3 December 2014
P. F. Strawson called his twentieth century exposition of Kant The Bounds of Sense. I have commented elsewhere what a appropriate title this is. The Kantian project (much like metamathematics in the twentieth century) was a limitative project. Kant himself wrote (in the Preface to the 2nd edition of the Critique of Pure Reason): “…my intention then was, to limit knowledge, in order to make room for faith.” Here is the entire passage from which the quote is taken, though in a different translation:
“This discussion as to the positive advantage of critical principles of pure reason can be similarly developed in regard to the concept of God and of the simple nature of our soul; but for the sake of brevity such further discussion may be omitted. [From what has already been said, it is evident that] even the assumption — as made on behalf of the necessary practical employment of my reason — of God, freedom, and immortality is not permissible unless at the same time speculative reason be deprived of its pretensions to transcendent insight. For in order to arrive at such insight it must make use of principles which, in fact, extend only to objects of possible experience, and which, if also applied to what cannot be an object of experience, always really change this into an appearance, thus rendering all practical extension of pure reason impossible. I have therefore found it necessary to deny knowledge, in order to make room for faith.”
Immanuel Kant, Critique of Pure Reason, Preface to the Second Edition
What lies beyond the bounds of sense? For Kant, faith. And Kant’s theological agenda drove him to seek the bounds of sense so that speculative reason could be deprived of its pretensions to transcendental insight. Thus Kant gives us an epistemology openly freighted with theological and moral concerns. Talk about the theory-ladenness of perception! It is, however, non-perception — i.e., that which cannot be the object of possible experience — that is the Kantian domain of faith.
Of course, this is the whole Kantian project in a nutshell, is it not? It is Kant’s design to show us exactly how perception is laden with theory, the theory native to the mind, the a priori concepts by which we organize experience. Kant propounds the transcendental aesthetic and the transcendental deduction of the categories in order to demonstrate the reliance of even the most ordinary experience upon the mind’s a priori faculties.
Kant was, in part, reacting against the empiricism of Locke and Hume — especially Hume’s skeptical conclusions, although Kant’s own rejection of metaphysics equaled if not surpassed Hume’s anti-metaphysical stance, as famously described in the following passage from Hume:
“When we run over libraries, persuaded of these principles, what havoc must we make? If we take in our hand any volume; of divinity or school metaphysics, for instance; let us ask, Does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames: for it can contain nothing but sophistry and illusion.”
David Hume, An Enquiry Concerning Human Understanding, “Of the academical or sceptical Philosophy,” Part III
For Hume, the bounds of sense and the limitation of reason entailed doubt; for Kant the bounds of sense and the limitation of reason entailed belief. There is a lesson in here somewhere, and the lesson is this: from a single state of affairs, multiple interpretations can be shown to follow.
Are the bounds of sense also the bounds of science? It would seem so. In so far as science must appeal to empirical evidence, and empirical evidence comes to us by way of the senses, the limits of the senses impose limits on science. Of course, this is a bit too simplistic to be quite true. There are so many qualifications that need to be made to such an assertion that it is difficult to say where to start.
It should be familiar to everyone that we have come to extensively use instruments to augment our senses. Big Science today sometimes spends years, if not decades, building its enormous machines, without which contemporary science could not be possible. So the limits of the senses are not absolute, and they are subject to manipulation. Also, we sometimes do science without our senses or instruments, when we pursue science by way of thought experiments.
While thought experiments alone, unsupplemented by actual experiments, are probably insufficient to constitute a science, thought experiments have become a necessary requisite to science much as instrumentation has become a necessary requisite to science. Sometimes, when our technology catches up with our ideas, we can transform our thought experiments into actual experiments, so that there is an historical relationship between science properly understood and the penumbra of science represented by thought experiments. And thought experiments too have their controlled conditions, and these are the conditions that Kant attempted to lay down in the transcendental aesthetic.
There is also the question of whether or not mathematics is a science, or one among the sciences. And whether or not we set aside mathematics as something different from the other sciences, we know that the development of unquestionably empirical sciences like physics are deeply mathematicized, so that the mathematical content of empirical theories may act like an abstract instrument, parallel to the material instruments of big science, that extends the possibilities of the senses. Another way to think about mathematics is as an enormous thought experiment that under-girds the rest of science — the one crucial thought experiment, an experimentum crucis, without which the rest of science cannot function. In this sense, thought experiments are indispensable to mathematicized science — as indispensable as mathematics.
At a more radical level of critique, it would be difficult to give a fine-grained account of empirical evidence that did not shade over, at the far edges of the concept, into other kinds of knowledge not strictly empirical. Empirical evidence may shade over into the kind of intuitive evidence that is the basis of mathematics, or the kind of epistemological context that is the setting for our thought experiments. Empirical evidence can also shade over into interoception that cannot be publicly verified (therefore failing a basic test of science) or precisely reproduced by repetition, and which interoception itself in turn shades over into intuitions in which thought and feeling are not clearly distinct.
Where does Kant’s possible experience fit within the continuum of the senses? What is the scope of possible experience? Can we make a clear distinction between extending the senses (and thus human experience) by abstract or concrete instruments and imposing a theory upon experience through these extensions? Does possible experience include all possible past experience? Does past experience include phenomenon that occurred but which were not observed (the famous tree falling in a forest that no one hears)? Does it include all possible future experience, or only those future experiences that will eventually be actualized, and not those that already remain merely shadowy possibilities? Does possible experience include those counterfactuals that feature in the “many worlds” interpretation of quantum theory? Explicit answers to these questions are less important that the lines of inquiry that the questions prompt us to pursue.
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7 May 2013
The Transcendental Aesthetic and the Finding of
Other Minds in Other Species
An extrapolation of the “problem of other minds” to other species
What philosophers call “the problem of other minds” is closely related to what philosophers call the “mind-body problem” (both fall within philosophy of mind), and both are paradigmatic metaphysical questions that have been with philosophy from the beginning. Lately I’ve written a good deal about the mind-body problem on my other blog (e.g., in Naturalism and the Mind, Of Distinctions Weak and Strong, Of Distinctions, Principled and Otherwise, Cartesian Formalism, etc.), and this has got me to thinking about the problem of other minds.
I have never found the idea of other minds in other species to be in the least problematic. When you look into the eyes of another living being, whether human being or other being, you are well aware of the moment of mutual recognition, and you are equally well aware at that moment of mutual recognition that you are sharing that moment with another consciousness (that is to say, you experience a social temporality).
In The Eye of the Other I wrote:
It is when we look into the eye of the other that we recognize the consciousness of the other. Even if we feel that the reality of other minds is beyond philosophical demonstration, even if we are skeptics of other minds, it would be extraordinarily difficult to look into the eyes of another and not experience that immediate reaction of recognition of another mind. When we look not only into the eyes of another being but also into the eyes of another species, there is simultaneously the recognition of the awareness of the other and of the alien nature of that awareness.
Some people feel obliged to deny this inter-species recognition of common consciousness on ideological grounds, although few ever think of speciesism as a ideology. As I have recently observed in relationship to geopolitics, which I characterized as an ideology that does not know itself to be an ideology, so too with speciesism: for many it is simply an unexamined presupposition and is never formalized as an explicit article of belief.
While I myself don’t find anything in the least problematic about consciousness in other species, and I think that anyone that takes a naturalistic point of view would be hard-pressed to deny it, I cannot deny that there are some persons who feel a real sense of moral horror in recognizing the consciousness of other species. I am fully aware of this moral horror, and I am utterly unsympathetic to it. To paraphrase Freud on the “oceanic” feeling, I am unable to discover this moral horror in myself.
Some of those who are uncomfortable with the ascription of consciousness to other species simply don’t like animals, and some of those similarly disposed are just completely uninterested in animals and find it peculiar that some human beings seem to be closer to their dogs and cats than they are to other human beings. Such persons sometimes become visibly discomfited at any mention of Johnson’s Hodge or Greyfriars Bobby or Hachikō, all memorialized by statues. I have personally heard individuals of this particular temperament indignantly lecture others (myself included) on the dangers of anthropomorphizing our companion animals. If I were to be so lectured today, I would lecture right back on anthropic bias in the philosophy of mind, which is utterly out of place and unbecoming of a philosopher (which in this instance includes anyone who makes, or who implies, philosophical assertions about mind, specifically, denying mind to certain classes of existents).
Such persons often live in an exclusively human world, and to them the animal world seems inexplicably alien. This in itself is an implicit recognition of an animal world, that is to say, a world constituted by animal consciousness. But, of course, not all who deny consciousness to other species can be so pigeon-holed. Some who have completely succumbed to anthropic bias in the philosophy of mind are in no sense living in an exclusively human world, and certainly when the dogma of human exceptionalism in consciousness gained currency, long before our industrial-technological civilization freed us from animal muscle power as the motive force of civilization, almost everyone lived intimately with animals.
In this latter context, prior to industrialization, there was always a theological overlay to the denial of consciousness to other species. Indeed, it is very likely that, if the terms of the philosophical problem of other minds were carefully explained, those with a theological world view might well without hesitation grant consciousness of other species, and simply deny they other species possess a “soul,” which is simply a theologically-legitimized devalorization. In practice, it comes to much the same as the denial of consciousness to other species and a sedulous distinction between the human and the animal realms.
I observed in The Origins of Physicalism that Cartesianism was the original “mechanical philosophy,” and while Cartesianism in the time of Descartes and immediately afterward incorporated human exceptionalism into the philosophy (i.e., it institutionalized anthropic bias in the philosophy of mind), the logical extrapolation of the theory was evident, and what the Cartesians practised upon other species later philosophers in the mechanistic tradition came to practise also upon human beings: the denial of consciousness.
Today we have a school of thought that is not exactly the denial of consciousness but rather the revaluation, or, better, the devaluation of consciousness, which latter is called a “user illusion” — at least, in techno-philosophy the denial of consciousness is called the “user illusion.” In traditional philosophy, the denial of the existence of consciousness is called “eliminativism,” since instead of seeking to reduce consciousness to something else that is not consciousness (and thereby exemplifying reductivism), eliminativism cuts the Gordian Knot and simply denies that there is any such thing as consciousness — meaning that there is nothing to be “explained away.” I am sure that I am not the only one who finds this to be a thoroughly unsatisfying “solution” to a perennial philosophical problem.
How then are we to understand the minds of other species, i.e., the problem of other minds as generalized to include non-human species? What philosophical framework exists that can provide a conceptual infrastructure for such an understanding? There are many possibilities, but today I would like to consider a Kantian approach.
If we take as the lesson of Kant’s transcendental aesthetic that the mind is being continually bombarded by a riot of sensations from all the various bodily sensory organs, and that the mind then constitutes a kind of conceptual sieve that shapes, channels and directs the mass of sensory experience into something coherent upon which an organism can act, we can recognize that much the same process occurs in other species. All mammals have more or less similar bodies and similar sensory endowments, so that all living mammals are constantly being bombarded by a riot of sensations which each creature must sort into coherent experience. The fact that we can play fetch with a dog, and both successfully interact in one and the same world, simultaneously recognizing the stick at the center of the game as an object that passes between two or more organism involved in a game of fetch, suggests that we and the dog constitute and cognize the world in a remarkably similar fashion.
The dog, like us, is receiving sensory signals from his eyes, ears, nose, and so forth, as well as experiencing kinesthetic sensations from the movement of his body as he exerts himself in lunging after the stick. From all of this sensation the dog successfully distills a world, and that world is remarkably similar to our world.
A few years ago I had an interesting experience that bears directly on games of fetch and shared experience, when I had an opportunity to feel what it was like to be a dog among dogs. I was at a vacation house on a river, and had brought my wetsuit along so I could swim. The river is fed by snow melt from Mt. Hood and it is one of the coldest rivers in which I have ever been swimming. I put on my wetsuit and got into the water just as others were beginning to play fetch with a large black lab that they had brought along. They threw a stick into the frigid waters of the river, and the lab plunged into to fetch the stick. The next time the stick was thrown I started swimming toward it the same time that the lab started swimming toward it. The lab looked at me and instantly saw me as a competitor for the stick. He swam all the harder and made it to the stick before me with an obvious sense of triumphalism.
Of course, most people have had experiences like this in life, and some people will dismiss such experiences as readily as Descartes dismissed his correspondent’s stories attempting to prove that animals are not mere mechanisms. However we interpret such experiences, we share and interact in a common world. Although this is utterly contrary to the spirit of Kant, I have to observe that any animal that could not distill coherent experience of the world out of its mass of sensation would never survive. Evolution selects for those organisms that can best hunt or avoid being prey in the common world in which predator and prey interact. This is a naturalistic point of view, whereas Kant’s point of view was decidedly that of idealism.
Even if one rejects Kant’s idealism, as I do, there seems to me to be some residual value in the idea of the mind being involved in the constitution of experience. I think that Kant was right that we have certain a priori intuitions that order our experience, but I think that this was much more fluid and pluralistic than Kant’s exposition of the transcendental aesthetic allows. While I wrote above that mammals all have a relatively similarly experience of the world, a function of a similar sensory and cognitive endowments, I would allow that there is some important variation. Sight plays a very large role in how human beings cognize the world; smell plays a disproportionate role in how dogs cognize the world; sound plays a disproportionate role in how dolphins cognize the world.
All terrestrial critters of a given level of cognitive complexity have to distill coherent experience of one and the same world out of a mass of sensation, but that mass of sensation differs among different species. I suspect that this sensory difference means that different species also have different a priori conceptions that help them to organize their experience into a coherent whole, and that, just sensory experience differs from species to species, but admits of degrees of greater or less, so too the a priori ideas of distinct species different from species to species but also admit of greater or less similarity. That is to say, smell may shape the world of a dog far more than it shapes our world, but we probably share far more in terms of sensory experience and organizing ideas with a dog than with a marine mammal, and probably we share much more with a marine mammal than with an octopus or other cephalopod. This is a function and an illustration of a point I recently tried to make about the relationship between mind and embodiment.
I tried to make this point in my above referenced post, The Eye of the Other, since when I unexpectedly looked into the eyes of a sealion, a marine mammal, we immediately recognized each other, and in the same moment of recognition also recognized the profound differences between the two of us. Common mammalian minds, differently embodied and living in profoundly different environments, will involve different sensory stimulation, different kinesthetic sensations, and different a priori concepts for organizing experience. But not too different. A shark, with a mind very different from a mammalian mind, can predate marine mammals, so that both sharks and marine mammals interact in the same marine environment just as human beings and tigers interact in the same terrestrial environment.
I suspect that, at least in some senses, the tiger’s mind and the human mind share concepts derived from their common terrestrial environment, while the shark and the marine mammal share concepts derived from the common marine environment, so that a tiger’s mind is more like a human mind than a sea lion’s mind is like a human mind, and, vice versa, a sea lion’s mind is more like a shark’s mind than it is like a human mind. Nevertheless, the human mind and the sea lion mind will share some concepts due to their common mammalian constitution. To employ a Wittgensteinian turn of phrase, the different sensations, concepts, and minds of distinct species overlap and intersect.
The recognition of consciousness in other species is no marginal and recondite inquiry; if, in the fullness of time, we encounter other intelligent species in the universe of extraterrestrial origin, we will need a philosophical framework in which we can integrate the idea of consciousness among other organic species, and if research into artificial intelligence and machine consciousness ever issues in a self-aware mechanism, fashioned by human hands in the same way that we might build a car or a house, we will again require a philosophical framework in which we can integrate the idea of consciousness even more generally, comprehending both naturally-emergent consciousness from organic substrates and artificially emergent consciousness of non-organic substrates.
We need a robust philosophy of mind that does not stagnate in questions of whether there is mind or whether minds can be reduced to other phenomena or eliminated altogether. Such doctrines are — would be — utterly unhelpful in coming to understand what Husserl called the “structures of consciousness.” It is likely that the structures of consciousness vary incrementally among individuals of the same species, vary a little more across distinct species, and will vary even more among minds derived from different sources — different ecosystems and biospheres in the case of organically-originating extraterrestrial minds, and different mechanisms of implementation in the case of inorganically-originating minds of machine consciousness.
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6 August 2012
Brouwer and Wittgenstein were contemporaries, with the whole of Wittgenstein’s years contained within those of Brouwer’s (Wittgenstein lived 1889 to 1951 while Brouwer lived the longer life from 1881 to 1966). It is mildly ironic that even as Brouwer’s followers were playing down his mysticism and trying to extract only the mathematical content from his intuitionist philosophy (even the faithful Heyting distanced himself from Brouwer’s mysticism), Wittgenstein’s writings reached a much larger public which resulted in the mystical content of Wittgenstein’s works being played up and the early Wittgenstein himself, very much the logician following in the tradition of Frege and Russell, presented as a mystic.
Not only were Brouwer and Wittgenstein contemporaries, but we also know that Brouwer played a little-known role in Wittgenstein’s return to philosophy. After having written the Tractatus Logico-Philosophicus and then disappearing into the mountains of Austria to become a village schoolmaster in Trattenbach, some of those philosophers that continued to seek out Wittgenstein in his self-imposed exile convinced him to go to a lecture in Vienna in March 1928. The lecture was delivered by Brouwer (Brouwer gave two lectures; Wittgenstein is said to have attended one of them). Wittgenstein was said to have listened to the lecture with a surprised look on his face (sort of like G. E. Moore saying that Wittgenstein was the only student that looked puzzled at this lectures). So it may be the case that Brouwer played a pivotal role in the transition from the thought of the early Wittgenstein to the thought of the later Wittgenstein. (Matthieu Marion has argued this thesis.)
Wittgenstein’s distinction between saying and showing, a doctrine that dates from the Tractatus (cf. sections 4.113 and following), is often adduced in expositions of his alleged mysticism. According to Wittgenstein’s distinction, some things can be said but cannot be shown, while other things can be shown but cannot be said. While to my knowledge Wittgenstein never used the term “ineffable,” that which can be shown but cannot be said would seem to be a paradigm case of the ineffable. And since Wittgenstein identified a substantial portion of our experience as showable although unsayable, the ineffable seems then to play a central role in his thought. This puts Wittgenstein firmly in the company of figures like, say, St. Symeon the New Theologian (also, like Wittgenstein, an ascetic), which makes the case for his mysticism.
An extract from St. Symeon on the ineffable: “The grace of the all-holy spirit is given as earnest money of the souls pledged in marriage to Christ. Just as a woman without a pledge has no certainty that the union with the groom will occur within a certain length of time, so does the soul have no firm assurance that it will be re-united to its God and Master for all eternity. The soul cannot be certain that it will achieve this mystic, ineffable union nor that it will enjoy its inaccessible beauty if it does not have the pledge of His grace and does not consciously have that grace within.” (Krivocheine, Basil and Gythiel, Anthony P., In the Light of Christ: Saint Symeon, the New Theologian 949–1022, St. Vladimir’s Seminary Press, 1986, p. 367)
Brouwer was a bit more explicit in his doctrine of ineffability than was Wittgenstein, and he repeatedly asserted that the language of mathematics was a necessary evil that approximated but never fully captured the intuitive experience of mathematics, which he understood to be a free creation of the human mind. This comes across both in his early mystical treatise Life, Art, and Mysticism, which is pervaded by a sense of pessimism over the evils of the world (which include the evils of mathematical language), and his more technical papers offering an exposition of intuitionism as a philosophy of mathematics. But, like Wittgenstein, Brouwer does not (to my limited knowledge) actually use the term “ineffable.”
There is another ellipsis common to both Brouwer and Wittgenstein, and that is despite Brouwer’s openly professed intuitionism, which can be considered a species of constructivism (this latter is a point that needs to be separately argued, but I will only pass over it here with a single mention), and despite the strict finitism of the later Wittgenstein, which can also be considered a species of constructivism, neither Brouwer nor Wittgenstein employ Kantian language or Kantian formulations. No doubt there are implicit references to Kant in both, but I am not aware of any systematic references to Kant in the work of either philosopher. This is significant. Both Brouwer and Wittgenstein were philosophers of the European continent, where the influence of Kant remains strong even as his reputation waxes and wanes over the generations.
Kant was an early constructivist, or, rather, a constructivist before constructivism was explicitly formulated, and therefore sometimes called a proto-constructivist — although I have pointed out an obvious non-constructive dimension to Kant’s thought despite his proto-constructivism (which I do not deny, notwithstanding Kant’s non-constructive arguments in the first Critique). Kant’s classic proto-constructivist formulation is that the synthetic a priori truths of mathematics must be constructed, or “exhibited in intuition.” It is this latter idea, of a concept being exhibited in intuition, that has been particularly influential. But what does it mean? Obviously, a formulation like this has invited many interpretations.
The approaches of Brouwer and the later Wittgenstein could be considered different ways of exhibiting a concept in intuition. Brouwer, by casting out the law of the excluded middle from mathematics (at least in infinitistic contexts), assured that double negation was not equivalent to the truth simpliciter, so that even if you know that it is not the case that x is false, you still don’t know that x is true. (On the law of the excluded middle cf. P or not-P.) The later Wittgenstein’s insistence upon working out how a particular term is used and not merely settling for some schematic meaning (think of slogans like “don’t ask for the meaning, ask for the use” and “back to the rough ground”) similarly forces one to consider concrete instances rather than accepting (non-constructive) arguments for the way that things putatively must be, rather than how they are in actual fact. Both Wittgenstein’s finitism and Brouwer’s intuitionism would look with equal distaste upon, for example, proving that every set can be well-ordered without actually showing (i.e., exhibiting) such an order — also, the impossibility of exhaustively showing (i.e., exhibiting in intuition) that every set can be well-ordered if one acknowledges an infinity of sets.
I give this latter example because I think it was largely the perceived excesses of set theory and Cantor’s transfinite number theory that were essentially responsible for the reaction among some mathematicians that led to constructivism. Cantor was a great mathematical innovator, and his radical contributions to mathematics spurred foundationalists like Frege (who objected to Cantor’s methods but not his results) and Russell to attempt to construct philosophico-mathematical justifications, i.e., foundations, that would legitimize that which Cantor had wrought.
The reaction against infinitistic mathematics and foundationalism continues to the present day. Michael Dummett wrote in Elements of Intuitionism, a classic textbook on basic intuitionistic logic and mathematics, that:
“From an intuitionistic standpoint, mathematics, when correctly carried on, would not need any justification from without, a buttress from the side or a foundation from below: it would wear its own justification on its face.”
Dummett, Michael, Elements of Intuitionism, Oxford University Press, 1977, p. 2
In other words, mathematics would show its justification; in contrast, the foundationalist project to assure the legitimacy of the flights of non-constructive mathematics was wrong-headed in its very conception, because nothing that we say is going to change the fact that non-constructive thought that derives its force from proof, i.e., from what is said, does not show its justification on its face. Its justification must be established because it does not show itself. This is what “foundations” are for.
Note: There is also an element of intellectual ascesis in Dummett’s idea of a conservative extension of a theory, and this corresponds to the asceticism of Wittgenstein’s character, and, by extension, to the asceticism of Wittgenstein’s thought — asceticism being one of the clear continuities between the earlier and the later Wittgenstein — like the implicit development of constructivist themes.
But it was not only the later Wittgenstein who reacted with others against Cantor. It seems to me that the saying/showing distinction of the Tractatus is a distinction not only between that which can be said and that which can be shown, but also a distinction between that which is established by argument, possibly non-constructive argument, and that which is exhibited in intuition, i.e., constructed. If this is right, Wittgenstein showed an early sensitivity to the possibility of constructivist thought, and his later development might be understood as a development of the constructivist strand within his thinking, making Wittgenstein’s development more linear than is often recognized (though there are many scholars who argue for the unity of Wittgenstein’s development on different principles). The saying/showing distinction may be the acorn from which the oak tree of the Philosophical Investigations (and the subsequently published posthumous works) grew.
For the early Wittgenstein, the distinction between saying and showing was thoroughly integrated into his idea of logic, and while in the later sections of the Tractatus the mysticism of what which can only be shown but cannot be said becomes more evident, it is impossible to say whether it was the logical impulse that prevailed, and served as the inspiration for the mysticism, or whether it was the mystic impulse that prevailed, and served as the pretext for formulating the logical doctrines. But the logical doctrines are clearly present in the Tractatus, and serve as the exposition of Wittgenstein’s ideas, even up to the famous metaphor when Wittgenstein says that the propositions of the Tractatus are like a ladder than one must cast away after having climbed up and over it.
Just as there is a mathematical content to Brouwer’s mysticism, so too there is a logical content to Wittgenstein’s mysticism. It is, in fact, likely that Wittgenstein’s distinction between saying and showing was suggested to him by what is now called the “picture theory of meaning” given an exposition in the Tractatus. Few philosophers today defend Wittgenstein’s picture theory of meaning, but it is central to the metaphysics of the Tractatus. For Wittgenstein, the logical structure of a proposition can be shown but not said. Since for Wittgenstein in his Tractarian period, “The facts in logical space are the world” (1.13), and “In the proposition the thought is expressed perceptibly through the senses” (3.1) — i.e., the proposition literally exhibits its structure in sensory intuition — thus, “The proposition is a picture of reality.” (4.01) One might even say that a proposition exhibits the world in intuition.
Today these formulations strike us as a bit odd, because we think of anything that can be formulated in logical terms as a paradigm case of something that can be said, and very possibly also something that may not be showable. For us, logic is a language is among languages, and one way among many to express the world; for the early Wittgenstein, on the contrary, logic is the structure of the world. It shows itself because the world shows itself, and after showing itself there is nothing more to be said. The only appropriate response is silence.
As we all know from the final sentence of the Tractatus, whereof one cannot speak, thereof one must remain silent. According to the Wittgenstein of the Tractatus, all scientific questions can be asked and all scientific questions can be answered (shades of Hilbert’s “Wir müssen wissen. Wir werden wissen.” — which Per Martin-Löf has called Hilbert’s solvability axiom, and which is the very antithesis of Brouwer’s rejection of the law of the excluded middle), but even when we have answered all scientific questions, the problems of life remain untouched.
As implied by the early Wittgenstein’s insistence upon the solvability of all scientific questions, the metaphysics of Brouwer and Wittgenstein were very different. Their common constructivism does not prevent their having fundamental, I might even say foundational, differences. Also, while Wittgenstein comes across in a melancholic fashion (a lot like Plotinus, another philosophical mystic), he is not fixated on the evils of the world in the same way that Brouwer was. If both Brouwer and Wittgenstein can be called mystics, they are mystics belonging to different traditions. Brouwer was a choleric mystic while Wittgenstein was melancholic mystic.
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27 April 2012
The thesis that epistemic space is primarily shaped and structured by geometrical intuition may be equated with Bergson’s exposition of the spatialization of the intellect. Bergson devoted much of his philosophical career to a critique of the same. Bergson’s exposition of spatialization is presented in terms of a sweeping generality as the spatialization of time, but a narrower conception of spatialization in terms of the spatialization of consciousness or of human thought follows from and constitutes a special case of spatialization.
One might well ask, in response to Bergson, how we might think of things in non-spatial terms, and the answer to this question is quite long indeed, and would take us quite far afield. Now, there is nothing wrong with going quite far afield, especially in philosophy, and much can be learned from the excursion.
There is a famous passage in Wittgenstein’s Tractatus Logico-Philosophicus about “logical space,” at once penetrating and obscure (like much in the Tractatus), and much has been read into this by other philosophers (again, like much in the Tractatus). Here is section 1.13:
“The facts in logical space are the world.”
And here is section 3.42:
“Although a proposition may only determine one place in logical space, the whole logical space must already be given by it. (Otherwise denial, the logical sum, the logical product, etc., would always introduce new elements — in co-ordination.) (The logical scaffolding round the picture determines the logical space. The proposition reaches through the whole logical space.)”
I will not attempt an exposition of these passages; I quote them here only to give the reader of flavor of Wittgenstein’s . Clearly the early Wittgenstein of the Tractatus approached the world synchronically, and a synchronic perspective easily yields itself to spatial expression, which Wittgenstein makes explicit in his formulations in terms of logical space. And here is one more quote from Wittgenstein’s Tractatus, from section 2.013:
“Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.”
I find this particularly interesting because it is, essentially, a Kantian argument. I discussed just this argument of Kant’s in Kantian Non-Constructivism. It was a vertiginous leap of non-constructive thought for the proto-constructivist Kant to argue that he could imagine empty space, but not spatial objects without the space, and it is equally non-constructive for Wittgenstein to make the same assertion. But it gives us some insight into Wittgenstein’s thinking.
Understanding the space of atomic facts as logical space, we can see that logical space is driven by logical necessity to relentlessly expand until it becomes a kind of Parmenidean sphere of logical totality. This vision of logical space realizes virtually every concern Bergson had for the falsification of experience given the spatialization of the intellect. The early Wittgenstein represents the logical intellect at its furthest reach, and Wittgenstein does not disappoint on this score.
While Wittgenstein abandoned this kind of static logical totality in this later thought, others were there to pick up the torch and carry it in their own directions. An interesting example of this is Donald Davidson’s exposition of logical geography:
“…I am happy to admit that much of the interest in logical form comes from an interest in logical geography: to give the logical form of a sentence is to give its logical location in the totality of sentences, to describe it in a way that explicitly determines what sentences it entails and what sentences it is entailed by. The location must be given relative to a specific deductive theory; so logical form itself is relative to a theory.”
Donald Davidson, Essays on Actions and Events, pp. 139-140
In a more thorough exposition (someday, perhaps), I would also discuss Frege’s exposition of concepts in terms of spatial areas, and investigate the relationship between Frege and Wittgenstein in the light of their shared equation of logic and space. (I might even call this the principle of spatial-logical equivalence, which principle would be the key that would unlock the relationship between epistemic space and geometrical intuition.)
Certainly the language of spatiality is well-suited to an exposition of human thought — whether it is uniquely suited is an essentialist question. But we must ask at this point if human thought is specially suited to a spatial exposition, or if a spatial exposition is especially suited for an exposition of human thought. It is a question of priority — which came first, the amenability of spatiality to the mind, or the amenability of the mind to spatiality? Which came first, the chicken or the egg? Is the mind essentially spatial, or is space essentially intellectual? (The latter position might be assimilated to Kantianism.)
From the perspective of natural history, recent thought on human origins has shifted from the idea of a “smart ape” to the idea of a “bipedal ape,” the latter with hands now free to grasp and to manipulate the environment. Before this, before human beings were human, our ancestors lived in trees where spatial depth perception was crucial to survival, hence our binocular vision from two eyes placed side by side in the front of the face. Color vision additional made it possible to identify the ripeness of fruit hanging in the trees. In other words, we are a visual species from way back, predating even our minds in their present form.
With this observation it becomes obvious that the human mind emerged and evolved under strongly visual selection pressure. Moreover, visual selection pressure means spatial selection pressure, so it is no wonder that the categories native to the human mind are intrinsically spatial. Those primates with the keenest ability to process spatial information in the form of visual stimuli would have had a differential survival and reproductive advantage. This is not accidental, but follows from our natural history.
But now I have mentioned “natural history” again, and I pause. Temporal selection pressure has been no less prevasive than spatial selection pressure. All life is a race against time to survive as long as possible while producing as many viable offspring as possible. Here we come back to Bergson again. Why does the intellect spatialize, when time is as pervasive and as inescapable as space in human experience?
With this question ringing in our ears, and the notable examples of philosophical logical-spatial equivalence mentioned above, why should we not have (parallel to Wittgenstein’s exposition of logical space) logical time and (parallel to Davidson’s exposition of logical geography) logical history?
To think through the idea of logical history is so foreign that is sounds strange even to say it: logical time? Logical history? These are not phrases with intuitive self-evidence. At least, they have very little intuitive self-evidence for the spatializing intellect. But in fact a re-formulation of Davidson’s logical geography in temporal-historical terms works quite well:
…the logical form of a sentence is to give its logical position in the elapsed sequence of sentences, to describe it in a way that explicitly determines what are following sentences it entails and what previous sentences it is entailed by…
Perhaps I ought to make the effort to think things through temporally in the same way that I have previously described how I make the effort to think things through selectively when I catch myself thinking in teleological terms.
In the meantime, it seems that our geometrical intuition is a faculty of mind refined by the same forces that have selected us for our remarkable physical performance. And as with our physical performance, which is rendered instinctive, second nature, and unconscious simply through our ordinary interaction with the world (all the things we must do anyway in order to survive), our geometrical intuition is often so subtle and so unconsciously sophisticated that we do not even notice it until we are presented with some Gordian knot that forces us to think explicitly in spatial terms. Faced with such a problem, we create sciences like topology, but before we have created such a science we already have an intellect strangely suited to the formulation of such a science. And, as I have written elsewhere, we have no science of time. We have science-like measurements of time, and time as a concept in scientific theories, but no scientific theory of time as such.
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Fractals and Geometrical Intuition
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12 February 2012
Today is Darwin’s birthday, and therefore an appropriate time to celebrate Darwin by a mediation upon his work. No one has influenced me more than Darwin, and I always find the study of his works to be intellectually rewarding. I also read (and listen to) quite a number of books about Darwin. Recently I listened to Darwin, Darwinism, and the Modern World, 14 lectures by Dr. Chandak Sengoopta. While I enjoyed the lectures, I sharply differed from many of Dr. Sengoopta’s interpretations of Darwin’s thought. One theme that Dr. Sengoopta returned to several times was a denial that Darwin had anything to say about the ultimate origins of life. Each time that Dr. Sengoopta made this point I found myself grow more and more irritated.
To say that Darwin had nothing to say about the ultimate origins of life may be technically correct in a narrow sense, but I do not think that it is an accurate expression of Darwin’s vision of life, which was sweeping and comprehensive. While it may be a little much to say that Darwin ever entertained ideas that could accurately be called “Darwin’s cosmology,” it is obvious in reading Darwin’s notebooks, in which he recorded thoughts that never made it into his published books, his mind ranged far and wide. It is almost as though, once Darwin made the conceptual breakthrough of natural selection he had discovered a new world.
In characterizing Darwin’s thought in this way I am immediately reminded of a famous letter that Janos Bolyai wrote to his father after having independently arrived at the idea of non-Euclidean geometry:
“…I have discovered such wonderful things that I was amazed, and it would be an everlasting piece of bad fortune if they were lost. When you, my dear Father, see them, you will understand; at present I can say nothing except this: that out of nothing I have created a strange new universe. All that I have sent you previously is like a house of cards in comparison with a tower. I am no less convinced that these discoveries will bring me honor than I would be if they were complete.”
Darwin, too, discovered wonderful things and created the strange new universe of evolutionary biology, though it came on him rather slowly — not in a youthful moment that could be recorded to a letter in his father, and not in a fit of fever, as the idea of natural selection came to Wallace — as the result of many years of ruminating on his observations. But the slowness with which Darwin’s mind worked was repaid with thoroughness. Even though Darwin was the first evolutionist in the modern sense of the term, he must also be accounted among the most complete of all evolutionary thinkers, having spent decades thinking through his idea with a Platonic will to follow the argument wherever it leads.
Given that Darwin himself thought that making the idea of natural selection public was like “confessing to a murder,” the fragments of Darwin’s cosmology must be sought in his latter and notebooks as much as in his published works. As for the origins of life, narrowly considered, apart from the cosmological implications of life, Darwin openly speculated on a purely naturalistic origin of life in a letter to Joseph Hooker:
“It is often said that all the conditions for the first production of a living organism are now present, which could ever have been present. But if (and oh what a big if) we could conceive in some warm little pond with all sorts of ammonia and phosphoric salts, — light, heat, electricity &c. present, that a protein compound was chemically formed, ready to undergo still more complex changes, at the present day such matter would be instantly devoured, or absorbed, which would not have been the case before living creatures were formed.”
Darwin’s 1871 letter to Joseph Hooker
What has widely come to be known as “Darwin’s warm little pond” sounds like nothing so much as the famous Stanley L. Miller electrical discharge experiment.
Darwin revealed his consistent naturalism in his rejection of teleology in a letter to Julia Wedgwood, where he indirectly refers to his slow, steady, cumulative mode of thinking (quite the opposite of revelation):
“The mind refuses to look at this universe, being what it is, without having been designed; yet, where would one most expect design, viz. in the structure of a sentient being, the more I think on the subject, the less I can see proof of design.”
Darwin’s letter of 11 July 1861 to Miss Julia Wedgwood
This same refusal continues to a sticking point to the present day, since, like so much that we learn from contemporary science, appearances are deceiving, and the reality behind the appearance can be so alien to the natural constitution of thue human mind that it is rejected as incomprehensible or unthinkable. That Darwin was able to think the unthinkable, and to so with a unparalleled completeness at a time when no one else was doing so, is testimony to the cosmological scope of his thought.
One of the most memorable passages in all of Darwin’s writings is the last page or so of the Origin of Species, which touches not a little on cosmological themes. Take, for instance, the “tangled bank” passage:
“It is interesting to contemplate an entangled bank, clothed with many plants of many kinds, with birds singing on the bushes, with various insects flitting about, and with worms crawling through the damp earth, and to reflect that these elaborately constructed forms, so different from each other, and dependent on each other in so complex a manner, have all been produced by laws acting around us.”
Besides anticipating the evolutionary study of ecology and complex adaptive systems long before these disciplines became explicit and constituted their own sciences, Darwin here subtly invokes a law-like naturalism that both suggests Lyell’s uniformitarianism while going beyond it.
Darwin places this law-governed naturalism in cosmological context in the last two sentences of the book, here also implicitly invoking Malthus, whose influence was central to his making the breakthrough to the idea of natural selection:
“Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.”
This famous passage from Darwin reminds me of a perhaps equally famous passage from Immanuel Kant, who concluded The Critique of Practical Reason with this thought:
“Two things fill the mind with ever new and increasing admiration and awe, the more often and steadily we reflect upon them: the starry heavens above me and the moral law within me. I do not seek or conjecture either of them as if they were veiled obscurities or extravagances beyond the horizon of my vision; I see them before me and connect them immediately with the consciousness of my existence. The first starts at the place that I occupy in the external world of the senses, and extends the connection in which I stand into the limitless magnitude of worlds upon worlds, systems upon systems, as well as into the boundless times of their periodic motion, their beginning and continuation. The second begins with my invisible self, my personality, and displays to me a world that has true infinity, but which can only be detected through the understanding, and with which . . . I know myself to be in not, as in the first case, merely contingent, but universal and necessary connection. The first perspective of a countless multitude of worlds as it were annihilates my importance as an animal creature, which must give the matter out of which it has grown back to the planet (a mere speck in the cosmos) after it has been (one knows not how) furnished with life-force for a short time.”
Both Darwin and Kant invoke both the laws of the natural world (and both, again, do so by appealing to grandeur of the heavens) and a humanistic ideal. For Kant, the humanistic ideal is morality; for Darwin, the humanistic ideal is beauty, but what Kant said of morality and the moral law is equally applicable, mutatis mutandis, to beauty. Darwin might equally well have said of “the fixed law of gravity” and of “endless forms most beautiful and most wonderful” that he saw them before himself and connected them immediately with the consciousness of his existence. Kant might equally well have said that there is “grandeur in this view of life” that embraces both the starry heavens above and the moral law within.
Darwin did not express himself (and would not have expressed himself) in these philosophical terms; he was a naturalist and a biologist, not a philosopher. But Darwin’s naturalism and biology were so comprehensive to have spanned the universe and to have converged on an entire cosmology — a cosmology, for the most part, not even suspected before Darwin had done his work.
There is a sense in which Darwin fulfilled Marx’s famous pronouncement, from this Theses on Feuerbach, such that: “Philosophers have only interpreted the world in various ways; the point is to change it.” Darwin, however, did not change the world by fomenting a revolution; Darwin changed the world by thinking, like a philosopher. In this sense, at least, Darwin must be counted among the greatest philosophers.
I would be a rewarding project to devote an entire book to the idea of Darwin’s Cosmology. I know that I have not even scratched the surface here, and have not come near to doing justice to the idea. It would be a rewarding project to think through this idea as carefully as Darwin thought through his ideas.
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Happy Birthday Charles Darwin!
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29 June 2011
The idea of collective security can be traced back at least to Kant, whose short and widely influential work Perpetual Peace is as clear and as easy to understand as the Critique of Pure Reason is opaque and difficult to understand. There are many visionary ideas in Kant’s essay, all of which were ahead of his time, and most of which still remain ahead of our time. Here is Kant’s formulation of collective security:
“Peoples, as states, like individuals, may be judged to injure one another merely by their coexistence in the state of nature (i.e., while independent of external laws). Each of then, may and should for the sake of its own security demand that the others enter with it into a constitution similar to the civil constitution, for under such a constitution each can be secure in his right. This would be a league of nations, but it would not have to be a state consisting of nations. That would be contradictory, since a state implies the relation of a superior (legislating) to an inferior (obeying), i.e., the people, and many nations in one state would then constitute only one nation. This contradicts the presupposition, for here we have to weigh the rights of nations against each other so far as they are distinct states and not amalgamated into one.”
Immanuel Kant, Perpetual Peace, Section II, “SECOND DEFINITIVE ARTICLE FOR A PERPETUAL PEACE”
After considering the vicissitudes of “lawless freedom” and the perversity of war, Kant continues:
“…there must be a league of a particular kind, which can be called a league of peace (foedus pacificum), and which would be distinguished from a treaty of peace (pactum pacis) by the fact that the latter terminates only one war, while the former seeks to make an end of all wars forever. This league does not tend to any dominion over the power of the state but only to the maintenance and security of the freedom of the state itself and of other states in league with it, without there being any need for them to submit to civil laws and their compulsion, as men in a state of nature must submit.”
While Kant is known as an “idealist” philosopher in the technical sense of idealism, which is to say that Kant sees the world as ultimately constructed out of ideas, this essay of Kant reveals Kant as an idealist as the term is commonly used in conversation. In fact, Kant deserves to be called an idealist in both senses. It is hard to believe that Kant believed in the practicality of his proposals in his Perpetual Peace essay, but I don’t think that there is any question that he did so believe. Kant also wrote a wonderful little essay, which I have quoted on several occasions, in which he argues quite explicitly against those who maintain the impracticality of theoretical ideals.
Surprisingly, perhaps even shockingly, the world has tried to put some of Kant’s ideas into practice. While the League of Nations didn’t work out so well, we still have the United Nations, and though it can’t accomplish much, it is at least a nod in the direction that Kant visualized. The idea of collective security, then, in familiar to all, and can be intuitively summarized in phrases such as there being strength in numbers, all for one and one for all, and the like.
I would like to suggest that beyond collective security in the familiar sense that there is also the possibility of collective economic security, and I would argue that the European Union constitutes an attempt to realize collective economic security. I can easily imagine how others might disagree with me on this. I recall some time ago I was reading a Stratfor analysis in which the writer (probably George Friedman) argued that the rationale behind the European Union was ultimately security, and that the unification of the European economy was only a means to the end of getting Europe to work together abandon its militaristic ways so there wouldn’t be any more blood-lettings like the world wars of the twentieth century.
That Europe is and has been a deeply fractured place was recently reiterated on Stratfor by Marko Papic in The Divided States of Europe:
“Europe has the largest concentration of independent nation-states per square foot than any other continent. While Africa is larger and has more countries, no continent has as many rich and relatively powerful countries as Europe does. This is because, geographically, the Continent is riddled with features that prevent the formation of a single political entity. Mountain ranges, peninsulas and islands limit the ability of large powers to dominate or conquer the smaller ones. No single river forms a unifying river valley that can dominate the rest of the Continent. The Danube comes close, but it drains into the practically landlocked Black Sea, the only exit from which is another practically landlocked sea, the Mediterranean. This limits Europe’s ability to produce an independent entity capable of global power projection.”
Nevertheless, I think that there is a certain segment of people who see strength in numbers economically, in way that that is not tied to security. Sometimes bigger is better, and especially so when one is attempting to deal with the consequences of mass society engendered by industrialization. It could be argued — in fact, I would argue — that the economic success of the US was due in no small part to is large (ultimately continental) contiguous land area under a single political regime. If North America had been political divided like South America, it is unlikely that its economic development would have taken the particular path that it did take.
I have mentioned in some previous posts that Gaddafi has argued on many occasions for a “United States of Africa,” and while this is perhaps impossibly visionary, if it could be made to work it would have great economic benefits for the continent. Similarly, the European Union is sometimes characterized as a “United States of Europe,” and with hope and the aspiration that its collective economic and technological clout might rival that of the US. So even though the term “collective economic security” is not used, the idea is out there, and has been the basis of practical policy objectives.
The Wikipedia article on collective security quotes A.F.K. Organski on five (5) basic assumptions of collective security:
● In an armed conflict, member nation-states will be able to agree on which nation is the aggressor.
● All member nation-states are equally committed to contain and constrain the aggression, irrespective of its source or origin.
● All member nation-states have identical freedom of action and ability to join in proceedings against the aggressor.
● The cumulative power of the cooperating members of the alliance for collective security will be adequate and sufficient to overpower the might of the aggressor.
● In the light of the threat posed by the collective might of the nations of a collective security coalition, the aggressor nation will modify its policies, or if unwilling to do so, will be defeated.
This is formulated in terms of security from military attack, but it could be reformulated, mutatis mutandis, to address collective security from an economic standpoint. Economically, the threat to economic security comes not primarily from a military assault but from an economic crisis. This should seem pretty intuitive to most people these days, since the global economy is only now pulling out of what is being called the “Great Recession,” which was triggered by the subprime mortgage crisis — a genuine financial crisis if there ever way one — and even more recently the Eurozone was been faced with major crises as Portugal, Ireland, and Greece have come close to defaulting on their debt payments. (Most of the today’s Financial Times was about the Greek debt crisis.)
Well, interpreting Organski’s basic assumptions in terms of collective economic security, we see that the idea turns into a disaster:
● In an economic crisis, member nation-states will be able to agree on the cause of the crisis.
● All member nation-states are equally committed to contain and constrain the crisis, irrespective of its source or origin.
● All member nation-states have identical freedom of action and ability to join in containment and de-escalation of the crisis.
● The cumulative power of the cooperating members of the alliance for collective economic security will be adequate and sufficient to contain the economic crisis.
● In the light of the economic power wielded by the collective might of the nations of a collective economic security coalition, the cause of the crisis will be intimidated into cooperation, or failing to do so, will be contained.
The amusing thing about this is that, while this remains a coherent set of principles when reformulated in terms of economic security, it is even more spectacularly impossible than when formulated (as in the original) in terms of politico-military security. This makes the disaster of these principles particularly interesting, because it shows us that a coherent body of thought can be utterly unworkable despite its coherency.
The reader may well respond to me by saying that I have no basis whatsoever for my claims about collective economic security, and this is not even a fair way to summarize the mission of the EU. I would agree that this is certainly not the be-all and end-all of the European Union, but on the other hand what I did explicitly say about was that the idea of collective economic security is out there.
The idea is out there, but it has not (perhaps, until now, unless I have been anticipated, which is more likely than not) been made fully explicit. What that means in practical terms is that the idea is present implicitly, and the implicit presence of an idea is an idea with deniability. People can and do think in terms of ideas that have not been made explicit, and when they do so they often think in a way that is sloppy, vague, imprecise, and riddled with fallacies.
One of the virtues of making an idea fully explicit is that weaknesses and faults become as obvious as strengths and virtues. When an idea is out in the open and is debated and discussed in explicit terms, its strengths and weaknesses can be compared in a rational and systematic fashion. When an idea remains in the shadows, by contrast, it has a subterranean influence without being critically assessed. This can be unfortunate, since a vaguely appealing implicit idea is not balanced by an explicit consideration of its limitations.
One of the reasons (though certainly not the only reason) that ideas are never made fully explicit is that they are “unthinkable” for some reason or another. It takes a visionary mind to think the unthinkable in explicit terms. Herman Kahn famously did this for nuclear war during the height of the Cold War. I am not suggesting that collective economic security has anything like the unthinkable character of nuclear war, but I am suggesting that we have not had an economist since Malthus who was willing to think through the economically unthinkable.
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28 September 2009
Everyone is familiar with optical illusions. A mirage of water on the horizon on a hot day, or the appearance of a stick being bent when it is put into water, or Fata Morgana, are examples of optical illusions that are so familiar that we learn to disregard them. There are also optical illusions that can be generated by a carefully crafted illustration, as in the works of M. C. Escher. Specialists of optical illusions make many interesting distinctions within the category, but we will not recount these here.
There is a sense in which optical illusions are also spatial illusions (mostly), while some of the optical illusions that involve movement could be said to illustrate temporal illusions. In movement, both space and time are involved so that properly optical illusions that involve motion are spatio-temporal illusions. But a spatio-temporal illusion suggests the possibility of purely temporal illusions. The very idea of a temporal illusion is unfamiliar, but it is a worthwhile conception and once we become familiar with the idea it can be useful to explain experiences for which we have no adequate language.
Once we think in terms of temporal illusions it is not difficult to think of experiences that involve temporal illusions. The most obvious example of a temporal illusion is when time feels as though it passes more slowly when one is waiting for something. There is an old saying to illustrate this: a watched pot never boils. The opposite observation is that time flies when you’re having fun. Psychologists have identified what they call “flow states” in which a person becomes so involved in their work that they cease to notice the passage of time. This is an instance of a temporal illusion.
For my part, I have noticed that when I drive down an unfamiliar road, and then am forced to backtrack along the same route, that the outbound drive always feels as though it takes significantly longer than the return drive. I have always assumed that this is because in the initial drive everything is unfamiliar and one never knows what to expect, while driving back out the same way one remembers at least some of the route. In other words, in a new experience one has a flood of new sensations that populate one’s subjective time consciousness at a higher level of density than familiar experiences. If this explanation has any bearing, it is merely a mechanism, but it does nothing to explain the feeling of time passing more slowly on the first leg of the drive as compared to the second leg of the drive.
The most abstract illusions pose the greatest difficulty for us. Those optical illusions that involve a Gestalt effect such as the Kanizsa triangle, in which one perceives a white triangle that is not an explicit part of the drawing, pose theoretical problems that are not posed by simple optical illusions such as a mirage. (I can imagine a quasi-Platonic explanation for the Kanizsa triangle that would appeal to the receptacle of a triangle that is embodied in such drawings — the receptacle plays a significant role in Plato’s Timaeus.)
The most abstract illusions of all are those that occur without reference to our senses, nor even to space or time. These are the illusions of our minds, of our conceptual scheme. This may sound a little beyond the concerns of most of us, but abstract illusions are actually quite common. We call them paradoxes. In my Variations on the Theme of Life I wrote that paradoxes are the optical illusions of the eye of the soul. I haven’t had time to follow up on this and flesh it out, but the obvious extrapolation would be that purely conceptual illusions like paradoxes are the theoretical basis of all illusions, and if we could formulate a complete theory of illusions we would find that sensory and experiential illusions could be explained by their basis in abstract illusions. Maybe. That remains to be seen.
Kant is remembered as an especially difficult philosopher to read, but we note that Kant elaborated the idea of purely conceptual illusions in the Critique of Pure Reason. In some translations such illusions are called transcendental illusory appearance. This is actually quite a good formulation to encapsulate the idea. Kant was driven to formulate transcendental illusory experience to account for the famous antinomies of pure reason that are central to the argument of the Critique. Kant argued that traditional metaphysics up to his time was bogus because when pure reason attempts to apply itself to matters upon which it is not competent — like the ultimate structure or origin of the world — it falls into paradoxes from which it cannot extricate itself.
Kant clearly not only saw the danger of abstract illusions, but mapped them out as well as he could with the intellectual resources available to him. After Kant, major conceptual upheavals like the development of non-Euclidean geometry and relativistic physics based in part on non-Euclidean geometry (Einstein used Reimann’s elliptic geometry as the setting for general relativity), as well as Cantor’s theory of transfinite numbers, called into question some of the specifics of Kant’s exposition, but the basic idea remains sound. However, contemporary re-statements of the Kantian position such as P. F. Strawson’s The Bounds of Sense and several phenomenological attempts to rehabilitate Kant’s philosophy of mathematics don’t have much to say about transcendental illusory appearance. This seems to me like a potentially very fertile field for philosophical research.
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