Transcendental Knowledge?

[Mudhammam]

...The fact that mathematics break down in the case of Singularities, however, casts doubt in my mind that even mathematics, though accurately descriptive about the reality within which our brains evolved to take advantage of, itself can be said to contain explanatory power, or necessary truths, about more fundamental levels of reality.

If that is indeed a fact then all bets are off and the very possibility of knowledge is in question, yes?

The very possibility of knowledge, with regards to certain facets of existence, as intelligibly formulated in the craniums of a certain ungrateful biped, I'm afraid so.

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...I have no idea what the hell you just said. I think I'd rather read the wall of text.

Seriously, can't people whose regularly employed vocabulary contains words such as "transcendental" be clear about anything?

I would recommend reading The Critique of Pure Reason, though I fear you might not get too far... (it's a genuinely difficult book to comprehend, but then when we're dealing with concepts attempting to cut through the very heart of conceptual understanding, we shouldn't expect it to be anything but challenging).

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What certain reasons?

Just to press the issue, as we may not actually disagree, allow me to suggest for starters:
Law of Identity
Law of Noncontradiction
And perhaps those that I already quoted

"two straight lines do not enclose a space.--Nothing happens without a cause.--3x7=21.--Matter can neither come into existence or pass way."

In the meantime......

Before, or even -in the absence of- is not "hence apart", at least insofar as I take the phrase. Let me explain this in an amusing way. Say I went back to the DOD with a proposal for an invisible attack helicopter. DOD says "great just show us some field trials." -So, being the enterprising soul that I am I haul my bird down to Benning and put it in front of 200 blind men, beat my chest and say "ha- success, now pay me!". I can't see it, or you can't see it, does not mean that it cannot be seen - that it is "apart". I don't think that sight even requires intelligibility or reason- in it's purest and simplest description. Any photoreactive cell can "see" - regardless of anything resembling intelligibility or reason.

Specific to sight, we needn't assume that anything about what makes sight possible were true before "we" came along to see it. The nature of light is such that if it were different at some point in the frame of reference before human eyes (and before reason or intelligibility) there would be a shitload of ways to detect that. Is it possible that light could behave differently than it does now? I don't know. Did it, at some point in the past here on this planet? No, and that's not an assumption. But suppose we didn't have that knowledge, would that assumption be required in order to do work? I don't see why. Seems like a cart and horse issue. We don't have to assume that such and such were true to give rise to the senses. We can propose that the senses are evidence that such and such was true at least by the time the senses arose (no mention of whatever came before). Or we could propose that such and such was not true before sense arose (plenty of ways to structure a claim along these lines)...but why would we propose that, and would it stand up to scrutiny?

I may have misunderstood the question, I'm sure a list of those certain reasons that must be assumed will clear it up though.

Invoking something "apart from the senses" invokes something wholly not in experience, and "inexperiencable". Something different than what we have here before us. Since logic arises out of our observations of how this place here, before us, appears to behave, and how we can feasibly conceptualize those relationships within that frame of reference, anything "apart from the senses" in principle is something apart from any reasonable expectation that logic applies. This whole "reasoning about that which is apart from the senses" is a shell game, imo. A person who puts it forward is going to appeal to their senses anyway - they just don't want to handle criticism that arises from sense experience.

"Why can't I see it, taste it, hear it, touch it, feel it, or smell it?"
-"oh, that's because it's -apart from sense-"
"Ah, I see, then shut your mouth, because you know nothing about it and -can know- nothing about it."

The examples I gave above are not discernible by sense; in fact, sense perception is only possible in light of their (even if unformulated) immutable a priori truth about our experienced reality, which we only know by understanding (which is why it's called transcendental knowledge).