Super quick and dirty response: I believe it exists, you believe it exists, and everyone you've ever spoken to believes it exists. You have massive evidence that it exists in the form of memories which seem far more likely to come from it actually existing than any other possibility. Is there a chance we're all wrong (or that you're hallucinating the rest of us, etc.)? Of course. There always is. If someone demands proof that it exists, they will be disappointed - there is no such thing as irrefutable truth. Not even "a priori" logic - not only could you be mistaken, but additionally your thoughts are physical, empirical phenomena, so you can't take their existence as granted while denying the physical world the same status.
If anyone really truly believes that the empirical world doesn't exist, you haven't heard from them. They might believe that they believed it, but to truly believe that it doesn't exist, or even simply that we have no evidence either way and it's therefore a tossup, they won't bother arguing about it (it's as likely to cause harm as good). They'll pick their actions completely at random, and probably die because "eat" never came up on their list. If anyone truly thinks that the status of the physical world is questionable, as a serious position, I'd like to meet them. I'd also like to get them help, because they are clinically insane (that's what we call people who can't connect to reality on some level).
Basically, the whole discussion is moot. There is no reason for me to deny the existence of what I see, nor for you to do so, nor anyone else having the discussion. Reality exists, and that is true, whether or not you can argue a rock into believing it. I don't care what rocks, or neutral judges, or anyone like that believes. I care about what I believe and what other humans and human-like things believe. That's why philosophy in that manner is worthless - it's all about argumentation, persuasion, and social rules, not about seeking truth.
Your argument is about as valid as "Take it on faith". Unless appealing to pragmatism, your argument is circular in using the belief of others when you can't justifiably assume their existence. Second, your argument is irrational in that it appeals to "Everybody believes X" to support X. Thirdly, a source claiming X to be so is only evidence for X being so if you have reason to consider the source reliable.
You are also mixing up "epistemic order" with "empirical order", to frame two new concepts. "Epistemic orde...
I have naturally read the material here, but am still not sure how to act on two questions.
1: I've been arguing out the question of Foundationalism v.s Coherentism v.s other similiarly basic methods of justifying knowledge (e.g. infinitism, pragmatism). The discussion left off with two problems for Foundationalism.
a: The Evil Demon argument, particularly the problem of memory. When following any piece of reason, an Evil Demon could theoretically fool my reason into thinking that it had reasoned correctly when it hadn't, or fool my memory into thinking I'd reasoned properly before with reasoning I'd never done. Since a Foundationalist either is a weak Foundationalist (and runs into severe problems) or must discard all but self-evident and incorrigible assumptions (of which memory is not one), I'm stuffed.
(Then again, it has been argued, if a Coherentist were decieved by an evil demon they could be decieved into thinking data coheres when it doesn't. Since their belief rests upon the assumption that their beliefs cohere, should they not discard if they can't know if it coheres or not? The seems to cohere formulation has it's own problem)
b: Even if that's discarded, there is still the problem of how Strong Foundationalist beliefs are justified within a Strong Foundationalist system. Strong Foundationalism is neither self-evident nor incorrigible, after all.
I know myself well enough to know I have an unusually strong (even for a non-rationalist) irrational emotive bias in favour of Foundationalism, and even I begin to suspect I've lost the argument (though some people arguing on my side would disagree). Just to confirm, though- have I lost? What should I do now, either way?
2: What to say on the question of skepticism (on which so far I've technically said nothing)? If I remember correctly Elizier has spoken of philosophy as how to act in the world, but I'm arguing with somebody who maintains as an axiom that the purpose of Philosophy is to find truth, whether useful or useless, in whatever area is under discussion.
3: Finally, how do I speak intelligently on the Contextualist v.s Invariantist problem? I can see in basic that it is an empirical problem and therefore not part of abstract philosophy, but that isn't the same thing as having an answer. It would be good to know where to look up enough neuroscience to at least make an intelligent contribution to the discussion.