Not even mathematical facts necessarily hold since there could always be a magical demon blurring your mind, making you make errors and making you blind at them.

That's a much weaker statement than the one you originally stated. This new statement says, basically, "you can never be 100% sure of anything", whereas before you seemed to be saying, "there exist no objective standards of truth at all, any story is as good as any other".

I suspect that most of the people decrying logic, axiomatic systems, etc. aren't objecting to reasoning in general so much as certain levels of formality...

Or, in my experience, specific topics. For example, such a person would say that reasoning does apply to topics such as deciding which car to buy, or which stock to invest to, or what the sum of the angles in a triangle is. Reasoning does not, however, apply to other topics such as deciding what to eat for lunch, which deity to worship (if any), whom to date, and which topics are subject to reason in the first place.

The above is a real example, BTW (assuming I understood the person's position correctly).

Oh, I found it. It wasn't a discussion here, it was a post on Scott Aaronson's blog: http://www.scottaaronson.com/blog/?p=232

“Listen,” Darwin says, more kindly now, “I have a simple notion for resolving your dispute. You say,” says Darwin, pointing to Mark, “that people’s beliefs alter their personal realities. And you fervently believe,” his finger swivels to point at Autrey, “that Mark’s beliefs can’t alter reality. So let Mark believe really hard that he can fly, and then step off a cliff. Mark shall see himself fly away like a bird, and Autrey shall see him plummet down and go splat, and you shall both be happy.”

Doesn't seem to apply here, because Randolf admits that reality doesn't care what nonsense he believes. The only problem is he seems intent on describing that nonsense as 'truth' and refusing to label what it is that reality is doing, which is what everyone else is calling 'truth'.

Hmm, well, if you truly believe that truth is subjective, then there's nothing I can do to dissuade you, by definition -- since my subjective opinion is as good as yours. Now if you'll excuse me, I've got to go build some hula-hoops, and then maybe take to the skies by will alone

Oh, you probably could. I'm not so fond on this definition. It's just something I have found most satisfying so far but it's still subject to chance (How ironic!).

That's a bit differend from what I'm trying to say. My word choosing of intuition was clearly bad, I should have talked about mental experiences. My point is that when I do the mathematics, when I, for example, use the axioms and theorems of natural numbers to proof that 1+1 is 2, I have to rely on my memories and feelings at some point. If I use a theorem proven before, I must rely on my memories that I have proven that theorem before and correctly, but remembering is just another type of vaque mental experience. I could also remember axioms of natural numbers wrong, even if it would seem clear to me that I remember them correctly. I have to rely on the feeling of remembering correctly. This is why I define truth as what you truly believe. Once you have carefully checked that you used all the axioms and theorems correctly, you will truly believe that you made no mistake. Then you can truly believe that 1 + 1 is 2, and it's safe to say its the truth.