Immanuel Kant (1724-1804)

Epistemology

Metaphysics

Copyright (c) 1996, 1998, 2000, 2002, 2003, 2004, 2006, 2008, 2009, 2010, 2015, 2016, 2017, 2018, 2019, 2020, 2022, 2023 Kelley L. Ross, Ph.D. All Rights Reserved

Immanuel Kant (1724-1804), Note 1

The full quote, with some of the sequel goes:

Either the object alone must make the representation possible, or the representation alone must make the object possible [Entweder wenn der Gegenstand die Vorstellung, oder diese den Gegenstand allein möglich macht]. In the former case, this relation is only empirical, and the representation is never possible a priori. This is true of appearances, as regard that [element] in them which belongs to sensation. In the latter case, representation in itself does not produce its object in so far as existence is concerned, for we are not here speaking of its causality by means of the will. [§14, A92, B124-125, Norman Kemp Smith, St. Martin's Press, 1929, 1965, p.125]

A correspondent recently brought to my attention that I had left out the word "alone" (allein) from my paraphrase above. I think that Kant is better off without the "alone"; for if he really means that "the representation alone must make the object possible," this would mean that, apart from the representation, there are no other necessary conditions for the presence of an object. But this cannot be right. Kant himself, in this very passage, says that representation alone "does not produce its object in so far as existence is concerned." Something else is responsible for the existence of an object, and in Kant's philosophy that will obviously be the thing-in-itself. Thus, the representation of an object that counts as knowledge is made possible both by the representation and by the existence of the thing-in-itself.

If representation produces an object that does not exist, this is called a "hallucination." If representation causally produces an object that does exist, this can happen in two ways in Kant's thought. The representation can, by means of the will, create an object, as Kant mentions. However, the will in us is subject to the laws of nature, which means we can only create objects by means of natural causality. Creation ex nihilo and other miracles are not allowed. And then there is "intellectual intuition." As I have discussed elsewhere, "intellectual intuiton" is a notion commonly misused. There is not a true Kantian intellectual intuition unless the production of a representation will also create an externally existing object. Thus, Kant would think that only God would have this facility. Our sensible intuition is passive or receptive, according to Kant, which means that our knowledge waits for and receives existing objects, rather than creating them.

The danger of the "alone" in Kant's statement at A92 is the temptation to disregard the independence of existence and things-in-themselves. If we do that, and imagine that representation effects the existence of its objects, but then we are aware that this process is not under the control of our will or individual imagination, the solution might be to postulate a meta-consciousness, a mind itself possessing intellectual intuition, of which we are merely a part. This is rather like what we find in Spinoza, and, more significantly, in Hegel. Kant's "alone" is thus a kind of aneurysm, whose failure can produce a hemorrhage of Absolute Idealism. The context and cautions that Kant provides should protect us from that, but he does create a weakness.

Kant's second theory was also about nebulae, of a different kind. Along with bright and dark diffuse nebulae and planetary nebulae (which have nothing to do with planets), there are spiral nebulae. In Kant's day, I don't believe that the telescopes could resolve these as spirals. But as "nebulous stars," die neblichten Sterne, Kant did distinguish the species, quoting Pierre-Louis Moreau de Maupertuis (1698�1759), as their presenting "the figure of ellipses more or less open [mehr oder weniger offene Ellipsen]" [note].

Immanuel Kant (1724-1804), Note 2;
The Philosopher's Walk

While Kant is the first philosopher to become famous for having a "walk," it is now not clear if the route of the walk was as regular as its notoriously regular timing. Since Königsberg has been occupied by the Russians, the Mediaeval city pretty much demolished, and most of the German population long deported (or "disappeared"), both the local memory of Kant's habits and the layout of the city no longer contribute a connection to Kant's story. Since the Soviet city, Kaliningrad, was long closed to foreigners, it's not like the locals were approaching tourists to tell them, "That's where the philosopher Kant used to walk." There were no tourists and, after the Russian treatment of the city, no particular reason for there to be any.

Instead, other cities have become known for having a "Philosopher's Walk." One is the university town of Heidelberg, infamously associated with student dueling and with Martin Heidegger, where the Philosophenweg seems to have become a tourist attraction in its own right. It is not clear that this was inaugurated by a specific philosopher, and the word itself is ambiguous, since Philosophen can be both the genitive singular and the genitive plural of Philosoph, "philosopher" (an ambiguity, with Herren, that also turns up in a featured quote from Nietzsche) So this is either the "Philosopher's Walk" or the "Philosophers' Walk" in English. The plural is probably more appropriate for the history and usage. Weg, of course, is the German cognate of "way."

The other "Philosopher's Walk" is in, of all places, Kyōto, Japan, along a scenic, tree-lined canal on the East side of town. This can be traced back to an individual philosopher of the Kyōto School, Kitarō Nishida (1870-1945). "Philosophy" in Chinese is , which in Japanese is read tetsugaku. "Way" is the familiar in Chinese, which can be read dō or michi in Japanese. So we don't actually get "philosopher's walk" but the "way of philosophy," , Tetsugaku-no-Michi in Japanese. This could even be written , without the Japanese possessive particle, or in a corresponding Chinese form as (哲學之道), but both are still read the same way in Japanese.

The University of Toronto also has its Philosophers [sic, now often written "Philosopher's"] Walk, which runs from Bloor Street south to Hoskin Ave. Signs along the route explain how it was once a stream bed, and a venue for pre-Columbian fairs and functions, but the bed dried up when the stream was diverted in the development of Toronto. Now it has been developed as a scenic park space, with a pleasant, meandering path.

There is no explanation, however, why it should be called a "Philosophers Walk." At this point, the tradition may be developing that any pleasant path through a university is going to be a "Philosopher's Walk," despite the walks through Königsberg, Kyōto, and Heidelberg not traversing any universities or schools, although the first two are associated, unlike the others, with specific philosopher individuals.

So Kant's own walk has become a bit of an orphan, not unlike the city of Königsberg itself; and it does not sound like either locals or tourists do or even are able to practice the same walk, unlike in Heidelberg, Kyōto, or even Toronto.

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Immanuel Kant (1724-1804),
Note on Kant's Astronomy

Before his Critical period, Immanuel Kant nevertheless had made a bit of a name for himself. Part of this was due to the Observations on the Feeling of the Beautiful and Sublime (1764), which shows a very different kind of Kant, as thinker and writer, than what becomes familiar in the later works. Indeed, Kant's moral observations in his four humor typology seem more sensible, realistic, and humane than the rigor of the Categorical Imperative.

Kant's most striking early contribution to knowledge, however, was his General Natural History and Theory of the Heavens (Allgemeine Naturgeschichte und Theorie des Himmels, 1755). Kant had two noteworthy theories in physics and astronomy. One was the "Nebular Hypothesis" of planetary formation. Kant reasoned that diffuse nebulae, dim clouds of dust and gas that were only first being well observed in his lifetime, would collapse under the force of gravity. As they did, they could begin spinning and would then spin out into a disk. From these spinning disks stars and planets would condense. Unlike the greatest of earlier German philosophers, Leibniz, Kant was not himself much of a mathematician, so the theory was not given a mathematical form until the great French mathematician Pierre-Simon Laplace (1749-1827) did so in 1796. Although there was still argument in my childhood about the formation of planets, it now seems to be generally accepted that both stars and planets condense out of nebulae and collapsed, spinning disks of dust and gas. There are stellar "nurseries" that can be examined in places like the Orion Nebula. Kant was right. The principal addition to Kant's theory may be that diffuse nebulae are now believed to begin collapsing and spinning because of shock waves from supernova explosions, which clear voids in nebulae and concentrate material at the edges. Unfortunately, some astronomy textbooks refer to the Nebular Hypothesis as the theory of Laplace alone, instead of the Kant-Laplace theory, and do not give Kant proper credit.

Laplace believed that these elliptical nebulae were actually the spinning disks of the Nebular Hypothesis. Kant had a different idea. In 1750 Thomas Wright had suggested that the Milky Way, the Galaxy, was a vast spinning disk itself, consisting of stars and everything else, and that the earth was part of this system. Kant had read a report of this theory, and his use of it actually first brought it to general attention. An observational confirmation of it came from the great astronomer William Herschel in 1785.

Kant's idea was that the dim, tiny nebulae were themselves external galaxies, "island universes" independent of the Milky Way. He says:

It is far more natural and conceivable to regard them as being not such enormous single stars but systems of many [stars], whose distance presents them in such a narrow space that the light which is individually imperceptible from each of them, reaches us, on account of their immense multitude, in a uniform pale glimmer. Their analogy with the stellar system in which we find ourselves, their shape, which is just what it ought to be according to our theory, the feebleness of their light which demands a presupposed infinite distance: all this is in perfect harmony with the view that these elliptical figures are just [island] universes and, so to speak, Milky Ways, like those whose constitution we have just unfolded. [op. cit., p.63, boldface added]
Weit natürlicher und begreiflicher ist es, daß es nicht einzelne so große Sterne, sondern Systemata von vielen sein, deren Entfernung sie in einem so engen Raume darstellet, daß das Licht, welches von jedem derselben einzeln unmerklich ist, bei ihrer unermeßlichen Menge in einem einförmichten blassen Schimmer ausschlägt. Die Analogie mit dem Sternensystem, darin wir uns befinden, ihr Gestalt, welche gerade so ist, als sie es nach unserem Lehrbefriffe sein muß, die Schwäche des Lichts, die eine vorausgesetzte unendliche Entfernung erfordert: Alles stimmet vollkommen überein, diese elliptische Figuren vor eben dergleichen Weltordnungen, und so zu reden, Milchstraßen zu halten, deren Verfassung wir eben entwickelt haben... [op.cit., p.266, A15-16]

There was really no evidence for this. It was just a guess. Nevertheless, it launched a great debate that lasted all the way until 1924. Astronomers were either Laplaceans or Kantians. Although Kant is said to have introduced the term "island universes," I do not see "island" in his text, just "universes," Weltordnungen. Nevertheless, the expression became associated with his theory.

The Great Debate

Thus, as late as 26 April 1920, there was a formal debate over the issue between Harlow Shapley (1885-1972, the Laplacean, at left) and H.D. (Heber Doust) Curtis (1872-1942, the Kantian, at right) at the National Academy of Sciences. It was the older scientist, Curtis, with the modern view.

However, the matter was not settled by the debate but by Edwin Hubble (1889-1953) in 1923-1924, using the recently completed Mount Wilson 100 inch telescope, in the San Gabriel Mountains above Pasadena, California -- a telescope whose mirror was made from crushed French wine bottles and was hauled up the mountain by mules. The dirt track that was used is still there and can be hiked. The site of the telescope is visible from the San Fernando Valley, although the building is over the crest of the ridge and surrounded by trees. The modern forest of radio and television towers on the mountain, however, is plainly visible.

Hubble was able to identify Cepheid variable stars in nearby spiral nebulae -- initially the Great Spiral Nebula in Andromeda, whose full extent covers three degrees of arc in the sky (six times the diameter of the sun or moon), although only the much smaller core is visible to the naked eye -- actually, the most distance object visible to the naked eye, at 2.38 million Light Years. With this kind of variable star, their period of variation is proportional to their absolute brightness. With their absolute brightness (M), compared to the apparent brightness (m), Hubble would know their absolute distance (m - M = 5 log (r/10), where r is in parsecs). They were far, far further away than the stars of the Milky Way Galaxy. They were in external galaxies. Kant was right.

Hubble's sensational results were presented to a meeting of the American Astronomical Union in December 1924. Now, since it was just a guess, how much credit can we give to Kant? A fair amount, since many great ideas in science begin as guesses, sometimes with little or contrary evidence behind them (as was the case with Copernicus, come to think of it). More importantly, if we ask who the first person was to conceive the form of the universe as we now see it, filled with "billions and billions" of galaxies (as Carl Sagan liked to say), the answer is just: Immanuel Kant, a man who never left East Prussia and who never saw a mountain (although he described them vividly).

Astronomical Ignorance and Falsehoods

Now, not only is it rare to see Kant given credit for his theory, but positive falsehoods can be found in public discourse. Thus, an episode of the History Channel program The Universe, "Beyond the Big Bang" [2007], credited Hubble with being the first person to conceive as well as prove that spiral nebulae are external galaxies, completely ignoring Kant and the long history of the controversy that culminated in the debate between Shapley and Curtis -- which, of course, is not mentioned. Nor is this shocking carelessness and distortion just the fault of the writers of the narrative (they often cannot be trusted on these shows), but we see the assertion seconded by featured talking-head scientists, like Michio Kaku.

Just a century ago, we thought that the Milky Way was all there was. Scientists called it our 'island universe.' For them no other galaxies existed. Then in 1924, astronomer Edwin Hubble changed all that.

I begin to wonder if Kaku himself is behind the promotion of this distortion. And it is a low blow to use the Kantian term, "island universe," for the very theory, that the Milky Way is the only galaxy, that Kant was contradicting.

Perhaps no one takes cable documentaries, or their recurring stars, seriously; but we now have Lawrence M. Krauss (whom we have seen endorsing George H. Smith's atheism) in his article "The Universe: 'The Important Stuff Is Invisible'," in The New York Review of Books of March 10, 2016. This is a lot more recent than my cable examples. Krauss, who is identified as the "Foundation Professor in the School of Earth and Space Exploration and the Physics Department at Arizona State [University, Tempe] and Director of its Origins Project," is reviewing the book Dark Matter and the Dinosaurs: The Astounding Interconnectedness of the Universe by Lisa Randall. Early in the course of this he writes:

...it is sometimes hard to appreciate that less than one hundred years ago the entire universe, as conceived by astronomers, consisted of a single galaxy, the Milky Way, surrounded by a possibly eternal static void. [p.37]

So here we have the same falsehood advanced six to nine years earlier by Michio Kaku, and the same ignorance of the history of astronomy, from Kant to Shapley and Curtis. As a physicist, perhaps Krauss cannot be expected to know the history of astronomy; but if he is writing about it, and saying things like "as conceived by astronomers," he should take some care to be informed. We must also worry that if there are fact-checkers at The New York Review of Books, they are not doing their job here. And with all these people, we should reflect that, not only are they ignorant of what happened, they also cannot appreciate the nature of Hubble's accomplishments. He was working against a background of lively debate, not a background of a complacent "static void" in astronomy.

Apart from this, Krauss seems to be a particularly militant and vicious atheist. Indeed, he has a piece in the New Yorker of September 8, 2015, entitled "All Scientists Should Be Militant Atheists." In 2018, the moral force of this has now been rather attenuated by multiple accusations of sexual misconduct against Krauss. Despite complaints that he did not enjoy ordinary legal protections in the inquiry by his institution, Arizona State University, something we have come to expect from the Star Chamber ethos of the modern university, he agreed to retire from his academic position. What this may have to do with his atheism, or his carelessness about the history of astronomy, I cannot say.

Atheism and Sophistry

Infantile Atheism

The Great George O. Abell

Is the problem in all this the result of simple ignorance, or of a positive bias against giving a mere philosopher a significant place in the history of science? There was certainly neither ignorance nor bias with the great UCLA astronomer George O. Abell (1927-1983). Abell will be long remembered for the catalogue he compiled, using the Palomar telescope, of clusters of galaxies, which now are identified by their "Abell" number.

Laurent de La Hyre (1606-1656), Allegory of Astronomy, 1649, Musée des Beaux-Arts, Orléans, France;
one of the seven Liberal Arts


Laurent de La Hyre (1606-1656), Allegory of Astronomy, 1649, Musée des Beaux-Arts, Orléans, France; one of the seven Liberal Arts

Yet Abell gave full credit to Kant in his astronomy textbook, The Realm of the Universe [Hold, Rinehart and Winston, 1976, pp.327-329 -- continued after his death, Abell, G.O., Wolff, S.C., and Morrison, D., Realm of the Universe, Saunders College Publishing, 5th edition, 1994].

Abell quotes Kant and inserts "island" in brackets into the text, just as I have done above.

Since the writers of textbooks tend to look at others in their field, and since scientists like Kaku or Krauss can be expected to have seen some astronomy textbook in the course of their education, if not Abell's own, that could be informed with Abell's knowledge, it hard to imagine that they simply don't know about the history of the theory of external galaxies. It is shocking to see them endorsing the distortion perpetuated in something like "Beyond the Big Bang" (which, of course, also perpetuates the calumny that geocentric astronomers were just bigoted fools) or "Alien Galaxies." Science education is bad enough in the United States without the History Channel, the Science Channel, and The New York Review of Books joining in with gratuitous misrepresentations.

I now see a curious case in 2021. On a new episode of Nova, "NOVA Universe Revealed: Milky Way," broadcast 3 October 2021, Cambridge astronomer Gerry Gilmore (b.1951) proclaims, "It was only 100 years ago people thought our Milky Way was the entire universe." This is a little ambiguous, since "people" could just mean some people; but the impression it gives is that all people thought this. Mere impression or not, it echoes a falsehood that should have been long banished.

The curious thing about this, however, is that Gilmore's statement is an outtake. It is included as teaser for the show, before the main title credits, but then it is entirely missing from the actual show, which ignores the whole question of when it was thought, let alone proven, that the Milky Way was not the only galaxy. This in it itself leaves the impression that the producers decided that they didn't need to get into it. If anything else was filmed about the theory of external galaxies, it was left on the cutting room floor. I'm not sure if that is progress, or what. If the show wasn't going to cover it, why include Gilmore's deceptive statement as a teaser? A teaser without a payoff. That is dishonest, a kind of "bait-and-switch."

If Nova is going to do astronomy episodes, one of its duties ought to be to clear up the misconceptions such as we have seen with Michio Kaku, Lawrence M. Krauss, and Gerry Gilmore. But, you know, if they can't do that with John Philoponus, how can we expect them to do it with Kant and Laplace? George O. Abell, where are you when we need you?

Ignorance and falsehoods about the history of astronomy live in 2023. John Horgan is identified by The Wall Street Journal as the Director of the "Center for Science Writing at Stevens Institute of Technology" (in Hoboken, New Jersey). His background is journalism rather than science; but he has been a writer and blogger for Scientific American, which may tell us more about that magazine than it does about him. He made a splash by claiming that there were going to be no more great discoveries in science or, apparently, in mathematics, which elicited widespread derision, as it should, for such folly.

In the Journal, he reviews two books, Simulating the Cosmos: Why the Universe Looks the Way It Does, by Romeel Davé, and The Universe in a Box: Simulations and the Quest to Code the Cosmos, by Andrew Pontzen. Whatever is in these books, and whatever Mr. Horgan may have learned elsewhere, he begins his reviews with these stunningly ignorant statements:

Little more than a century ago, humans believed that our universe consisted solely of the Milky Way, the swirl of stars that houses our solar system. But in the 1920s telescopes got bigger, and so did the universe. Astronomers spotted other galaxies far beyond the edges of our own. Isn�t that awesome? ["The Cosmologist's Craft," The Wall Street Journal, September 9-10, 2023, p.C9]

As we have seen, the idea the Milky Way was thought to be the whole universe is common, despite Kant suggesting otherwise more than a century earlier, which set off a lively debate that was not settled until Edwin Hubble. But Mr. Horgan represents a new level of achievement in ignorance by saying that in the 1920's, "astronomers spotted other galaxies," which of itself revealed the truth. Of course, it was because the galaxies had already been "spotted" in the 18th Century that Kant would propose his theory.

Horgan then introduces and trivializes Hubble by saying he was, "One such astronomer," i.e. with all those (dozens? hundreds?) who "spotted other galaxies." He then credits Hubble with discoverying the Red Shift, skipping over the proof, let alone the controversy, about the existence of external galaxies in the first place. Horgan could at least have told us who was the first astronomer who "spotted other galaxies."

Horgan's final remark, "Isn�t that awesome?" is the sort of breathless, gee-whiz rhetoric that plagues some kinds of documentaries, and perhaps is now unfortunately taught at the Stevens Institute of Technology.

Years ago, with the naked eye, I was able to "spot" the Great Spiral Nebula in Andromeda, which had turned out to be an external galaxy, in fact the first to be proven by Hubble to be one. I didn't need any telescope, much less a "bigger" one, to do that -- just a dark sky, which, back then, was available on the edge of Austin, Texas. Indeed, the Andromeda Galaxy is the most distant object that can be seen with the naked eye. Mr. Horgan should try it some time.

As it happens, Googling "Great Debate" turns up multiple webpages on the debate between Shapley and Curtis, which have full information. Sometimes, however, this debate is still referenced in documentaries without any explanation of its background, or any mention of Kant or Laplace. Thus, despite the occasional (or frequent) sins on television, anyone who pays attention to the matter can be informed of the truth. I am tempted to add to the resumé of George O. Abell that he was a great astronomer in part because he was accurately informed about the history of astronomy.

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Copyright (c) 1996, 1998, 2000, 2002, 2003, 2004, 2006, 2008, 2009, 2010, 2011, 2013, 2016, 2017, 2018, 2019, 2021, 2022, 2023 Kelley L. Ross, Ph.D. All Rights Reserved

Immanuel Kant (1724-1804),
Note on Kant's Astronomy; Note

Immanuel Kant, Universal Natural History and Theory of the Heavens, translated by W. Hastie, Introduction by Milton K. Munitz, Ann Arbor Paperbacks, University of Michigan Press, 1969, p.62; in German: Immanuel Kant, Vorkritische Schriften bis 1768, 1, Werkausgabe Band 1, edited by Wilhelm Weischedel, Suhrkamp, 1960, 1977, p.265, A13.

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Analytic and Synthetic:
Kant and the Problem of First Principles

Except for outright Skeptics, Aristotle's solution to the Problem of First Principles, that such propositions are known to be true because they are self-evident, endured well into Modern Philosophy. Then, when all the Rationalists, like Descartes, Spinoza, and Leibniz, appealed to self-evidence and all came up with radically different theories, it should have become clear that this was not a good enough procedure to adjudicate the conflicting claims. This awkward situation was then blown apart by Hume, under whose skeptical examination, reviving the critique of al-Ghazālī, even the principle of causality crumbled.

Kant does not directly pose the Problem of First Principles, and the form of his approach tends to obscure it. Thus, the "Transcendental Logic" in the Critique of Pure Reason is divided into the "Transcendental Analytic" and the "Transcendental Dialectic." The "Dialectic" is concerned with the fallacies produced when metaphysics is extended beyond possible experience. The "Analytic," about secure metaphysics, is divided into the "Analytic of Concepts" and the "Analytic of Principles." "Principles" would be Principia in Latin, i.e. "beginnings," "first things," "first principles," where now in English, thanks to the drift in the meaning of "principle," the term must be reduplicated with an etymologically redundant "first." Kant, however, is here writing in German, and in place of Principia we have Grundsätze (singular Grundsatz, "principle," "axiom" -- literally "ground sentence"). The examination of the Grundsätze, however, is deferred until after the "Analytic of Concepts." Thus, were the Problem of First Principles to be raised, it seems like that would come after an examination of concepts. Since it is not raised at all, one is left with the impression that it has somehow, along the way, actually already been dealt with. It has. [note]

The peculiarity of Kant's approach, from an Aristotelian (or Friesian) point of view, is not idiosyncratic. Kant approaches the matter as he does because he is responding to Hume, and one of Hume's initial challenges is about the origin of "ideas." While the Problem of First Principles is about the justification of propositions, Hume's Empiricist approach goes back to asking about the legitimacy of the very concepts, of which the propositions are constituted, in the first place. The Rationalists never worried too much about that. For Descartes, any notion that could be conceived "clearly and distinctly" could be used without hesitation or doubt, a procedure familiar and unobjectionable in mathematics. It was the Empiricists who started demanding certificates of authenticity, since they wanted to trace all "ideas" back to experience. Locke was not aware, so much as Berkeley and Hume, that not everything familiar from traditional philosophy (or even mathematics) was going to be so traceable; and Berkeley's pious rejection of "material substance" lit a skeptical fuse whose detonation would shake much of subsequent philosophy through Hume, thanks in great measure to Kant's appreciation of the importance of the issue.

Thus, Kant begins, like Hume, asking about the legitimacy of concepts. However, the traditional Problem has already insensibly been brought up; for in his critique of the concept of cause and effect, Hume did question the principle of causality, a proposition, and the way in which he expressed the defect of such a principle uncovered a point to Kant, which he dealt with back in the Introduction to the Critique, not in the "Transcendental Logic" at all. Hume had decided that the lack of certainty for cause and effect was because of the nature of the relationship of the two events, or of the subject and the predicate, in a proposition. In An Enquiry Concerning Human Understanding, Hume made a distinction about how subject and predicate could be related:

All the objects of human reason or enquiry may naturally be divided into two kinds, to wit, Relations of Ideas, and Matters of Fact. Of the first kind are the sciences of Geometry, Algebra, and Arithmetic; and in short, every affirmation which is either intuitively or demonstratively certain [note: these are Locke's categories]. That the square of the hypothenuse is equal to the square of the two sides, is a proposition which expresses a relation between these figures. That three times five is equal to the half of thirty, expresses a relation between these numbers. Propositions of this kind are discoverable by the mere operation of thought, without dependence on what is anywhere existent in the universe. Though there never were a circle or triangle in nature, the truths demonstrated by Euclid would for ever retain their certainty and evidence.
Matters of fact, which are the second objects of human reason, are not ascertained in the same manner; nor is our evidence of their truth, however great, of a like nature with the foregoing. The contrary of every matter of fact is still possible; because it can never imply a contradiction, and is conceived by the mind with the same facility and distinctness, as if ever so conformable to reality. That the sun will not rise to-morrow is no less intelligible a proposition, and implies no more contradiction than the affirmation, that it will rise. We should in vain, therefore, attempt to demonstrate its falsehood. Were it demonstratively false, it would imply a contradiction, and could never be distinctly conceived by the mind. [Enquiries, Selby-Bigge edition, Oxford, 1902, 1972, pp.25-26]

Both paragraphs warrant quoting in full. The first now would seem properly more a matter of embarrassment than anything else. Whatever Hume expected from intuition or demonstration, it would be hard to find a mathematician today who would agree that "the truths demonstrated by Euclid would for ever retain their certainty and evidence." If Hume's fame rests on this point, there would be little to recommend it. The second paragraph, however, redeems the impression by giving us a logical criterion to distinguish between truths that are "relations of ideas" and those that are "matters of fact": A matter of fact can be denied without contradiction.

This was the immediate inspiration to Kant, who can have asked himself how something "demonstratively false" would "imply a contradiction." A contradiction means something of the form "A and not-A." If a proposition expressing a matter of fact can be denied without contradiction, then the subject and the predicate of such a proposition cannot contain anything in common, otherwise the item would turn up posited in the subject but negated in the predicate of the denial. On the other hand, a proposition that cannot be denied without contradiction must contain something in the predicate that is already in the subject, so that the item does turn up posited in the subject but negated in the predicate of the denial. This struck Kant as important enough that, like Hume, he founded a whole critique on it, and also produced some more convenient and expressive terminology. Propositions true by "relations of ideas" are now analytic ("taking apart"), while propositions not so founded are synthetic ("putting together").

This clarified distinction Kant could then turn on Hume's own examples of "relations of ideas." Can geometry be denied without contradiction? Kant did not see that the predicates of the axioms of geometry contained any meaning already expressed in the subjects. They were synthetic. They could be denied without contradiction. Geometry would thus not have an intuitive self-evidence or demonstrative certainty that Hume claimed for it. Kant still thought that Euclid, indeed, would have certainty, but the ground of certainty would have to located elsewhere. Nevertheless, Kant is rarely credited, and Hume rarely faulted, for their views of the logic of the axioms of geometry. If the axioms of Euclid can be denied without contradiction, this means that systems of non-Euclidean geometry are logically possible and can be constructed without contradiction. But it is not uncommon to see the claim that Kant actually denied this, and it is Kant, not Hume, who is typically belabored for implicitly prohibiting the development of non-Euclidean systems. This distortion can only come from confusion and bias, a confusion about the meaning of "synthetic" (even in Hume's corresponding category), and a bias that the Analytic tradition has for British Empiricism, by which the glaring falsehood of Hume's statements is ignored and Kant's true and significant discovery misrepresented. This curious and reprehensible turn is considered in detail elsewhere.

Kant, as it happens, also did not see how arithmetic could be analytic. In his own example of "7 + 5 = 12" (p. B-15), if "7 + 5" is understood as the subject, and "12" as the predicate, then the concept or meaning of "12" does not occur in the subject. This was rather harder to swallow than the point about geometry, for it seems rather "intuitively" certain that "7 + 5 = 12" cannot be denied without contradiction. Kant must have missed something. Hope for demonstrating the analytic nature of arithmetic came with the development of propositional logic, since a proposition like "P or not P" clearly cannot be denied without contradiction, but it is not in a subject-predicate form. Still, "P or not P" is still clearly about two identical things, the P's, and "7 + 5 = 12" is more complicated than this. But, if "7 + 5 = 12" could be derived directly from logic, without substantive axioms like in geometry, then its analytic nature would be certain. In their Principia Mathematica (1910-1913), Russell and Whitehead and, in the Tractatus, Wittgenstein thought that they could indeed derive arithmetic from logic. Their demonstrations, however, were flawed, and it turned out that substantive axioms were necessary, just like in geometry. The axioms are now those of axiomatic Set Theory, and it is Set Theory that concerns the foundations of arithmetic. Kant turned out to be right again, though, curiously, he is again rarely credited for this.

Kant's discovery, however, can be trivialized if it turns out that there are simply no analytic propositions at all. This task was undertaken by Willard Van Orman Quine ("Two Dogmas of Empiricism," 1950). The approach, simply enough, was Nominalistic. If we say that "red is a color" is an analytic proposition, where is "color" in "red"? I don't see it. If we say that the meaning "color" is in the meaning of "red," where are these "meaning" things? I don't see them. Thus, if language consists of words but not abstract meanings, then we don't have to worry about one meaning containing another. "Red is a color" is just a convention of our language, which is even what we can say about "P or not P." Besides the general failings of Nominalism, Quine's particular critique is well refuted by Jerrold Katz.

In Kant there is little left in the category of "analytic." Definitions and truths of logic are going to be about it; and the definitions themselves will be suspect when the concepts defined may or may not be legitimate. The meaning within a concept must also in some sense be "put together," and the ground of this will raise the same questions as the ground of synthetic propositions. Thus, Saul Kripke began to speak of "analytic a posteriori" propositions, when the meanings in the subject are themselves united on only a posteriori grounds, i.e. the basis of experience. Indeed, dictionary definitions of natural language words are prima facie of conventional usage, e.g. how a pot is different from a pan, and the meaning of any words can be simply stipulated for some appropriate purpose, e.g. a "designated hitter" can go to bat for some particular member of a baseball team (usually the pitcher), without otherwise replacing him in other play. Thus, a big fight over the existence of analytic propositions doesn't in the end make that much difference. Synthetic propositions are the key anyway, as they were if Kant wanted to answer Hume's critique of causality.

For, indeed, outside of an axiomatized logic itself, the First Principles of Demonstration will be synthetic. However Kant can explain the truth of non-empirical synthetic propositions, i.e. those that are a priori instead of a posteriori, that will be his answer to the Problem of First Principles. They are clearly now, after Hume, not going to be self-evident. Yet Hume himself is often poorly understood. While it is common to say that Hume denied the existence of synthetic a priori propositions, there is some question about whether he actually does. He says that the relationship of cause and effect is not discovered or known by any reasonings a priori, but that is not the same thing. A synthetic a priori proposition is not known from any reasonings. In fact, Hume does not see that the relationship of cause and effect is discovered or known from anything, since it is not justified by experience, in which there is no necessary connection between cause and effect, and there is in fact nothing in the cause to even suggest the effect, much less that the effect must follow. Hume's famous explanation was a psychological one, that we become accustomed to the association of certain events ("causes") with others ("effects"); but this, obviously, carries no weight whatsoever about the nature of things, which is what makes Hume, very properly, a Skeptic.

At the same time, Hume had no doubts whatsoever of the necessity of cause and effect. This is where he is commonly misrepresented. People assume that because he was a Skeptic, then he must have thought it possible for causes to occur without effects, i.e. for the principle of causality to be contradicted in actuality. He never had any such expectation, and in fact he ruled out a priori, not only miracles, but also chance and free will just because they would violate (a very deterministic) causality. Confusion over this occurs because people do not appreciate that Hume as an "Academic" Skeptic, holding that lack of knowledge (the meaning of "Skepticism") does not rule out "reasonable" beliefs. Causality is a "reasonable" belief because, as Hume says, "All reasonings concerning matter of fact seem to be founded on the relation of Cause and Effect" [Enquiry, op. cit., p. 26]. So without it, we would have no basis of reasoning in daily life. Thus, Hume says:

Nor need we fear that this philosophy, while it endeavors to limit our enquiries to common life, should ever undermine the reasonings of common life, and carry its doubts so far as to destroy all action, as well as speculation. Nature will always maintain her rights, and prevail in the end over any abstract reasoning whatsoever. Though we should conclude, for instance, as in the foregoing section, that, in all reasonings from experience, there is a step taken by the mind which is not supported by any argument or process of the understanding [i.e. from cause to effect]; there is no danger that these reasonings, on which almost all knowledge depends, will ever be affected by such a discovery. [ibid., p. 41]

Kant therefore understood that Hume's problem was not with the quid facti, that there were causes and effects, and necessary connection, but with the quid juris, the epistemic justification of the principle. While some philosophers spent much of the 20th Century congratulating Hume for having discovered that causality might not exist, they never seem to have noticed that he explicitly denied having done anything of the sort. Kant already knew the type, who "were ever taking for granted that which he doubted, and demonstrating with zeal and often with impudence that which he never thought of doubting..." [Prolegomena to Any Future Metaphysics, p. 259, Lewis White Beck translations, Bobbs-Merrill, 1950, p.6].

Kant's solution to the quid juris in the Critique of Pure Reason was the argument of the "Transcendental Deduction" (in the "Analytic of Concepts") that concepts like causality are "conditions of the possibility of experience," because they are the rules by which perception and experience are united into a single consciousness, through a mental activity called "synthesis." Once the existence of consciousness is conceded (which not everyone, e.g. behaviorists, might be willing to do), then whatever is necessary for the existence of consciousness must be conceded.

This is a strong argument and, decisive or not, is heuristically of great value, especially when we untangle it from the earlier views of perception in the Critique. However, it suffers from a couple of serious drawbacks. One is that, like Hume's own explanation, it is a psychological approach that does not necessarily tell us anything about objects, i.e. consciousness may be united in a way that is irrelevant to external things. Kant seemed to recognize this himself when he said that none of this gives us any knowledge of things-in-themselves. This problem was never properly sorted out by Kant, and is considered independently in "Ontological Undecidabilty".

The second drawback of Kant's argument is that it would only work, indeed, for the "conditions of the possibility of experience," and not for any other matters which might seem to involve synthetic a priori propositions. Hume himself was just as concerned about morality as about causality, and found himself in the same Skeptical position in both matters. The only comparable thing that Kant can do for morality, however, would be to employ a principle of the "conditions of the possibility of morality." But this would require conceding that morality exists, which is something that a very large number of people in the 20th century, far beyond behaviorists, would not be willing to do. Nor does it make one a Kantian merely to vaguely appeal to human "rationality" (e.g. John Rawls) as a basis for morality, since this really just begs the question of justification -- besides violating Hume's famous observation that propositions of obligation ("ought," imperatives) cannot be logically derived from propositions of fact ("is," indicatives).

Keeping in mind that First Principles cannot be proven, and that synthetic propositions can be denied without contradiction, the conspicuous historical alternatives seem to be to deny one or the other. Hegel denied the first, by taking the equivalent of Kant's Transcendental Deduction as itself a part of metaphysics and a proof, by means of novel principles of "dialectical" logic, of moral and metaphysical truths. To an extent, Hegel may also have denied the second, as Leibniz certainly did, treating any moral or metaphysical truth as analytic, if only from the point of view of divine omniscience. Either such move, however, cannot escape the original embarrassments of Rationalism, or avoid the devastation inflicted by the criticisms made by Hume and Kant.

Less conspicuous historically was Jakob Fries, who could accept the proper meanings of "First Principle" and of synthetic propositions. The Friesian theories of deduction and of non-intuitive immediate knowledge make it possible to preserve the advances of Hume and Kant without falling back into Rationalism or heading for the Nihilism (so different from Hume's Skepticism), relativism, scientism, pragmatism, etc., so conspicuous in the 20th century. Later, Karl Popper proposed a special solution for the Problem in that science, by using falsification, does not need to worry about a positive justification of First Principles at all. This enables scientific progress to heedlessly continue, as it has, regardless of the status of any philosophical solution.

Thus, Kant gave us the real elements of the solution of the Problem of First Principles, even though he could not complete and seal the matter himself. Indeed, no one can hope to do that, even as new elements and new understanding of the solution emerge over time.

Epistemology

The passage also displays a bit of evidence that Kant takes the derivation of universal propositions from experience through induction as unproblematic. He cannot have been unaware of the Problem of Induction, having read Hume, but had not worked out, as no one would until Karl Popper, that there is a solution.

Copyright (c) 2000, 2004 Kelley L. Ross, Ph.D. All Rights Reserved

Analytic and Synthetic:
Kant and the Problem of First Principles, Note

In his earlier writings, in Latin, Kant had actually used the Latin expression principia prima, "First Principles." In the Critique of Pure Reason, we get an explicit discussion of principia only at the beginning of the "Transcendental Dialectic":

The term 'principle' [Prinzips] is ambiguous, and commonly signifies any knowledge [Erkenntnis] which can be used as a principle [Prinzips], although in itself, and as regards its proper origin [Ursprung], it is no principle [Principium]. Every universal proposition, even one derived from experience, through induction [Induktion], can serve as major premise [Obersatz] in a syllogism; but it is not therefore itself a principle [Principium]. [Norman Kemp Smith translation, St Martin's Press, 1929, 1965, p.301, A 300]

Here the difference between Kant's use of the German term and the Latin is, shall we say, lost in translation -- an entirely unnecessary loss, since the Latin term could have been used in English just as in German. Kant explains the drift in meaning of "principle," but instead of contrasting principium with principium primum, as in English we can contrast "principle" with "first principle," he contrasts German Prinzips with Latin Principium. By translating both the German term and the Latin one as "principle," Kemp Smith obscures the difference between a principle, in the modern sense, and a first principle. This may reveal that Kemp Smith actually isn't very sensitive or interested in either first principles or the Problem of First Principles. Indeed, Anglo-American philosophy, with its empiricist tendencies, has not been attracted to anything so un-empirical as first principles.

Kant's Transcendental Idealism

The obscurity of Kant when it comes to his theory of empirical realism and transcendental idealism is largely due to his terminology and the difficulties of reconciling parts of his theory. Since "transcendental" is contrasted with "empirical," the two terms are epistemological and mean "independent of (i.e. transcending) experience" and "immanent in experience." Since "realism" is contrasted with "idealism," those two terms are ontological and mean "independent of my existence" and "dependent on my existence." Berkeley was for Kant the characteristic "idealist," and undoubtedly an empiricist, while Descartes was a "realist," believing commonsensically that objects exist independent of us, but who also thought that we could only know their essences through "clear and distinct" innate ideas, not experience -- while experience is unreliable because our only connection to external objects is through causation, which can conceal multiple possible causes, including the "Deceiving Demon." This made Descartes a "transcendental" realist.

If we try to construct a square of opposition using Kant's two distinctions, we have some trouble. A strictly constructed square of opposition would look like the one at right. "Transcendental" (ē) is the negation of "empirical" (e), and "idealism" (r̄) is the negation of "realism" (r). The structure we get, however, does not work for Kant's theory. Transcendental idealism and empirical realism would be contradictories and so cannot both be true, as Kant requires. Similarly, transcendental realism and empirical idealism are also contradictories and so cannot both be false, as Kant requires. The features of the square of opposition that we would expect Kant's theory to conform to would be that "contraries," the two upper members, are both false, while the "subcontraries," the two lower members, are both true.

If we want such a square of opposition, it will have to be rearranged without regard for the strict logical properties of the terms. We can save the distinctions and do that by recalling that opposites contradict each other only when applied to the same objects. Black coal and white snow are not contradictions. Kantian realism and Kantian idealism are thus reconciled by a distinction, that between phenomena and things-in-themselves. The former applies to the former, and the latter to the latter.

We can then produce a square like the one at right, which allows for the traditional truth values. In this version the definition of "transcendental idealism" has actually been left out. Kant's position, although terminologically embracing the two lower members, is really well defined by only one of them, empirical realism. However, saying that the objects of knowledge are immanent in experience and independent of our existence involves a paradox. How can something be independent in existence and yet dependent or immanent in our experience, our representation?

...the representation alone must make the object possible... ...representation in itself does not produce its object in so far as existence is concerned... [A 92]

The common sense, direct acquaintance with objects, part of this is what Kant appears to mean by his empirical realism, while the paradoxical, "in me but not of me," metaphysics is what he means by "transcendental idealism." This is the paradox addressed by Schopenhauer and by "Ontological Undecidability."

However, using the strict definitions, "transcendental idealism" means something else, as reproduced in the entry at left. If "transcendental" means, epistemically, "independent of experience," but "idealism" means, ontologically, "dependent on subjective (my) existence," then "transcendental idealism" would have to mean knowledge of objects that are dependent on my existence but independent of my experience. This seems to be, not just a paradox, but an out and out contradiction, since if something exists as an epiphenomenon of myself, it hardly seems like it could be independent of my experience. Berkeley's principle was "to be is to be perceived," but this kind of "transcendental idealism" would require that something is because of my existence but then is not perceived. This might work on the basis of Spinoza's metaphysics, where my existence is God's existence, but God's knowledge far transcends mine. Nevertheless, since anything is God, God is part of my experience after all.

What this peculiar meaning of "transcendental idealism" reveals are the loosest ends of Kant's thought. The terminology of "transcendental," "empirical," "realism," and "idealism" does not seem well ordered for Kant's purposes, in part because those purposes are unsettled. The contradiction of the strict rendering of "transcendental idealism" might be resolved if we say that there is simply no knowledge in this case, which is pretty much what Kant says about things-in-themselves -- the soul certainly depends on my existence but is not part of my experience because I don't have any knowledge of it. But then Kant doesn't want to go all the way with that. Morality doesn't fit into empirical reality, but then maybe that isn't too bad, since morality is really "regulative" rather than "constitutive" (of metaphysical entities). What is bad are "God, freedom, and immortality," which totally upset the applecart. If there are such things, they are about transcendent objects which, at least in one case, are independent of my existence. If they are only objects of "faith," we want to know how that is motivated; and if they are motivated as necessary conditions of the Moral Law, then it seems like they would be as much matters of knowledge as the necessary conditions of experience, i.e. causality, substance, etc.

My view is that the way out of this is through Friesian epistemology. Nevertheless, Kant's theory, as an approximation, is superior to any that have come since -- let alone the dismal exercises in nihilism, scientism, and scholasticism that are now so popular.

Since writing the foregoing treatment, I have tried tackling "Transcendental Idealism" again twice. The first was in 2010, when I added a section to this essay. I have now moved that to a footnote, which can be examined independently. This is a treatment that may be of interest in its own right, but it doesn't salvage a square of opposition with Kant's original terminology.

Now, in 2020, I have been rethinking Kant's terminology again and have a new solution. This is in footnote two of "A Deuternonomy of Kant-Friesian Metaphysics." There I have scrapped "Transcendental Idealism" altogether, accepting that is contains a self-falsifyng contradiction, and have suggested that there is a place for "Transcendental Realism" in Kant's system, although not in the form we find in Descartes.

Metaphysics

Kant's Transcendental Idealism, Note;
Update, 2010

Since I have not been happy with the logic of Kant's terminology concerning transcendental idealism and empirical realism, I have been trying to think of different ways to restate it. This diagram is another square of opposition, but the truth values are not determined by the properties of the square. Instead, we are looking at certain concepts, which themselves are no more than features of particular theories. While the concepts thus obey the principles of the square, they leave the truth of the theories underdetermined, which means that the truth or falsehood of the theories is a separate issue and is not reflected in the logic of the square.

The concepts in the square are "subject" ("s") and "object" ("o"); and what they reflect is the idea whether the existence of subject and object transcend the contents of consciousness (appearances, phenomena). Thus, in Transcendental Idealism, the existence of both subject and object transcends appearances. This is the right idea, and the true theory, in Kantian terms.

The opposite of this ("s̄ō") is that the existence of neither subject nor object transcends appearances, i.e. phenomenal reality is all that there is and there are no things-in-themselves. This is actually the form of Hegel's metaphysics. Since the terms of this diagram are purely metaphysical and not epistemic, calling Hegel's theory "empirical realism" has a very different meaning from the way Kant uses it. It is also now false, with all the evil consequences, such as judicial positivism, of Hegel's philosophy.

If the existence of the subject transcends appearances, but that of the object does not ("sō"), we find something like Berkeley's metaphysics, where matter does not exist, and objects have no independent reality, but there is a soul. We can call this, as Kant does, "empirical idealism."

Finally, if the existence of the object transcends appearances, but that of the subject does not ("s̄o"), we have a take on the metaphysics of Descartes. Now, at first blush, this characterization looks paradoxical and wrong for Descartes, who, after all, famously posited the existence of the soul over and above that of matter. However, Descartes saw the existence of the soul in a certain way: it was part of the external order of objects in space and thus possessed a location in relation to matter and was supposed to physically interact with it. This is the source of a veritable eruption of paradoxes and embarrasssments in the Cartesian system. Thus, while the essence of the Cartesian soul is subjectivity, it is part of what ontologically is an external order of things.

We therefore have a new way to think about these distinctions. "Internalism" is the transcendence of the subject from appearances; and "externalism" is the transcendence of the object from appearances. In Descartes, the transcendence of the subject is misconceived in externalist terms. This produces something that is one of the major paradoxes of Cartesian philosophy: the whole mess looks more sensible than the more logically coherent constructions of Spinoza and Leibniz, let alone Hegel. What we do get in Hegel, then, is the rejection of both internal and external transcendence. We might characterize the result as an "immanentalist" phenomenalism.

Kant's theory, as a result, preserves both internal and external transcendence. And it does so without reducing one to the other. This is a considerable achievement, since the structure looks unnatural and unstable. We want to know, is existence really internal? or external? I have expressed precisely this balance, and our inability to reduce internal or external to the other, as Ontological Undecidablity.

The Crooked Timber of Humanity

...aus so krummen Holze, als woraus der Mensch gemacht ist, kann nichts ganz Gerades gezimmert werden.
Out of timber so crooked, as from which man is made, nothing entirely straight can be built.
Immanuel Kant, "Idee zu einer allgemeinen Geschichte in weltbürgerlicher Absicht," "Idea for a Universal History with a Cosmopolitan Intent" [1784, Was ist Aufklärung, Felix Meiner Verlag, 1999, p.10; Perpetual Peace and other essays on Politics, History, and Morals, translated by Ted Humphrey, Hackett Publishing, 1983, p.34; translation based on Isaiah Berlin, The Crooked Timber of Humanity, Princeton, 1990, p.v].

But what is government itself but the greatest of all reflections on human nature? If men were angels, no government would be necessary. If angels were to govern men, neither external nor internal controls on government would be necessary. In framing a government which is to be administered by men over men, the great difficulty lies in this: You must first enable the government to control the governed; and in the next place, oblige it to control itself. A dependence on the people is no doubt the primary control on the government; but experience has taught mankind the necessity of auxiliary precautions.
James Madison, Federalist Paper No. 51

Our rulers are theoretically "our" representatives, but they are busy turning us into the instruments of the projects they keep dreaming up. The business of governments, one might think, is to supply the framework of law within which we may pursue happiness on our own account. Instead, we are constantly being summoned to reform ourselves. Debt, intemperance, and incompetence in rearing our children are no doubt regettable, but they are vices, and if left to generate their own consequences, vices soon lead to the pain that corrects. Life is a better teacher of virtue than politicians, and most sensible governments in the past left moral faults alone. Instead, democratic citizenship in the twenty-first century means receiving a steam of improving "messages" from authority. Some may forgive these intrusions because they are so well intentioned. Who would defend prejudice, debt, or excessive drinking? The point, however, is that our rulers have no business telling us how to live. They are tiresome enough in their exercise of authority. They are intolerable when they mount the pulpit. We should never doubt that nationalizing the moral life is the first step toward totalitarianism.
Kenneth Minogue, The Servile Mind, How Democracy Erodes the Moral Life [Encounter Books, 2010, pp.2-3]

Vade Retro Satana, Nunquam Suade Mihi Vana;
Sunt Mala Quae Libas, Ipse Venena Bibas.
Get thee behind me Satan!
Never tempt me with your vanities!
What you offer me is evil.
Drink the poison yourself!
Medal of St. Benedict

The great liberal political philosopher Isaiah Berlin has popularized Immanuel Kant's "crooked timber of humanity" phrase. It is a telling phrase, most appropriately coupled with the quote by James Madison that I have provided. These are among the most important statements that can be made in political philosophy, and that is because they forestall utopian visions in human affairs. The 20th century was full of ideologies that promised "heaven on earth." But they did a much better job of providing hells on earth, with mass murder, poverty, terror, starvation, vast prison systems, "reeducation" camps, slave labor camps, and extermination camps. Yet the utopian appeal remains, and even much of the same ideology, with vicious dinosaurs like Fidel Castro still celebrated by trendy leftists. We find public intellectuals such as Garry Wills arguing that distrust of government, as we see in Madison's statement, is "a tradition that belittles America" [cf. A Necessary Evil: A History of American Distrust of Government, 1999].

Wills, indeed, represents a Hegelian movement in American political thought, going back to John Dewey ("Things gain meaning by being used in a shared experience or joint action") and earlier, that exalts the collective and the state and sees the imperfections of man as something that can be overcome with the perfection of the government. Kant and Madison, aware that a government is something "which is to be administered by men over men," would find this movement perfectly senseless and dangerous. The idea that politicians and bureaucrats are disinterested servants, to whose wisdom and goodness absolute power can safely be entrusted, is a notion so preposterous that most persons of adult perspicacity see through it easily -- even if they do not know about rent seeking and Public Choice economics. Why an intellectual like Garry Wills is deceived may be due to an effect familiar since Plato: the tempting answer to all politics that the only real problem is that the wrong people are in charge, while the right people, of course, would be someone like themselves (e.g. Plato, Wills, etc.). This has tempted many of the naive and self-deceived, not only into folly, but into evil.

The statement by Madison is so appropriately coupled with Kant because Kant believed that moral perfection was only possible with an "angelic will," a will in which the imperative of rational morality is not obstructed or compromised by irrational influences. Where these irrational influences come from is clear enough. As sensation contributes the material for synthesis, perception, and empirical knowledge, it also contributes the sensual and self-interested temptations that conflict with rational duty. In short, the phenomenal world is the place of the Fall, where our nature is so compromised that the moral perfection of God or the angels is impossible. This seems to me the most Christian feature of Kant's thought, or perhaps the only Christian feature. However, were Kant a Christian, he would know that Fallen human nature can be redeemed through Jesus Christ. But we see no such thing allowed. Instead, it is an important part of Kant's argument for immortality as a Postulate of Practical Reason that the absolute command of the Categorical Imperative, to be perfect, can only be met if we are given infinite time, i.e. immortality, to meet it. Come to think of it, the requirement of perfection has a Biblical basis also: "Be ye therefore perfect, even as your Father which is in heaven is perfect" [Matthew 5:48]. My understanding is that eternal life in Christian thought is a reward for faith and for repentance. For Kant, however, eternal life is simply the way to deal with our hopeless imperfection. Repentance and redemption don't seem to figure in at all, though Kant is not unaware of what he formulates as his own question, "What can we hope?" An eternity of futile moral improvement sounds more Sisyphean than hopeful.

The imperfection of the world contradicts a principle that is the opposite of the Kantian, namely moral heteronomy, that the standard, the paradigm, and the authority of the right and the good stand outside of us in the world. Where the world can contain no such thing, then our knowledge of the standard of the good comes from within, a matter of Kantian autonomy. Heteronomy is what we see in Aristotle and Hegel, with the former because virtue is a matter of achieving good habits by imitation, with the latter because, where the "real is rational," the state embodies that rationality. For Kant, the rationality of the world is evident in science, but the rationality of morality tends to be contradicted, not affirmed, by the world. We are thus in the world, but not of it, as Plato might have been the first to say. Autonomy is then a principle of conscience and of political freedom. There is nothing in the world that can claim absolute obedience, because there can be nothing in the world that, by its perfection, can be worthy of such obedience. Knowing how government and the law often actually work, no one could be deceived that any blind obedience is owed to it. As Madison said, "No government, any more than an individual, will long be respected without being truly respectable" [Federalist Paper No. 62].

An imperfect government in an imperfect world of autonomous individuals means that the aims of life are not going to be the business of government. The government is thus not, in Michael Oakeshott's terms, a teleocracy, rule that has some end (telos) in view. It will only be a nomocracy, a government of abstract laws (nomoi) that limit the means of action, regardless of the ends. That is then conformable to a Lockean and Jeffersonian view of government as existing to secure the natural rights, the negative rights as Berlin said, that protect individuals from others. The Kantian moral respect for the will and rational nature of others contrasts with the Hegelian sentiment that "All worth which the human being possesses -- all spiritual reality, he possesses only through the State." To find meaning in something larger than oneself is noble, but this becomes poisonous when the "something larger" is interpreted as only meaning government and the state, to the point where a particular kind of political activism becomes viewed by educators (following Dewey?) as the only moral and enlightened thing. Mussolini's conception of "totalitarianism," after all, was simply that all meaning is found in the "totality," the collective. It is ironic that a favorite leftist accusation against those suspicious of government action is that they don't "care" about other persons -- when their own idea of "care" is the action of something, the government, that always has the sanction of force behind it. The individual uncooperative with the "care" of government is liable to find men with guns breaking into his home. This has happened to people like Peter McWilliams who after becoming gravely ill have discovered that marijuana has medicinal value. The state disapproves; and Peter is dead.

Where Kant goes very wrong is with the notion that the imperfection of the world is simply due to sensation and the sensible nature of our experience. This is pregnant, not just with the moralism that otherwise troubles Kant's ethics, but with the anaesthesia and anhedonia, the denial of the value of art, beauty, and pleasure, to which moralism tends. It is not surprising then that Kant should have moved from the aesthetic realism of his Observations on the Feeling of the Beautiful and Sublime to the doctrine of the Critique of Judgment that aesthetic feeling is subjective and simply a result of a "harmony of the faculties" between perception and morality. We might see this as another Christian characteristic of Kant if we agree with Nietzsche's thesis to any extent that Christianity is anaesthetic. Indeed, an ascetic impulse in any religion or politics will tend to anaesthesia and anhedonia.

Kant's error can be partially corrected by returning to Plato, or advancing to Schopenhauer. With both of them, beauty is the clue, the reflection, or even the "participation" of a different order of reality. It is the very direct presence of something which stands in stark contrast to all other imperfection in the world. Certainly, the world is not perfected thereby, and Schopenhauer would not think of beauty as indicating a separate reality to which we could go. However, all we need is Kant's own famous quote, "Two things fill the mind with ever new and increasing admiration and awe, the oftener and more steadily we reflect on them: the starry heavens above me and the moral law within me." This combines moral autonomy with "starry heavens" (der bestirnte Himmel, "the bestarred heaven") that are, to be sure, objects of scientific knowledge, but also fascinating images of beauty -- that only thing that would draw, indeed, such enthusiasm ("admiration and awe") as we see in the quote. Even a more realistic appreciation of beauty, however, does not quite do the job. Pleasure has never quite recovered from Mediaeval anhedonia. Nevertheless, the smug attitude happy to blame religion for this faces the difficulty that modern political moralism is fully as anhedonic as any religion. The leftists (and conservatives) who fulminate against "consumerism" really mean the pleasures that are fostered by -- in Plato's phrase and theirs -- the "unnecessary desires" created by advertising and modern production. At least Ted Kaczynski, the Unabomber, was willing to give up modern technology (except in the interests of his Terrorism, when he was ready to use airplanes, the postal system, etc.), while I doubt that most critics of "consumerism" are.

So, unfortunately, the bottom line on pleasure may still be Aristotle:

Men erring on the side of deficiency as regards pleasures (hēdonás), and taking less than a proper amount of enjoyment (khaírontes, "enjoying") in them, scarcely occur; such insensibility (anaisthēsía) is not human (anthrōpiké) [Nicomachean Ethics, Book III, xi, 7, Loeb Classical Library, Harvard U. Press, 1926-1982, pp.180-183].

Both religious and political anhedonia are, especially when forcefully imposed on others, "not human." With Kant's "crooked timber," it is hard not to see the crookedness contributed in great measure by the existence of pleasure. Yet pleasure is a good. Like all goods, it may or may not become a moral issue. Nor is moral evil always the result of self-interest, sensuality, or pleasure. The path to hell is paved with good intentions, and in both religion and politics some of the most dangerous and vicious people are the ascetic and the disinterested. Doing good for others sometimes can visit the greatest evils upon them.

Kant's principle thus gives us one way to forestall political utopianism and totalitarianism, but it is also not quite the right idea, and its further implications must be examined carefully.

Political Economy

Intuition and Mysticism
in Kantian Philosophy

While Kant's term "intellectual intuition" is thrown around rather casually in post-Kantian philosophy, the usage rarely conforms to Kant's meaning. Kant contrasts "intellectual" with "sensible" intuition (Anschauung) on the basis of the active or passive role of the object. Thus, while objects are presented to a (passive) sensible intuition, objects are created by an (active) intellectual intuition. To Kant himself, this meant that only God would have an intellectual intuition. In the history of philosophy, the "active intellect" of Aristotle and Neoplatonism may be the antecedent of the idea of intellectual intuition, though this would tend to blur the difference between the self and God, since it looks like there is only one active intellect -- which was precisely the point for a system of mysticism like Neoplatonism.

Kant, of course, had no interest in mysticism, famously pillorying the Swedish spiritualist, Emanuel Swedenborg ("Dreams of a Visionary, Explained by Dreams of Metaphysics," 1766), but it is important to note what mysticism would be in Kantian philosophy. Any kind of mysticism is going to be a kind of immediate knowledge that is an intuitive understanding, i.e. the opposite of a discursive understanding, where an intuitive understanding is immediate and unarticulated, while a discursive understanding is mediate and articulated. There is going to be no intuitive understanding in Kantian philosophy -- i.e. no understanding that stands on its own as knowledge, an understanding that is a ground for substantive truths. An intuitive understanding which is not knowledge is the common and essential experience of insight which is ordinarily and non-technically called "intuition," e.g. "My intuition is that murder is wrong" (in German, Nelson called it Intuition in contrast to Kantian Anschauung). This kind of "intuition" is not evidentiary, i.e. it doesn't prove anything. In Socratic/Platonic terms, it is only opinion. It can only be justified when analyzed, reduced to discursive understanding, and grounded accordingly [note]. Were ordinary "intuitions" evidentiary, and so items of knowledge (Erkenntnisse, cognitions), then this would be "intuitionism," the theory that knowledge is grounded by such intuitions [note]. The self-evidence of Aristotelian first principles is a theory of this kind, with the proviso that intuitive self-evidence follows, rather than precedes, discursive understanding. Other forms of intuitionism may claim intuitive understanding prior to discursive, if the latter is considered even possible.

While mysticism is a form of intuitionism, not all intuitionism is mysticism. The difference, again, will be in the objects. Mysticism is intuitive knowledge of transcendent concrete objects, i.e. not the phenomenal or material concrete objects of ordinary perception. The mystic sees things that are not part of ordinary experience. In Kantian terms, transcendent objects cannot be understood because they cannot be consistently articulated. For Kant, a theory of transcendent objects ("dialectic") generates antinomies. If a Kantian theory allowed for mystical knowledge, it would have to be unanalyzable, unrenderable into a system of discursive understanding of transcendent objects. This is rather like what many mystics say, since they gain knowledge which is ineffable and inexpressible. On the other hand, mystics also claim to intuitively derive knowledge which is analyzable and expressible, although only intuitively justified, since, for instance, al-Ghazzali (1059-1111) finds specific justification of Islām and its doctrines through mystical insight.

The intuitive apprehension of abstract objects does not rise to the level of mysticism, since abstract objects do not have independent existence -- except when substantialized in Platonism, a theory rarely followed since. Intuitions of abstract objects concern meaning, and in general the ordinary sense of "intuition" (Intuition) applies to this. Such intuitions, when analyzed, are the basis of analytic truths, but whether the meanings apply to existence is a separate question (pace St. Anslem and Descartes), which requires an evidentiary basis. The mystical claim would have to be that an intuitively apprehended abstract object is also intuitively known to apply to existence, in a way, analyzable (as in Anselm's "ontological argument") or unanalyzable, that transcends ordinary perception and experience.

An important distinction in mystical claims will be between objects which are independent and which are identical to the subject of mystical knowledge. This itself is an analyzable characteristic of mystical intuition. In monotheistic religions, God will tend to be seen as independent. This was not an open question, and the Christian mystic always ran the risk that contrary truths learned through mystical intuition might conflict with Orthodoxy -- but the Catholic Church never denied that such an avenue of knowledge existed, as with St. Teresa of Ávila (1515-1582). Other mystics, however, paid the price of their experiences at the stake. In Judaism and Islām, with looser institutional authority over doctrine, the drift of claims towards extinction of self and identity with God is conspicuous. Some efforts were made in Islām to suppress this, like the execution of al-Ḥallāj (in 922), but the precedent was powerful. An artifact of this in Judaism remained with the philosopher Spinoza, whose sense of identity with God is crystal clear, but who cannot properly be considered a mystic, since his God is not transcendent, but immanent, identical with all the objects of perception, and who does not claim intuitive knowledge beyond the minimal Aristotelian claims about first principles. Nevertheless, Spinoza retains a strong mystical affect, the "intellectual love of God," which helps explain the meaning to him of a system that otherwise is rationalistic and seems devoid of religious appeal.

The distinction between independent and identical objects can be seen to overlap Kant's between intellectual and sensible intuition. Only a sensible intuition could relate one to an independent transcendent object, since such a thing clearly cannot be created by one's knowing it. However, if the mystic is identical to the transcendent object, this could allow for an intellectual intuition, depending on the metaphysics of the object. It is possible for God's existence to be presented to him passively, in which case he would have sensible knowledge of himself; or, God may actually create his own existence, like that of anything else, merely by knowing it. This fits Spinoza's principle of a substance, namely God (Spinoza's only substance), being self-caused. There, if the mystic is identical to God, who also creates everything else through intellectual intuition, all mystical knowledge will be of the nature of an intellectual intuition.

This is even simpler in Buddhism, where there are no substances and, at least in some forms of Buddhist philosophy (e.g. Yogacara), all things are clearly created by Mind. In Pure Land Buddhism, an important meditative practice is the visualization of the Pure Land of the Buddha Amitabha. It is always possible to interpret this as unrelated to the independent, or even real, existence of the Pure Land, but the metaphysics clearly allows that the Pure Land is actually created by the act of visualization, since all things are Mind dependent. This would be an intellectual intuition in a strong Kantian sense, and a form of mysticism, with the transcendence of the Pure Land, in which the identity with the mystical object is facilitated by the absence of any substantial independence of things whatsoever. Similarly, the Tibetan "Book of the Dead" urges the deceased to realize that the visions of the hereafter are not independent but created by their own Mind. Thus lies the path to Enlightenment and Salvation.

In light of this examination, we should revisit the charge of mysticism against Rudolf Otto. Since Otto does not claim intuitive knowledge of transcendent objects, he clearly is not a mystic. The natures of transcendent objects, to the extent that they can be theorized at all, are matters of rational Kant-Friesian metaphysics (after the fashion of Kant's "postulates of practical reason," which resolve some antinomies); and Kant-Friesian metaphysics tends to dismiss more substantive doctrine from historic religions (e.g. the Trinity, transsubstantiation, etc.). Otto's famous theory of "numinosity" is about a property, and so an abstraction, whose existence is certified by its presence in the objects of experience, but which in an important way is not a natural property, since it is invisible to science and is unrelated to mundane utility. The numinosity of God is natural to Otto, but his God comes from the Kantian Ideas, besides historic religions, and divine numinosity derives from no more than a phenomenology of such religions.

So is there mysticism? Of course, there actually are mystics, most of whom are clearly sincere and deeply moved or transformed by their experiences. But there is no philosophical mysticism in the sense that philosophy could, as the Neoplatonists believed, certify, verify, and theorize the results of mystical intuitions. Given a Kantian epistemology and metaphysics, no rational or intelligible system can be built from mystical intuitions, analyzable or unanalyzable. This, however, should be no more than what we would expect given the contradictory claims of mystical or dogmatic authorities in world religions. The antinomical choices between mystical intuitions as intellectual or sensible, of independent or identical objects, of a divine substance (personal or impersonal) or ultimate Emptiness, cannot be resolved on the evidence of mystical knowledge, since the knowledge of different mystics confirms each of these and, as Hume would say, the evidence of one tends to refute the evidence of the other. This in itself is one of the most important features of human existence, since it leaves us without any rational certainty that there are transcendent objects at all. The mystic may just be hallucinating (or lying), whether beholding the Virgin Mary or visualizing the Buddha Land. As considered elsewhere, however, this simply leaves us faced with the choices of the right and the good without any confidence in the ulterior considerations of reward and punishment. Behind our veil of ignorance, it is character and benevolence that are proven.

Faith, Works, and Knowledge

Epistemology

Philosophy of Religion

Intuition and Mysticism in Kantian Philosophy, Note 1

Problems of justification are covered elsewhere. In Kant's theory, complications arise over Kant's original, "architectonic," conception of intuition (Anschauung) because, as considered in the main essay on Kant, perception itself comes to be seen (in the Transcendental Deduction) as a product of mental activity. If perception is itself active and intellectual, then the simple distinction between sensible and intellectual intuition, or even between intuition and thought, becomes confused. Friesians like Nelson don't deal with this very well and tend to take over Kant's own naive version of the theory.

However, as is examined in detail in The Origin of Value in a Transcendent Function ("Intuition and the Immanent Object), the immediacy of intuition that is lost when we consider perception to be the result of active mental synthesis returns when we realize that this synthesis is an activity that cannot occur in the conscious mind. Perception is spontaneously produced by a preconscious activity; and even if it is governed by Kant's "pure concepts of the understanding" as rules of synthesis, these concepts do not accompany the results as conceptual or semantic content. Perception can occur without being understood, without particular things being seen, or without a particular recognition determined by the percept -- as in the Gestalt tricks where different things (e.g. faces or candlesticks) can be seen in the same shapes. The difference between conceptual meaning and perceptual object must be maintained, even when the empiricist tabula rasa is rejected and mental processes are allowed into the formation of perception. It is thus possible to continue speaking of intuition pretty much as Kant and the Friesian do, even after taking into account the way that the Transcendental Deduction undermines Kant's original view of intuition. There is also the ontological aspect to this, that the phenomenal objects immanent in perception are undecidably both real/external and subjective/internal.

Intuition and Mysticism in Kantian Philosophy, Note 2

In arguments about mathematics and set theory, "intuitionism" tends to mean something else, which can be very confusing. Mathematical intuitionists don't like mathematical or logical constructions that cannot be visualized (hence, "intuited") and so tend to be wary or disapproving of infinities. Such scruples, however, which may be empiricist in origin, seem to have had little effect on the practice of mathematics and, if taken seriously, would make much of modern mathematics, including non-Euclidean geometry, suspect. While Kant might be said to be a kind of intuitionist in this sense, since he thinks that the axioms of geometry and arithmetic are grounded by visualization, there is nothing to prevent the logical extension of mathematics beyond our capacity for visualization, which in fact is what has occurred. While Kant's mathematics is somewhat intuitionistic in the modern mathematical sense, it is not necessarily intuitionistic in the traditional epistemic sense, since our mathematical "intuitions," e.g. "that looks like a triangle," can be wrong. The Kantian mathematical intuition is much more like perception, an empirical intuition, than it is like a true self-justifying, evidentiary intuition -- a Kantian mathematical intuition, like an empirical intuition, can be misunderstood, while the evidentiary intuition of (epistemic) intuitionism is itself a kind of infallible understanding. To prevent confusion, the mathematical sense of "intuition" and "intuitionism" is not used in the text.

The Most Knowable
and the Most Real

To Plato and Aristotle, there is no doubt that the most knowable things to us are also the most real things in the universe. This would mean the Forms in Platonism, while that would be God to Aristotle. Thus, as our knowledge increases, we get closer to the foundation and the essence of all existence. In Ancient and Mediaeval philosophy the only contrary word about this would have come from the Skeptics, or from theology in which the nature of God transcends our possible knowledge, mainly because God is infinite and our knowledge finite. There was another twist, however. William of Ockham believed that God in his omnipotence could even violate the principle of non-contradiction. This scandalized Aristotelians, since allowing the equal reality of contradictions destroys just about the most basic principle of knowledge.

In Modern philosophy there is correspondingly little doubt that knowledge penetrates to the fundaments of reality until we encounter, indeed, the Skepticism of David Hume, who says, about the objects of scientific inquiry, "These ultimate springs and principles are totally shut up from human curiosity and enquiry" [Enquiry Concerning Human Understanding, Shelby-Bigge edition, Oxford, 1902, 1972, p.30]. Now, it was reading Hume, Kant says, that awakened him from his dogmatic slumber. Kant's "Copernican Revolution" then not only reverses the roles of representation and object in human knowledge but it radically reverses the overall relation of knowledge and reality -- not a Skeptical denial of knowledge as in Hume, but a kind of restructuring of reality itself.

The simplest form of this is familiar enough. Kant believes that our knowledge is of phenomena, the objects of appearance, while reality ultimately is with the things-in-themselves. If we ask what is the most knowable thing for us, the answer in Kant would be mathematics. There are a couple of things about mathematics that put it in this position. (1) Its abstraction. It is easier to know something of abstract rather than concrete content, though if mathematics cannot be completed (according to Gödel), we are limited by the finitude of our knowledge. (2) Kant believes that mathematics is based on the "pure intuition" of space and time, something that underlies phenomenal objects in space and time but does not extend to things-in-themselves. Thus, although Kant sees mathematics as describing the foundations of the phenomenal world, he does not have a Platonic view of mathematics as taking us to the highest levels of reality. Kant might outdo Plato in one respect, saying that mathematics is the "purest" kind of positive human knowledge, owing nothing at all to experience, despite its application being limited to phenomenal objects. For Plato, the purest and highest kind of knowledge would be of the Form of the Good. After mathematics, positive, theoretical knowledge for Kant would mean science. This opens vast expanses, as we have certainly seen since Kant's day.

When it comes to things-in-themselves, Kant believes that the only kind of positive knowledge we can have is by way of morality. Thus, like Plato, priority is given to the good. Kant, however, does not have the kind of concrete and aesthetic view of the good that Plato has. We only know the good by way of the Moral Law, the Categorical Imperative. This is itself a very severe abstraction, based on Kant's view of reason as expressed in the forms of logic, whose application is supposed to generate the imperatives of morality. This is all very dubious, though Kant's good sense overlays it with formulations with more substantive content. Kant then believes that morality provides clues to the Ideas of Reason -- God, freedom, and immorality -- which then give us some notion about realities among thing-in-themselves. Aesthetic value itself is reduced to a subjective sense of the "harmony between the faculties," reconciling theoretical knowledge (science) and practical (morality).

In matters of value, Kant's Copernican reversal does not go as far and is not as consistent as with theoretical knowledge. Aesthetic value, which is resistant to analysis, is presumably less knowable than the abstract content of morality, yet Kant removes it from any connection to external reality at all. Kant's Copernican Revolution in this respect is thus not completed until Jakob Fries. In Fries, we have the distinction between Wissen, Glaude, and Ahndung, where Wissen ("knowledge") is the positive knowledge of mathematics and science, Glaube ("belief") consists of the abstract clues to things-in-themselves that Kant sees in morality, and then Ahndung ("intimation") consists of the positive aesthetic feelings that relate us directly to things-in-themselves. Where Kant only saw religion, "within the limits of reason alone," as consisting of morality, Fries allowed for religion a content of feeling and aesthetic value in addition to that. Needless to say, these aesthetic feelings represent no clear or demonstrable kinds of knowledge.

Although on the right track, the shortcoming of Fries's treatment is that, like Kant's, it is still reductionistic. In the Qurʾān, the Prophet Muhammad denies that he is a poet. Poetry is not prophecy, and religion is not merely art plus morality. Within the framework of Friesian philosophy, this is finally understood by Rudolf Otto. What is characteristic of religion is the sacred or the holy, and the characteristics and feelings associated with this are rather different than the merely aesthetic, or even the aesthetic sense of the sublime. To Otto, one basic feature that will always distinguish the numinous from the merely beautiful or sublime is the uncanny, an eerie sense that seems to accompany something supernatural. The power and splendor of a thunderstorm will seem beautiful, sublime, and terrifying, but it does not convey quite the same kind of fear as a quiet cemetery at night.

Otto thus completes Kant's Copernican Revolution and the reversal of the knowable and the real. Morality now stands in a kind of complete equality with mathematics, yet it does not give rise to the endlessly growing system that mathematics does. Morality has a kind of incompleteness that can only be remedied with a different kind of positive content. Fries returns us to the kind of aesthetic realism found in Plato, while holding that the merely aesthetic is closer to reality than Plato would have allowed (beauty is a clue to the Forms). Finally, Otto identifies something, common to all religion, that is nevertheless difficult to characterize without invoking something contrary to the customary course of nature -- something which thus bespeaks an order beyond the world of experience and science, that which, in the words of the Mandukya Upanishad, is "without an element, what cannot be dealt with or spoken of, the cessation of the phenomenal world, auspicious, nondual."

Here is a graphic I produced for "A New Kant-Friesian System of Metaphysics." This matches up a Friesian metaphysic with the theory of "magnetic substates" in quantum mechanics. It presents a model for how the more knowable varies inversely with the more real. Thus, the long arrow, representing the angular momentum vector in quantum mechanics, might here be called the "moment of necessity." In an absolute sense it is equal for all modes of necessity. However, its component in the z axis varies from the full value (positive or negative) to zero. In atoms, the z axis is identifiable in the presence of a magnetic field (hence "magnetic substates"). Here, the z axis represents the phenomenal world in consciousness, which is a fragment of the reality of things-in-themselves. Thus, the full value of the moment of necessity is apparent to us only where it falls entirely in the phenomenal world, which is the case with logic (analytic necessity) and morality. Otherwise, the vector falls outside the phenomenal world, with a larger or smaller component in it. To the extent that the moment of necessity is not reflected in the z axis, it contains content that is concrete and resistant to abstract analysis. On the side of value, the most familiar case is with beauty, where "there is no disputing taste" (de gustibus non disputandum), but where there nevertheless is at least a hierarchy of taste (since "pushpin" is not as good as poetry, pace Jeremy Bentham), and there are regularities of beauty that can identified in a formal and experimental way. On the theoretical side, "conditioned" necessity is the nomological necessity of natural law. If it is possible for the laws of nature to be different in different universes, which is a popular idea these days, then there is an arbitrary element in the natural laws of our universe. Physicists and mathematicians find this offensive, but we are probably stuck with it. The arbitrary element is what cannot be reduced to an abstract formalism. It is less intelligible. For the numinous, the vector's magnitude is only apparent in the transcendent, which leaves its phenomenal content, at zero, entirely irrational and unintelligible. Its presence, of course, is felt in the phenomenal world, which is the difference between a Kantian theory, where phenomena are simply the appearance (in consciousness) of things-in-themselves, and a Platonic theory, where the transcendent is in another world.

Metaphysics