I guess I'd have to disagree with the idea that "all of philosophy and logic point to a reason or cause for everything." There's certainly no argument from logic as such; it's perfectly consistent to say that some events are genuinely random. Some philosophers have held that there's a reason (not necessarily a cause in the physical sense, BTW) for everything, but the arguments are not very good.
On the other hand... quantum mechanics is a remarkably well-confirmed physical theory that, at least as standardly interpreted, gives us excellent reason to think that some things happen one way rather than another with no reason or cause for which way they turned out.
An example: suppose we send a photon (a quantum of light) through a polarizing filter pointed in the vertical direction. We let the photon travel to a second polarizing filter, oriented at 45 degrees to the vertical. Quantum theory as usually understood says that there's a 50% chance that the photon will pass this filter and a 50% chance that it won't. But quantum theory itself provides no account whatsoever of which will actually happen. And on the usual interpretation, there is no reason or cause; it's really random.
Now the usual interpretation of quantum mechanics could be wrong. There are deterministic interpretations, most notably "many worlds" or Everettian quantum mechanics, and Bohmian mechanics. No one is in a position to rule either of those out; all I can say is that neither of those approaches is to my taste. But even though both of them restore determinism, that's not really their motivation. Most people who work in foundations of physics are not bothered by the very idea of indeterminism and in fact, indeterminism wasn't by any means Einstein's biggest issue with quantum mechanics.
So to sum up: I don't think there are any good general arguments against randomness. I think the concept is coherent, and that it's a plausible fit for our best physical theory. It also happens to suit my own prejudices about quantum mechanics, but that's just icing on the cake. ;-)
There are two questions here: first, can Descartes' cogito be doubted—is it open to doubt that "I" exist? Second, more generally, is there anything that's not open to legitimate or reasonable or rational doubt? (What people are psychologically capable of doubting maybe another matter.)
On the first, may philosophers would say yes. Even if it's certain that there's thinking going on, it doesn't follow that there's some one or some thing doing the thinking. Consider the Buddhist/ Humean "no self" view. On that way of understanding things, there's no substantial self. There is, as the Humean might say, just a bundle of perceptions. "I think," on this account, is just a manner of speaking. We can't get from "there is thinking" to "I exist."
So maybe it's open to doubt that I exist. Is it open to doubt that there's thinking going on when it seems that there is? Maybe not, though I don't doubt that some clever philosopher could offer an interesting argument to the contrary. What else? Can it be rationally doubted that anything that exists is self-identical? Some might say it depends on whether there are "things" to be self-identical.
At this point, however, I feel more like a philistine than a philosopher; I'm not sure I care. Maybe there's something beyond all possibility of rational doubt, or maybe there's not. But even if there isn't, real epistemic life will go on as it always has. We'll continue to believe things, reasonably in my view, and, I'm willing to say, we'll even know some of them. Here my sympathies are broadly with G. E. Moore. The arguments that one has to come up with to adopt wholesale skepticism are a lot more fragile and open to doubt than the innocuous thought that we actually know some stuff, even if we're not entirely sure just what.
It's a good question and the answer seems pretty plausibly to be yes. The impression that people have of themselves can often be off the mark, and that can be shown by how they actually behave. Someone who thinks he's generous might really be stingy, always finding excuses not to contribute his fair share. Someone who thinks she's not very smart might actually have a lot of insight, as those who know her can plainly see. And on it goes. We're complicated beings. There's no reason a priori to think that the part of our minds that tries to make sense of ourselves overall is likely to be especially good at it. No doubt there are some things about ourselves that we're in a better position than others to know, but when it comes to the larger patterns and dispositions that go into making us who we are, disinterested outsiders may well be in a better position than we are to get things right.
I think the simplest answer is this: empiricists think beliefs about matters of fact should be grounded in empirical evidence; they don't think the evidence always has to be direct. I've never been to New Zealand, but I have a considerable amount of indirect empirical evidence that it exists. To take just one bit of that evidence: people whom I know to be otherwise reliable and honest tell me they've been there.
On the other hand, I don't even have indirect evidence that Middle Earth exists. What I have is evidence for is that J. R. R. Tolkien wrote stories about a fictional place called Middle Earth, which neither he nor anyone else claimed was real.
The (small) larger point is this: the one-word name of a view is not always the best way to figure out what the view actually comes to. Very few, if any, self-described empiricists have said that evidence always has to be direct to be relevant.
You say that love is an emotion, and in some sense we can grant that. But saying it suggests that love is a feeling, and that, in turn, suggests that it's like a warm sensation in one's tummy -- something that we can simply detect by introspection and that we can't (or can't easily) be wrong about. But it's more complicated than that. If I love someone, I can still have moments when I feel angry at them, for example. But my momentary anger -- a non-loving feeling -- isn't the same as not loving them. Love is, among other things, a complicated set of dispositions. Some of them are dispositions to feel a certain way in certain situations, and others are dispositions to behave in certain ways. I might be momentarily angry with my daughter, for example, but it might be true that if anything were to happen to her, I would be beside myself with grief. I might also be willing to make considerable sacrifices for her well-being. I might worry about her, take time to check up on her, and do all of this not just out of some sense of duty. Those dispositions are much better indicators of my love for her than my momentary feeling of anger.
On the other hand, if I wouldn't grieve the loss of my daughter, wouldn't go out of my way to help her, didn't care whether I spent time with her and so on, the fact that I would say I love her wouldn't count for much. Indeed, the fact that I believed I loved her might best be seen as a kind of self-deception due, perhaps, to my wanting to think well of myself. Similar comments apply to romantic love, of course.
Because love is a lot more than a feeling, people are quite capable of being wrong about whether they love someone. They can tell themselves that they don't love someone when they really do (think of someone who swears they no longer love their ex-lover when it's obvious to everyone else that they do), and they can tell themselves that they do love someone when they really don't. The connection with behavior is clear. If love involves dispositions to feel and to act, then the actions someone actually performs can be signs of their real dispositions.
Of course, this is only a small part of the story. The notion of love is both complicated and not entirely precise. It's certainly possible to love someone and yet not to be the jealous type. It's certainly possible to love someone and not be willing to go along with all of their wishes or principles; the examples you cite seem pretty clearly to be compatible with really loving someone. But if A treats B with reliable cruelty, for example, it would take a very complicated story to make sense of A's claim to really love B. This is so even if A really believes that s/he loves B.
The more general point is this: there are some things about our minds that we know better than others do. But there's a good deal about our minds that we can't discover just by introspection. We can be quite wrong about our selves in various ways. Add to that the fact that our psychologies have such an important role in producing our behavior, and it's not hard to see why sometimes others are in a better position than we are to make judgements about our own psychologies. The case of love is just one among many.
If I read you correctly, your point is this: if you're prepared to assert P, you should be prepared to assert that you know that P. And the converse is even clearer: if you are willing to assert that you know that P, you're willing to assert that P is true. That's an interesting and important observation, but it doesn't show that the standard analysis of knowledge is circular. Suppose I'm prepared to assert that P. Do I actually know that P? That depends. Even if I'm prepared to make a sincere assertion -- and hence believe that P -- I might not really be justified or P might not actually be true. In either case, the classical analysis says, I don't actually know that P. The analysis of knowledge doesn't make any reference to what people are prepared to assert. On the contrary: it points out how there can be a gap between what we're prepared to assert and what we actually know.
We could turn this into a slogan: saying it's so is saying you know, but that doesn't mean you do.
There are a couple of ways we might think about the questions you're raising. One is by trying to look for an Archimedean Point, so to speak, that provides some sort of absolute or incontrovertible answer. The other way is to look at how we actually think about these sort of things -- look from the inside. Since I have no Archimedean point available to me, I'll offer the latter sort of response.
What we think does depend on what we've experienced, but even though my life is different from yours, we have lots of common ground to appeal to. Obvious sort of case: if you and I were both to look out my office window, then even though your experience is not just like mine, we'd agree that there's a building directly across from us. We'd also agree that there's a large grassy area behind it, and that there are people wandering around in the vicinity. Other cases of ho-hum agreement among people are more complicated, but we could multiply examples indefinitely.
We can also agree that some people are better positioned to have a view. If I look at an x-ray, my opinion about what I see isn't worth much. I know that, and so does anyone who knows that I have no medical training. But a radiologist can tell a lot. I'll defer to her opinion, and so should any sensible person in my position.
And on it goes. Our ordinary notions of evidence, reasoning and so on clearly can carry us a long way. Add the refinements of science and math and we get even further. By those lights, some people really are more justified in believing certain things than others, and we can come to reasonable consensus about who is who. Some of what "led you to being who you are today" was sound: soaking up the deliverances of your senses, thinking carefully about evidence, taking counsel from those who know more than you.
Two things, however. One is internal to the whole system. There are hard cases, and there may even be unresolvable cases -- from the point of view of our usual conceptions of evidence and reasoning. True though that may be, however, it doesn't undermine the fact that we know a lot, and that not everyone is equally expert on everything.
The other point may be closer to your worry. We could toss everything up in the air and become skeptics about all our usual beliefs and standards. We could do that, but the mere fact that it's possible doesn't give us much of a reason to. There's a larger point here. We can look at knowledge, belief, expertise, etc. notions that call for the sort of Archimedean perspective that we noted above and duly set aside. Some philosophers think that unless we can find such a point (and we can't), then skepticism is the only reasonable response. Most philosophers, for better or worse, think that that's a hopeless approach.
So in short: from the point of view of our usual standards and practices, we have all sorts of reasons to think that some opinions are better than others. If we toss all those standards and practices aside, we're radically adrift. But there's no compelling reason to give ourselves over to the currents.
Initial disclaimer: I am no epistemologist. But I'm not sure I quite understand. First, why are all assumptions about basic beliefs, etc. dogmatic? Are you perhaps demanding that one must be certain of such things? Why isn't it good enough to say "I know Peter was at the meeting because I was there and I spoke with him?" People who say things like that could be mistaken, of course. But suppose that as the world turns out, I'm right: I did attend the meeting and I did speak with Peter. Then don't I know that he was there? If not, why not?
Perhaps the worry is that I don't know that I know this (doubtful in this case, but happens sometimes.) But it's long been doubted that knowing X requires knowing that you know X. Perhaps the thought is that to know X always requires being able to give some particular sort of justification. But reliabilists wouldn't buy that. On their view, I know something (roughly) if my beliefs about it come to be in a reliable way, even if I have no clue what the mechanism is.
So while certain sorts of projects in epistemology fail, the field is still thriving, near as I can tell. But in any case, it seems to me that one sensible version of the epistemological enterprise takes it for granted: we know lots and lots of stuff. The project isn't to prove this, but to provide plausible analyses and accounts of what this amounts to. Seems like a reasonable project to me.
I could come up with an argument that you don't exist, but it would be harder for you to. Descartes' point is that even in doubting that I exist, I seem to presuppose that I actually do. Descartes claimed that in any moment when I reflect on it, I know for sure that I exist.
That said, this shows much less than it might seem to. In particular, it doesn't show that there is any unified "self" that has a continued, coherent existence over time. The existence of that sort of "I" has been doubted by many thinkers, going back at least to the Buddha, but also, famously, by David Hume and more recently by Derek Parfit. Views of this sort are sometimes called "bundle theories" because they replace the idea of a unified self with a picture according to which we are an ever-changing bundle of sensations and thoughts.
Here's a link to the section of Hume's Treatise in which he sets forth his views on the self. Enjoy!