Transcendental Knowledge?

[Neo-Scholastic]

Then I challenge you to invent your own personal form of mathematics.

It is done all the time by mathematicians. Create some axioms, some rules of inference, and boom! new formal system with new theorems and new truths.

All those do is place limits on what mathematical truths can be drawn from those specific limitations. They have no effect on mathematical truths as a whole.

[Chas]

It is done all the time by mathematicians. Create some axioms, some rules of inference, and boom! new formal system with new theorems and new truths.

All those do is place limits on what mathematical truths can be drawn from those specific limitations. They have no effect on mathematical truths as a whole.

There is no "mathematical truths as a whole". That is an incoherent concept.

There are only truths within formal systems.

[Mudhammam]

Just because we only know the world by means of the senses does not mean that you cannot reason about the parts of reality that exist apart from the senses. Form this process someone can know of real things that exist apart from particular knowing subjects. For example, the truthes of mathematics are discovered, not invented. They are necessary truths that do not depend on a knowing subject for their validity. Secondly, perceptions are contingent upon the existence of an independent perceiver. The perceiver must exist prior to its perceptions, unless you posit a perfectly self-perceptive preciever ;-) or a real unifying and insensate principle that binds experiences into identifiable knowing subjects.

Necessarily true as in a transcendental truth?
I take that to mean that true mathematical statements are necessarily true insofar as they relate to certain dimensions of space (three, for sure, I don't know a damn about 11-dimensions) and change that is successive (as in time)... because anything else is simply inconceivable to me. 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.

Is it true that the object of consciousness ceases to exist apart from a knowing subject? Again I would refer to the truths of mathematics whose objects are immaterial and thus can be known by the intellect apart from any particular sensible form.

I would agree. I'm not sure if idealists would suggest that objects of consciousness wholly cease to exist apart from a knowing subject, only that they're existence as subjectively perceived would cease to be...leaving something analogous to objects, that is, completely unknown, in a state of infinite potentiality? Again, I'm a bit unclear as to what Idealists think exists outside of perception (there seems to be different strains or degrees of idealism).

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Ignoring the wall of text and focusing on the thread title, there's no such thing as "transcendental knowledge" (or "transcendental" anything, really, but that will become obvious in a second).
"Transcendental" means that it transcends everything. Your thread title literally means "Knowledge that transcends knowledge". This is nonsensical.

It means (forgive my repeated quotations), a judgement that "rests not merely on experience but on the conditions of the entire possibility of experience which lie within us. For the judgement is determined precisely by that which determines experience itself, that is either by the forms of space and time intuitively perceived by us a priori, or by the law of causality known to us a priori. Examples of such judgments are propositions such as: two straight lines do not enclose a space.--Nothing happens without a cause.--3x7=21.--Matter can neither come into existence or pass way." They transcend knowledge only in the sense that (according to this author) they're truths (like logical axioms) that exist independent of experience, are required for experience, and we have an intuitive understanding of them (on which empirically true statements depend).

Da fuck is going on with my quotes?
Edit: fixed.

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Just because we only know the world by means of the senses does not mean that you cannot reason about the parts of reality that exist apart from the senses.

Good luck with "reasoning" about anything that exists "apart from the senses" - care to explain how this is even possible? Why would you assume that reason even applies to things "apart from the senses" even if there were such things in this category in principle...and how have you determined that there are?

Yet it seems we must assume that certain reasons are unconditionally true when describing the nature of reality as it existed before (and hence, apart) from the senses, in order to give rise to the senses (which, in turn, discovered or gave intelligibility to the reasons). No?

[Neo-Scholastic]

...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?[/quote]

[The Grand Nudger]

Yet it seems we must assume that certain reasons are unconditionally true when describing the nature of reality as it existed before (and hence, apart) from the senses, in order to give rise to the senses (which, in turn, discovered or gave intelligibility to the reasons). No?

What certain reasons? 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."

[One Above All]

It means (forgive my repeated quotations), a judgement that "rests not merely on experience but on the conditions of the entire possibility of experience which lie within us. For the judgement is determined precisely by that which determines experience itself, that is either by the forms of space and time intuitively perceived by us a priori, or by the law of causality known to us a priori. Examples of such judgments are propositions such as: two straight lines do not enclose a space.--Nothing happens without a cause.--3x7=21.--Matter can neither come into existence or pass way." They transcend knowledge only in the sense that (according to this author) they're truths (like logical axioms) that exist independent of experience, are required for experience, and we have an intuitive understanding of them (on which empirically true statements depend).

...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?

[Neo-Scholastic]

...something "apart from the senses" invokes something wholly not in experience, and "inexperiencable".

As for me "apart from the senses" applies the Aristotelian concept that forms and propositions do exist and are real, not in their own realm, but immanently across multiple manifestations. They are immaterial in the sense that they do not depend on any particular material to instantiate, i.e. a wooden triangle and a pencil sketch of three joined and straight lines, both partake of the form of triangularity. Likewise, there is a common meaning to "I am." and "Je le suis" even though the form of the proposition is entirely different. In both cases you do not directly perceive the forms or propositions as objects of sense; but rather the objects of sense allow you to know the existence of the forms and propositions.

[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).

[The Grand Nudger]

Identity - absolutely discernible by sense and in fact rooted in sense. How do you know that the law of identity is true, give me an example?

Non-contra..same as above. If I say that something is flying, and you say that it is not - we will be able to determine this by sense, and we will be able to determine that it is not both - and cannot be both, simultaneously, again by sense. Without sense, sure, why couldn't something be flying and not flying simultaneously? How would we know, and how would we know that it;s a problem to conceive of things this way?

(You aren't going to find a single logical statement that you won't be able to apply sense to, because that's how we figured out what the laws of logic were in the first place..using our senses to parse statements. There is absolutely no removing reason from sense, it's built out of it and depends upon it.)

Nevertheless, "sense perception" is not dependent upon those principles, our being able to use reason is dependent upon those principles (and as above, reason is derived from our "sense perception"). If some other universe behaved in some other way you're telling me that you think that sense perception would be impossible in that universe? Rather than, idk..just different?

[Mudhammam]

Identity - absolutely discernible by sense and in fact rooted in sense. How do you know that the law of identity is true, give me an example?

Non-contra..same as above. If I say that something is flying, and you say that it is not - we will be able to determine this by sense.

I only know they are true because all thought, including the individuation of percepts by means of concepts, is conditioned on their being true. Can any sensible experience violate these laws? If not, aren't these laws prerequisite for sense, and hence, sense rooted in them rather than vice versa?