| | Daniel:
>>Actually, can you just clarify? From what I can make out, your position is >>either:
>>1) The problem of induction exists, but you have now solved it.
>>2) The problem of induction does not exist, and I am wrong to say it does.
Nathan:
>That depends upon what you mean by "exists."
Hey, you're not going to come over all verbalist with me now...?;-)
>>Either way, it would at the very least be interesting for you to produce here what you think actually SOLVES a problem you believe exists, irrespective of whether I've invalidated it or not.
OK. Perhaps I'll put the issue another way, so it will emerge more clearly. I'll break this down by-the-book, as simply yet thoroughly as I can make it. Sorry, it will have to be long-ish.
You can put the problem of induction this way - as the question of the *truth of universal laws or statements* (eg"All swans are white") which are *based on experience*. Yet obviously an "experience" can be only singular statement ("A swan is white") not a universal one. So, when people say a universal law is "known by experience" what they are really saying is the truth of a universal statement can be reduced to the truth of singular statements, which are known by experience to be true; which, in turn, is simply a way of asking *whether inductive inferences are logically justified*.
With me so far?
But obviously if we want to find such a way of justifying such inferences, we will need to establish *a principle* for doing so: *a principle of induction*. This would be a statement which would put inductive inferences together to form a universal truth. But – one slight problem. How are we to know the “principle of induction” is itself true? If we try to regard its truth as “known from experience”, then the same problem will arise all over again. To justify this principle, we will have to use inductive inferences; thus assuming a higher principle which is true; which in turn will require inductive inferences, and so forth. So the attempt to show that a principle of induction is actually *true based on experience* breaks down, as it leads to an infinite regress.
So any principle of induction – which is a theory of truth based on experience – *cannot itself be shown to be true based on experience*!
And *that* is why it is not logical. OK? It's not some kind of clash of two internally consistent systems.
Hume, a dedicated rational empiricist himself, was distressed by this finding. Like you, he could not conceive of human knowledge without induction. Yet there was no escaping it – *there was no rational reason to believe induction was true*. So he decided belief in induction must be a kind of irrational human habit. Faced with the same conundrum centuries later, Bertrand Russell came at it from a different angle, deducing that as we seemingly need it so much for science, induction must be some kind of un-analysable, free-standing logical principle, impervious to both normal logic and experience.
Of course, both approaches unwittingly open the door to irrationalism. For if you can have an un-analysable, freestanding principle for discovering truth, a principle that is impervious to both logic and experience, well then so can I, L Ron Hubbard, the Reverend Sun Yung Moon and both their dogs!
Popper, however, viewed the whole problem as being misguided. No-one, he said, ever seriously considered that we might be able to get along *without* induction – that there might be a method of empricism that might be logically justifiable.
This method, he proposed, was falsifiability. He noticed the assymetry between confirmation and falsification – how no amount of white swans could establish a universal law with certainty, but one black one could falsify it with certainty. And of course, there is nothing "inductive" about *one* observation!
So what he proposed was this: *we may propose hypothetical laws or theories on any basis* – on something we saw once, twice, a thousand times or never! (like Einstein’s theory of relativity) It may be something we dreamed, read about, someone told us, we misread – anything. Unlike induction, the source of our theory is irrelevant.
What we must then do is *test our theory rigorously* by both argument (like logic) and experience (experiment, observation). Not to prove it is true, which we cannot, *but to prove it is false*! If it survives our testing, which should be as imaginative and rigorous as possible, we may assume it is true, but we will never be absolutely certain. *We can only be certain that it is false* (and of course, even that "certainty" has the same issues of instrument precision, reliability of observation etc that induction has, so we may discount that particular sense of the word in comparing them).
Now Popper suggests that in fact *falsification* – proposing theories and testing them – is what humans have been doing all along. It just *looks like induction*. So humans *are* actually rational after all, and don’t require illogical beliefs as sources of knowledge.
To see the comparison, let’s take a banal example like eating apples. The inductivist assumes that we only know "eating apples is good" because we’ve eaten some non-specific number of them, and have therefore inferred that they were good. The falsificationist replies that we have got the idea from anywhere that apples are good – perhaps our mother told us, perhaps we read it somewhere, perhaps we like the colour red, perhaps we are guessing rather optimistically because we are hungry! We eat one – and it is good. So our proposed theory that "apples are good" survives. Now that theory may get tested several times – in fact we may develop the psychological expectation that apples are good. But of course this in no way guarantees that the next apple we eat might not be bad – and indeed, our theory that apples are good will be falsified by the first bad apple we eat, and must then be amended to “apples are good, except ones with large worms in them”. So you can see we are perfectly able to get along without induction. And even better, we don’t have to worry about theories being true with “absolute certainty”, as you quite rightly point out. It is simply not necessary – the quest for it is “the central mistake” of philosophy as Popper says.
Finally – and this is one of the things that makes Popper’s theory not just powerful, but beautiful - unlike induction, where the scientist is a kind of chartered accountant of the universe, dutifully logging examples which turn inexorably into theories, falsification brings into imagination into play in a vital role in growing human knowledge. Imagination proposes, reason disposes. The scientist is no longer a fleshy pocket calculator, but now is a kind of artist – an exceptionally rigorous one!
So that’s it, as brief and clear as I could make it. Phew. Now I need to test my theory that beer is good after lots of typing...;-)
- Daniel
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