So, he "elsewhere undermines as a basis for such inferences" the perception of the memory and senses. How does that translate to "correlation is the sole basis for causation"?
The reason this is relevant is because
the impossibility of certain knowledge
refers to the impossibility of identifying causes directly.
Because you still are saying Hume is your source for this claim, and you still have not shown the quote where he says so.
I don't really feel like leafing through my enormous annotated copy of the
Treatise of Human Nature and quoting huge tracts of the work for you. Instead I'm going to present quotes from some online sources:
According to Hume, we reason inductively by associating constantly conjoined events, and it is the mental act of association that is the basis of our concept of causation . . . Hume held that we have no perceptual access to the necessary connection . . . but we are naturally compelled to believe in its objective existence
This refers to our natural propensity to infer causation based on correlation.
Causes and effects are discovered, not by reason but through experience, when we find that particular objects are constantly conjoined with one another . . . Even after we have experience of causal connections, our conclusions from those experiences aren't based on any reasoning or on any other process of the understanding. They are based on our past experiences of similar cases, without which we could draw no conclusions at all
This refers to causation being inferred solely based on correlation.
When we examine experience to see how expectations are actually produced, we discover that they arise after we have experienced ?the constant conjunction of two objects;? only then do we ?expect the one from the appearance of the other.? . . . Custom or habit ?determines the mind?to suppose the future conformable to the past.? . . . ?either we have no idea of force or energy, and these words are altogether insignificant, or they can mean nothing but that determination of the thought, acquir'd by habit, to pass from the cause to its usual effect?
This is a combination of both of the above.
Now if need be, I am prepared to wheel out my Norton edition of the
Treatise and quote from the introduction (which is considerably easier than trying to quote large swathes of Hume's actual text). However, what would be better for both of us is if you actually read the
Treatise. Consider it an exercise in self-improvement.
Hume expresses in several parts the enormous complications of the process of jumping from "perception of our memory and senses" to a reliable "causality". This is the total opposite of what you are saying, that the whole process can be reduced to one simple mathematical or statistical concept, which is the correlation.
First of all, Hume never arrives at "a reliable causality". For Hume, we identify causes because we are naturally inclined to do so based on the seemingly constant correlation of events. Secondly, the bolded point has never been my argument. You are referring to the statistical definition of causation, whereas I have clearly been using the word correlation in its general sense.
And a model with clear cause-effect relationships is "certain knowledge". If you can infer it from correlations, it is not impossible to get to certain knowledge. If you take the stance of the impossibility of certain knowledge, then you have to say that nothing can infer causality, because knowledge of causality is certain knowledge.
Uh, yes? You do realise why Hume is considered the ultimate skeptical philospher, don't you?
As most of the time for you FE'ers, you are saying people that they do not understand because they do not read when you cannot give an answer. But please end this discussion once and for all, showing us where Hume (or anyone other than the FE'ers) says "correlation is the sole basis for inferring causation".
No trig, the simple truth is that you don't know what you're talking about. I have now presented quotations from other sources demonstrating my point. The Stanford Encyclopedia of Philospophy article I have quoted in support of my argument contains references to the relevant sections of the
Treatise. If that isn't enough for you, then I'm not sure I can be bothered to quote the same sections myself.
Lord Wilmore, can you summarize your/Hume's position? I assume that the underlying idea relevant to the topic is that the show possibly establishes correlation, but this is not equivalent to demonstrating causation? 
I think the above summarises Hume's position quite well. Here's another summary of the argument which puts it quite well:
David Hume described the problem in An Enquiry concerning Human Understanding, ?4, based on his epistemological framework. Here, "reason" refers to deductive reasoning and "induction" refers to inductive reasoning.
First, Hume ponders the discovery of causal relations, which form the basis for what he refers to as "matters of fact." He argues that causal relations are found not by reason, but by induction. This is because for any cause, multiple effects are conceivable, and the actual effect cannot be determined by reasoning about the cause; instead, one must observe occurrences of the causal relation to discover that it holds. For example, when one thinks of "a billiard ball moving in a straight line toward another,"[7] one can conceive that the first ball bounces back with the second ball remaining at rest, the first ball stops and the second ball moves, or the first ball jumps over the second, etc. There is no reason to conclude any of these possibilities over the others. Only through previous observation can it be predicted, inductively, what will actually happen with the balls. In general, it is not necessary that causal relation in the future resemble causal relations in the past, as it is always conceivable otherwise; for Hume, this is because the negation of the claim does not lead to a contradiction.
Next, Hume ponders the justification of induction. If all matters of fact are based on causal relations, and all causal relations are found by induction, then induction must be shown to be valid somehow. He uses the fact that induction assumes a valid connection between the proposition "I have found that such an object has always been attended with such an effect" and the proposition "I foresee that other objects which are in appearance similar will be attended with similar effects."[8] One connects these two propositions not by reason, but by induction. This claim is supported by the same reasoning as that for causal relations above, and by the observation that even rationally inexperienced or inferior people can infer, for example, that touching fire causes pain. Hume challenges other philosophers to come up with a (deductive) reason for the connection. If he is right, then the justification of induction can be only inductive. But this begs the question; as induction is based on an assumption of the connection, it cannot itself explain the connection.
In this way, the problem of induction is not only concerned with the uncertainty of conclusions derived by induction, but doubts the very principle through which those uncertain conclusions are derived.