a universal inference from enumerative induction. We only draw a general inference from enumerative induction. And the generality of the inference isn’t based on induction alone.

We don’t subscribe to the uniformity of nature. Rather, we subscribe to ordinary providence (which allows for miracles).

We don’t believe in natural regularities simply because we observe them. Rather, we believe in them because that’s the kind of world which God made for us to inhabit.

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