It's not our perception of space that's at issue, I'd say. The propositions of geometry are closely tied to physics, by my reading. Because our intuition follows mathematical laws we are also able to apply those mathematical laws to objects, which are themselves within our intuition.

Strictly speaking it's not perception which intuition is trying to explain, but rather intuition is one half of the elements of cognition which explains how knowledge of objects is possible. Clearly there are relations between perception and cognition, and granted the intuition's description relies heavily upon visual imagery (like a lot of Western philosophy), but the reason why mathematical laws are able to be posited and discovered in the phenomenal world is because our cognition relies upon this form. It sort of explains why we are able to make predictions which are actually caused -- meaning the "necessary connection" between two events -- in the first place, rather than merely the constant conjunction of non-related events believed by force of habit.

So if it turns out that Euclidean geometry is not the form of intuition it would seem to upend the notion that we have synthetic a priori knowledge of the form of intuition. Same goes for the physics based upon that synthetic a priori knowledge. However, if Euclidean geometry were merely empirical, an approximation of our cognitive faculties as Newton was an approximation, then I'd say that the aesthetic is saved.

But in either case, it's not how we perceive that's at issue. It's how we are able to know math and why it applies to the objects of our perception in the first place. Kind of a hair-thin distinction, but I'd say it's important because in one case we are dealing with phenomenology and psychology, and in the other we are dealing with the possibility of knowledge which seems to fit more in line with the whole Critique. — Moliere

Ptolemization, I see X-) - when it doesn't work, we'll add new fudge factors to make it work... Kind of ironic, given that this was supposed to be a Copernican revolution >:O

But why is suffering "just" the nature of life? That's a cop out. — Noble Dust

Because we don't control every bad thing that can happen to us, nor can we control it. Obviously.

Exactly. Peterson and co. just treat the cause of suffering as being the fault of or caused by no one, or if anyone caused it it's the people who are being hurt by it caused it. Nope, there's no such thing as a prejudiced system wherein some people are given preference for reasons other than competency. — MindForged

Well let's see... suffering. You love someone, they don't love you back, you get sick, you suffer pain, you get bored, there are diseases, illnesses, handicaps, there are accidents that can occur, you lose loved ones, etc. Need I go on? This has nothing to do with society, it's suffering that is intrinsic to the nature of existence.

Like literally every 'ontological argument for God' ever, the OP assumes its conclusion. All the argument can show - all every such ontological argument can show - is that if God existed, the argument would hold true. — StreetlightX

Notice the material conditional, 'if'. The passage should read: 'If God existed only in our imaginations, he wouldn't be the greatest thing we can think of, because, if he existed, God in reality would be greater. Therefore, if God existed, God would exist in reality".

Every 'ontological argument for God' engages in this slight of hand: beginning with a material conditional and then silently dropping it along the way. Once you know to look out for it, its kinda fun to play the 'spot the illicit shift from conditioned to unconditioned (from 'if' to 'existence') in all 'ontological arguments'. The OP's phrasing, 'God in reality would be greater', actually retains the conditional lanaguge even as it pretends not to notice it. — StreetlightX

No. There is no "if" or material conditional at all. That's just a way to rephrase the content of the argument.

Take a look at Plantinga's formulation:

(1) God exists in the understanding, but not in reality (assumption for reductio).
(2) Existence in reality is greater than existence in the understanding alone. (premise)
(3) A Being having all of God's properties plus existence in reality can be conceived. (premise)
(4) From (1) and (2), a being having all of God's properties plus existence in reality is greater than God.
(5) From (3) and (4), a Being greater than God can be conceived.
(6) It is false that a Being greater than God can be conceived (by definition).
(7) Hence, it is false that God exists in the understanding, but not in reality. — Alvin Plantinga

Can't you replace "God" with any x? — anonymous66

No, you cannot replace God with any finite thing. It is one mark of finitude for an object to be different than its concept - or for the thought to be different from the being. A unicorn (as a concept) can be different from a unicorn as a being. A unicorn (as a concept) exists. It doesn't follow from that that the unicorn (as a being) must also exist. The same cannot be said about God (the infinite Being).

https://www.bu.edu/wcp/Papers/Mode/ModeDeLo.htm

Yes, I mean what ordinary people mean by intuition, not what Kant means . He uses words too weirdly for me. — andrewk

(1) What ordinary people mean by intuition cannot be used to defend Kant, who uses that word differently, and thus means different things by it than ordinary people.
(2) The way ordinary people use "intuition" and others words that are derived from it is extremely vague. In ordinary language, an "intuition" is just when I throw up my hands and tell you "I know it is this way, but I can't say why". Very often, habit can entrench thoughts, principles, and the like in people's mind, and they easily recall them, and feel very certain in them, but are unable to give justification for them.

Yes. It may be, as you say, cos I'm a mathematician. Or maybe I'm a mathematician cos I look at things that way. — andrewk

Which way?

If I could explain it, it wouldn't be an intuition. — andrewk

For Kant intuition means something closer to perception. So I assumed you were using that term, otherwise, it has no bearing on what Kant was writing about anyways. So is non-Euclidean geometry perceptible in your mind's eye / imagination?

The other postulates seem obvious and undeniable to me. That one doesn't. I suppose it must be just the way my brain's wired. — andrewk

Why doesn't the parallel postulate also seem undeniable? There must be a reason for it, otherwise, I think we will have to attribute it to habit. Are you a mathematician? If so, perhaps you have trained for long enough in non-Euclidean geometry that this training has become second-nature to you.

For me, Euclid's parallel postulate seems undeniable. I am not a mathematician, and from early on I was taught geometry according to Euclid. Euclid's postulates are second nature to my practice of geometry and thinking about geometric problems. Indeed, this may be exactly why I find it easy to perceive the truth of Euclid's parallel postulate, and not to perceive the opposite. It may just be habit, as Hume said, that has entrenched these unprovable things that we take for granted, that Kant now pulls out of the hat as a magician, and calls them "synthetic a prioris". There have also been other critiques of Kant along Marxist lines which claim that Kant's Categories themselves are conceived in the praxis of economic exchange, and then philosophy (& science) is misled to consider them properly basic.

At least I can tell you why it took so long to discover the other geometries though. It's because it wasn't just a question of removing the parallel postulate. It needed to be replaced by something, otherwise we're taking away too much. In fact, what was needed was a complete re-axiomatisation, starting with a completely new set of axioms that does not resemble the existing ones at all. In fact a completely new language was needed, involving things called manifolds, vector spaces, tensors and metrics.

That was a very difficult task, and needed to wait for some extremely clever people to first realise that's what was needed, then secondly work out how to do it. — andrewk

So this new reconceptualisation was not a pure intuition as per Kant's definition of the term? It arose by means other than intuition, such as conceptualisation, right? It took several minds to adjust the conceptualisation so that it all made sense.

Some Platonist ideas are common to all Western philosophy. All the comment was about, was the distinction that Schopenhauer recognises between ‘truths of reason’ and empirical observations. It does indeed reflect a distinction which is basic to philosophy, generally. — Wayfarer

Yeah, this isn't controversial.

The love is palpable. — Noble Dust

Yes, TimeLine has moved to a new form of philosophy, whereby we show what we mean through our way of acting, not through what we say X-)

Let me break LOVE down for you. — TimeLine

>:O >:O >:O

Your theories on love are somewhat hilarious :P

I think the distinction 'pure and not empirical' is significant, as it refers to any principle which is immediately evident to intuition itself without reference to any empirical or sensory object. This reflects the Platonist distinction between the intellectual intuition which is able to grasp ideas directly, with sensory perception which is of a lower order in only grasping its objects mediately. — Wayfarer

Ummm, no. Plato's intellectual intuition goes more with Kant's Understanding and the categories than with the forms of sensibility. The forms of sensibility ARE sensuous or sensory in nature. So space and time are not like, say, causality, which is a category of the Understanding. And the forms of sensibility are in no way "lower order" or "higher order" - there is a difference in kind between the content of sensibility and the form of sensibility. The latter is a form - it is the organising principle of the matter, the matter is given through it. And the former is the matter or content itself. On the other side, the Understanding provides the organising principles of our judgements.

You keep doing a mishmash of Plato and Kant and this is totally wrong - these two thinkers are not on friendly grounds in most regards. The Eastern / Schopenhaurian Platonic reinterpretation of Kant fails along with the failure of transcendental idealism.

Yeah, recently, there is a lot of competition over Descartes here it seems. You, @PossibleAaran and @Hanover all like Descartes :P

Personally, as I said in my previous reply in this thread, I find the method of doubt problematic.

Unless I'm missing something, the 5th postulate would also be true for an elliptic surface, such as the surface of a sphere. In order to exclude elliptic geometries, the words ',and not on the other side' would have to be added at the end of the sentence. — andrewk

I don't see why "and not on the other side" must be added when "on the same side" and "on that side on which are the angles less than the two right angles" already exists. This is implicit.

locally perfectly flat. — andrewk

And globally?

Problem solved! Immanuel Kant has been vindicated. X-) — andrewk

:-}

As an aside, my source pointed out that, even in the Swarzschild coordinate system that is more typically used near a planet, the spatial curvature near Earth would be about one part in a billion, and probably not possible to detect with current equipment. — andrewk

But it still exists, hence invalidating Kant.

And you still haven't explained:

Why don't you find it intuitive? When you imagine space, isn't this how you necessarily would imagine it? I lean towards saying that my intuition is thoroughly Euclidean, and non-Euclidean geometry wasn't discovered for so long precisely because we don't have an intuition / direct perception of it. Otherwise, why did it take non-Euclidean geometry so long to be discovered? — Agustino

You keep repeating that Euclid's parallel postulate is not intuitive, but you don't explain why.

I would say there is no "physical space" for Kant; space is not a physical object. — Janus

Yes, I am already aware of that. It's necessary for me to talk of "physical space" because Kant was wrong.

The space studied by physics is this phenomenal, empirically real space (which of course is a contradiction - Kant wouldn't claim physics studies space, that would be the job of mathematics). — Agustino

space is not a physical object. — Janus

Sure.

Can you provide a citation that supports your idea that Kant was specifically concerned with showing "why mathematics is so effective at describing physical space"? — Janus

Well, for Kant, there is only one space and mathematics (geometry) describes it with apodictic certainty.

Of course geometry is effective at describing perceptual space, because it just consists in formulations of our intuitions of the nature of our visual perception. — Janus

Nope. This is wrong on two counts. (1), our perception may not be Euclidean. Parallel lines do meet, in our perception, at the horizon. So if you want to argue for this point (that our natural intuition of space is Euclidean), with which I actually agree, you cannot appeal to the "nature of visual perception". (2), there is no "perceptual" space as differentiated from "physical" space (the space we encounter when we do our physical experiments) in Kant - there is only one space.

For Kant space is a pure form of intuition, it is not given empirically, rather it gives the empirical. — Janus

Yeah, or rather, the empirical is given by means of space. Space is the form, and the empirical is the content or matter of that form.

Euclidean geometry is the direct intuition of the characteristics of perceptual space. — Janus

I've already tackled this above.

Non-Euclidean geometries are not empirically given either but are intuitively derived models of how geometrical principles would diverge form the Euclidean on curved two-dimensional planes. — Janus

This is incoherent. Can you perceive non-euclidean geometries? If you can't, then they are not intuitive per Kant's understanding. andrewk has still not told us how he "intuitively" perceives that Euclid's parallel postulate is not a priori.

The curvature of space-time is also not empirically given, but is a hypothetical construct, whose predictions have been very precisely confirmed and measured. The point is, though, that spacetime is not the same as space and time understood as pure forms of intuition; it is something else, we know not what, something that we cannot even visualize. — Janus

Space-time is empirically given, that's why it can be empirically validated.

Can you quote a passage from Kant where he clearly claims that all experimental results must be in accord with our synthetic a priori conceptions of the pure forms of intuition? — Janus

No, and you can't give any to the contrary.

But in Kant's system I can tell you for certain that it can be no other way.

"Therefore in one way only can my intuition anticipate the actuality of the object, and be a cognition a prioir, viz., if my intuition contains nothing but the form of sensibility, which in me as subject precedes all the actual impressions which I am affected by the objects"

Kant conceives the intuition as "anticipating" the actuality of objects, since it already has the cognition, a priori, of space, which precedes & organises the sense impressions of the objects. So objects are given in space, and we know space a priori. Thus, objects necessarily must conform to this space. It follows from this that physics - or anything else - cannot invalidate or cause us to revise our conception of space, if it is a priori given. The only way we could revise it is if it's not a priori. At minimum, space must be more than transcendentally ideal.

did Kant ever specifically insist that Euclid's parallel postulate was part of our a priori processing of intuitions? — andrewk

There is a remark about something similar:

Suppose that the conception of a triangle is given to a philosopher and that he is required to discover, by the philosophical method, what relation the sum of its angles bears to a right angle. He has nothing before him but the conception of a figure enclosed within three right lines, and, consequently, with the same number of angles. He may analyse the conception of a right line, of an angle, or of the number three as long as he pleases, but he will not discover any properties not contained in these conceptions. But, if this question is proposed to a geometrician, he at once begins by constructing a triangle. He knows that two right angles are equal to the sum of all the contiguous angles which proceed from one point in a straight line; and he goes on to produce one side of his triangle, thus forming two adjacent angles which are together equal to two right angles. He then divides the exterior of these angles, by drawing a line parallel with the opposite side of the triangle, and immediately perceives that be has thus got an exterior adjacent angle which is equal to the interior. Proceeding in this way, through a chain of inferences, and always on the ground of intuition, he arrives at a clear and universally valid solution of the question. — Kant

In addition, there are the remarks of Kant's student, Schopenhauer, more clearly about the same subject:

In fact, it seems to me that the logical method is in this way reduced to an absurdity. But it is precisely through the controversies over this, together with the futile attempts to demonstrate the directly certain as merely indirectly certain, that the independence and clearness of intuitive evidence appear in contrast with the uselessness and difficulty of logical proof, a contrast as instructive as it is amusing. The direct certainty will not be admitted here, just because it is no merely logical certainty following from the concept, and thus resting solely on the relation of predicate to subject, according to the principle of contradiction. But that eleventh axiom [11th axiom is equivalent in the context of Euclidean geometry with Euclid's Fifth Postulate] regarding parallel lines is a synthetic proposition a priori, and as such has the guarantee of pure, not empirical, perception; this perception is just as immediate and certain as is the principle of contradiction itself, from which all proofs originally derive their certainty. At bottom this holds good of every geometrical theorem. — Schopenhauer WWR Vol II §8

So all evidence available seems to point to the fact that Kant (& Schopenhauer) did consider Euclid's parallel postulate to be a synthetic a priori.

One last thing. The parallel postulate says that there exist pairs of straight lines that never meet, and that pairs that do meet only do so at one place. I, and generations of mathematicians before me, do not find that particularly intuitive, whereas Euclid's other axioms do seem intuitive. That's why people wondered for centuries whether that aximo was necessary in order to do geometry at all. Gauss's brilliance was to show that it wasn't. — andrewk

Why don't you find it intuitive? When you imagine space, isn't this how you necessarily would imagine it? I lean towards saying that my intuition is thoroughly Euclidean, and non-Euclidean geometry wasn't discovered for so long precisely because we don't have an intuition / direct perception of it. Otherwise, why did it take non-Euclidean geometry so long to be discovered?

I've spent quite a lot of time studying Kant, but it's not something I'm proud of, since it is disappointing that he could be so wrong. The first time I encountered Kant's system, I literarily thought he was a genius, who had advanced philosophy far beyond what anyone had before him. But with time, the more carefully I studied Kant and these issues, I came to see that Kant had made some serious mistakes, that despite the initial beauty and order of his system, could not be maintained. Transcendental idealism as developed even more by Schopenhauer was the first philosophical system that I thought was correct, and we fundamentally gained new knowledge from it. The first time I felt that "this must be right" in philosophy, because it was so well closed, and there were few dangling bits, unlike most other philosophical systems which have many dangling bits. Most of that knowledge was in understanding how things fit together, and why things are as they are - for example, why mathematics describes the physical universe so well. But it turns out that those certainties were mere appearance. Ever since then, I have not found a philosophical system with as much internal coherence as that one.

So pure intuition refers to the perception of space and time. They are pure, because we cannot "not perceive" them. Kant goes through the thought experiment of taking all sensations away, "heavy", "red", etc. and finds that he cannot get rid of space. Even when one imagines nothing, one imagines that nothing in space.

I apprehend some inconsistency here. In the first, you describe space as a "form of pure intuition". In the second you describe space as one of the "forms of sensibility".

As a form of "sensibility", I would assume that space is a condition for the possibility of sensation. But "intuition" I would think only arises from a being which has sensation. So if space is an intuition, then sensation would be prior to space as an "intuition".

Therefore one or the other cannot be correct. Either space is an intuition, in which case it occurs after sensation, or, space is a condition for the possibility of sensation, in which case it is prior to sensation and cannot be an intuition, which only occurs to creatures which already have sensation.

Edit: This is probably why there is such variance in interpretation of Kant on this issue. — Metaphysician Undercover

Kant uses intuition in a technical sense. It's not what we mean by intuition in common language. In Kant, intuition is something closer to what we mean in common language by perception.

And so, in Kant's system, there is no inconsistency though my language was a bit convoluted by saying "form of pure intuition" instead of just "pure intuition". Kant says:

Transcendental Aesthetic - Introduction:

"The pure form of sensibility I shall call pure intuition"

The a priori synthetic truths may be certain from the perspective of our sensations but does this really make them logically necessary? — Perplexed

According to Kant, the a priori synthetic truths must be certain from the perspective of the phenomenon and our experience. One repercussion of this is that you could not do a physics experiment which did not obey the laws of geometry.

No, that wasn't my point of disagreement.

that if you doubt whatever cannot be justified non-circularly — PossibleAaran

The problem with this method is when do you stop doubting? When is there enough certainty for something to be justified?

If I see a flower outside my window, then do I have enough justification to believe there is a flower there just by seeing it? Or do I need to perhaps approach it and touch it? Smell it too? Move it, and interact with it in different ways?

In other words, with the method of doubt, how do we decide when to stop doubting?

doubting P requires some evidence against P — PossibleAaran

I tend to agree with the statement. If I doubt something, I must have grounds for doubting it. Though I have to admit, that if I am honest, I don't often behave that way in practice. The reason why I adopted belief in the proposition quoted is because I was suffering from generalised anxiety disorder, OCD and hypochondria back then - so I determined to establish a philosophical method for when to worry and when not to worry (worry being somewhat similar to doubt). So then I learned, using that, not to worry (or doubt) in the absence of evidence, but only in the series of worries/doubts that were troubling me.

If I am honest, I continued to doubt other things even in the absence of evidence. It has been quite a methodological means for me to determine what can go wrong, and what can be done if it does go wrong. For example, I typically and often do this in my work and business. I doubt whether the work is good enough, or I doubt whether X or Y will do the right thing with the paperwork I need them to do for me, etc. So there is a certain degree of hypocrisy for me in holding to that belief. On the one hand, it did help me overcome an anxiety condition, on the other, I still practice it in many aspects of my life, where it yields results. But on a theoretical level, I cannot distinguish between when it's right to practice doubting and when it's not.

true reality of space — Hanover

Also it is a grave error to think that there is any "true reality" to space according to Kant. Space is transcendentally ideal, given by the forms of our sensibility. There very likely is no space at all out there - external to our phenomenal, empirically real experience. The space studied by physics is this phenomenal, empirically real space (which of course is a contradiction - Kant wouldn't claim physics studies space, that would be the job of mathematics).

Meh, you miss the point. — Hanover

Sorry, but I will disagree with you on this.

Kant says nothing of reality (noumena) — Hanover

Reality is a hazy word. Why is the noumenon reality, and the phenomenon not? Don't forget that it is the phenomenon that is the empirically real according to Kant, not the noumenal. Kant's notion of a noumenon, at any rate, is confused. He talks of the noumenon causing the phenomenon, which is nonsense, since causality is a category of the understanding, and hence can only apply to the phenomenon. It takes Schopenhauer to clarify this aspect of Kant.

Space is a precondition of understanding — Hanover

Precondition of the sensibility, not of the understanding. Kant talks of space (and time) in the Transcendental Aesthetic, and labels them as forms of the sensibility (as opposed to the matter or content of the sensibility, the sensations themselves), which comes before he goes into the categories of the Understanding.

Did he do that? I don't know. I never read the original, being a secondary-source kind of chap. — andrewk

Exactly... If you had, you'd be amazed by how often Kant mentions the "apodictic" nature of geometrical propositions.

Non-Euclidean geometries are just as intuitive (synthetic a priori) within their contexts as Euclidean geometry is within the context of everyday experience, so I don't see the problem. — Janus

Nope. This is a mistaken view. Kant was trying to show why mathematics is so effective at describing physical space - if mathematics is just a human construct, its effectiveness cannot be accounted. So Kant resolved the problem by saying that it is not just a human construct. We have this form of pure intuition, space, from which we derive the axioms of geometry. So they are synthetic, since we can imagine the opposite to be the case, but they are a priori, because they stand as being true prior to experience. His point was that I don't need to run a physical experiment to see that Euclid's Fifth Postulate holds (which of course turned out to be false). It is simply impossible, according to Kant, for Euclid's Fifth Postulate not to hold - not due to its synthetic nature, but due to its a priority, and the role the pure form of sensation (space) has in constituting all (spatial) experiences, and hence any possible experimental result.

Kant considered all of mathematics and geometry to be synthetic a priori knowledge, unless I am mistaken. — Janus

That is correct.

People will go to any heights of absurdity to prove that what they want to believe is true, instead of admitting to the truth.

There’s an essay on it here. — Wayfarer

That essay is a pile of manure.

The Euclidean nature of our imagination led Kant to say that although the denial of the axioms of Euclid could be conceived without contradiction, our intuition is limited by the form of space imposed by our own minds on the world. While it is not uncommon to find claims that the very existence of non-Euclidean geometry refutes Kant's theory, such a view fails to take into account the meaning of the term "synthetic," which is that a synthetic proposition can be denied without contradiction.

>:O And Kant wasted his time saying that the propositions of geometry are synthetic in order to tell us they can be denied without contradiction, because that certainly proves the reliability of mathematics when applied to physics (which is what Kant was trying to do - just open a page of the Prolegomena, instead of reading 20,000 secondary sources who don't know what they're talking about). Of course, this isn't what Kant did. Kant aimed to say that the propositions of geometry don't derive their CERTAINTY (because he took their certainty for granted) due to the law of non-contradiction (hence the synthetic part). Rather they derive their certainty from their a priority, rooted as they are in the pure form of sensation, space.

I think the people (which is everyone here pretty much) who think that non-Euclidean geometry is not a problem for the Kantian have not carefully read what Kant (and other transcendental idealists, like Schopenhauer) wrote about the axioms of geometry. Some people who have posted in this thread have read a lot of secondary works about Kant, but not the actual Critique itself - they are lazy thinkers.

There is an old thread about this I opened here:

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"Both Schopenhauer and Kant take space to be an a priori form of representation, applied by the cognitive faculties to the senses. They understand this to mean that the propositions of geometry are synthetic a priori judgements, and are therefore apodeictic - certain.

Space is not an empirical concept which has been derived from outer experiences. For in order that certain sensations be referred to something outside me (that is, to something in another region of space from that in which I find myself), and similarly in order that I may be able to represent them as outside and alongside one another, and accordingly as not only different but as in different places, the representation of space must already underlie them. Therefore, the representation of space cannot be obtained through experience from the relations of outer appearance; this outer experience is itself possible at all only through that representation — Kant

Space is not something objective and real, nor a substance, nor an accident, nor a relation; instead, it is subjective and ideal, and originates from the mind’s nature in accord with a stable law as a scheme, as it were, for coordinating everything sensed externally — Kant

Space is a necessary a priori representation that underlies all outer intuitions. One can never forge a representation of the absence of space, though one can quite well think that no things are to be met within it. It must therefore be regarded as the condition of the possibility of appearances, and not as a determination dependent upon them, and it is an a priori representation that necessarily underlies outer appearances. — Kant

Space is not a discursive, or as one says, general concept of relations of things in general, but a pure intuition. For, firstly, one can represent only one space, and if one speaks of many spaces, one thereby understands only parts of one and the same unique space. These parts cannot precede the one all-embracing space as being, as it were, constituents out of which it can be composed, but can only be thought as in it. It is essentially one; the manifold in it, and therefore also the general concept of spaces, depends solely on limitations. It follows from this that an a priori intuition (which is not empirical) underlies all concepts of space. Similarly, geometrical propositions, that, for instance, in a triangle two sides together are greater than the third, can never be derived from the general concepts of line and triangle, but only from intuition and indeed a priori with apodeictic certainty — Kant

Schopenhauer follows Kant in conceiving of space (and geometry - the study of space) as transcendentally ideal:

Perception, partly pure a priori, as establishing mathematics, partly empirical a posteriori as establishing all the other sciences [...] We demand the reduction of every logical proof to one of perception. Mathematics, on the contrary, is at great pains deliberately to reject the evidence of perception peculiar to it and everywhere at hand, in order to substitute for it logical evidence. We must look upon this as being like a man who cuts off his legs in order to walk on crutches [...] Whoever denies the necessity, intuitively presented, of the space-relations expressed in any proposition, can with equal right deny the axioms, the following of the conclusion from the premises, or even the principle of contradiction itself, for all these relations are equally indemonstrable, immediately evident, and knowable a priori — Schopenhauer WWR Vol I §14-15

Now Schopenhauer's ontological idealism (and I refer here to the phenomenon/noumenon distinction largely) critically requires that the stage on which experience occurs be transcendentally ideal, for this stage being transcendentally ideal is what enables experience to be called the veil of Maya - appearance - and hence necessitates the noumenon, the thing-in-itself. Without space, time and causality (which constitute the stage in/on which experience occurs) being transcendentally ideal, the distinction between noumenon/phenomenon is in danger, as is idealism - for if at least part of the stage on which experience occurs is real, then Schopenhauer's ontological idealism is false.

Schopenhauer laughed at mathematicians trying to prove Euclid's Fifth Postulate, thinking that it is known from pure perception a priori:

In fact, it seems to me that the logical method is in this way reduced to an absurdity. But it is precisely through the controversies over this, together with the futile attempts to demonstrate the directly certain as merely indirectly certain, that the independence and clearness of intuitive evidence appear in contrast with the uselessness and difficulty of logical proof, a contrast as instructive as it is amusing. The direct certainty will not be admitted here, just because it is no merely logical certainty following from the concept, and thus resting solely on the relation of predicate to subject, according to the principle of contradiction. But that eleventh axiom [11th axiom is equivalent in the context of Euclidean geometry with Euclid's Fifth Postulate] regarding parallel lines is a synthetic proposition a priori, and as such has the guarantee of pure, not empirical, perception; this perception is just as immediate and certain as is the principle of contradiction itself, from which all proofs originally derive their certainty. At bottom this holds good of every geometrical theorem — Schopenhauer WWR Vol II §8

Non-Euclidean geometry came along, and it turns out that we have empirical proof that Euclid's Fifth Postulate is actually false, with regards to space as investigated by physics. Now the curvature of space cannot be perceived - we perceive objects in space - things in space curve - but how can space itself curve - that is anathema to our perception. What does this mean for Schopenhauer? Well for one, Euclid's Fifth Postulate isn't apodeictic, and neither is it a priori - contrary to what Schopenhauer thought. So Schopenhauer was wrong at least about this one truth of mathematics, and if he was wrong about this one, why should the other mathematical propositions that he was certain of be anymore certain than this? Indeed, it is his method that is wrong. Grounding mathematical propositions in a priori perception without appeal to experience is wrong. As Einstein said:

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality

More importantly, there is one feature of space - its non-Euclideanness which is NOT a synthetic a priori, but rather a synthetic a posteriori, and therefore not transcendentally ideal, but empirically real - for it takes experience (physical experiments) for us to know of it. This means that at least part of the stage on which experiences occur isn't imposed on reality as a structure by our cognitive faculties, but rather is empirically real. If part of the stage is empirically real, then Schopenhauer's ontological idealism falls apart."

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To summarize - read the 10 or so pages of the Transcendental Aesthetic. Kant is very clear about this - space and time are the pure forms of the sensibility and they are not derived from the contents of sensation. They are NOT empirical intuitions.

I mean what makes geometry - if anything - certain? Before, it was taken to be certain since it was merely the reflection, in the understanding, of the a priori spatial form of the sensibility, and as such, there was nothing "external" involved in it, but rather everything external had to conform to it. — Agustino

From axioms and postulates. — Response

And where do the axioms and postulates get their certainty from?

In Euclid's Elements Book I, Euclid gives definitions, postulates, common notions and propositions (the latter of which are derived from the definitions, postulates and common notions or each other).

There are 5 postulates given:
1. To draw a straight line from any point to any point. {this is to be read in the sense of "it is always possible to draw a straight line from any point to any other point"}
2. To produce a finite straight line continuously in a straight line.
3. To describe a circle with any centre and distance.
4. That all right angles are equal to one another.
5. That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which there are angles less than two right angles.

My question is "which of these 5 postulates are synthetic a prioris, which are synthetic a posteriori, and which are analytic"? — Agustino

The answer will be forced to be either synthetic a priori or synthetic a posteriori, and one must be given a reason why. If all axioms are synthetic a prioris, except for the 5th one, then why is it that the fifth one isn't, and yet Kant and Schopenhauer thought it is? Because clearly, non-Euclidean geometry demonstrates beyond a shadow of a doubt that the 5th postulate is not a synthetic a priori, despite what Kant and Schopenhauer thought.

If the axioms are synthetic a posteriori, then geometry is not apodictic - it is not certain. This means that outer space does not have to obey our geometrical constructs (since clearly, those constructs are not some a priori forms of our sensibility that exist in the mind and through which all phenomenal experience is given). Then the whole of Kantian thought collapses since space is not an A PRIORI form of the sensibility, and therefore (probably) must be determined by the senses itself (or at any rate, by the senses + a (reconceptualized) understanding), being a synthetic a posteriori.

It's that that you comment on form my post? — Banno

Yes, because the rest was a pile of unargued manure.

I watched quite a bit of the film somewhat horrified. — Banno

Why horrified at Peterson's speech?

Can you expand on this? — Noble Dust

Well, it's a difference of attitude. One claims that suffering is part and parcel of the nature of existence as we experience it now, and thus cannot be eliminated completely (it can only be fought against, held at bay, etc.) while the other party thinks that someone is responsible for the badness of existence, and if those people or agents are removed, then existence will be good.

Didn't Marx hold that advances in production, technology, and so on would result in new kinds of thinking? — Bitter Crank

Actually, he held the dialectical view, that advances in thinking and advances in production go hand in hand, and one spurs the other. Quantitative progress leading to qualitative progress in a loop sort of way. And sure, I agree with that view. When new possibilities of behaviour open up (that's what new technology does), then thinking changes to take those into account, which again opens up new possibilities of technology, etc. etc.

Somehow, I don't think most members of "the left" who you consider to be behind all these identity schemes would recognize a communist or a socialist if their lives depended on it. It's a strange kind of Marxism, if you ask me -- perverse. — Bitter Crank

The issue is precisely that the left campaigns on these points - they may not be responsible for them, but they certainly create unrest and add fuel to the fires. The left as it exists today, not the left in principle, because remember, I am somewhat left-leaning too as the many political tests I've done 1 year or so ago illustrate.

It isn't the case that Marx focussed on conflict between haves and have nots: He focussed on the conflict between producers and owners -- the working class and the bourgeoisie. The WRONG that Marx identified wasn't that some people had more than others, it was that those who produce all wealth (the workers) do not benefit proportionately, and that those who benefit DISPROPORTIONATELY (the bourgeoisie) do no work at all. EDIT: They perform work putting things together, but once assembled, they hire people to make sure it stays put together. — Bitter Crank

I think that the underlying issue is that people have grown accustomed to (or perhaps are forced to?) sell their labour instead of sell what they produce. For many, that is because they never learned how to produce anything. The social environment does a lot of harm here since it trains people to be handicapped. Basically, from the moment you enter the gates of your school, you are trained to sell your labour, not the products of your labour. You are told to stay in the schooling system, follow the path they lay out for you, get that degree, or get that job they help you to get, etc. You are never told "listen, you have useful things to give for society. You must concentrate on producing what is useful for your fellow human beings" - no, the message is always to trade your labour for money, instead of your products for money.

So the issue that many on the left don't get is that it's not business and the trading of commodities, goods and services that is problematic. It's the trading of labour. So the entrepreneur is actually the person who most often understands this - that the so-called exploitation happens when one trades their labour for money instead of their production for money. Labour is intrinsically tied to time - you need to spend time to labour. But production isn't. Production can happen without spending time, thanks to automatisation, or in the case of software, reproducing your product is essentially free, regardless of the number of copies you sell. So in the decoupling of production from labour, therein lies the "surplus value" that the entrepreneur takes for himself. And this decoupling is done at multiple chokepoints. One of them is in terms of means of production directly (the factory is owned by you, and your workers effectively pay you rent to use it to sell their labour), or in the distribution channel, in connecting client with product.

So all good entrepreneurship runs on the "rent" model. Getting paid for "renting" some means of production or means of distribution. Entrepreneurship is premised on the idea of passivity - all entrepreneurs want passive income, it is almost the Holy Grail. Passive income is determined by the amount of time required to make it. Rent, software, and money itself are very passive. Rent, you don't have to do much to collect it. Software, easy to reproduce, and resell, takes almost no work. And money, well, if you have lots of money, you give it to the speculators, and they breed it, so that it produces lots of babies for you.

What enables this kind of entrepreneurship is simply the fact that not everyone is an entrepreneur. If everyone became an entrepreneur, and nobody sold their labour, but rather the products of their labour, then there would be no problem. Hence distributism. So entrepreneurship is the solution, not the problem, which is what the left of today doesn't understand.

Another thing we have to take into account about Peterson is his milieu: Peterson is a college professor. College campus are exactly the kind of place where one would expect ideological excess because on campus are thousands of students (well... hundreds, anyway) who are anxious to try on radical new theories in a relatively safe environment (they are, after all, paying customers).

The wannabe radicals may be right, wrong, or not even wrong, but they can't, don't, and won't affect society very much. Once they get out of college and get hired to work in a large corporation, they will find they are not allowed anywhere close to the levers of power. If they attempt college stunts at work they are likely to get fired.

Peterson has perhaps been overly influenced by what happens on his (and other) campuses. It's a very lively but unrepresentative school playground. — Bitter Crank

I wouldn't say that those people aren't destructive once they exit University. Their attitudes influence elections, they influence workplace environments, and so on.

-How do you know the hierarchy is based on competency? Most people stay within their income bracket (and near where there parents were). So it could be that nearly everyone is incompetent, but it seems more likely that those who held power (whether political or economic) in the past has a strong relationship with who has it in the future. I'll just let you know that white people did not eliminate nepotism, not from politics nor in economics. — MindForged

I would say that over time the hierarchy always shifts towards competency. This doesn't mean that there cannot be cases, some of them even for hundreds of years, when incompetent people maintain positions of power. That is quite frequent - look at Justin Trudeau - no competency, he's there just because of his father.

Many people look at things in this way, but it's just a short-term thing. It's not sustainable - and when I say sustainable, I'm referring to the fact that it's not sustainable over many generations.

Regarding the concrete example you provided. Statistically, people may stay within their income bracket, but that isn't what interests me. What interests me is the possibility of moving from one income bracket to another. That isn't something that you can assess statistically because it presupposes that all people (or at least most people) are willing to do what it takes and desire to move from one income bracket to another. And of course, this just isn't true. Most people grow comfortable in their income bracket over time, and this is a personal observation I've made.

-Even if it is in fact the case that hierarchies cannot be eliminated, that does not entail that no specific hierarchy cannot be eliminated. Nor does competency need to entail privilege unless you are just something like social Darwinist ("those who succeed are the ones who are competent" seems to fit the bill) — MindForged

Hierarchies cannot be eliminated, but sure, they can be changed.

I never said competency entails privilege. But competency naturally translates in greater power to influence your surrounding environment. That's why things fell apart in the Eastern Soviet bloc, because people were promoted solely based on political connections and ideological reasons, and not on competence. Such a structure cannot survive in the long-run.

-So wait, you do acknowledge the existence of the Bourgeoisie??? Marxists define (it's not the full definition) that as the class which by whatever means necessary perpetuates their ownership of the means of production. — MindForged

Sure.

-Oh, lol, so we just exclude corruption? Hm, I guess when businesses (all of the most successful of which) sprinkle campaign donations on dozens of politicians we can just exclude that as counting against the idea of them being competent (otherwise they needn't manipulate the political process to their benefit by using their money). — MindForged

Yeah, I excluded it because corruption is a problem and needs to be addressed separately from whether or not someone is successful in their business. Someone can be successful without being corrupt.

But I think the phrase 'the lie of white privilege' is silly. — andrewk

Sure, it's just clickbait, just like my own thread title - a marketing element.

White privilege is simply not having to wonder whether a stranger will suddenly start to abuse you on the bus, just because of what you look like. — andrewk

The problem here is that I don't think that being white, in and of itself, prevents a stranger from abusing you on the bus. First of all, it depends on the geographical area we're talking about. And it also depends on many other features - if you have something that stands out - a weird looking nose, etc. - you may get people abusing you, regardless of your skin color. If you're a super big, muscular, strong and tough-looking black guy, you most likely won't get people abusing you on the bus. That's why I say that it really depends - we can't frame it as "white" privilege, as if this sort of privilige belonged only to whites and not people of other skin colors too. I think that, instead, it ought to be framed as being a decent human being and not abusing others, regardless of why the perpetrators claim to do it.

In the US it is also not having to fear a police officer every time one comes near, that they may stop and search you, or even shoot you, because of what you look like. One would have to live under a rock to think that such a privilege does not exist. — andrewk

Yeah, that is probably right, the US is a strange society in that regard.

Does this mean you're a republican? — Joshs

Yes, on most issues of American politics apart from healthcare, environmental policies and some economic issues.

Yes, being a Black American can provide unique experiences that help better qualify someone to discuss and debate political issues related to Black/minority America than a White American who has not had similar experiences. — Maw

Okay, I see. That's reasonable, but then it's a double-edged thing, since every demographic has its own problems. So even white people would confront problems that other demographic groups don't, etc.

racist, misogynistic, and repeatedly failed businessman — Maw

I don't think Trump is racist or misogynistic or a failed businessman. Out of those three, the most disputable one is the racist one. That one is debatable because it is plausible to say that at minimum he disconsiders African nations, though probably many US Presidents did that, whether they openly said so or not. For example, Obama called Libya a "shit show", very similar to Trump's "shithole" remarks.

But I don't think he disconsiders black Americans though. I have not seen evidence for that. So I would say even in that case Trump is more nationalist than racist.

The misogynistic - I don't really buy that. Trump has a view of women that is typically portrayed in popular culture. He doesn't see women as inferior, but he does buy into the popular image of the rich man being successful with women, and just the popular and ubiquitous way of viewing sexual issues. I don't think Trump has sexual morality though, and that's probably the biggest negative about him for me.

As for being a failed businessman, I find that one to be definitely and indisputably false. A lot of people say this, but many are not aware of just how difficult it is even to maintain one's wealth while actively investing it and managing it yourself. So if all Trump did was keep up with the S&P500 and beat inflation over his life while actively being engaged in the management of his fortune (which he did), he would be classified as successful, though not incredibly successful.

Otherwise, no serious modern Presidential candidate, Clinton, Obama, or otherwise, have claimed that their political qualifications stem simply from the color of their skin, or gender. — Maw

So political qualifications don't stem simply from skin color or gender, but the latter can contribute to it? Is that what you mean by the use of the word "simply"?

what would be worrying is if America voted for a white male president regardless of qualifications and competency. — Maw

That would be worrying, yes. As worrying as voting for a woman President or a black president regardless of qualifications and competency.

the most unqualified Presidential candidate in modern American history to capture the White House. — Maw

Why do you think a successful businessman is unqualified to be President?

It is impossible to imagine Obama or Clinton acting even remotely similar to Trump, and get anywhere near the candidacy. Otherwise, no serious modern Presidential candidate, Clinton, Obama, or otherwise, have claimed that their political qualifications stem simply from the color of their skin, or gender. — Maw

Sure, but you know why that is? Because much of the left media has been hypocritical for many years, and the voters are just sick of it.

And by the way, I think that if someone says "Vote for me because I'm (insert Gender, Skin Color, etc.)" then they are racist, sexist and the like, and there are no excuses for this. It doesn't matter if they are black or white, male or female. It's as bad in either case. As if having a certain skin color or gender ought to qualify you for being President :s - as if your skin color or gender was relevant to your competency for the job. It is the foundational trait of racism, sexism and the like to claim that gender, race, etc. instead of competency, qualifies someone for the job. We're really on some dangerous territory here if we think that this postmodernist absurdity makes any sense.

Barack Obama — Bitter Crank

But, unlike with regards to Bush, I don't have a lot of negative things to say about Obama, precisely because he was a career politician who stuck to the party line. What can I say? He did what Presidents usually do. That's it. The problem, of course, is that it's rare to have a good President.

Uncultured barbarians who have the means generally want entre to the class with matching amounts of money. The Cultured barbarians who got there first generally want to fence in their estates to keep new money out. Yes, it is snobbism, of course. This is an old problem for new money. As you become a wildly successful uncultured barbarian, rolling in cash from your various entrepreneurial activities, you will want to join the cocktail party / dinner party / dance party / board room circuit along with the other successful people. — Bitter Crank

I don't know, I don't think I'd like many of those things or be interested in them tbh. I don't like spending non-work related time around or talking to rich people.

How do you do that? You probably don't have a pedigree which would win you admission (no recent tzars, dukes, or earls in your family tree). Being white isn't privilege enough. Academic degrees definitely won't cut it. What you will do is fake a background. There are standardized methods of doing this. You live in the right kind of mansion, wear the right kind of clothes, go to the right church, give generously to the right charities, volunteer your services on the right committees, and in 30 years you might be accepted, grudgingly. Then your sons and daughters will reap the reward. They will be accepted as scions of money old enough not to still stink.

And per George Bernard Shaw, you also talk the right way. Very important to get the accent and idiom down cold.

Agustino Jr. can then marry the daughter (or son, if they turns out gay) of the leading family. It's a long range project. Good luck. — Bitter Crank

Well, my whole life I have fought against hypocrisy & convention, it would really be a shame to become one myself.