You have a very classical-philosophy kind of tone and seem to be following a very similar line to thinking to a few 17th century philosophers I've read, but you run into the same problem as they did:
You speak so highly of knowledge being from physical experience in order to separate yourself from the irregularities of mental experience, but in doing so you functionally ignore mathematics, logic, and all other a priori studies.
Returning to an earlier example, imaginary numbers clearly cannot be said "properly" exist, but they can be used to reproduce exactly the behavior of harmonic oscillators across a number of physical forms. If I calculate a resonance pattern, is that merely "conjecture"? Mathematics has proven itself far too disciplined and concrete in its conclusions to accept that kind of demotion-- if anything, mathematics is truer than human senses.
Something is true or not as it properly represents some aspect of reality. Reality is the final arbiter. If you want to know if something is true, you ask reality, not your mind or mathematics. This is central to science of any kind. You create a theory or an hypothesis and then where do you go to find out if it is true? Reality. That what testing is for.
Non-contradiction is the proper principle to integrate concepts because things in nature do not contradict themselves. If your math or your logic contradicts reality then they are wrong, not the basis of thought, but the conclusions you come to with the fundamentals we all must use, or the improper use of reason and logic. I do not ignore the fundamentals of these as you do. You are finding contradiction in advanced particle physics and improperly ascribing it to the universe as a whole and other parts that are not at the limits of our perception.
You accuse me of being classical. You're skipping over philosophy and science 101. One doesn't look at reality and ask their mind or math if it is true. One does your math and then asks reality if it is true. The existence of entities that we perceive are more real than some arbitrary abstract concept. I can draw and 8 on its side and call it forever and that is not more true than something I can perceive and repeatedly demonstrate. As if a negative amount of apples could actual exist.
Mathematics is a mental construct that depends on existence existing and a consciousness to perceive identity. Without this process, there would be no math. A brain during its early years must perceive a thing and then another in order to build the concept of the number two. If existence did not surely exist, we could not have brains and if we did not have brains we could not perceive patterns of perceptual stimuli and form objective concepts, like the number 2, from them. The concept of two could not exist without first existence existing and then subsequently there being a consciousness to perceive some aspects of reality, and then two aspects.
That an abstract concept is useful practically does not mean that it exists as an existent. An imaginary number only represent a relationship between things interacting in a complex fashion. No concept could exist without the physical world. Concepts are formed from perception, which again, necessitates something with a particular identity to be observed, something that is, for sure, some things and not others.
Math, science and logic come from our ability to form, store, compare and contrast different patterns of patterns of perceptual stimuli. They all require, assume and presume a real world that exists, for sure, and behaves in a certain way, for sure. It is wrong to then attempt to use these things to state that the world isn't necessarily there. That really is preposterous.
I am not attempting to separate myself from the irregularities of mental experience. As if that makes any sense. You're a platonic mystic. Knowledge comes from the real world, not some ethereal mental realm. There is one source of knowledge and that is the noncontradictory integration of perceptual evidence. First, the world, then the brain and then knowledge. Knowledge, by the brain, of the world and only the world.
Ah, I see that we may have been discussing contradiction in two different ways. I generally recognize it as logical compatibility, and hence my treatment of it as an a priori property. Your description is much closer to what I would call continuity, where physical structures cannot be discontinuous at macroscopic scales but mental structures often are. If that's the case, then I would agree with your a posteriori usage.
But you missed the next point: humans look at reality and ask philosophy if it is true; they ask math what it could become; and they ask science if they covered everything. It's definitely not common for people to assume everything they see is absolutely true, especially since psychology has done a good job of demonstrating that our minds lie about that kind of stuff.
And could you explain to me where exactly in the axioms of mathematics it states that physical existence and human perceptions are necessary for math to be meaningful? It's quite the opposite, actually, as the basic nature of a priori knowledge is that it can (and must) be determined in systems as a prerequisite for containing data.
This necessarily means that the entirety of all a priori knowledge was accessible prior to the birth of the universe (though there would have been no sentient beings to actually learn it).
Do not mistake the sequences of mental function for the sequence of knowledge itself. The two do not match, so it's critical to distinguish between them when describing the physical world.
Math and Logic function regardless of any existence, so they don't fit your conclusion (they're a priori methods, again). Science does not actually require a 'real world', it only requires a predictable world. That exact point has been covered historically with the conclusion that the whole universe could be an illusion-- but so long as the illusion follows uniform laws of action it can still be explored by scientific means. So while our existence is generally assumed for simplicity, it's by no means required or justified by science.
Look, I'm not even arguing my own points on this. These issues have been discussed at great length by many of the most accomplished thinkers in the past 400 years and they've covered just about every significant line of thought on the matter. Your epistemology is too narrow for reasons that were beat to death in the 17th century when the Empiricists tried it.
Or in the reverse, I can exactly reproduce everything contained within your framework and then surpass it with equally solid analysis of the structure and operation of the mind; the origin of the universe; and the interrelation between physics, biology, and social behaviors. At no point am I confounded by 'preposterous' or 'unthinkable' but nevertheless persistent concepts or phenomena because I built my framework upon a demonstrably complete epistemology.
I'm not saying you have to agree with or adopt my framework, but if you won't even strive to match that level of sophistication then your approach is a non-contender. I'm pushing at the areas you haven't covered as philosophic encouragement, but there's a certain point where a dogmatic refusal to advance your ideas is just an intellectual dead-end. We're slowly covering more of the grounding for your current framework, but unless you actually present the argument from first principles then this kind of horizontal shifting is pointless.
So make a choice: lay your ante on specific points where you may take a loss, present your core framework as a stand-alone argument, try expanding your framework with new ideas, or we're done here.
The whole universe an illusion? Come on. Like the sunrise maybe, but the Sun and Earth exist, while we may not have understood their proper orientation, suggesting that the Sun, the Earth or the universe may not exist is ridiculous.
If you expect me to think you have any idea what you are talking about when you can't even acknowledge that the universe definitely exists or that it is impossible for trees to rollerblade, you're mistaken. Science existing without human consciousness? Preposterous. You've thrown the baby out with the bath water. Or more concretely, you ignore what you learned as a child and deny what you implicitly know and must to even form a sentence, for favor of phantasmagorical postmodern confabulation.
"And could you explain to me where exactly in the axioms of mathematics it states that physical existence and human perceptions are necessary for math to be meaningful?"
-Meaning entails a human having a goal and there being some relevance to that. Only a human can ascribe meaning to something. I don't need an understanding of axioms to know that there is no meaning without consciousness and before life on Earth, there was no consciousness, no meaning, no math and no science. These are human activities that depend on the brain recognizing entities with identity and storing these distinct patterns of perceptual stimulation into concepts and further organizing them into contextually valid knowledge when they can be reduced to perceptual evidence without logical contradiction. No fancy pattern of neo-logic can show that this process is not valid because it is the process of validation.
You have no means of fundamentally proving that your mental perceptions are a literal and complete representation of the things external to you as the 'real world' could be any combination of factors which result in those perceptions.
One illustrative example is a metaphorical demon which feeds you an illusory 'virtual reality' meant to deceive you into thinking it's a real world (yes, The Matrix ripped off some past philosopher's musings). As your only proof is the mental perceptions themselves, you cannot prove the 'real world' you perceive actually exists without circular reasoning. That's where DesCartes came in with his "Cogito ergo sum" line of argument.
Don't misconstrue 'meaningful'. If mathematical analysis does not require physical experience beyond the 'fuel' we used to perform the mental operations, then mathematical knowledge remains valid regardless of the presence or absence of humans or their experiences.
Again, this is textbook material. You don't have to agree with the historical conclusions, but you do have to acknowledge and respond to the arguments they introduce.
Where have you found suggestion of First Cause ideas in my statements? No, I argued exactly against that concept in favor of an Uncause, or the very idea that causality is incomplete (thus eliminating the recursion that spawned the First Cause sentiment).
All of your 'impossible' examples are showing a consistent pattern: You mention an analytic a posteriori Identity of some form (I'll call mine "Bob"), then proceed to describe synthetic a posteriori interactions which are incompatible with that Identity (like Bob stealing ice cream from a kid). But it's all farcical Straw Men because I'm saying that you're ignoring a priori knowledge and you're countering with a posteriori anecdotes.
All discussion of the pre-temporal universe-in-potentia are a priori in nature, so they're obviously not based on a posteriori methods. We're not arguing on that point. The issue I see is that you will not acknowledge a priori methods such as mathematics and logic for the analytical tools they are, so you remain certain that we have no such tools.
Your whole "cognition necessarily requires both non-contradiction and causality" argument should be properly presented in a separate thread in the Philosophy forum. It does little good to keep dancing around it here without the full argument to deconstruct. If you can provide an air-tight argument that these are "necessary axioms" then you could have a real impact on other's thinking, but it won't do anything to spout conclusions without the supporting logic.
But you're consistently misreading my suggestions towards self-reflection and such as attacks on your personal identity. Disregard that, because it's not what I'm doing. I've been trying to convey professionally-focused advice for refining your presentation and verifying the soundness of your arguments. In the above paragraph, I'm being about as direct with it as possible: write it all out so we can actually discuss it, and maybe in a fresh thread. This 'arguing on many fronts' style simply won't work if we don't resolve the fundamental issues first.
"The entire universe carries the structural imprints of its origin,"
-Does this not imply a first cause? The universe carries the structural imprints of causality maybe, not a beginning.
Dividing knowledge into a priori and a posteriori is not uselful here, imo. Both must be programmed from perception to begin with. Without reality existing, perception existing and conceptualization existing first, neither a priori or posteriori could be. Discussions about pre-temporal anything are not about knowledge about the real world. They are not a priori or a posteriori, they are simply irrational. I clearly acknowledge the use of math and logic, just not to invalidate the axioms that allow them to be in the first place. Math and logic depend on existence existing and a consciousness being aware of a things with identity.
I should not have to deconstruct this any more than I have. Maybe you are not getting the fundamental nature of identity. For something to exist, it must be somethings and not others. You know this already implicitly. You have enough information to know it explicitly. It must stand out from other things around it, for us to perceive it. When a brain is first presented with reality, it must perceive things with identity, to recognize them. And when a human can couple a things structure to its behavior, they have grasped, implicitly, the corollary of identity that is causality. You implicitly grasp that things do only what is dictated by their structure and momentum. You now have enough knowledge to know this explicitly. Example, balls roll, books slide. The implicit recognition of the fact that the universe works this way is what allows us to group things according to their essential similarities and form a concept after we discard their arbitrary differences. If a balloon filled with helium could go up or down in this atmosphere, when let go, we could not recognize the essential elements of helium and balloons and atmosphere and nothing of what we see would make enough sense to form concepts, let alone debate the truth of them. And since we are debating them, existence must exist, for if it didn't we would not be members of Atheist Nexus. And you, sir, keep avoiding, the inevitable conclusion of your assertions which is that it is possible that we are not now members or that the impossible is possible.
"I've been trying to convey professionally-focused advice for refining your presentation and verifying the soundness of your arguments."
-By telling me I'm biased by my own position?