Kurt Gödel [A World Without Time, p.140] Palle Yourgrau, an associate professor of philosophy at Brandeis University, seems to think that Kurt Gödel, one of the most important, perhaps even the most important, of the logicians and mathematicians of the 20th century, was also actually a better philosopher than many of the people who are otherwise celebrated in 20th century philosophy, or who now dismiss Gödel's own philosophical insights or significance. In this, I expect he is quite right. Gödel's greatest drawback as a philosopher is that he was relucant to openly state and develop his views. It is a shame that someone did not bring Leonard Nelson to Gödel's attention. Nelson, indeed, had already died (1927) before Gödel's most important work, but many people in Gödel's circle knew about him, like fellow logician Paul Bernays, mentioned by Yourgrau [note]. Instead, Gödel was drawn to Husserl, with whom Nelson differed sharply, and whom Gödel also found somewhat unsatisfactory, but obviously was aware of no alternative. The problem with Husserl was his intuitionism. Now, Kant and Nelson had allowed that there were mathematical intuitions, in which there was agreement with both Gödel and Husserl, but they had denied that there are conceptual intuitions in the cognitive, evidentiary, probative, and substantiating ways that intuitionists like Husserl usually mean it. In other words, intuition as immediate knowledge is denied by Kant and Nelson apart from perceptual and mathematical intuitions. Nevertheless, the way the method that Gödel gets from Husserl is described, it sounds more Friesian than intuitionistic:
Reflecting on our own conceptual acts sounds a lot less like an intuition of the objects, the referents, of the concepts (the ground of ad rem truth) than it does as a version of Fries's anthropologische reflective and psychological "Critique." If it is "our own acts" rather than the objects, then we are the closest to Kant's "subjective deduction" of the Critique of Pure Reason and its descendants, as in Fries.
But what Husserl then lacks is the theory of non-intuitive immediate knowledge. This explains why attention must be to "our own acts" rather than to the objects. If real intuition were available, then the objects, not our own acts, would be the focus. And it is clear here what is happening. Yourgrau says:
Understanding is not a kind of intuition in the Kantian sense because it is not immediate, evidentiary, and probative. Because of this, Nelson distinguished between Anschauung, Kant's word for intuition in the Kantian sense, and Intuition, intuition in the sense of a spontaneous opinion, understanding, or insight about some conceptual matter. Husserl and Gödel (or Yourgrau) do not make that distinction. More importantly, they cannot distinguish between intuitive and non-intuitive immediate knowledge. Like most epistemologists, they assume that "intuitive" is synonymous with "immediate." But the difference is crucial. Immediacy posits the cognitive ground, i.e. something not fallible or corrigible, but a non-intuitive immediacy means this is only accessible indirectly, by reflection on "our own acts." Intuitive immediacy means that the ground need only be, in Wittgenstein's words, "shown." Nelson calls that "demonstration," as opposed to "proof" -- formal derivation -- and "deduction," the critical evaluation of reflection on "our own acts."
By not distinguishing between immediacy and intuition, or between intuitive and non-intuitive, Gödel is led into some difficulties. For instance, Yourgrau says, in referring to the critique of Gödel by Warren Goldfarb:
It is not clear whether Yourgrau accepts this assessment. He asserts that Gödel's treatment of Kant is based on "a deep understanding of Kant," but then he doesn't say whether Gödel thought that intuitions in metaphysics are comparable to intuitions in mathematics. As Goldfarb says, there is no hint that they are different, and if intuition is simply intuition to Gödel, they cannot be. Kant knew there was a difference, explained, as Nelson liked to point out, in his "Enquiry into the Clarity of the Principles of Natural Theology and Morality" [1762, 1764; see Nelson's discussion in Progress and Regress in Philosophy, Volume I, Basil Blackwell, 1970, pp.104-109]. But the epistemological problem is not resolved by Kant, but only by Fries and Nelson.
There is also another problem with Husserl, that his phenomenology is not supposed to be metaphysical at all. Husserl practices a Pyrrhonian epochê, the "suspension of judgment" or the "bracketing" of metaphysical questions. This disqualifies Husserl's own intuitionism from serving as metaphysics. In the same passage quoted, we also get Yourgrau making what seem like incommensurable claims. First, that, "Gödel had a profound understanding of Kant, which enabled him to demonstrate a striking and previously unsuspected connection between Kantian idealism and Einsteinian relativity" [p.169]; and, second, "that Gödel, though he accepted certain elements of Kant's philosophy, systematically rejected its main thrust, which assimilated knowledge to the knower, not the known, and thus gave Kant's philosophy a subjectivist cast" [pp.169-170]. But wouldn't this make Husserl equally "subjectivist"? Indeed, but then Kant was nowhere near as agnostic as Husserl.
Now, it turns out that Gödel's "connection" between Kantian idealism and Einstein was the rejection of the intuitive nature of time, which is simply assimilated to the nature of space. This is the title of Yourgrau's book (i.e. A World Wihout Time). Since this rejects the intuitive (in the Kantian sense) nature of time, and is said by Yourgrau himself to vindicate Kant's idealism (!), I would take it to give to Gödel's metaphysics "a subjectivist cast." On the other hand, regarding Kant as "subjectivist" is to gravely mistake, as indeed many do, the thrust of his thought. Yourgrau and Gödel both seem to have accepted the plain "unknowability" of things-in-themselves, overlooking, as perhaps many do, the exceptions that arise in the Critique of Practical Reason.
The problem with time is indeed the heart of Yourgrau's book, both for his evaluation of Kant and of Gödel. Yourgrau argues rightly that the Gödel Universes, where it is possible to travel into the future and arrive in the past, mean that time, as ordinarily understood, doesn't exist.
Yourgrau says,
Actually, I fail to see why this is a "rational choice." It is more like a reductio ad absurdum. If "Einstein's theory is inconsistent with the existence of the A-series, with the reality of time in the intuitive sense" [p.132], then it looks like we would have a prima facie falsification of that theory. The choices are between a theory in physics, that of Einstein, which implies universes without time, and our ordinary, intuitive apprehension of the world as something that is only present to us at one point in time, the present. The alternatives are then between chalking up an anomaly for Relativity and deciding, as Yourgrau says, "that our sense of intuitive time is founded on a misunderstanding or misapprehension" [p.138]. But if time doesn't exist, then the whole history of the universe should be present to us at once, simultaneously, as it is to God in Leibniz (one of Gödel's favorite philosophers). How could our inability to access the simultaneous universe possibly be a "misunderstanding" or "misapprehension"? This is not the kind of thing we would just by chance fail to notice. Instead, people have always tried to intuit the future; and while prophetic claims get made, they are rarely and only poorly substantiated.
Yourgrau's wording makes for a nice comparison with Kant; for while one might think of Kant's theory as having a "subjectivist cast" because, as he says, "the representation alone must make the object possible," Kant goes on to say in the same passage, "representation in itself does not produce its object in so far as existence is concerned" [B124, Critique of Pure Reason, Norman Kemp Smith translation, St. Martin's Press, 1969, p.125]. When it comes to existence, there is no difference between phenomena and things-in-themselves in Kant. Yet, for all his disparagement of the "subjectivist cast" in Kant, Yourgrau eagerly seizes a "Kantian" condemnation of time as "ideal" just in the sense that existence, physical existence, is radically different from its phenomenal appearance. This would seem to violate both a Husserlian phenomenology and a pretty basic version of scientific method. A world without time implies the simultaneous appearance of the history of the universe. This should be something that is observable, in a good observational test of a scientific theory, like observing a solar eclipse to test General Relativity. Since past, present, and future are not equally present to consciousness, experience, or observation, this is falsifying evidence against the theory. If there is something about physical reality and/or the senses that limits our perception to one point in time, then this is much more than a "misunderstanding" and calls for a substantive explanation, nothing of the sort of which is provided either by Gödel or Yourgrau. Obviously, Yourgrau would rather not have to provide such an explanation, but this is either a grave oversight or disingenuous.
Yourgrau realizes that this procedure is the opposite of that Gödel took in his incompleteness proofs.
Thus, in mathematics Gödel proves that intuition transcends formalism, but in physics a particular theory refutes, well, common sense. Why this turnabout is rationally motivated or even a good idea is really never explained by Yourgrau, as I doubt it can be. Indeed, the possiblity that Relativity would not capture specific attributes of real time is evident from one of the most overt characteristics of the theory: Einstein's field equations, like the equations of Newton or Maxwell, do not distinguish the directionality of time and can be run forwards and backwards just as easily and indifferently. Given a theory that clearly doesn't capture an essential characteristic of time, it is not surprising that predictions might be derivable from it that violate those characteristics. Is there, indeed, any evidence in science that time is directional? Well, yes. It makes some scientists neverous, but when we bring in issues of order and entropy, the direction of time makes all the difference. It is an attribute of the phenomenal world that broken glasses do not spontaneously reassemble themselves -- and an argument that they could, but that this is just very unlikely, looks like a merely hopeful reach. A Rubic's Cube can be easily scrambled -- anyone can do it, even an infant -- but some people, intelligent and accomplished people, have taken years trying to restore its original form, without success.
Perhaps we see the confusion in the continuation of the passage just quoted:
But Gödel is here very confused about what is a "fact." The fact is that we only perceive the present. But the "fact" with which Gödel challenges this is only the deduction of a theory in physics. Gödel is taking the prediction of a theory to refute observation, not observation to refute the prediction of a theory. Whether or not Gödel is a philosopher, a logician, or a mathematician, it is clear from this that he is not a scientist. In science, observation supplies the facts, to which theory must be adjusted. But Gödel surveys the world as an abstract, mathematical entity, and he simply doesn't notice, as Yourgrau fails to either, that the result is preposterous.
The final sentence of the quoted passage is, "This for Gödel, was the point of intersection between Kant's idealism and the temporal idealism implicit in Einstein's physics" [p.137]. But Yourgrau is not always so kind to Kant's "idealism":
Still, idealism is idealism, whether British or German. [p.106] These comments are dismissive and approach ridicule, leaving us to think that a term like "transcendental" is just a muddle and a fog that conceals no real difference between Berkeley and Kant. Since Yourgrau doesn't bother defining the word, it clearly makes no difference to him. But the term is irrelevant. Yourgrau knows quite well what the difference is between Berkeley and Kant, and he says so in his following sentence, that Kant believes in an independently existing reality, while a positivist like Ernst Mach (or Berkeley) does not. Yourgrau simply does not see why this makes a difference, since the independent existence of things, as "things-in-themselves" is "unknowable." But this a paradoxical complaint from Yourgrau, who otherwise claims that Gödel vindicates Kant's idealism. And if "idealism is idealism," this would mean that there is no independently existing reality, something denied by both Einstein and Gödel, and Kant. This seems to me the most incoherent aspect of Yourgrau's presentation.
Einstein, Gödel, and Yourgrau perhaps seize on the paradox that Kant couples the unknowability of things-in-themselves with the knowledge that they exist. Perhaps this is like the Skeptic claiming to know that there is no knowledge. But what critics commonly miss is that Kant always believed that reason itself relates us directly to things-in-themselves. And if we ask where Kant proves this, we miss one of his fundamental distinctions, between the quid facti and the quid juris, between the matter of fact or the discovery, and the justification [A84, B116, Kemp Smith p.120]. In the Critique of Pure Reason, we get no knowledge from the application of our concepts "in general," without the limitations of possible experience, but then we discover in the Critique of Practical Reason that there are clues, through morality, to characteristics of things-in-themselves that we do not get through merely theoretical reason. It was thus always a matter of fact that reason applied to things-in-themselves, but it was only through practical reason that we get positive knowledge of this and the justification became evident.
There is thus a grave and not at all paradoxical qualification to the "unknowability" of things-in-themselves. Reason defines both the conditions of possible experience and, in general, the conditions of possible knowledge. When Gödel, Einstein, or Roger Penrose assert (as in the epigraph above) that an anti-realist or postivist view of knowledge is simply senseless, contradicting the very meaning of knowledge, they are making not just a Platonic but a Kantian objection. If Yourgrau, or Gödel, has missed this, the worst effect is to simply head back to speculative Rationalistic metaphysics. That had, to be sure, been tried, and would be tried again (e.g. Hegel), but the result was never more than to demonstrate the truth of Kant's Antinomies. Indeed, just between Einstein and Gödel, we have a preference in the former for the metaphysics of Spinoza, and in the latter for those of Leibniz. This does not seem surprising, that the scientist should like the determinist where God is identical with Nature, while the mathematician likes, well, the mathematician. But Spinoza and Leibniz are opposites in much fundamental ontology: one the monist, the other the pluralist; one the determinist, the other the teleologist; one for whom all is perfect, the other for whom all is perfectible; etc. In these terms, Gödel is indeed "pre-critical," but not, of course, in the way the Positivists, Wittgensteinians, etc. would have it.
Missing the nuances of Kant is one thing, though it seems to leave Yourgau somewhat undecided whether vinicating Kant's "idealism" is good or bad; but missing Nelson and the Friesians is something else -- the path by which intuitionism and metaphysics do not simply mean a return to classical Rationalism. In the same way, Jerrold Katz, for all his insight, seemed to contemplate no alternative -- his book, Realistic Rationalism, tells the tale. After the debacle of 20th century philosophy, when people like Yourgrau and Katz are feeling their way back to realism and metaphysics, it is annoying and worse to imagine that this will simply repeat the old mistakes and absurdities of speculative Rationalism. Only Fries and Nelson, in my view, represent a continuation of Kant without falling into either Rationalism or Positivism.
He knew he was not one of the club and that his preferences were contrary to most of the philosophical Zeitgeist. That Gödel took academic philosophers so seriously, was intimidated by them, and did not challenge them forthrightly on their own ground, is perhaps the only reason to think of him more as a logician and mathematician than as a philosopher. Also, considering the issues that Gödel raised, and the explanations they made necessary, he didn't make much of an effort to provide the explanations by way of either original metaphysics or epistemology. Perhaps that limits his value as a philosopher. Either way, Yourgrau, himself an academic philosopher, is obviously trying to toss a bomb into the middle of the inappropriate complacency and condescension that he sees his colleagues directing towards Gödel. In many ways, he knew better than they do.
Husserl called his new way "phenomenology," which Gödel described as a method by which we can "focus more sharply on the concepts concerned by directing our attention in a certain way, namely, onto our own acts in the use of these concepts." if we are successful, said Gödel, we achieve "a new state of consciousness in which we describe in detail the basic concepts we use in our thought." [p.170]
But concepts, of course, aren't physical objects. We can't literally see them. Rather, says Gödel, "we perceive objects and understand concepts. Understanding is a different kind of perception." He adopted the Kantian terms "intuition" for the quasi-perceptive grasping by the mind's eye of concepts and other "ideal objects." [p.173]
Goldfarb continued: "There is no hint" in what Gödel wrote, he said, "that the truths of metaphysics are problematic in any special way, or pose special problems of our access to them." [p.169]
Gödel would conclude that the space-time structure in such a world was clearly a space, not a time, and therefore that it, the temporal component of space-time, was in fact another spatial dimension -- not time as we understand it in ordinary experience. [p.115]
We can have a world in which there is time or a world in which there is existence, but not both. Gödel made the only rational choice: a world without time. [p.132]
For Gödel, the devices of formal proof are too weak to capture all that is true in the world of numbers, not to say in mathematics as a whole. When it came to relativistic cosmology, however, he took the opposite tack. The consequence of his discoveries for Einstein's realm was not that relativity was too weak to encompass all that is true about time, but rather that relativity is just fine, whereas time in the intuitive sense is an illusion. [pp.136-137]
Relativity, by Gödel's lights, does not capture the essence of intuitive time, because when it comes to time, our intuitions betray us. "As we present time to ourselves," he said," it simply does not agree with fact. To call time subjective is just a euphemism." [p.137]
The "Copenican Revolution" in epistemology inaugurated by Kant consisted in the radical doctrine that the known must conform to the knower. The hard-nosed, ultraempiricist Mach had derived his positivism from Kant, who was not a realist but an idealist, albeit of the deep, German, transcendendal variety, not (as Kant saw it) of the shallow British strain of George Berkeley.
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| Gödel and Einstein walking to work at the Institute for Advanced Study |
While at the Institute for Advanced Study in Princeton, Gödel was for a time a member of an elite -- a very elite -- discussion group, consisting of himself, Einstein, the German physicist Wolfgang Pauli, and Bertrand Russell, one of the founders of modern "analytical" philosophy. Russell reacted badly to the discussions, finding them too philosophical in the "old fashioned sense." (The failings of an entire century are crystallized in this fact.) In an unpleasant aside he vented his frustration: "All three of the others were Jews and exiles, and in intention, cosmopolitans," he wrote later, "[who shared] a German bias for metaphysics." [p.13]
The "bias for metaphysics," of course, is simply a natural desire for knowledge of reality, something that Russell either never had or had managed to suppress. It is to the most enduring credit of Gödel and Einstein that they were interested in knowledge of reality. That Russell wasn't will certainly mean insignificance for his thought in the long run. Just what bothered him about "cosmopolitans" or, for that matter, Jews, is unclear -- and Gödel actually wasn't Jewish ( -- "though I don't think this question is of any importance," he said [p.13] -- although before finally leaving Austria to move to Princeton himself, Göedel was once beaten up by toughs for looking Jewish).
Metaphysics without repeating the experience of the Rationalists is clearly what is now needed. It is also obvious that the place to start is with the philosopher, Kant, who was the original person who wanted metaphysics without repeating the experience of the Rationalists. Picking up the matter with Kant, as obviously Einstein and Gödel were themselves doing, however, involves two needful things: (1) avoiding common misunderstandings or misinterpretations of Kant. For instance, from the evidence of Yourgrau's book, he has apparently spent not a second rethinking the received wisdom on Kant's theory of geometry. What this would mean is examined in detail elsewhere. Without having done this, Yourgrau is bound to perpetuate grave misunderstandings. That Nelson could already have helped in this area leads to: (2) making use of Fries and Nelson, who also wanted to avoid Rationalism and Positivism, and who introduced new ideas into the development of Kantian theory. It is sad that Gödel, for all the people they had in common, was not aware of Nelson and the value of what he represented. That Yourgrau is not aware is not surprising, simply part of the tragedy of 20th century philosophy, which ignored the Friesian alternative. But it is about time that people like him, disillusioned with the likes of Russell and Wittgenstein, began finding their way.
Past, Present, and Future, A Philosophical Essay about Time, by Irwin C. Lieb, Illinois, 1991
