• What would Kant have made of non-Euclidan geomety?
    I don't think so. Einstein's model of the universe, for example, makes use of certain non-Euclidean geometries, but that doesn't mean the model is accurate. Astronomers don't know for certain whether the universe is Euclidean or non-Euclidean. — Thorongil
    What do you mean it doesn't mean the model is accurate? If that model makes certain predictions (such as light bending around massive objects) and we go out there and test that, and the test confirms the predictions of the model, in what sense is the model "not accurate"?

    You're missing the forest for the trees, or perhaps for what you regard as a few dead trees in the Kantian forest. Here is Schopenhauer, from which I derive the thought you quoted of me: — Thorongil
    I don't see how this part of Schopenhauer is relevant. I claim that Kant's way of deriving the phenomenon/noumenon distinction is not valid, though Plato's is. As Schopenhauer likes to say, the right conclusion, from the wrong premises ;)

    Time, space, and causality are not determinations of the thing in itself, but pertain only to its phenomenon, insofar as they are nothing but our cognitive forms.
    If space was real, then transcendental idealism cannot hold. Space must be a faculty of the mind and must be imposed by the mind, in order to be able to claim that the plurality found through (amongst others) space is not, in the end, real (just like space itself).

    So all the machinations of physics in both relativity and quantum mechanics - and certain aspects of quantum mechanics, such as the proposed loop quantum gravity theory which doesn't even have continuous space and has no time at all - must be accounted for by a transcendentally ideal philosophy.

    Now, my opinion, if I were to try to defend Kant, is that we must insist that our pure intuition is Euclidean, and even non-Euclidean geometry we represent based on our Euclidean geometry. I asked Moliere to show me the equivalent of the "sketching figures" which is the intuition we use with regards to coming up with Euclidean geometry when it comes to non-Euclidean. I don't think he, or anyone, will be able to. Indeed, if you think how we construct non-Euclidean geometry, we do so by analogy, from within Euclidean geometry. We look at the properties of geometric shapes on the 2D surface of a sphere which curves in the 3rd dimension and infer from that, by analogy, what it would mean for a 3D surface to curve in the 4th dimension (and further dimensions from there). Now, this non-Euclidean geometry is not revealed to us by our pure intuition - we deduce it by analogy and extrapolation based on our pure intuition. So Euclidean geometry remains synthetic a priori.

    What about non-Euclidean geometry? What is its mathematical status, if Euclidean geometry is synthetic a priori? Well, granted that we know that non-Euclidean geometry must always be at least locally Euclidean, and at any rate, non-Euclidean geometry always presupposes the Euclidean one in its derivation, then we know for sure that it cannot be synthetic a priori. So it must be either synthetic a posteriori, or analytic a priori. But non-Euclidean geometry isn't something that requires experience in order to be derived. Therefore it is a priori, and it must be analytic, built by analogy to Euclidean. This means that there is no grounding either in experience or in the forms of intuition for non-Euclidean geometry (except, as it were, by analogy).

    This is all fine and good, but notice what happened. Just like the dogmatists before Kant were led into metaphysical (or transcendental) illusions because they applied their concepts outside of the area of the phenomenon, so too this non-Euclidean geometry is a mathematical illusion that comes about when the concepts of Euclidean geometry are applied outside of their rightful realm of application, where they can be grounded in the form of the pure intuition. Because non-Euclidean geometry, according to Kant, is as you say, a fiction.

    The weird thing that begs for explanation though is, how come that this fiction is useful in predicting events in the real world? How come we can use this fiction to determine how a ray of light bends around the sun? (and I mean determine its exact path!) Is this use merely instrumental (as andrewk speculated here: https://www.physicsforums.com/threads/spacetime-doesnt-really-exist-does-it.487794/ )? If so, how come that it works - we would, by all means, not expect a fiction to tell us about reality. And if it's not merely instrumental, and it really describes the structure of empirical reality, how is this at all possible?

    If Kant warned about transcendental illusions, then it seems fair that a warning about mathematical illusions is also necessary. And what are all the physicists doing who have built entire explanatory frameworks based on these mathematical models? They claim to be describing the structure of empirical reality - how is it possible that such mathematics apply to the structure of empirical reality? There are also Euclidean models which can explain all that general relativity explains, the issue is just that they are more complex. So what is happening? Are we using what is convenient for faster calculation, and not what is most likely to describe the actual structure of reality? Or are we describing the actual structure of (empirical) reality?

    How does bending spacetime, or quantum entanglement, etc. cash out?

    Or, was Kant wrong, to begin with, in restricting the sphere of application of our concepts? And so, non-Euclidean geometry is derived from Euclidean (and there is nothing wrong with this) just as the metaphysical conclusions of dogmatists are derived from concepts that are extrapolated beyond possible experience, and there is nothing wrong with them?

    Other interesting material:
  • What would Kant have made of non-Euclidan geomety?
    ↪Moliere
    Thanks.
  • What would Kant have made of non-Euclidan geomety?
    Our expositions, consequently, teach the reality (i.e., the objective validity) of space in regard of all which can be presented to us externally as object, and at the same time also the ideality of space in regard to objects when they are considered by means of reason as things in themselves, that is, without reference to the constitution of our sensibilities.
    We maintain, therefore, the empirical reality of space in regard to all possible external expereince, though we must admit its transcendental ideality; in other words, that it is nothing, so soon as we withdraw the condition upon which the possibility of all experience depends and look upon space as something that belongs to things in themselves     — Kant
  • What would Kant have made of non-Euclidan geomety?
    Can anyone gain access to this article?

    https://www.degruyter.com/view/j/kant.1970.61.issue-1-4/kant.1970.61.1-4.5/kant.1970.61.1-4.5.xml
  • What would Kant have made of non-Euclidan geomety?
    ↪andrewk
    You should listen to the last few minutes of this for a more detailed explanation on the same matter that I was talking about above:

  • What would Kant have made of non-Euclidan geomety?
    Can you elaborate about what you mean by this reference to how reality happens to be? — andrewk
    So to be more clear, by reality I mean the empirically real, that which physics addresses and that which we encounter in experience, whether directly through our sense organs, or mediately, through scientific instruments. I don't mean Kant's noumenon.
  • Being or Having: The Pathology of Normalcy
    When you look at the saying I do not only see the rose, the rose also sees me, the rose itself is no longer an object because there is a genuine reciprocal unity. — TimeLine
    A beautifully worded statement, but just because it's beautiful doesn't mean it's true. In what sense does the rose "see me"?

    This is impossible if our relatedness to others has no substance, is not rooted with feeling but rather viewing others as merely objects that one can acquire and dispose of. — TimeLine
    I don't see how consumerism implies that you treat others as objects. The world is as much a forum for action, as it is a place for things. The rose is a thing - how I relate to that thing is a different question from what the rose is.
  • What would Kant have made of non-Euclidan geomety?
    My understanding of the TA is that it is not about how reality happens to be — andrewk
    Only if you take reality to be the noumenon. But if reality is the phenomenon, or the empirically real, then what you're saying here is false.

    Many people do not get this very well. They imagine we have representations, and then there is this noumenon which causes the representations, which is actually very similar to the representations themselves. That's wrong as Schopenhauer illustrates. Since space and time are pure intuitions, they cannot apply to the noumenon, so the noumenon is neither spatial nor temporal. So "reality" (if by that we understand the noumenon) is neither spatial nor temporary. Physics doesn't deal with "reality". It deals only with the empirically real, with the phenomenon, which is exactly what the form of intuition of space applies to.
  • Currently Reading
    Prologemena To Any Future Metaphysics - Kant — Noble Dust
    Awww, poor you, you just spent some hours reading a text that may not be relevant anymore in light of non-Euclidean geometry ;)
  • What would Kant have made of non-Euclidan geomety?
    between the thing-in-itself and the phenomena, in Kantian jargon. This, to me, seems to remain quite untouched. — Thorongil
    It is touched for the Kantian if the transcendental aesthetic falls apart. For the Platonist, yes, it does remain untouched.

    there is no problem if non-Euclidean geometries are purely fictitious. I think they are, for they were "discovered" by fiddling with axioms, not from empirical observation. — Thorongil
    But yet, there is empirical observation that confirms such geometries to be the case. How is it possible for them to be purely fictitious given that this is the case? Kant's argument would indeed be unaffected if these non-Euclidean geometries were, as you say, purely fictitious. Kant's position is that geometry is synthetic, so it is possible to form a concept of non-Euclidean geometry, since there is nothing logically contradictory in such a concept. However, Kant would claim that such isn't a science anymore, since it is a purely empty concept, which does not rely on the pure intuition of space.
  • Being or Having: The Pathology of Normalcy
    Only then can we be enabled with the right solutions to make real changes. As mentioned, a person could consciously enjoy the consumerism, have a perfect life, partner, family and everything could be great, but they are deeply miserable and are unable to ascertain why. — TimeLine
    No. This is outright BS. The only reason why consumerism is bad is because it leaves you vulnerable to the loss of the pleasure of consuming, through your susceptibility to loss of health, loss of money, loss of friends, loss of social status, etc. If it didn't leave you vulnerable to those things, or if you could be invulnerable to them, then it wouldn't be bad. But life is so structured, that suffering is an intrinsic aspect of it, and consumerism doesn't help to minimise it.

    You seem to try to get Buddhism on your side, but it's actually quite the opposite I believe. I'm not sure how deep your understanding of metaphysics is, but metaphysics is certainly relevant here. You never usually engage in discussions of metaphysics here though.

    There is no "hidden" despair as such, because there is nothing to do in life. One is free to either do or not do.
  • What would Kant have made of non-Euclidan geomety?
    That doesn't follow. The difference between a perfectly flat space and one that is curved very, very slightly would make no difference at all to the ability to communicate. — andrewk
    In principle it could. Since this is at all possible, space cannot be a priori. We're talking about how reality happens to be, not how we encounter it in our limited region of space and time. So yes, the fact that our principles are contradictory means that we can't both be right with respect to reality. Unless you want to claim we inhabit two different realities, that is.

    What's your preferred method? I find ouija boards OK but Automatic Writing tends to be quicker. — andrewk
    :lol: - well, I only meant that from my reading of him, I'm sure Kant would have found such an idea ludicrous, and pulling in a completely opposite direction to what is aimed at through philosophy. We aim to reach the truth - not opinions.
  • What would Kant have made of non-Euclidan geomety?
    No. Just as placing dots on a paper to demonstrate counting or addition, or drawing a triangle to demonstrate a triangle do not make mathematical knowledge a posteriori, so too with light. In terms of the intuition it is no different from using a ruler. — Moliere
    Sure, so tell me how you "place dots on a paper" (or the equivalent) to demonstrate non-Euclidean geometry (specifically intrinsic curvature). What is the "intuition" relevant to non-Euclidean geometry?

    Also, how is using the empirical behaviour of light (that it cannot go faster than a certain speed) the same as placing dots on a paper?

    So? How does that have anything to do with the modality of the copula, in Kant's logic? — Moliere
    Everything. A necessary judgement is one which must be thought to be true. Euclidean and non-Euclidean geometries cannot both be thought to be true since one allows possibilities that the other denies. Therefore they cannot both be necessary.

    Your saying "necessary" means not mistaken -- or, perhaps more strongly, not even possible to be mistaken. I am saying "necessary" means to give assent to by everyone, and hence be objective. — Moliere
    No, I don't agree "necessary" means assent by everyone to Kant. Please quote Kant where he says something like this. As far as I know, this is what later neo-Kantians would claim (ex, Husserl).

    According to Kant, the modality of apodeictic judgements involves one necessarily having to assent to the truth of the proposition when considering it. And it is necessary because one appeals to the intuition. So now, you have to show, as I asked you before, how one appeals to the pure intuition to "construct" non-Euclidean geometries.

    Yes, we could. — Moliere
    Yes, it can. — Moliere
    I asked you to tell me how that is possible though.

    It's like "necessary" and "certain" mean the same thing to you -- if some proposition is necessary then it is not possible for it to be false. But truth and falsity have nothing to do with necessity, in Kant'. — Moliere
    I think this is incorrect. Necessary means that we must think that proposition true, we must assent to it. Do you have a quote to prove that this isn't the case in Kant?

    I mean, of course these things can change in Kant's system -- especially considering that necessity, being a category, isn't even time-dependent. What happens in time can change when some proposition is necessary. — Moliere
    I see this the other way around. Precisely because it is not time-dependent, what happens in time cannot change the necessity of the proposition.

    He doesn't really go into psychology very much. But mathematics seems to form the heart of his philosophy of science. So it would just be the fact that it's not a science, that we can be wrong, and so forth. It's a mundane answer, but I don't think there is a deep answer. Kant's dealing with the structure of the mind, a structure we all share as compared to the contrast class of an intellectual intuition. It's not really about our subjectivity as much, though Kant uses the word "subjective" in his own way that fits within the philosophy.

    The self and subjectivity and all of that just aren't really there to be talked about. And psychology and anthropology are only mentioned in passing.     — Moliere
    Sure.
  • What would Kant have made of non-Euclidan geomety?
    If causality is an a priori form of the understanding, then we cannot but conceive of the noumenon causing the phenomenon, even though such a relation may not obtain in reality. — Thorongil
    Ok.

    Haven't looked at the rest of the thread, as it's beating a very dead horse. I've said my piece about space. — Thorongil
    I don't think so. At minimum, I think you should read my exchange with Moliere, starting from here:
    https://thephilosophyforum.com/discussion/comment/152158

    Non-Euclidean geometry strikes at the very possibility of the Transcendental Aesthetic.
  • What would Kant have made of non-Euclidan geomety?
    2. its necessity is individual-dependent, so that we could both be correct and it is necessary for you but not for me.

    I find the second one palatable but my secondary sources tell me that Kant was adamant that his a priori intuitions like the TA were not subjective. If that's correct then I think he'd roll in his grave at suggestion 2.     — andrewk
    Not only Kant, but I also, find suggestion (2) to be ridiculous. Reality has to be a certain way, and it is the job of philosophy to investigate it. It would be contradictory if geometry was different for each different person, since then we would be unable to share a world and communicate at all.
  • What would Kant have made of non-Euclidan geomety?
    Yes, true. I just mean how we categorize something, not what it is. — Moliere
    So then this is just about categorising statements, not about how things really are?

    Well, it's a priori because it does not rely upon particular experience -- it is non-empirical. Space itself is classified as non-empirical. We don't come to know it through inference. Space, like time, is unique in this way: that it is both part of our intuition, and that it is non-empirical. — Moliere
    The correct answer would be due to universality and/or necessity according to Kant I think.

    What makes it knowledge is that we then compare our propositions generated in the understanding to the form of intuition. And since it is knowledge of the form of intuition it is also universal and necessary. — Moliere
    I've asked this before, but for completeness sake, I'll ask it again to the above: how can we be wrong about judgements which are universal and necessary?

    If we are wrong, it seems to follow as the night follows day that they were not universal and necessary. And yet, lo and behold, we can be mistaken about statements being universal and necessary. But we determine that they are universal and necessary by appealing to our intuition. So then our intuition must be wrong. Or we must have appealed to something other than our intuition, when we thought we were appealing to our intuition.

    What is contradictory in them? Perhaps we are wrong in thinking that. — Moliere
    Euclid's 5th postulate precludes forms of geometry that are actually possible in non-Euclidean geometry. Thus the two must be contradictory. If one is true, then the other cannot be true, except, maybe, in a limited situation.

    Apodeictic certainty just means that a proposition must be true to the consciousness who holds it to be true. — Moliere
    If it must be true in the consciousness that holds it as true, and if it is true in virtue of appeal to the form of intuition, then it cannot ever cease to be true.

    To use your question later on -- why was Aristotle wrong about the categories? — Moliere
    Ehmmm X-) - I don't think he was.

    It seems to me that we can be wrong about all manner of things, though. And in this case, with geometry, if the two geometries appear very similar within the world as we are presently living in it then there simply wouldn't be a reason to think there is another one. But then we lived in a different way and someone had some ideas and it turned out to be that we were wrong in some of our predictions. — Moliere
    Here you forget that we cannot appeal to experience at all to justify a priori knowledge, and hence neither can we appeal to experience to disconfirm it.

    Why exactly do you think we can't be wrong? Simply because the knowledge is universal and necessary? — Moliere
    Yes.

    Of the noumenal world nothing is known, period. So the proposition "The noumenal world is lacking space", while truth-apt, cannot be judged. There is no basis upon which such a judgment can rest. The noumenal world may have space, it may not. We simply do not know nor can we judge in either direction. To believe something along those lines would be to be doing metaphysics, which our understanding is incapable of turning into a science. — Moliere
    Agreed for the sake of this discussion. (I take the most coherent version of Kantianism to be the one outlined by Schopenhauer, so I actually disagree here).

    It seems to me, paired with your balking about being wrong about subjectivity, that you're harboring some Cartesian sympathies for knowledge of the self.

    That's fine and all, but if we're talking about Kantian philosophy then the self is not so central in his philosophy. Subjectivity is. But knowledge of the self is not given priority. It is not more certain. In fact, the most certain knowledge in Kantian philosophy is of mathematics and physics, and not psychology :D. (Kant didn't even think chemistry was a science proper.)     — Moliere
    No, not really. I'm fully aware that we don't have knowledge of our own subjectivity in many regards (Freud's unconscious, etc.). However, I wanted you to explain how this works according to Kant.
  • What would Kant have made of non-Euclidan geomety?
    Geometry is a science which determines the properties of space synthetically, and yet a priori.
    What, then, must be our representation of space, in order that such a cognition of it may be possible?
    It must be originally intuition, for from a mere conception, no propositions can be deduced which go out beyond the conception, and yet this happens in geometry. But this intuition must be found in the mind a priori, that is, before any perception of objects, and consequently must be pure, not empirical,
    intuition. For geometrical principles are always apodeictic, that is, united with the consciousness of their necessity, as: "Space has only three dimensions"     — Kant
    Another one. Apparently, geometrical principles are united with the consciousness of their necessity - I don't see how that is the case with Euclid's 5th postulate. If we had the consciousness of its necessity, then we couldn't be wrong, could we? That consciousness cannot just vanish can it? So my prior question remains significant - how is it even possible to be mistaken about our a priori cognition as it relates to our pure intuition? This cognition is necessary, if it is necessary, then we cannot be mistaken about it - that seems to follow, necessarily, if I may say so.
  • What would Kant have made of non-Euclidan geomety?
    it would still be necessary, — Moliere
    Although I disagree it would be necessary. Again - Euclid's 5th postulate contradicts non-Euclidean geometries by not allowing cases that non-Euclidean geometry does allow. Therefore, it cannot be necessary. So why was it that we thought it necessary in the first place? How is such a mistake at all possible (to use Kant's transcendental language :P )?
  • What would Kant have made of non-Euclidan geomety?
    Plus, we developed other means of probing the shape of space which were not available in Kant's time — Moliere
    Does it mean that it is a posteriori if we have to "probe the shape of space" for it? :s
  • What would Kant have made of non-Euclidan geomety?
    it would still be necessary, but not universal. — Moliere
    Thus it would be a priori according to Kant. It is sufficient for a proposition to be either necessary or universal to be a priori.

    "Now, in the first place, if we have a proposition which contains the idea of necessity in its very conception, it is a if, moreover, it is not derived from any other proposition, unless from one equally involving the idea of necessity, it is absolutely priori [...] Necessity and strict universality, therefore, are infallible tests for distinguishing pure from empirical knowledge [...] But as in the use of these criteria the empirical limitation is sometimes more easily detected than the contingency of the judgement, or the unlimited universality which we attach to a judgement is often a more convincing proof than its necessity, it may be advisable to use the criteria separately, each being by itself infallible."
  • What would Kant have made of non-Euclidan geomety?
    ↪Moliere
    To build for a second on what I said above. To find out whether analytic statements are true, we appeal to the meanings / definitions of our words. To find out whether synthetic a posteriori statements are true, we appeal to experience. And to find out whether synthetic a priori statements are true, we appeal to the intuition (with regards to geometry at least). So we appeal to the intuition and find out that Euclid's 5th postulate is true. And yet, you claim that we were merely wrong about our intuition... but it doesn't make sense to be wrong about our intuition when it is our intuition to which we appeal to determine whether Euclid's 5th is true or not, isn't it?
  • What would Kant have made of non-Euclidan geomety?
    I will address the rest of the post soon, but first:
    I think you're conflating a priori with analyticity here. The principle of non-contradiction is the hallmark criteria, for Kant, of analyticity. a priori just means without experience. All analytic statements are a priori, but not all a priori statements are analytic (according to Kant). — Moliere
    Sure. Analytic statements are a priori because we don't need to appeal to experience to know that they are true. If geometric statements are also a priori, then we don't need to appeal to experience to know that they are true, correct? And if we don't need to appeal to experience to know that they are true, then experience cannot disconfirm them. But experience is able to disconfirm Euclid's 5th postulate. Thus it cannot be a priori, and yet we have mistaken it for a priori. How is it possible to know if the other geometric postulates we have aren't also mistaken to be a priori, when in truth, they really aren't? And if we can't know that they are a priori, then on what basis can we claim that space is a form of our intuition?
  • What will Mueller discover?
    do you think Trump rows his own boat? — tim wood
    No, no, absolutely not :B - here's the rower and the boat:

    jet-set-trump-putin.jpg

    *shakes head*
  • What will Mueller discover?
    Paul Manafort and Kellyanne Conway ran a "standard campaign"? Isn't Manafort a prime suspect for "nonstandard" campaign? — Metaphysician Undercover
    PM joined late, after the campaign was already well underway.
  • What will Mueller discover?
    Just so. — unenlightened
    You have not justified this attempt to invert the logic :P
  • What would Kant have made of non-Euclidan geomety?
    https://plato.stanford.edu/entries/kant-mathematics/
    https://plato.stanford.edu/entries/kant-spacetime/     — Moliere
    Thanks, I had a quick look and will read in more depth soon.

    Originally my thought was that any geometry upon which natural phenomena are predicted would count as the synthetic a priori geometry, whereas previous geometries would be considered approximations of the a priori -- and therefore empirical, since they are no longer necessary (at least for predicting physical phenomena occuring within the forms of space and time). — Moliere
    This doesn't make sense. Either the geometry is a synthetic a priori, or it's not. It cannot merely "count" as a synthetic a priori at one point, and not at another. If it is a priori, then it is always a priori. We can, on the other hand, be mistaken about which geometry is the a priori geometry. And if we can be mistaken, I have to ask that you specify how we can know if we are mistaken about it. And the further question, how can we know that (the geometry we have) it is a priori? Because knowing that, would seem to require infinite time, since a particular geometry (like the Euclidean) can always prove in the future not to have been complete.

    But now I'm wondering if it's possible that both could be considered synthetic a priori -- since we can demonstrate either geometry within the non-empirical intuition by means of either physics. It would still count as a cognition regardless of the physics we use. — Moliere
    This doesn't make much sense to me. Both geometries are contradictory to each other. Two contradictory statements cannot both be true, hence they cannot both be a priori, since a priori truths are necessary, and hence always true.

    "Sensible" as in why does it make sense and is reasonable? — Moliere
    Yes.

    If so, then it would just be a matter of the fact that propositions are truth-apt. — Moliere
    Propositions may be truth-apt, but if something is true in an a priori fashion, then it follows that it cannot fail to be true, regardless of what happens in the world. Like "it is raining or it is not raining".

    My first inclination was to say that any geometry upon which the physical sciences rests would count as the synthetic a priori geometry, and would thereby be certain. — Moliere
    Why? Why does the fact that physics "rests" (what does that even mean?) on it guarantee it certainty?

    Yes and yes. — Moliere
    Can you explain how you can be wrong about your own subjectivity, and what you mean by that idea?

    But now I'd also note that certainty isn't quite as important in Kant as other epistemologies. Certainty is obtained subjectively or objectively -- and the difference between the two is subjective certainty is where one person holds something to be true, and objective certainty is when everyone does. I had to look up certainty in A Kant Dictionary to come up with that, though. It's by Howard Caygill, and just like the above articles certainly relies upon a certain interpretation to help readers through Kant -- but unfortunately I didn't mark in my CPR where Kant talks about the conditions of certainty :D. So I found it hard to find. — Moliere
    I doubt this. Kant does talk about apodeictic certainty innumerable times with regards to mathematics. Part of the TA project, as far as I see it, is to secure where the certainty of mathematics comes from - and for Kant, it comes from the (synthetic) a priority of its propositions.

    Though space is the form of outer intuition, and is so for everyone with an intellect like ours, knowledge cannot be obtained except by the use of both our understanding and intuition. Space is an intuition, and knowledge of space only comes about by use of the understanding. — Moliere
    Right, I definitely agree with you here. This is undoubtedly correct from a Kantian point of view. So then, our geometrical judgements (Euclidean geometry) can be wrong. What exactly is the relationship between the intuition and the understanding that causes us to be capable of forming wrong concepts based on the former?

    More or less, yes. — Moliere
    So, if space is transcendentally ideal, then there is no noumenal space, correct?

    But mathematical knowledge relies upon the form of intuition. — Moliere
    Ok.

    The way that acting in the world helps us gain the knowledge is that we compare concepts to our intuitions, and the form of intuition is the basis for geometry. — Moliere
    So why is it that it took so long for us to discover non-Euclidean geometry? According to this development of Kant, we gain knowledge by comparing our concepts with our intuition. Do you claim that, in our intuition, we knew that non-Euclidean geometry is possible? If we did, then why did it take so long for us to compare our concepts (Euclidean geometry) with our intuition, and find out that they were different?
  • What will Mueller discover?
    It's inevitable. Success is the obsession of the fool. Far better to fail attempting the right thing than to succeed at the wrong. — unenlightened
    How did it go... hmmm, let me remember... wasn't it that the fox who cannot reach the grapes, calls them sour? X-)
  • What will Mueller discover?
    Trump wasn't running it. Pretty sure it's the campaign manager that runs it. And winning doesn't take intelligence, only popular appeal. — Michael
    So you think the "campaign manager" would have run the incredibly controversial and non-traditional campaign that Trump ran? Sorry, "campaign managers" cannot do that - they just know how to do standard campaigns. The rest comes through the guidance of the person running for office. They have to ASK them to do things differently.
  • What will Mueller discover?
    Timely wisdom from a biscuit.
    And Trump has all the wisdom of a fortune cookie.     — unenlightened
    Is it possible for wisdom not to lead to success though?

    Sure, success does usually bring a reputation for wisdom, but why is that? Isn't it because it takes wisdom to be successful?
  • What will Mueller discover?
    Because Trump was elected President and McMaster wasn't. It has nothing to do with intelligence. — Michael
    Takes intelligence to run that campaign and win.
  • Currently Reading
    Any good book of comparative religion between Christianity and Buddhism? (I am mostly interesting in something that has a philosophical side to it, mostly from the Thomist perspective) Thanks.
  • What will Mueller discover?
    https://www.vox.com/world/2017/11/20/16680190/hr-mcmaster-trump-idiot-kindergartner — Michael
    Is that why Trump is McMaster's boss, because he's less intelligent than him?
  • What will Mueller discover?
    ↪ProbablyTrue
    As if just about any dumb Joe could do either of those things.
  • What will Mueller discover?
    ↪ProbablyTrue
    No, but I'm underlining how ridiculous it is to claim that someone who has built a billion dollar empire and won the Presidency of the United States "is not good at grasping anything complicated" - absolute nonsense.
  • What will Mueller discover?
    Trump is not good at grasping anything complicated. — Wayfarer
    Oh, and you are? Is that why Trump built a billion-dollar real estate empire, and you didn't? :-}
  • On Meditation
    At least in theory, you're using the techniques that draw one into the divine, but using those techniques for one's own accomplishment in a temporal life which end's with death. Which is essentially demonic. — Noble Dust
    I don't see how that is demonic. Didn't Abraham and his sons all pray to God and engage in spiritual practices to better guide them in their worldly activities? Of course they did.
  • The Last Word
    What you are saying is that he has resigned himself to no longer thrive but just to exist? A eternal version of "It is what it is?" — ArguingWAristotleTiff
    Well, what else can you do in that situation?

    Waiting 5 hours for a diaper change at 75 is not the way it should be. Two showers a week even when my Dad had 5 straight days of a stomach illness is unacceptable. — ArguingWAristotleTiff
    Not surprising, this seems to be the trend in most parts of the world. My grandfather had a stroke this summer (he is 91 years old), so he had the unfortunate necessity of spending time in hospital. In third world countries though, you can get better treatment - if you give the dollars to the right people. But not much better. It is only for the short duration of giving the $3 - then they give you a shower. To change the catheter - another $3. To change diapers - well, another $3. Not to mention that the whole place smells of uncleaned urine. Some people don't have even the $3 to give - so then their relatives are pretty much left to die there :( From my experience, and seemingly from yours too, these are not good places to leave sick people in.
  • On Meditation
    So, it’s intersting to note that theosophy, and then New Ageism (growing out of theosophy) grew out of a more magical approach to mysticism. Which would put secular meditation, yoga, etc, purely in the camp of magic, not mysticism. Spiritual practice for personal power and gain, not for a movement towards union with the divine — Noble Dust
    What's wrong with spiritual practice in order to improve your efficiency and capacity in the world?
  • On Meditation
    fluffy bunny feet — TimeLine
    With the same shoes everyday :P
  • On Meditation
    Demanding does not necessarily include expecting, and not being satisfied does not necessarily include frustration. :) — Janus
    Absolutely, you are right, how could I have made such a mistake. Of course demanding does not necessarily include expecting, and not being satisfied does not necessarily include being frustrated...

    Reveal
    except in like 99% of cases >:)
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