Frege's views about truth are complex, and there is a great deal of controversy concerning their proper interpretation. (Robert May and I have recently written a paper trying to outline Frege's views.) So I won't try to go into this in detail. But the first point to remember is that, for Frege, a "thought" is not any kind of mental episode. Frege means by a a "thought" roughly what other philosophers mean by a "proposition". So "truth is factual thoughts" would have to mean something like "truth is factual propositions", which probably sounds rather less exciting.
It's been shown in several studies that political views vary with how much education you have had. People who have a post-graduate degree of any kind tend to be to the left of people who have only a high school or college degree. In the 2004 US presidential election, for example, people with only a high school or college degree voted about 53-46 for Bush, the Republican, whereas people with a post-graduate degree voted 55-44 for Kerry, the Democrat. Indeed, I do not have access to the numbers, but if you focus on people with PhDs, as opposed to doctors (MDs, DDs, etc), lawyers (JDs), and business school types (MBAs), then the difference is even more dramatic. Since philosophers do tend to have PhDs, then, of course they trend with that group.
Does education make you more leftist? Or do people inclined to be more leftist just seek more education? These are interesting questions, but, obviously, they are empirical questions, so I will not try to answer them.
I don't know anything about Hegel, but I have several friends who reject the Law of Non-contradiction, and they're all perfectly respectable analytic philosophers, with lots of friends who are also analytic philosophers. So I doubt that the claim that Hegel rejects the Law of Non-contradiction, in so far as it is made by analytic philosophers, is one they make because they don't like Hegel. Most of them don't know any more about Hegel than I do, I'll wager.
Personally, I'm a big fan of the Law of Non-contradiction, and I think there are good reasons not to reject it. But doing so, as I've indicated, isn't completely nuts. If you want to know about this approach to logic, read the article on dialetheism at the Stanford Encyclopedia.
Richard's response is helpful and interesting, but perhaps I would put matters a bit differently. He makes it sound as if Quine accepts the distinction between analytic and synthetic truth and goes on to argue that nothing counts as a truth of the first kind (perhaps "mellowing" his view about this later on). But Quine's position (early, middle, and late) is rather that he can make no sense of the distinction at all. His challenge isn't to the analyticity of logical or mathematical truth; it's rather to the intelligibility of sorting truths into these categories – to the very categories themselves – as the traditional philosopher conceives of them.
Your thought that the distinction can be given some sense in the context of an artificial language is a natural one. Quine explicitly turns to this suggestion in section 4 of "Two Dogmas of Empiricism."
I thought about the article idea. And, back in the day, one might have had an off-print for someone to sign. (I once saw an off-print that had apparently belonged to Henry Sheffer, he of the Sheffer stroke, signed by Gottlob Frege!) But it does seem odd to ask someone to sign a photocopy of an article. Anyway, it's nonetheless true that some people like to collect autographs, and that a blank card is often the format of choice, and there's nothing wrong with that. But don't do the napkin. ;-)
This doesn't seem at all clear. First of all, the argument assumes that, to know whether we know, on Nozick's account, we would have to know whether a certain counterfactual is true. But this isn't obvious. Water is H2O, but it doesn't follow that, to know whether something is water, you have to know whether it is H2O. Similarly, even if knowledge is (say) Nozick-style tracking, it does not follow that, to know whether you know, you have to know whether you track Nozick-style. That might follow if Nozick's account is construed as providing some kind of conceptual analysis, but even then there are issues that tend to go under the heading "The Paradox of Analysis".
Second, even if the foregoing is waived, I don't see why we can't know "whether the subjunctive condition Nozick deems necessary for knowledge is fulfilled". Surely we do have lots of knowledge about possibility, necessity, and counterfactuals. Of course, the epistemology of modal knowledge is a vexed issue, but so is the epistemology of everything else.
This is a thorny topic, and I doubt there is any detail concerning philosophers per se. But for some data, see the Harris Poll on Americans' Religious Beliefs, which found that people with post-graduate degress are somewhat less likely to believe in God. But the difference isn't very impressive: 85%, as opposed to 90% for the general population. There are larger gaps concerning belief in miracles, which is perhaps not so surprising, either.
As Richard suggests, the success or failure of arguments of this sort depends on the success or failure of arguments about the nature of the content of our beliefs and other thoughts.
So, for example, in his later writings Davidson made clear that his account of (as he called it) the veridicality of belief--his account of why by their very nature the vast majority of our beliefs must be true--depends on his defense of a version of a doctrine that philosophers call "externalism," and which asserts that the content of our beliefs and other thoughts is (in part) determined by the very external objects those thoughts purport to be about.
If this view of the content of our beliefs is correct, then the thought that the world might be completely different from what we perceive it and believe it to be would be mistaken in a rather strong sense: despite appearances, massive error of that would turn out to be unintelligible.
Understanding whether or not any one view of content is correct is a complicated affair that involves many philosophical challenges. So, exploring the type of argument you raise in your question requires quite a bit of work. If you are interested in knowing more about Davidson's argument about the veridicality of belief, a good place to start is with the work of his teacher and mentor, Quine. Even though Quine's and Davidson's accounts of the nature of the content of our belief are quite different from each other, Quine's text *Word and Object* is a fairly accessible starting place that lays out some ideas that are key to Davidson's account.