As it stands, the supposition is hopelessly vague. You would need to make it more precise, I would think, to render it falsifiable: what are the relevant respects in which past and future are to be compared? What are the time periods we are talking about? And what counts as resemblance or lack thereof in each of these respects? Without answers to these questions, it's hard to know what would count as evidence pro or con. For example, can the averge price-to-earnings ratio of the S&P500 be relevant to the sought falsification? If so, what's the relevant past period that the future might resemble or not? How far must this ratio stray from the past range for there to be non-resemblance? How long must the deviation last? Are we to look at annual averages or daily fluctuations? Does discontinuation of the index count as non-resemblance? Is non-resemblance of this ratio sufficient to falsify the supposition, or must there be other respects as well in which the future is different? Etc.

You are asking whether it is true that T=K (knowledge and truth are the same). From your asking this, I conclude that you don't know whether T=K. If truth and knowledge were the same, then lack of knowledge would be lack of truth. So, assuming T=K is true, we derive the conclusion that T=K is false. Better then to suppose that knowledge and truth are not the same. And of course they aren't. Something may be true and yet not be known by many or not be known by anyone at all. For example, take the following two sentences: "with optimal play, white can always win in chess" and "it is not the case that, with optimal play, white can always win in chess". One of these sentences is certainly true; but no one yet knows which one it is. (Or, if anyone does now, they haven't told me, so I don't know which is true.)

Well spotted! Nozick holds that, in order for you to know p, it must be the case that, if p were false, you wouldn't believe p. This condition is not fulfilled when p is "it is not the case that I am a brain in a vat on Alpha Centauri being stimulated to have my present experiences": if p were false (if I were a brain in a vat on Alpha Centuri being stimulated to have my present experiences), then I would nonetheless be believing p. But this condition may well be fulfilled when p is "I am typing." It is fulfilled if, were I not typing, I wouldn't believe that I am. With this move, Nozick takes himself to have shown at least how knowledge is possible: it's possible that I am really typing and that, if I weren't typing, I wouldn't believe that I am. But do I know that I am typing or do I not? Well, according to Nozick, this depends on what I would believe if I weren't typing now. Nozick assumes that there's a definite answer to this question, a fact of the matter. But, even if we grant this,...

As with other great works in the history of philosophy, Kant's Critique of Pure Reason -- the single greatest work of philosophy ever written, in my view -- is valuable more for the questions it poses and the ways it develops for pursuing these questions than for the answers. These questions and methods are understood and reflected in the best work done by philosophers today. Still, much current work in philosophy is not at this level -- mistakes of the kinds Kant exposed are still frequently made, esp. ones that are so "natural" to our ordinary ways of thinking. (For example, it is very natural to believe that you just know the temporal order of the events in your mental life ... until someone presses you to explain how a being with a plurality of mental items in her mind could possibly get from these the notion of time and some specific ordering of her mental items in time.) Kant explored so much new ground in this book, pioneering the language needed in this exploration as he went along...

Let's begin by distinguishing two senses in which something might be said to be unknowable. In some cases something is said to be unknowable because it isn't the kind of thing about which, in principle, knowledge could be had. For example, do you know the minimum number of hairs a man must have on his head to escape being bald? Well, there is no such minimum number to be known or discovered, because the concept of baldness is too vague for this. Do you know what time of day it is now on the sun (Wittgenstein)? Would you be happier dead? Again, there's nothing to be known or discovered in these regards. Philosophers have said about such cases that "there is no fact of the matter." Let us set these cases aside, because they are not the ones that interest you. In the cases that interest you, there is a fact of the matter. And the claim is then either that it is impossible for us (human beings including all future generations) to know this fact or even, more dramatically, that it is in principle...

Immanuel Kant comes pretty close to articulating the points you make here. In one of his last writings, Kant tells the story of a man who stands in front of the mirror with his eyes closed (or almost closed). Asked what he is doing there, the man responds that he wants to see what he looks like when he is asleep. The story is funny because the man is attempting the impossible: When his eyes are really shut (as in sleep), then he will see nothing and, in particular, will not see what he looks like. And when his eyes are just a little bit open, then he will see himself alright, but with his eyes slightly open (not as in sleep) . The morale of this funny story is that the desire to know what the world is like apart from our faculties of knowledge is incoherent: We want to know, hence engage our faculties of knowledge, and yet know without these faculties of knowledge and presumably even without any faculties of knowledge at all. The story is meant to reconcile us to the fact...