I'm well aware of the problem of induction. In my estimation, the real "problem" is saying how, given that the conclusion of a line of inductive reasoning is never logically necessary, but also given that inductive reasoning undeniably works, how is it that it works if the conclusions are never assured?
The conclusions are assured, but only ever in the present. You can never be certain when going to bed at night that you will be there alive and well in the morning. And the same applies to all things composed of form and matter for eventually they are seen to degrade, wither and perish. And added to that inductive conclusion is the logical argument that every speck of matter can be conceived to be annihilated. In sum, there is no logical reason why the world as a contingent truth must obtain, which is further supported by scientific models cautioning that the world, already universally accepted as finite, may end with heat death or the Big Freeze.
Sure- as above, it works. As per your Russell quote, even though we cannot examine future futures, we can remember past futures, and while we can't have positive confirmation of an inductive inference, we can certainly imagine negative evidence- for instance, if it had happened that one day the sun failed to rise, we would have lost alot of confidence in our inductive inference that it would continue to rise in the future.
And past futures, have there been instances of that negative evidence of which you speak, and do we have reliable experience of every single millennia going back to time immemorial on which to build our inductive inferences?
But once again, you're exposing the operative presupposition; you ask from what argument does it follow- you're using the language of deductive reasoning. You're simply arguing that only logical consequence can attain the epistemic status of knowledge or reasonable belief- in other words, that deductive reasoning provides the gold standard which all other forms of reasoning must satisfy.
That doesnt answer my question. Certain truth would be the elusive Gold Standard, but which experience can never attain, and so there is no argument that can be made that from the world existing today it must therefore continue to exist tomorrow.
Who went from one extreme to the other? Up til this point, you appear to be arguing that there cannot be any knowledge based on induction, because induction is always fallible- which would entail that the vast majority of what we colloquially refer to as "knowledge" (virtually the entirety of the results of empirical science) would fail your test and thus not count as knowledge any longer. Now you appear to forswear any such argument- which is it? Indeed, the fact that "experience serves us well"- or, as I've said, that induction works, is the reason for supposing that somehow, induction is able to be a reliable form of reasoning about or knowing the world we find ourselves in.
Then it seems you misunderstand me! My standpoint is and has always been fundamentally that of empiricism (tendentiously, as per my post: #86); I take the view that we learn through cause and effect and experience, despite there being no innate or a priori knowledge. Or as Freddie Ayer said: the fact that the validity of a proposition cannot be logically guaranteed does not entail that it is irrational to believe it. On the contrary what is irrational is to look for a guarantee where none can be forthcoming; to demand certainty where probability is all that is obtainable.
And I'm not saying it gives us indubitable knowledge; I'm saying that "indubitable knowledge" is not redundant since some types of knowledge are fallible and open to doubt.
Some types of knowledge? So may I ask what knowledge isnt fallible and open to doubt?
"Trust"? Again, it is a matter of probability, rather than logical consequence- and once again you're presupposing what counts as knowledge; perhaps you should lay out exactly what your criteria for knowledge is?
In simple terms Ive been pressing the point that unless anyone can show me differently there is no certain knowledge, either to affirm or deny that the sun will rise or that the supernatural exists. So to ask me for a criterion of knowledge is to suppose that I can somehow know what Ive been consistently arguing cant be known!
But I'm arguing that these are not necessarily mutually exclusive- that one asserts or even knows some X doesn't exclude that ~X is nevertheless possible.
Then once again this demonstrates your misuse of the term. It is self-evidently a contradiction to claim to know a thing to be the case while in the very same sentence allowing that it might not be the case.
Evidence which could not fail to exist if the claim in question were true; we're basically inquiring into the truth-conditions for a given belief, and what the necessary conditions are. But To use an example I used in a similar context elsewhere, take the claim that my house has been burglarized; necessary evidence of a burglary would be some missing property- if I have been burglarized, it is necessary that something has been taken (otherwise it would be trespassing, not burglary), and so the necessary evidence of a burglary would be some missing property.
But what is to count as your necessary evidence of absence of the supernatural, because the analogy doesnt offer an explanation in those terms?
So can we never have knowledge of facts, since they are "only probable" and never certain?
Yes thats what Im saying, although not in the way that youre using knowledge by conflating the term with present and/or past experience as an argument to the future.
Well, but what good are such explanations or hypotheses, if they "lie outside the experiential world"? Would this make them distinctions which make no difference? For instance, how would one distinguish between a good hypothesis that "lies outside the experiential world" from a bad hypothesis that "lies outside the experiential world", seeing as our only tribunal for evaluating competing explanations just is the experiential world?
But we are able to distinguish between what you refer to as good or bad hypotheses. Speculative metaphysics and arguments for a transcendent reality have their internal truths and logical conclusions and can still be subject to analysis and reasoned argument, a testament to that would be some of the discussions and ideas explored in this thread. The experiential world isnt a boundary or an obstacle to what can be thought. For as Wittgenstein remarked: In order to draw a limit to thinking, we should have to think both sides of this limit.