Post with 3 notes
Kantian Non-constructivism
Kant is not infrequently called a “proto-constructivist,” by which is meant that Kant staked out positions that are constructivist in spirit but which preceded the explicit formulation of constructivism by more than a hundred years. I believe that there are good reasons for calling Kant a proto-constructivist, given his insistence upon the exhibition of objects in intuition. I have argued elsewhere (in an unpublished manuscript) that in fact this Kantian focus on exhibition in intuition is the authentic core of constructivism.
Nevertheless, even as a proto-constructivist (a constructivist before constructivism was cool), Kant was far from a thorough-going constructivist. In fact, I just realized today that Kant makes a spectacularly non-constructive argument in his transcendental aesthetic, which lays the foundation for the whole of his philosophy that followed.
Near the beginning of the Critique of Pure Reason, when Kant gives an exposition of the concepts of space and time in the transcendental aesthetic, Kant offers parallel formulations of the two concepts. Here is Kant’s exposition of space:
Space is a necessary a priori representation, which underlies all outer intuitions. We can never represent to our- selves the absence of space, though we can quite well think it as empty of objects. It must therefore be regarded as the con- dition of the possibility of appearances, and not as a determina- tion dependent upon them. It is an a priori representation, which necessarily underlies outer appearances.
And here is Kant’s exposition of time:
Time is a necessary representation that underlies all intuitions.
We cannot, in respect of appearances in general, remove time
itself, though we can quite well think time as void of
appearances. Time is, therefore, given a priori. In it alone is
actuality of appearances possible at all. Appearances may, one
and all, vanish; but time (as the universal condition of their
possibility) cannot itself be removed.
In his twin expositions of space and time, Kant asserts that, while we cannot imagine objects outside space or time, we can nevertheless imagine space and time without objects. Kant makes this assertion, but he does not demonstrate how space or time without objects can be constructed, not does he exhibit empty space or empty time in either sensory or intellectual intuition. Here the Kantian insistence upon exhibition is utterly absent.
I can still remember how I was struck by this passage the first time I read it. It has stayed with me all these years. Philosophers today consider the ideas of empty space and empty time to be problematic; indeed, the defense of these concepts has become a minority (if not a marginal) view. (In the interest of full disclosure, I will state here I find the concepts of empty space and empty time to be perfectly legitimate, but even in so saying I know that it is a minority view made all the more marginal by the most common interpretations of relativity theory.)
C. S. Pierce’s comment on his study of Kant is quite interesting in this context, so I will quote Pierce at some length:
The first strictly philosophical books that I read were of the classical German schools; and I became so deeply imbued with many of their ways of thinking that I have never been able to disabuse myself of them. Yet my attitude was always that of a dweller in a laboratory, eager only to learn what I did not yet know, and not that of philosophers bred in theological seminaries, whose ruling impulse is to teach what they hold to be infallibly true. I devoted two hours a day to the study of Kant’s Critic of the Pure Reason for more than three years, until I almost knew the whole book by heart, and had critically examined every section of it. For about two years, I had long and almost daily discussions with Chauncey Wright, one of the most acute of the followers of J. S. Mill.
The effect of these studies was that I came to hold the classical German philosophy to be, upon its argumentative side, of little weight; although I esteem it, perhaps am too partial to it, as a rich mine of philosophical suggestions. The English philosophy, meagre and crude, as it is, in its conceptions, proceeds by surer methods and more accurate logic.
Despite many years of study of one of the most difficult books ever written, Pierce found Kant to be “of little weight” when it came to argument. Well, I will admit that the argument of the transcendental aesthetic is pretty weak, and I say this on general principles, and not because it is a non-constructive argument. However, I can imagine that Pierce, with his “pragmatic” turn of mind, may have discerned the non-constructive core of Kantianism and found it to be a weak argument.
Post with 1 note
Intuitively Clear Slippery Concepts
Or, into the conceptual wild…
The above phrase, “intuitively clear slippery concepts” just appeared today on the FOM (foundations of mathematics) listserv, as used by Hendrik Boom.
Here’s some context:
“…well-founded is one of these intuitively clear slippery concepts that goes awry when things become too general.”
This appeared in the tread, “iterative conception/cumulative hierarchy,” so this phrase that I ripped out the context of a sentence is also ripped out the context of a long discussion on the foundations of set theory.
Philosophers have used a variety of terms to indicate imprecise concepts and their manipulation: open-textured concepts, loose concepts, fuzzy concepts, and the like. This is the first time I’d seen “slippery concepts” used in this kind of context, but of course we all know what “slippery” means when it is used in colloquial speech. A slippery concept is difficult to pin down.
At the same time, philosophers have used a variety of terms of indicate intuitively clear concepts. The above phrase, “intuitively clear slippery concepts,” has the virtue of combining both the wide recognition that some concepts are intuitively clear, some concepts are slippery, and some concepts are both intuitively clear and slippery at the same time. One might hope or expect intuitively clear concepts to not be slippery, but sad experience has shown us that some of the least slippery concepts are counter-intuitive.
Moreover, Boom adds the caveat that these concepts, “go awry when things become too general.” In other words, in a suitably restrictive context, we ought not to have much trouble with concepts both intuitively clear and slippery, but once let out into the conceptual wild, as it were, things can go wrong.
This is a constructivist theme. In a couple of posts here, P or not-P and What is the relationship between constructive and non-constructive mathematics? (also inspired by posts on FOM), I have discussed constructivist thought in a general context.
For several years I have been thinking about how to characterize constructivist thought is absolutely general terms, so that all the diverse forms of constructivism can be brought together in a principled unity under a single concept. One obvious approach (which also has obvious problems) is to characterize constructivistic reasoning in terms of the limitations that it places on classical formal reasoning.
For example, “P or not-P” — the law of the excluded middle — doesn’t cause many problems in finite contexts, but once you try to apply it in unlimited or transfinite contexts its seems to generate paradoxes. The more rigorously we limit our reasoning (and this is one of the functions of axiomatization) the more we can be certain about what we say and what it means.
This is especially the point that I tried to make in What is the relationship between constructive and non-constructive mathematics?, as I there suggested that finite mathematics is a common core shared by constructivist and non-constructive thought alike.
That is to say, despite profound philosophical differences, there is a little bit of logic and mathematics upon which all (or almost all) formal thought can agree. It is when we go further afield, “when things become too general” as Boom wrote, or we head out into the “conceptual wild” (as I put it above), that differences emerge. The farther afield we go the more these differences harden into ideological differences informed by a “party spirit.”
In so far as almost all philosophies of mathematics can recognize the intuitive clarity of finite mathematics, but differences emerge once we pass beyond this restrictive boundary, the whole of mathematics could be said to consist of intuitively clear slippery concepts.
Post with 3 notes
Cities: the Constructive Kluge
I’ve just started to listen to the book on CD version of Edward Glaeser’s The Triumph of the City, which I wrote about shortly after starting this second blog, since I had just read a review of this book. I am happy to say that the book is much better than the review, which just goes to show that one ought never to give too much credence to reviews.
I particularly enjoyed this quote:
“Many of the ideas in this book draw on the wisdom of the great urbanist Jane Jacobs, who knew that you need to walk a city’s streets to see its soul. She understood that the people who make a city creative need affordable real estate. But she also made mistakes that came from relying too much on her ground-level view and not using conceptual tools that help one think through an entire system.”
I have many times referenced Jane Jacobs in my own ruminations, so it was interesting to see that this is one of Glaeser’s important influences. I was even more interested in Glaeser’s characterization of Jacob’s perspective as “ground level,” as this touches on what I recently wrote in Nazca to Ica:
The two perspectives offered on the Nazca lines by the tower and an airplane flyover also reminded me of a point that I imperfectly attempted to make in my post on Epistemic Orders of Magnitude, in which I employed aerial photographs of cities in order to demonstrate the similar structures of cities transformed in the image of industrial-technological civilization. This similarity in structure may be masked by one’s experience of an urban area from the perspective of passing through the built environment on a human scale — i.e., simply walking through a city, which is how most people experience an urban area.
Now, in light of what I have subsequently written about constructivism, I might say that our experience of a built environment is intrinsically constructive, except for that of the urban planner or urban designer, who must see (or attempt to see) things whole. However, the urban planner must also inform his or her work with the street-level “constructive” perspective or the planning made exclusively from a top-down perspective is likely to be a failure. Almost all of the most spectacular failures in urban design have come about from an attempt to impose, from the top down, a certain vision and a certain order which may be at odds with the organically emergent order that rises from the bottom up.
One could say, then, that Jacobs accepted the intrinsically constructive “ground-level view” of urbanism without supplementing that point of view with a non-constructive view from on high, which Glaeser suggests can be attained through the use of “conceptual tools.”
Glaeser also worried aloud about, “Why do so many smart people enact so many many foolish urban policies?” This immediately made me think of the book to which I just finished listening, Kluge: The Haphazard Evolution of the Human Mind by Gary Marcus. Here’s one of my favorite quotes from Marcus’ book, in partial answer to Glaeser’s rhetorical question:
“Put the contamination of belief, confirmation bias, and motivated reasoning together, and you wind up with a species prepared to believe, well, just about anything.” (p.57)
This is all too true, but, of course, natural selection puts a brake the scope of belief, since if a belief becomes too maladaptive it will contribute to negative selection pressure — something that Marcus knows well, as the book is very much imbued with the spirit of evolutionary psychology, though he makes several explicit criticisms of the discipline throughout his book.
But if the human mind is a kluge, haphazardly assembled, with layers of functionality stacked on top of older layers sometimes at cross-purposes to that which is built on top of it, certainly the city is the ultimate kluge. I have observed many times that planned cities are usually the result of utopian schemes that in implementation all too often become dystopian nightmares. The healthy, thriving, successful city is a kluge — as is the economy that drives it.
Post with 62 notes
What is the relationship between constructive and non-constructive mathematics?
A few days ago in P or not-P I mentioned a discussion concerning constructivism on the FOM listserv. In that post I quoted Frank Waaldijk, and gave my response to this. Since then I have been honored with a response, which follows herein:
I think that to compare classical mathematics to science fiction is not the same as to dismiss it. Actually I’m quite appreciative of good science fiction. And I also think it is important to dream. I just stated that it is also important to return to reality from time to time.
Connes’ image above suggests that constructive math and classical math actually study the same mathematical earth, from a different point of view. For very important parts of mathematics, I can more or less live with this image although I also consider it too simplified and too charitable. However, the unrestricted axiom of choice gives rise to whole galaxies which are not studied in detail by constructive mathematicians (because to them these galaxies are rather wild science fiction, with little realistic content). Perhaps a nice short paper to also read is `Reality and Virtual Reality in Mathematics’ by Douglas Bridges (http://www.math.canterbury.ac.nz/~d.bridges/files/real.pdf).Apart from that, my more important point was and is that there could be a better balance between the large number of classical mathematicians which swarm in the sky and the handful of constructive mathematicians who try to validate what has been glimpsed from above. So my intention was not to dismiss classical mathematics (since I value its helicopter view also) but to emphasize that for a better understanding of reality, we need constructive mathematics. And for this we need more researchers in this field, and we also should teach constructive views already in high school, not exclusively like I said, but for comparison. One should not forget that all constructive mathematicians have had a heavy training in classical math… but vice versa?This to me seems the deeper implication of the foundational crisis that Frank Quinn mentioned. Some progress can be noted, since nowadays acceptance of constructive mathematics seems much better than in Brouwer’s time. On the other hand, one still finds occurrences of Zorn’s lemma (equivalent to axiom of choice) being used in texts on number theory to prove the existence of a maximal ideal, where a simple constructive proof can also be given… This means that generally, mathematicians have little feel for the constructive level/content of what they are doing. Reverse mathematics then helps only so much.
For the record, I agree that constructivist methods should be taught in schools as early as it is reasonable to suppose that students can grasp the essential ideas behind constructivism. I think it would be great improvement simply to make students aware of the difference between constructive and non-constructive reasoning, and this distinction is pervasive throughout formal thought but is little known beyond mathematics and philosophy. The mathematical curriculum would be the perfect opportunity to inculcate this distinction.
Given, then the virtues of knowing both what classical, non-constructive methods are, and the constructivist reaction that they have precipitated, what exactly are the essential ideas of constructivism? While most mathematicians, like most scientists, eschew philosophical thought (perhaps this is a reason to classify mathematics among the sciences), this is a paradigmatically philosophical question, and it cannot be answered without some significant effort.
When I was corresponding with Torkel Franzén in 1997, I wrote to him:
“Do the intuitionists have a replacement for set theory, or is this wrongly construing the entire intuitionist project? What, in this context, does ‘replacement’ mean?”
And he responded to me that:
“It means, quite simply, that everybody stops doing, teaching, and using classical mathematics and instead does, teaches, and uses intuitionistic mathematics.”
There is a kind of mathematical positivism in this response, and I have encountered this attitude elsewhere. It is as though intuitionism here had no philosophical content at all, whereas in fact it is fundamentally the expression of a philosophical perspective on mathematics.
How then are we to understand constructivist mathematics in relation to classical mathematics? If the distinctive feature of constructivism is that it limits the forms of mathematical reasoning, may we conclude that constructivist thought is wholly contained within classical thought, as in the following Venn diagram?
Here I have colored constructivist mathematics is a bright Bolshevik red because Frank Ramsey spoke of the “Bolshevik menace” of Weyl and Brouwer — although I seem to recall that someone told me Ramsey was converted to intuitionism shortly before his untimely death at a early age. I’ve also used the exotic “aliens ate my mom” font to emphasize its nontraditional character.
I don’t think that many philosophers would say that constructivist thought is merely a subset of classical thought. There is an interesting quote from Michael Dummett (very recently deceased, rest his soul) from his “Concluding Remarks at the Cerisy conference” that, in its brief compass, touches on several important themes:
“…the new non-realist conception demands a change in the logic with which we operate. Brouwer of course developed intuitionistic mathematics not only by restricting proofs to the modified logic his conception validated, but by introducing new notions and new principles governing them. With these a beautiful new version of mathematics was born…” (One Hundred Years of Intuitionism, pp. 341-342)
Dummett here emphasizes Brouwer’s novel contributions to mathematics, which implies that intuitionist mathematics contains elements that are lacking in classical mathematics, which implies in turn that intuitionist mathematics is not wholly contained within classical mathematics. Of course, if classical mathematics took up the intuitionist ideas and made them its own, then, like Hinduism declaring the Buddha to be an Avatar of Vishnu, all would be classical mathematics again. But intuitionist ideas like bar induction and the fan theorem seem to be mostly confined to intuitionist thinkers.
W. V. O. Quine made the argument that a change in logic entails a change in meaning, and therefore implies a change in subject. Quine wrote in his Philosophy of Logic:
They think they are talking about negation, ‘~’, ‘not’; but surely the notation ceased to be recognizable as negation when they took to regarding some conjunctions of the form ‘p & ~p’ as true, and stopped regarding such sentences as implying all others. Here, evidently, is the deviant logician’s predicament: when he tries to deny the doctrine he only changes the subject.
Quine is here discussing the principle of non-contradiction — “not (P and not-P)” — rather than the law of the excluded middle — “P or not-P” — but the Quinean objection is invariant across laws of logic. In fact, the whole point in Quine’s making this assertion is to insist upon the invariance of classical logic, which implies the invariance of classical mathematics if mathematics follows from logic.
If Quine is right about this (and I myself have never agreed with the “change in logic; change in subject” thesis), and if constructivist mathematics can be correctly defined as a body of formal truths derived from a uniquely intuitionistic logic (perhaps derived from the ur-intuitions posited by Brouwer, but using Brouwer’s logic), then Brouwer has simply changed the subject (when he thought he was changing mathematics, or, as Dummett puts it, creating a new version of mathematics) and classical mathematics and intuitionistic mathematics are incommensurable, as in the Venn diagram below:
Here classical mathematics and constructive mathematics wholly disjoint, and this seems a little extreme to me, and I don’t think that many philosophers of mathematics would argue for this position — though no doubt there are a few who would so argue.
The next most obvious relationship would be that classical mathematics and intuitionistic mathematics overlap and intersect (to invoke a classic Wittgensteinian formulation), and I have a ready answer for the field of their intersection: this would be what I previously called “macroscopic mathematical intuitions” as familiar as counting with cardinal numbers.
This is a good as far as it goes, but it can’t be quite right. This Venn diagram implies that classical mathematics and intuitionistic mathematics have nothing in common except macroscopic mathematical intuitions, and this seems clearly mistaken. There are finite inferences from macroscopic mathematical intuitions, made with as much logic as classical and intuitionist reasoning have in common (i.e., logic without tertium non datur), that would constitute a body of mathematical knowledge distinct from macroscopic mathematical intuitions but held in common by classical and intuitionist thought.
Beyond the problem of the relation of intuitionism or constructivism to classicism — which is, it must be admitted, a difficult problem — there is perhaps the yet more difficult problem of the relationship of intuitionism to constructivism. I have indirectly alluded to this already by the ambiguity of the previously language, sometimes speaking of “intuitionism” and sometimes speaking of “constructivism” without making a clear distinction or defining either one relative to the other. This is just as much a disputed philosophical question as the above question of the relationship between classicism and non-classical thought.
Intuitionism has been unproblematically associated with constructivism and it has been explicitly denied any association with constructivism. For my part, the denial the intuitionism is a species of constructivism is sort of like Heidegger and Jaspers denying that they were existentialists — but in so far as the Sartrean maxim is that a writer should not allow himself to be turned into an institution, they were justified in doing so. We could call this philosophizing under erasure.
Here we come to a parallel sequence of problematic relationships, similar to those mentioned above in trying to determine the relationship of classicism to its non-classicist other. Are constructivism and intuitionism incommensurable?
Is intuitionism wholly contained within constructivism, so that intuitionism is a particular species of constructivist thought, but not the whole of constructivist thought?
These positions on the interrelationship seem as unlikely as the parallel formulations above, which brings us to constructivism and intuitionism overlapping and intersecting. If this is the proper model of how constructivism relates on intuitionism, what exactly is the common core, why is it common to them, and how is it to be distinguished from classicism?
The next step ought to be an attempt to see classicism, constructivism, and intuitionism all together, and again I can appeal to macroscopic mathematical intuitions as the common ground of all three schools of thought. Beyond that, their interrelationships are less clear.
If this is correct — or even approximately correct, if you’d like to grant me some latitude — what, then, is mathematics?
Is mathematics this whole structure — classicism, constructivism, and intuitionism taken together — plus whatever else is done in the name of mathematics?
Post with 1 note
P or not-P
The past few days has seen an interesting discussion emerge on the Foundations of Mathematics listserv (FOM), which grew out of link to a recent article by Frank Quinn in Notices of the AMS, “A Revolution in Mathematics? What Really Happened a Century Ago and Why It Matters Today.”
Quinn’s article highlighted the role of the Law of the Excluded Middle (also known as tertium non datur) in mathematical reasoning. The Law of the Excluded Middle is a logical law that is usually stated, “P or not-P.” Though this sounds simple enough, it has been a sore spot in mathematics because it allows one to “prove” the existence of something that one can neither construct or exhibit — once all the alternatives are eliminated (and with classical negation, there is only one alternative), one is left with the mathematical equivalent of the last man standing.
Dutch philosopher of mathematics L. E. J. Brouwer formulated one of the most influential schools of constructivist thought, intuitionism, by jettisoning the Law of the Excluded Middle and simply doing without it.
Frank Waaldijk (like Brouwer, from the Netherlands) wrote on the FOM list:
The revolution in mathematics spreads much further than `just´ methodology. The revolution is about the concepts underlying all of our thinking about math, science and reality.
And my preliminary conclusion is: we still know nothing for sure. We are stumbling in the dark.I therefore cannot take Quinn’s stance on the role of `excluded middle´ in mathematics very seriously. Classical mathematics, in its full-fledged embrace of excluded middle, can be compared to science fiction…or dreamland if you would like a stronger metaphor. It’s nice to dream, and nice to be able to conjure battlestars and time travel and black hole mining and…But it is also important to return to reality from time to time. This is where constructive mathematics comes in. Constructive mathematics and classical mathematics are not always at odds per se…it is `just’ a major difference of focus and perspective. But I am personally convinced that we need constructive mathematics for a better understanding of our physical world and physical reality. And constructive views on excluded middle should already be taught in high school, not exclusively but at least for comparison.
Panu Raatikainen responded to Frank Waaldijk writing:
These are strong claims, and we’ve heard them now and then before, but it would be nice to hear some convincing arguments supporting them… I’ve honestly tried hard to find one for some time, but have so far failed…
Today I wrote the following (though with additional material added below) to the FOM list:
Perhaps a more charitable conception of the relationship between classical eclecticism and its tolerance of non-constructive modes of reasoning on the one hand, and on the other hand the many species of constructivism that have been proposed in order to place limits on classical eclecticism, is to be found in an image proposed by the mathematician Alain Connes:
“Constructivism may be compared to mountain climbers who proudly scale a peak with their bare hands, and formalists to climbers who permit themselves the luxury of hiring a helicopter to fly over the summit.”
(Conversations on Mind, Matter, and Mathematics, Changeux and Connes, Princeton, 1995, p. 42)
On the next page Connes says, continuing the image,
“…the uncountable axiom of choice gives an aerial view of mathematical reality — inevitably, therefore, a simplified view.”
If we think of the constructivist perspective very roughly as a “bottom up” approach, like a mountain climber who starts at the base and clambers over every cliff and every ledge on the way up, and non-constructive methods as a “top down” approach, an aerial view of mathematics, perhaps lacking in definite detail, but giving the big picture of the scene, then the two approaches are complementary.
An adequate conception of mathematical reality must include both constructive and non-constructive approaches, rather than dismiss classical mathematics as science fiction or dreamland.
I suggest that the top-down perspective of classical mathematics and the bottom-up perspective of constructivism meet in the middle, and that middle is constituted by macroscopic mathematical intuitions — the familiar instances of mathematical knowledge and experience like counting with cardinal numbers.
The classical foundationalist project plunges down from the heights and seeks to immerse itself in the details of mathematical knowledge from above. The relationship of the foundationalist to foundations established regressively (in Russell’s sense) from macroscopic mathematical intuitions is analogous the relationship believed by the classical mathematician to hold between macroscopic mathematical intuitions and the mathematical reality from which they are thought to descend. Thus the foundationalist project is a project to bring down the truth of macroscopic mathematics down its foundations.
The constructivist is no believer in the truth or truth-giving properties of macroscopic mathematics, which he regards as riddled with errors. The constructivist seeks to build from below only what can be built step-by-step, content to neglect the big picture and therefore blind to the landscape in which he patiently builds. To the constructivist, and foundationalist is falling off a cliff when he plunges downward; to the classical mathematician, the constructivist is so absorbed in this life on firm ground, with his feet in the mud, that he has ceased to dream and no longer looks up at the stars.
To put the distinction between the two in a quasi-scientific idiom, constructivism “explains” macroscopic mathematical intuitions as being constructed from ur-intuitions (as, for example, from Brouwer’s first and second acts of intuitionism), while classical eclecticism “explains” macroscopic mathematics intuitions from the top down, with reference to the abstract mathematical entities, from which flow macroscopic mathematical intuitions when the mind directly “perceives” mathematical reality (as in Gödelian mathematical realism, where the mind possesses a special faculty for “perceiving” mathematical reality).
The constructivist, who is a mathematical fox and knows many little things, many details of mathematics, and the classical mathematician, who is tolerant of non-constructive methods and as a mathematical hedgehog knows one big thing, need each other.
Link with 3 notes
Sir Michael Dummett obituary →
Sir Michael Dummett has died at the age of 86 on 27 December 2011. He was one of the most renowned philosophers of his generation. He sometimes characterized late-twentieth century analytical philosophy as Post-Fregean philosophy, and although he wrote voluminously about Frege and acknowledged the obvious influence, Dummett’s own philosophy diverged considerably from Frege’s unapologetic realism in regard to abstract objects.
Dummett wrote Elements of Intuitionism, which is a classic textbook on basic intuitionistic logic and mathematics, and then went on to apply his generally constructivistic and specifically intuitionistic views to wider vistas of philosophy in The Logical Basis of Metaphysics. These works might be informally characterized as “Frege meets Brouwer.”
Although Dummett’s work came after the great heyday of mid-century linguistic philosophy, his work embodied the “linguistic turn” even when writing about logic, mathematics, and metaphysics. Dummett emphasized the central role of language and of meaning in philosophical theories, and here, too, Frege was a touchstone and a crucial influence. His first major publication was Frege: Philosophy of Language.
Putting this linguistic turn into practice, in The Logical Basis of Metaphysics he wrote:
“…we must attain a clear conception of what a meaning-theory can be expected to do. Such a conception will form a base camp for an assault on the metaphysical peaks: I have no greater ambition in this book than to set up a base camp.”
Post with 3 notes
A Pop Culture Exposition of Constructivism
Recently I watched the film Limitless, loosely based on the novel The Dark Fields by Alan Glynn. Despite several irritating features of the film, I liked it, primarily for two scenes. For two good scenes to convert me to liking a film from an initial sense of irritation is rather unusual.
The film begins with an unsuccessful writer experiencing writer’s block. If there’s anything I hate, it is writers indulging themselves by talking about writer’s block. If you don’t have anything to say, get an honest job; don’t complain about having nothing to say. If you do have something to say, it will pour out of you regardless.
There is a beautifully written blog, HUnter4086: An open notebook, that conveys this remarkably well in the form of a short story. In Neighbor the author has written:
Of the artists I was acquainted with, I was accustomed to a different sort of behaviour than Debbie’s unassuming productivity. The ones I knew had something to prove. They took pleasure in the indulgences society affords artists, or our notion of them: they put on airs, were evasive, and liked flaunting their unconventionality, and fell all over themselves talking about how they felt and how they saw things. Actual production seemed incidental.
And so it is with writers who complain of writer’s block: it is a way of talking about how endlessly fascinating one is and marginalizing one’s actual literary production to the point that the writing itself becomes incidental.
The protagonist, however, overcomes his writer’s block by using a drug that augments his cognitive capacities. At one point in the film the protagonist describes himself as a man with a four-digit IQ. And what does he do with his impressive mental abilities? He gets sex, friends, money, and eventually political power, in that order.
I would like to write an alternative screenplay, based on precisely the same premise, but with the protagonist, having come to full consciousness of his mental powers, turning his newly powerful mind to pure speculation and a heroic quest to understand the deepest mysteries of the world. Obviously, something like this wouldn’t get made into a film, but it is a fun idea. It is probably also closer to the truth.
In the novel, which I have skimmed since I saw the film, the original writer emphasizes how, once the protagonist begins taking his cognitive enhancement drug, people hang on his every word, and they want to be his friend. The original novel also characterizes his gaining control of his newly inspired conversational ability as follows:
“I tried to analyze what this was, and could only conclude that maybe a combination of my being enthusiastic and non-judgemental — non-competitive — might have struck some kind of chord in people.” (p. 114; italics in original)
Possessing special mental abilities is not likely to win friends and influence people. It is much more likely to be off-putting than attractive, though the author of the novel apparently felt otherwise.
What we have in this vision of what a person might do with a greatly expanded intellect is an account of what a thoroughly mediocre man would do with such an intellect. This may sound a bit odd, but I think it’s important, so I’m going to try to illustrate what I mean by it.
Recently, on my other blog, in The Role of Science Fiction in Industrialized Civilization, I quoted Bertrand Russell’s comparison of the Platonic vision of another world and the Apostle’s vision of another world:
“…mathematics, though not applicable to the mundane scene, is a vision, at once reminiscent and prophetic, of that better world from which the wise have come and to which they will return. Harps and crowns had less interest for the Athenian aristocrat than for the humble folk who made up the Christian mythology; nevertheless Christian theologians, as opposed to the general run of Christians, accepted much of Plato’s account of heaven.”
Bertrand Russell, The Art of Philosophizing: and other essays, “How to become a mathematician,” p. 111
Like much of Russell’s writing, an important point is hidden within a witticism: for Plato, the other world was an abstract, almost mathematical construction; for the “humble folk” responsible for Christianity, their vision of the other world — a better world — was one of harps and crowns.
Another illustration: I once said to a friend of mine that I always thought that Tolstoy’s writing was that of a mediocre man with exceptional literary gifts. As I recall, my friend was a little angry about this, and scolded me, but I was not chastened. Tolstoy was able to capture so well the life of his times because of his deep sympathy for the concerns of the ordinary man. All great literature and poetry is based on this principle.
Here is a passage from War and Peace that particular strikes me:
“He looked at the approaching Frenchmen, and thought but a moment before he had been galloping to get at them and hack them to pieces, their proximity now seemed so awful that he could not believe his eyes. ‘Who are they? Why are they running? Surely not towards me? Surely they’re not running towards me? But what for? To kill me? Me, whom everyone loves so much?’ He recalled his mother’s love for him, the love of his family, his friends, and it seemed impossible that the enemy could intend to kill him.” (Chapter XIX)
There are probably a lot of people who go through life with this deluded, self-centered sense of being loved by everyone, but anyone who has paused for a moment to think critically about life, and about their own lives in particular, will no longer suffer from this delusion.
This same kind of mediocre, self-centered, and self-satisfied vein runs through the thoughts and aspirations of the protagonist of Limitless as he is revealed in the film. Nevertheless, the film ultimately rises above this mediocrity with a couple of inspired scenes.
Now, after these criticisms, what I liked about the film: It did not give in to the temptations of lowbrow moralizing, which is typical for a Hollywood film. It did give in to some of these temptations, but in the penultimate scene of the film, the protagonist is shown to have mastered his situation, taken control of his life despite the drug that drove his success, and he characterizes himself as “fifty steps ahead of everyone.” This is a strikingly confident ending. The Wikipedia article on the film says that the final scene of the film leaves it open as to whether or not the protagonist is still using his cognitive enhancement drug, but this is now beside the point. Whether or not he is using it, he has demonstrated the discipline to use it or not use it to his advantage. The protagonist has achieved autonomy.
For a contemporaneous example of a film that did give in to every temptation of lowbrow moralizing (although in the context of economics rather than drug use), I will cite the example of The Company Men. I enjoyed this film. It was remarkably true to life and quite raw in its depiction of human failings and foibles. In this particular sense, it was a much more honest film than Limitless. However, all of the film’s honesty was squandered in its rush to confirm the public’s judgment — to tell the people what they want to hear, to speak truth to the masses — in regard to contemporary economic difficulties.
The scene that I liked best in Limitless, however, was near the middle of the film, when the Carl Van Loon character (played by Robert DeNiro) lectures the protagonist on the nature of his intellectual mastery. What fascinated me about this was that the Van Loon character essentially made a distinction between constructive and non-constructive thought, although I doubt that either the author of the novel (I couldn’t find the scene in the novel, but that doesn’t mean it isn’t there, as I only skimmed it) or the screenwriter knew that that was what they were doing.
Here is the Carl Van Loon monologue, contrasting the speaker’s constructive perspective to the protagonist’s non-constructive perspective:
“You do know you’re a freak? Your deductive powers are a gift from god, or chance, or a stray shot of sperm, or whatever or whoever the hell wrote your life script — a gift, not earned. You do not know what I know because you have not earned those powers. You’re careless with those powers and you flaunt them and you throw them around like a brat with his trust fund. You haven’t had to climb up all the greasy little rungs, you haven’t been bored blind at the fund raisers, you haven’t done the time in that first marriage to the girl with the right father; you think you can leap over all in a single bound; you haven’t had to bribe or charm or threaten your way to a seat at that table; you don’t know how to assess your competition because you haven’t competed. Don’t make me your competition.”
Roughly — very roughly — constructivism is a bottom-up perspective on the world, while non-constructivism is a top-down perspective on the world. While constructivism is usually the result of a conscious decision to adopt a distinct perspective, usually because one has come to think that constructivism is “right” or that non-constructivism is “wrong,” non-constructive thinking, on the other hand, is usually thinking without any particular commitment to any particular position on the nature of thinking. (Torkel Franzen aptly called this “classical eclecticism.”)
Both of these aspects — the bottom-up perspective and the almost careless attitude of the top-down perspective — come out in the Van Loon monologue, and I think this is a really striking scene that illustrates a deep point in an intuitively accessible manner. And this is ultimately the aim of art.
Just as I thought that The Company Men was spoiled despite its many honest scenes, so I found that Limitless saved itself despite its many irritating scenes.
