Kant-the five senses and noumena

Reply to Arthur Rupel

Kant discusses sensory perception from one and only one context.....the possibility of, and the theoretical conditions for, empirical knowledge.

Kant uses three pages to say how and why noumena are logically possible, followed by two pages on how and why noumena can never be of any use to the human rational or moral agent.

If you’re studying Kantian philosophy seriously you’ll need to understand what he says about them; if you’re not....forget noumena. They have no place in intuitive metaphysics. It follows necessarily from that, that Quoting Arthur Rupel

"representation" or "appearance" of phenomena from noumena

is unintelligible. There ain’t no such thing.

From what I understand noumena is the external reality, "the real of the "real." We can never have knowledge of noumena. You are right, we have no use to us other than it is the external reality upon which our reality is based. We can never have an appearance from nothing. It must come from something (Kant's statement) and that something is the "thing in itself," one view of noumena.

The question then is how do we get phenomena from noumena. It must first be given by senation (Kant's word).

Ref:MWR Can you please advise where these pages are.

Thanks

Quoting Arthur Rupel

Or does he discuss sensory perception from another context.?

The entire 'Transcendental Aesthetic' in the CPR is more or less dedicated to the question of sensory perception, which Kant generally groups under the name of 'sensibility' more broadly. A20/B34 lays out the broad strokes of how sensation figures in the architectonic:

"The capacity (receptivity) for receiving representations through the mode in which we are affected by objects, is entitled sensibility. Objects are given to us by means of sensibility, and it alone yields us intuitions; they are thought through the understanding, and from the understanding arise concepts. ... The effect of an object upon the faculty of representation, so far as we are affected by it, is sensation. That intuition which is in relation to the object through sensation, is entitled empirical. The undetermined object of an empirical intuition is entitled appearance."

Importantly, for Kant, sensibility involves both what he calls 'matter' and 'form'. 'Form' involves the a priori conditions of space and time, while 'matter' involves 'sensation in general':

"That in the appearance which corresponds to sensation I term its matter; but that which so determines the manifold of appearance that it allows of being ordered in certain relations, I term the form of appearance. That in which alone the sensations can be posited and ordered in a certain form, cannot itself be sensation; and therefore, while the matter of all appearance is given to us a posteriori only, its form must lie ready for the sensations a priori in the mind, and so must allow of being considered apart from all sensation." (A20/B34).

"Space and time are its [intuition's] pure forms, and sensation in general its matter. The former alone can we know a priori, that is, prior to all actual perception; and such knowledge is therefore called pure intuition. The latter is that in our knowledge which leads to its being called a posteriori knowledge, that is, empirical intuition. The former inhere in our sensibility with absolute necessity, no matter of what kind our sensations may be; the latter can exist in varying modes" (A43/B60).

So yeah, read the 'Transcendental Aesthetic' carefully, and you might find what you're looking for. There's alot there regarding the status of appearance, representation, and what can be known, especially in the bit titled "General Observations on Transcendental Aesthetic", (A42/B59).

Quoting StreetlightX

Importantly, for Kant, sensibility involves both what he calls 'matter' and 'form'. 'Form' involves the a priori conditions of space and time, while 'matter' involves 'sensation in general':

do you think there's an echo of A-T hylomorphic dualism here? Do you happen to know if this a question which has been explored?

Reply to Wayfarer I don't think it would be unfair to say that hylomorphism informs Kantian philosophy from end-to-end: “Matter and Form - These are two concepts which lie at the basis of all other reflection, so very inseparably are they bound up with the use of the understanding. (A 266/B 322)." The key difference is that Kant's hylomorphism is 'transcendental', rather than ontological: Kant shifts 'form' from the things themselves (as it were), to the human subject: it is the subject which in-forms the possible objects of knowledge and judgement, and indeed, makes them "possible objects" at all to begin with.

Reply to StreetlightX :ok:

Quoting Arthur Rupel

From what I understand noumena is the external reality, "the real of the "real." We can never have knowledge of noumena. You are right, we have no use to us other than it is the external reality upon which our reality is based.

Sorry, Arthur, but this understanding is self-contradictory. If noumena were the external reality then it would be of use to us necessarily. Noumena are not that which our reality is based, that being the thing-in-itself, which is the real empirical object that affects our sensibility. This understanding highlights a common misinterpretation, in as much as because no knowledge of two disparate conceptions is at all possible, those two conceptions are the same.
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Quoting Arthur Rupel

We can never have an appearance from nothing. It must come from something (Kant's statement)

.......

This is correct, as shown here: “...For, otherwise, we should require to affirm the existence of an appearance, without something that appears—which would be absurd....”. In other words, there are real objects external to us. That’s all he is saying. Kant was, after all, an empirical realist.

......Quoting Arthur Rupel

and that something is the "thing in itself,"

......

Only in the most liberal interpretations. When you’re talking about Kantian reason, all you can talk about is that which is internal in us, and nothing whatsoever concerning that which is external to us, except for the fact that’s its there. It follows that appearance is not so much the thing-in-itself, which is external, but that which is passed on from perception, which is internal. Thus, appearance, in and of itself, simply stands for that “something” that has caused perception to react to an affectation on it.

Properly speaking, the “thing-in-itself” is a term of knowledge, not of cognition. Think of counting to ten in the most logical way, in which you start at one. If knowledge is the ten, then the affect on perception is the one. At one, the “thing-in-itself” has no meaning. At ten, what we know is what reason has told us, and reason only tells us anything, by means of itself. That which affected our senses, that which appeared to us, tells us nothing at all about itself, other than it is there. In effect, what we know, is a determination from appearances alone, if for no other reason than that’s how the human cognitive system works. Which of course, has always begged the question.....what tells us what we know from appearance is not exactly the same as what we would know about the thing that appeared. Such may indeed be the case, but in this particular speculative metaphysics, if reason is the source of knowledge, the thing-in-itself cannot be, because if we had two sources we would have no means to determine which was correct in the event of a conflict between them.
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.......Quoting Arthur Rupel

one view of noumena.

Yeah, I suppose it could be one view, but it most certainly is not Kant’s view. One of the greatest feats of Kantian theoretical epistemology is its completeness, meaning that guy had an answer for every-damn-thing. Well, if there are only two possible sources of knowledge, knowledge of the empirically real and knowledge of the rationally thought, and if the “thing-in-itself” is proved to be a limitation on the former, then there absolutely must be a limitation on the latter, if only for the sake of logical consistency. Empirical knowledge is derived from sensibility, rational knowledge is derived from the understanding. Therefore, that which limits rational (a priori) knowledge must be a limit on understanding. Kant limits the faculty of understanding by positing its pure conceptions, called categories, can only be applied to phenomena, which, from the above, are shown to come from the faculty of intuition. But noumena are merely thought in general a priori, which means they have no object of intuition to represent them, which means the categories cannot be applied to them, which means we can have no cognition of them, hence they are meaningless. But......what are they, if they can be thought? We can’t say. We could say, if we had a mode of non-empirically grounded intuition to which the categories could be applied, but we don’t, so understanding is brought up short. He goes on to grant the possibility of “intellectual” intuitions, but nonetheless, the categories still couldn’t synthesize a mere intellectual object into either an empirical or rational cognition without devolving the entire system into an irreconcilable inconsistency.

All this because of the common misunderstanding, that because both the thing-in-itself and noumena are unknowable, they are the same thing. They are very far from the same thing, and even though Kant himself confuses everybody by actually calling them out identically, within the context of his doing that, he does not mean them to be the same thing. Thought of the same way, perhaps, but never thought of as being the same thing.

So.......Quoting Arthur Rupel

how do we get phenomena from noumena.

By having a faculty of intuition other than the one we actually have, which makes explicit....we don’t.

“......But if we understand by it an object of a non-sensuous intuition, we in this case assume a peculiar mode of intuition, an intellectual intuition, to wit, which does not, however, belong to us, of the very possibility of which we have no notion—and this is a noumenon in the positive sense of the term. The doctrine of sensibility is also the doctrine of noumena in the negative sense, that is, of things which the understanding is obliged to cogitate apart from any relation to our mode of intuition, consequently not as mere phenomena....”

Print reference: CPR, B307, 1787, in Meiklejohn, 1855, B307 slightly re-worded in Kemp Smith, 1929, but irrespective of translator, Sec I, First Division, Book II, Chapter III.

Good luck and have fun with it.

Ref : Mww
Thanks for your response. What I am exploring is how "real" is quantum field theory."

Kant seems to give a low priority to sensation stating that it is meaningless without the apriori concepts of space and time.

But there is one thing that I am confused about.

The only bridge there is between us and noumena is sensation. There must be an implicit order given given by noumena to sensation, otherwise even the unity of sensation with the apriori concepts could never give meaning

Since this order already comes peep prepackaged with sensation, we can, as with noumena, never be aware of it. Only that it is there.

All this says simply that the real external world has order and structure. Sensation and this "inherited' order come to us already prepackaged.

As an analogy: we are given a book of numbers. If the listing of numbers is random, we can never make sense of it. If the listing of numbers have order to it, we can create our own order from it.

As an aside: Kant states that space and time are apriori concepts that make sense of sensation.
Judging how space and time are handled in quantum field theory, Kant may have a point. We can speculate that the mathematics of quantum field theory are like sensations and it is only with our apriori concepts of space and time that we can make sense of them. Space and time have no external reality within quantum field theory.

This user has been deleted and all their posts removed.

I believe, and this may be only my opinion, that noumena is what exists when we are not. Deprive all perception from an object or eliminate, a more extreme example, all conscious life from the universe and a universe will still exist, a noumenal universe beyond any possibility of our ever perceiving it.

Why? Because "our world" depends upon perception. The universe exists without any perception of i and we will never of any idea of what it is.

Quoting Arthur Rupel

The only bridge there is between us and noumena is sensation.

If you think that is the case, I have no problem with it; a guy can think whatever he likes. In keeping with the title of the thread, I will insist such thinking is unjustified, because according to Kant, if there were such a thing as a bridge between us and noumena, implying some methodology for the thinking subject (us) to connect to noumena, it would be the function of understanding, not sensation. But there is no such connection, so the notion of a bridge is moot.
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Quoting Arthur Rupel

Kant seems to give a low priority to sensation

You could say Kant gives low priority to sensation, but he actually means to give low priority to perception. Perception is passive; it is the affect on its respective organs. What that affect is, is called sensation. It’s like a sieve, perception is on one side, the organs are the sieve, and sensation is on the other side. Sensation gives appearance to perception, perception cannot give appearance to itself. Minor point, to be sure. Either way, it is correct that perception/sensation is meaningless without the a priori conceptions of space and time.
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Quoting Arthur Rupel

There must be an implicit order given given by noumena to sensation, otherwise even the unity of sensation with the apriori concepts could never give meaning

Again, think what you like, but this isn’t the Kantian system. In it, sensation doesn’t unite with anything, and the a priori concepts in intuition, space and time, are necessary conditions for the existence of objects for us, but do nothing to tell us what they are, so technically they don’t unite anything either, and certainly do not impart any meaning. The a priori conceptions that do tell us about objects, reside in understanding and are called categories.

Meaning is a judgement, and all judgement derives from the unity of phenomenon which resides in imagination with its concept which resides in understanding as schema. Sensation itself has long since become moot.
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Quoting Arthur Rupel

All this says simply that the real external world has order and structure. Sensation and this "inherited' order come to us already prepackaged.

Oh, you think so, huh? Well, riddle me this, Batman: with respect to humans at least....which we happen to be, coincidentally enough....if it is absolutely impossible to say anything whatsoever, without exception, about the world without first thinking about it....how can you tell the difference between the world having intrinsic structure and order, or structure and order being given to the world simply by the way it is thought in order for us to access its intelligibility?

The world may indeed have intrinsic structure and order, but as long as it is a human asking questions, it can never be proven with apodeitic certainty. The very best we will ever be able to do, currently, is find no contradiction between the world as it is and the way the world seems to us.

BOOM!!!!! (Grin)

AR,

Some Christian Existentialists' [including myself] would interpret noumena as a metaphysical construct. Meaning the idea of noumena is a force of energy that possibly exists outside the human mind. For example the nature of Christian Revelation [revelatory thoughts] and everyday knowledge/wisdom associated with our states of consciousness (Ontology/Epistemology).

How if effects our cognition could also be from a cosmological context. For instance, the nature of mathematical truth's appear to us a priori (without sensory experience). The how's and more importantly the why's of this phenomenon are the existential questions. Like why does mathematics/geometry exist? Is it independent and outside of our knowing it?

All we know is that it works, yet it's powerful and useful truth that exists without experience. In other words, no amount of sensory experience will change its truth value (2+2=4 never changes).

So my interpretation is that Kant's noumena would represent a metaphysical question to me: if noumena could somehow be the source of mathematical truth's why does it exist? Why does it describe the universe so well? And what would its nature be...?

Reply to Arthur Rupel Reread Kant. He talks about noumena in the positive sense and the negative sense ... which is confusing because we can only ever talk of such in the ‘negative’ sense, because there is no ‘noumena’ (which was his point).

It does sound confusing so it is common for people to misunderstand.

I agree that Kant does not say much about noumena and uses it in different ways.
However let's look at the main interpretation of noumena, "the thing in itself."

Strip all perceptions from an object and something still remains.
My only point is that this is not a gray nothingness but must have an existence external to us.

Unless we are willing to believe that all existence is in our minds, as the good Bishop Berkeley believed, we must postulate an external reality upon which our reality is based. Otherwise everything is in our minds.

My main point, is that there is a fundamental basis of reality which we can never be aware of but which is represented by perception and an implicit order in perception which is based upon an implicit order in noumena. This is beyond what is stated Critique but I believe it can be extrapolated from it.

Kant studies phenomena or what is human knowledge. What is not studied is what characteristiics noumena might have. This is a subject worth looking into.

One of the fundamental points about noumena is that it is absolutely separate from awareness.
In the terms of set theory the set of awareness (phenomena) is disjoint from the set of noumena (external truths), but there is a relationship between them which we will never know.
.

The original meaning of 'noumenon' is taken from the Platonic distinction between appearance and reality. Intelligible principles, such as geometric forms, were 'objects or reason', before they were 'objects of sense'; that was the original meaning of 'noumena'. In other words, mind (nous) grasps the concept of 'the triangle' independently of any particular triangle as it is a universal (and the same can be said for all manner of ideal objects) although that way of describing it is characteristic of later philosophy and was not explicit in Plato.

[quote=Wiki] The Greek word ???????o? nooúmenon (plural ???????? nooúmena) is the neuter middle-passive present participle of ????? noeîn "to think, to mean", which in turn originates from the word ???? noûs, an Attic contracted form of ???? nóos[a] "perception, understanding, mind."[3][4] [/quote]

So, in Platonic thought, generally, the 'noumenal' is related to 'the form', whilst the particular - this or that man, triangle, or whatever - is what is perceived by the senses (the 'sense-able'). So in Aristotelian dualism (preserved in scholastic philosophy), each act of perception combines the intellectual (noetic) perception of the form of the thing, with the sensory perception of the particular.

Now, interestingly, I think Kant inherited this idea, but changed it in specific ways. He doesn't endorse the reality of forms, per se - no 'ideal objects' in his schema - but nevertheless, as per the quote StreetlightX provided above.

That in the appearance which corresponds to sensation I term its matter; but that which so determines the manifold of appearance that it allows of being ordered in certain relations, I term the form of appearance. That in which alone the sensations can be posited and ordered in a certain form, cannot itself be sensation; and therefore, while the matter of all appearance is given to us a posteriori only, its form must lie ready for the sensations a priori in the mind, and so must allow of being considered apart from all sensation." (A20/B34).

The ordering grasp of sensation and perception is what allows us to perceive the world as 'a world' and is reliant on what is inherent in the faculty of the understanding. And that, according to the rationalist tradition of philosophy, is innate to the intelligence. Where Kant departed from that tradition was in the requirement that knowledge is equally informed by perception, hence his famous aphorism, 'percepts without concepts are blind, concepts without percepts are empty'.

Quoting Arthur Rupel

One of the fundamental points about noumena is that it is absolutely separate from awareness.

So in light of the above, I don't think this absolute distinction holds. It is really more a dualist philosophy.

....sure Auther, it's worth exploring the notion that all events must have a cause as it were.

I think metaphysics is enjoying a little resurgence. Quantum physics was not fully explored during Kant's time. Science has made the connection to the 'observed and observer' on a quantum level, where it has been declared an interactive phenomenon of hide and seek (and indeterminate change).

So one takeaway from say from an ethics point of view (how to live a happy life) , is that a new analogy relating to quantum states of consciousness has emerged in the form of the so-called ' law of attraction ' theory.

So yes, some things are worth exploring even on a less scientific level.

Noumena is a Greek word that is plural. Which is weird if one wanted to translate it as a place where other stuff happened or not. Maybe more than one thing is "noumena."

Chances are, this is one of those topics where people tend to accept terms at cross purposes.

Aurther, I failed to mention an important driving force behind one other metaphysical theory that may help. Theoretical Physicist Paul Davies has postulated that knowing the laws of physics (knowing mathematics) has no evolutionary advantage, only the manifestations of them do. It's a compelling case...

So maybe if Kant would have postulated a similar theory vis a vis his noumena, he too might have theorized same. Again, all of this kind of stuff is theretical but as you said worth exploring... .

Quoting 3017amen

Quantum physics was not fully explored during Kant's time

Could this be because it wasn't discovered until about 300 years after he died? Just sayin'.....

LOL, thanks Wayfarer, I officially stand corrected !!!! To this end, do you know to what extent there were any similar breakthroughs... ?

Reply to Arthur Rupel

Have at it.

Quoting 3017amen

LOL, thanks Wayfarer, I officially stand corrected !!!! To this end, do you know to what extent there were any similar breakthroughs... ?

Have a look at this page.

You:
Quoting Wayfarer

requirement that knowledge is equally informed by perception

Him:
“....In whatsoever mode, or by whatsoever means, our knowledge may relate to objects, it is at least quite clear that the only manner in which it immediately relates to them is by means of an intuition...”

I’m curious to know what you mean by equally informed. The apparent disparity in my understanding, between your position and his, might be removed if you could clarify how perception is an equal informant of knowledge, when Kant apparently doesn’t think so.

And this relates to your aphorism, where your use of “percepts”, re: Quoting Wayfarer

percepts without concepts are blind, concepts without percepts are empty'.

......in which “percepts” I must take to be short for perceptions because the alternative, precepts, is even more inconsistent with the more familiar aphorism found irrespective of translator in A52/B76:

Guyer/Wood, 1998: “...thoughts without content are empty, intuition without concepts, blind...”
Kemp Smith, 1929: “...thoughts without content are void, intuition without concepts are blind...”
Meiklejohn, 1855: “....thoughts without content are void; intuitions without conceptions, blind....”

Problem solved if you could refer me to the similar assertorial that uses percepts, so I could grasp the context, or, failing that, clarify what you intend by substituting your own terms. I mean......if percepts are indeed short for perception, then, if nothing else, “concepts without percepts are empty” is utterly false because there are certainly a priori conceptions, re: categories (i.e., quantity), with content intrinsic to them, re: schema (i.e., numbers), are therefore not empty but nevertheless have nothing whatsoever to do with sensibility in general nor perception in particular.

As I said.....curious. Not argumentative, or correctional.

Reply to Arthur Rupel

Here's a fun exercise. I'll first try some definitions and add assumptions. (“All A is C; all B is A; therefore, all B is C.” )

Noumena= partly mathematical secrets that define our existence & contains the laws of nature/theory of every-thing.

Mathematics= an objective truth (a priori) that presumably always existed, which does not necessarily confer any evolutionary advantage.

1. Mathematics is an a priori objective truth
2. Noumena transcends human phenomena but is considered an a priori objective truth (mathematics).
3. Therefore Noumena is...

I'm not sure I have that correct...but you can see that metaphysical statements usually won't produce any meaningful results just by their definition. So I suppose it begs maybe one question, how do we discover any-thing? What did Kant say about that?

Quoting Mww

As I said.....curious. Not argumentative, or correctional.

Very perceptive comment! All I can say is, that version that I quoted using the terms 'percepts and concepts' was the way I first learned about the idea. 'Percepts' is an unusual word, but I take it to be 'perception of sense-able objects'. The Web definition is 'an object of perception; something that is perceived.' I don't find it a problematic word.

The SEP entry on this subject gives this account:

Intuition and concepts … constitute the elements of all our cognition, so that neither concepts without intuition corresponding to them in some way nor intuition without concepts can yield a cognition. Thoughts without [intensional] content (Inhalt) are empty (leer), intuitions without concepts are blind (blind). It is, therefore, just as necessary to make the mind’s concepts sensible—that is, to add an object to them in intuition—as to make our intuitions understandable—that is, to bring them under concepts. These two powers, or capacities, cannot exchange their functions. The understanding can intuit nothing, the senses can think nothing. Only from their unification can cognition arise. (A50–51/B74–76)

I think if you had been deprived of sensory experience since birth, as it were, you would nevertheless not be able to form any kind of concept of what numbers, categories, and the like, mean, even if they are in some sense innate to the intellect. I think the intellect has to be 'primed' by experience, as it were.

I take Kant's critique here to mean that neither 'the rationalists' or 'the empiricists' are correct in their own right, and that cognition relies on and combines elements of both the rational categories, etc, and the sensible particulars that are only ever known by experience (a posteriori). This paragraph gives a good account of it.

Now, while we're on the subject, you might care to peruse this blog entry on Aristotelian-Thomist dualism. This is what caused my earlier question about the sense in which Kant's work is derived from earlier scholastic dualism. I find this particular passage both profound and intriguing, although it hasn't elicited much response here when I've mentioned it previously.

Quoting Wayfarer

Percepts' is an unusual word, but I take it to be 'perception of sense-able objects'.

Good. I couldn’t see it otherwise, myself, and agree it is not problematic in itself. Still, we are left with the fact “percepts” do not belong in the aphorism, if it is to remain true to the Kantian methodology. This becomes quite apparent in context, for the passage sets the groundwork for justifying both the distinction and inter-connectedness of disparate forms of logic, by showing the distinction and inter-connectedness of the faculties of intuition and conception in the aphorism, by their employment of them respectively.

And all that was set by the premise that, not so much that both idealists and empiricists were incorrect with their respective philosophies, but rather, they were insufficient, because neither could explain the universal necessity for, and reliability of, a priori knowledge. This is the whole raison d’etre for Kantian speculative metaphysics, aimed at Hume in particular as the foremost era-specific philosophical empiricist, and all dogmatic subjective-dominant philosophies in general, as the idealists. As this makes quite clear, Kantian epistemological dualism has little to do with the Augustine/Aquinas theological dualism system per se, which is entirely predicated on some transcendent reality.

Of course, Kant could not argue against theological dualism and retain professorial tenure or hope to be published. His work-around was to ground the dualistic nature of knowledge within the thinking subject himself, thus removing the transcendent from the participation in human reason. In effect, while granting the current idea of the god of his time, at the same time attributing the power of rational thought, and everything that arising from it, to man alone.

Not that you didn’t already know all that........
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Quoting Wayfarer

I find this particular passage both profound and intriguing, although it hasn't elicited much response here when I've mentioned it previously.

With respect to the passage itself, parts of which are still relevant, I would suspect it hasn’t garnered much support because philosophers since, have gone to great pains to separate form from substance, rather than maintain they are necessarily inseparable. Beginning with Descartes culminating in the paradigm-shift in Kant, all because of that little ol’ sump’n sump’n called mathematics. Gotta admit....against pure logic on the one hand and astrophysics/quantum reality on the other, old fashion theology doesn’t stand much of a chance.

Were philosophy able to do away once and for all with the dualisms of form and matter, substance and accident, essence and existence, it would for once be able to claim a result. Until then it'll remain the history of a sad failure.

Reply to StreetlightX

Yeah, maybe, but it can’t. Damn Mother Nature anyway......making us wee humans prone to tripping over its own metaphysical feet.

Reply to Mww Sure we can. There's lots out there that has. But humans are stupid for the most part and like sticking to the tried and tired ways. It would be nice to abolish 'nature' too while we're at it.

Reply to StreetlightX

Lots out there that has..... what.....figured out how to do away with those sets of dualisms? This presupposes lots out there realize there are dualisms to do away with. What else thinks like we do?

I dunno about stupid. Termites been here longer than we have, but while our caves and grass huts have become ostentatious high rises, their mounds are still just piles of dirt. And even if dolphins and orcas communicate to coerce sardines into becoming bait balls, none of them have been on an obscenely expensive guided tour of Paris.

From Terry Pinkard's book: German Philosophy 1760-1860

The distinction between “things-in-themselves” and “noumena” is tricky. The former are the things that are the unknowable sources of our sensible intuitions; the latter are concepts of the world as intelligible to reason alone, apart from any experience, and a rerepresentations of certain “wholes” or supersensible objects that traditional metaphysics thought could be grasped by reason alone. As such, noumena function as limiting concepts, as reminders and cautions about the impossibility of extending rational accounts of the world in ways that contradict the conditions under which those accounts can be given.

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