A Fine-Grained Overview

5 December 2016



Constructive and Non-Constructive Perspectives

Whenever I discuss methodology, I eventually come around to discussing the difference between constructive and non-constructive methods, as this is a fundamental distinction in reasoning, though often unappreciated, and especially neglected in informal thought (which is almost all human thought). After posting Ex Post Facto Eight Year Anniversary I realized that the distinction that I made in that post between detail (granularity) and overview (comprehensivity) can also be illuminated by the distinction between the constructive and the non-constructive.

Two two pairs of concepts can be juxtapositioned in order to show the four permutations yielded by them. I have done the same thing with the dual dichotomies of nomothetic/ideographic and synchonic/diachronic (in Axes of Historiography) and with weak panspermia/strong panspermia and theological/technological (in Is astrobiology discrediting the possibility of directed panspermia?). The table above gives the permutations for the juxtaposition of detail/overview and constructive/non-constructive.

In that previous post I identified my theoretical ideal as a fine-grained overview, combining digging deeply into details while also cultivating an awareness of the big picture in which the details occur. Can a fine-grained overview be attained more readily through constructive or non-constructive methods?

In P or Not-P I quoted this from 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.”

Changeux and Connes, Conversations on Mind, Matter, and Mathematics, Princeton, 1995, p. 42

This image makes of constructivism the fine-grained, detail-oriented approach, while non-constructive methods are like the overview from on high, as though looking down from a helicopter. But it isn’t quite that simple. If we take this idea of constructivists as mountain climbers, we may extend the image with this thought from Wittgenstein:

“With my full philosophical rucksack I can climb only slowly up the mountain of mathematics.”

Ludwig Wittgenstein, Culture and Value, p. 4

And so it is with constructivism: the climbing is slow because they labor under their weight of a philosophical burden. They have an overarching vision of what logic and mathematics ought to be, and generally are not satisfied with these disciplines as they are. Thus constructivism has an overview as well — a prescriptive overview — though this overview is not always kept in mind. As Jean Largeault wrote, “The grand design has given way to technical work.” (in the original: “Les grands desseins ont cédé la place au travail technique.” L’intuitionisme, p. 118) By this Largeault meant that the formalization of intuitionistic logic had deprived intuitionism (one species of constructivism) of its overarching philosophical vision, its grand design:

“Even those who do not believe in the omnipotence of logic and who defend the rights of intuition have acceded to this movement in order to justify themselves in the eyes of their opponents. As a result we find them setting out, somewhat paradoxically, the ‘formal rules of intuitionist logic’ and establishing an ‘intuitionistic formalism’.”

…and in the original…

“Ceux-la memes qui ne croient pas a la toute-puissance de la logique et qui défendent les droits de l’intuition, ont du, eux aussi, céder au mouvement pour pouvoir se justifier aux yeux de leurs adversaires, et l’on a vu ainsi, chose passablement paradoxale, énoncer les ‘regles formelles de la logique intuitioniste’ et se constituer un ‘formalisme intuitioniste’.”

Robert Blanché, L’axioimatique, § 17

But intuitionists and constructivists return time and again to a grand design, so that the big picture is always there, though often it remains implicit. At very least, both the granular and the comprehensive conceptions of constructivism have at least a passing methodological familiarity, as we see in the table above, on the left side, granular constructivism with its typical concern for the “right” methods (which can be divorced from any overview), but also, below that, the philosophical ideas that inspired the constructivist deviation from classical eclecticism, from Kant through Hilbert and Brouwer to the constructivists of our time, such as Errett Bishop.

These two faces of methodology are not as familiar with non-constructivism. In so far as non-constructivism is classical eclecticism (a phrase I have taken from the late Torkel Frazén), a methodological “anything goes,” this is the granular conception of non-constructivism that consists of formal methods without any unifying philosophical conception. This much is familiar. Less familiar is the possibility of a non-constructive overview made systematic by some unifying conception. The idea of a non-constructive overview is familiar enough, and appears in the Connes quote above, but it this idea has had little philosophical content.

There is, however, the possibility of giving non-constructive formal methodology an overarching philosophical vision, and this follows readily enough from familiar forms of non-constructive thought. Cantor’s theory of transfinite numbers, and the proof techniques that Cantor formulated (and which remain notorious among constructivists) is a rare example of non-constructive thought pushed to its limits and beyond. Applied to a non-constructive overview, the transfinite perspective suggests that a systematically non-constructive methodology would insistently seek a total context for any idea, by always contextualizing any idea in a more comprehensive setting, and pursuing that contextualization to infinity. Thus any attempt to think a finite thought forces us to grapple with the infinite.

A fine-grained overview might be formulated by way of a systematically non-constructive methodology — not the classical eclecticism that is an accidental embrace of non-constructive methods alongside constructive methods — that digs deep and drills down into details by non-constructive methods that also furnish a sweeping, comprehensive philosophical vision of what formal methods can be, when that philosophical vision is not inspired to systematically limit formal methods (as is the case with constructivism).

Would the details that would be brought out by a systematically non-constructive method be the same fine-grained details that constructivism brings out when it insists upon finitistic proof procedures? Might there be different kinds of detail to be revealed by distinct methods of granularity in formal thought? These are elusive thoughts that I have not yet pinned down, so examples and answers will have to wait until I have achieved Cartesian clarity and distinctness about non-constructive methods. I beg the reader’s indulgence for my inadequate formulations here. Even as I write, ideas appear briefly and then disappear before I can record them, so this post is different from what I imagined as I sat down to write it.

Here again I can appeal to Wittgenstein:

“This book is written for such men as are in sympathy with its spirit. This spirit is different from the one which informs the vast stream of European and American civilization in which all of us stand. The spirit expresses itself in an onwards movement, building ever larger and more complicated structures; the other in striving after clarity and perspicuity in no matter what structure. The first tries to grasp the world by way of its periphery — in its variety; the second at its center — in its essence. And so the first adds one construction to another, moving on and up, as it were, from one stage to the next, while the other remains where it is and what it tries to grasp is always the same.”

Ludwig Wittgenstein, Philosophical Remarks, Foreword

These two movements of thought are not mutually exclusive; it is possible to build larger structures while always trying to grasp an elusive essence. It could be argued that anything built on uncertain foundations will come to naught, so that we must grasp the essence first, before we can proceed to construction. As important as it is to attempt to grasp an elusive essence, if we do this, we risk the intellectual equivalent of the waiting gambit.

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Constructivism and Non-constructivism

P or Not-P

What is the Relationship between Constructive and Non-Constructive Mathematics?

A Pop Culture Exposition of Constructivism

Intuitively Clear Slippery Concepts

Kantian Non-Constructivism

Constructivism without Constructivism

The Vacuous Identity Principle

Permutations of Infinitistic Methods

Methodological Differences

Constructivist Watersheds

Constructive Moments within Non-Constructive Thought

Gödel between Constructivism and Non-Constructivism

The Natural History of Constructivism

Cosmology: Constructive and Non-Constructive

Saying, Showing, Constructing

Arthur C. Clarke’s tertium non datur

A Non-Constructive World

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Wittgenstein wrote, “With my full philosophical rucksack I can climb only slowly up the mountain of mathematics.”

Wittgenstein wrote, “With my full philosophical rucksack I can climb only slowly up the mountain of mathematics.”

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Grand Strategy Annex

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Risk and Knowledge

9 May 2013


Fifth in a Series on Existential Risk

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Thinking about the Epistemology of Risk

A personal anecdote

What is risk? I have considered this question several times, in different contexts, as, for example, in Risk Management: A Personal View and more recently in Moral Imperatives Imposed by Existential Risk, but today although I want to consider some highly general philosophical ideas about risk, and I am going to start with a highly personal anecdote — a human interest story, if you will. Ultimately I need to make the philosophical effort to bring together these many threads of risk into something more general and comprehensive — but first, the personal story.

When my mother retired, she had for a few years been paying into a private retirement annuity. Upon her retirement she was in a position to begin drawing from this annuity, so I spent some time on the telephone with the financial representative. We had some long calls before we settled on an option that would best serve the financial interests of my mother. The amount she had saved up was not large, but it was enough that she was able to arrange for a fixed monthly payment in perpetuity, in return for handing over the lump sum of her annuity to the financial services company into which she had been making contributions to her annuity.

My mother was surprised to find that if she surrendered her capital to the financial institution with which she had the annuity, that they would promise to pay her a certain amount every month for the rest of her life, regardless of how many payments they had to made. I explained that financial institutions hire professionals called actuaries who calculate the likelihood of how long individuals will live and when they are likely to die. The actuaries make their judgments from statistics, not knowing the individual person. I assured by mother than she is far more healthy than the average person of her age, that the actuaries don’t know any details about an individual’s life, how active they are, what foods they eat, how the individual responds to stress, and so forth.

The actuary as non-constructivist

The actuary engages in classic non-constructivist thought in asserting that a certain number of persons of a certain age will die within a certain period of time, within identifying exactly which individuals are the ones who will die and which individuals are the ones who will live. The actuary sees the big picture (the aerial view of populations, as it were), and from the perspective of investing billions of dollars and insuring the financial security of millions of people, it is the big picture that matters. While life and death is everything to the individual, it is fungible to an institution, and the actuary embodies the institutional point of view.

While it would be possible for an insurance company or a financial institution to pursue a constructivist methodology, in practice this would be unwieldy and inefficient. A constructivist actuary would need to start from the ground up with the facts of the life of each individual, building a detailed profile from verified data. All of this requires time, and time is money. No insurance company or financial institution that pursued this method on a large scale could make a profit, because any gains from the strategy would be offset by the additional costs incurred by information gathering effort.

Actuaries can be extremely accurate on a statistical basis, considering populations on the whole, even while they can be completely wrong in regard to individuals who are members of a given population. Some individuals who are part of a population that dies, on average, at 65, may well live to be 75, 85, or 95 and still not skew the average for the population on the whole. Another individual might die much younger than the average without skewing the average on the whole.

If you know individuals personally, and you know that, for example, someone tends to drive in an erratic and dangerous manner that very well might get them killed, then you have knowledge that the actuary does not have — knowledge, in fact, that the actuary doesn’t even try to address. The actuary might control for age, gender, marital status, geographical location, and all the ordinary information you might put on a questionnaire. Just this much information can be very valuable. With more information, much more can be done, but no financial institution or insurance company could pay to have agents follow investors or policy holders to learn their personal habits, and therefore build a more accurate risk profile for the insured.

The individual possesses knowledge that the institution — financial, insurance, governmental, or whatever else — does not possess, and the individual can leverage this ellipsis of knowledge in order to get a better deal for themselves.

Leveraging knowledge to manage risk

This is an obvious application of the distinction between uncertainty and risk. The more knowledge one has, the less one’s picture of the world is about uncertainty and the more it is about known risks, which are quantities for which one can take preventative or prophylactic measures. To make it personal, if you know someone is an awful driver, you avoid riding with them, and if you know someone becomes aggressive and belligerent when drunk, you avoid going drinking with them, or you take other measures that will protect you from the consequences of beings around a belligerent drunk. If you are especially cunning, you can even turn such known risks to your advantage (transforming a risk into an opportunity), employing calculated risks in a ruse or as a distraction. We all know people like this, and we know that they, too, are a danger to be avoided.

The lesson here is that when you have detailed personal knowledge about a situation, the calculation of risk can change dramatically. Or, to be more precise, matters that are given over to uncertainty in one model become objects of knowledge and therefore in a more epistemically intensive model are transformed from uncertainty into risk, and as risk are amenable to rational calculation. The scope of the calculus of risk expands and contracts, waxing and waning in proportion to knowledge. (Even the actuary, with all that he does not know, knows enough about what matters to his institution that he is dealing with a controlled, calculated risk and not uncertainty.)

Another personal anecdote about investing

Another personal story to illustrate how knowledge bears upon risk: recently in Rationing Financial Services I discussed the different financial services that are available to the working class, of a very basic if not rudimentary character, as compared to the advanced and sophisticated financial services available to the wealthy and the well-connected.

I also mentioned in this post how far my views are from the mainstream, and in my earlier post on Risk Management: A Personal View I mentioned a personal anecdote about how a financial adviser had expressed surprise by the risks that I was taking, when I didn’t believe myself to be taking any risks of particular note. In my most recent consultation with a financial professional, as I was asking questions about various investment products, one banker actually said to the other banker, “I don’t think that these [investments] will be risky enough for him.” I smiled inside. You would think I had been riding a superbike at 90 MPH on a winding mountain road without wearing a helmet. Not quite.

My tolerance for risk is not based on a thrill-seeking personality — I’m not about to take up BASE jumping — but rather upon knowledge. And in so far as I leverage my knowledge to shift the epistemic balance from uncertainty to risk, I am taking a calculated risk, against which I might insure myself (if I felt inclined to do so), but I am not plunging myself into blind uncertainty — in other words, I’m not a fool rushing in where angels fear to tread. The more knowledge one has, the less uncertainty one faces, the more one is presented with calculated risks in place of uncertainty.

When it comes to the investment products available to the individual of ordinary means, the options were really Hobson’s choice — i.e., the choice between what is offered and nothing. The process gave the appearance of choice, because there were a great many funds in which one could invest, and reams of information describing these investments, but really what it all came down to is that they were widely distributed funds of funds that would approximately track the market. I said to my banker than buying into these funds is simply the same as placing a bet on the S&P. If it goes up, you do well; if it goes down, you lose. End of story. I didn’t want the appearance of choice, I wanted the reality of choice.

I asked my banker if any of the funds focused on any particular industry, or resource, or were invested in any particular country or region of the world. No. None of the choices had any distinguishing features of this kind. They were all strategies for, one way or another, gaming the domestic US market to try to get a few more percentage points of profit than the next fund. In this case, having detailed knowledge of the world made no difference at all. If one cares to guess at the direction of the S&P, or if one feels that one has studied the domestic US market sufficiently to predict the direction of the S&P, then you have knowledge that is appropriate to this investment climate. Otherwise, your knowledge is useless and can’t be leveraged to your financial benefit. (I could, of course, become a day-trader, but I really don’t think that’s my thing.)

Knowledge and statistical probability

If you have both real knowledge and real options, your investment portfolio can be less at risk than placing a single bet on the direction of the US market, but my attitude in this respect was treated as one of welcoming more risk — because the requisite knowledge was not taken into account. Knowledge is a factor in the calculation of risk. In fact, knowledge constitutes one among “all factors not really indeterminate” which Frank Knight identified as being crucial to the determination of statistical probability (cf. Addendum on Existential Risk and Existential Uncertainty).

If you lack knowledge about the structure and functioning of the global economy, then your ability to choose wise investments is not likely to be any better than your ability to guess the direction of the US market average, and this is the presumption of ignorance that is built into the kind of investment options available to most people. Or if you think you know what is going on, but your knowledge is merely illusory, you might be lucky or you might by unlucky in investing, but your chances are no better than an up or down gamble. But if you have the knowledge of many different sectors of the global economy, and of many different industries and of regions of the world, it really isn’t much of a challenge to be able to improve your chances over the 50/50 guesswork involved in a bet on the S&P.

A curious parallel

Our collective situation as a species is in some ways not unlike my individual situation as an investor: being “stuck” on the surface of the earth, we have Hobson’s choice when it comes to existential risk management and mitigation: the earth or nothing. Take it or leave it. That’s not much of a choice, and it is curiously parallel to my own lack of choices in investments. And this lack of choices gives us no opportunity to leverage our growing knowledge of the cosmos from recent gains in space science in order to get the edge of existential risk. Our knowledge of the universe, at present, makes no difference at all in mitigating existential risk.

The more knowledge that we have of the cosmos, and of the human position within a cosmological context, the more knowledge we will have concerning the exact existential risks that we face. That increase in our knowledge will serve to transmute existential uncertainty into existential risk, sensu stricto, and in so doing will possibly present us with clearcut options of “insuring” against the existential risk in question. But our civilization, in its present form, has a presumption of ignorance built into it. There are countless existential risk mitigation and management options that we simply cannot pursue because we are planet-bound.

Existential risk mitigation aspects of space-based science and industry

When, in the future development of earth-originating extraterrestrial civilization, we begin to construct large-scale scientific instruments off the surface of the earth — say, a large radio-telescope array on the far side of the moon, sheltered from the EM spectrum noise generated by our busy earth — our ability to see deep into the cosmos (farther and more clearly in terms of distance, and therefore also in terms of time) our knowledge of astronomy, cosmology, and astrophysics will increase by an order of magnitude beyond the kind of observations that are possible from the surface of the earth.

Thus large space-based scientific installations will have a two-fold value in the mitigation of existential risk:

1) such facilities would be a function of space-based industry, which in turn would be a function of space-based human presence, and it would be a sustainable human presence in space that would be the first step in overcoming the manifest vulnerability of a species confined to a single planetary body, and …

2) the knowledge yielded by such facilities would significantly increase our knowledge of the universe, and hence of our place in the universe, which knowledge, as we have seen above, is crucial in transforming unactionable uncertainty into actionable risk

In fact, these two existential risk mitigation aspects of space-based science and industry are integral with each other: the space-based position allows us to exploit opportunities not available on the surface of the earth, and the knowledge gained from this enterprise will raise our awareness of opportunities now only dimly perceived.

To adequately assess our existential uncertainty and transform it into existential risk that might be mitigated and managed, we need to acquire existential knowledge — that is to say, knowledge of the existential milieu of human beings, a cosmological equivalent of situational awareness. What situational awareness is to the individual facing existential threats, knowledge of existential risk is to the species facing existential threats.

The more existential knowledge that we have, the better we can calculate our existential risk, and the better we can manage and mitigate that risk.

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danger imminent existential threat

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Existential Risk: The Philosophy of Human Survival

1. Moral Imperatives Posed by Existential Risk

2. Existential Risk and Existential Uncertainty

3. Addendum on Existential Risk and Existential Uncertainty

4. Existential Risk and the Death Event

5. Risk and Knowledge

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ex risk ahead

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Grand Strategy Annex

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Nazca to Ica

23 January 2012


A short distance north of Nazca, along the Panamericana, and situated between the designs of the “hands” (“manos“) and the “tree” (“arbol“), there is a tower (the “Torre Mirador”) that can be climbed, probably about 40 or 50 feet in height, in order to view some part of the lines of Nazca without flying over them. This close-up view of the lines clearly reveals the construction methods that I quoted yesterday (in Lines in the Desert) from Mason’s The Ancient Civilizations of Peru — stones have been removed from within geometrically defined areas and the removed stones have been piled at the edges of the designs. The piled stones not only represent the space cleared, but the piles themselves serve to make the demarcation between cleared and non-cleared areas all the more obvious, making the distinction more visually striking.

This construction technique was also used at nearby Palpa, and continues to be effective in the present day, as driving along the Panamericana (once outside the archaeologically preserved area) one sees a variety of messages spelled out in the desert, from the initials and names of individuals to fairly elaborate advertisements for small roadside stores.

In my naïveté I though that any intrepid visitor of sufficient curiosity might walk out into the desert and and look at the construction of the lines for themselves, but the desert has been fenced off along the Panamericana to prevent further damage to the lines, and once made aware of the threat it becomes immediately obvious how damaged many of the lines and figures are, which accounts for some of the difficulty in seeing some of the patterns from the air. Some — but not all.

Much is revealed by a close inspection (as one can gain from the tower along the Panamericana) that is lost in a distant view from the air, just as much is revealed in a distant inspection from the air that is close in the close-up view from near the ground. This is a perfect concrete illustration of what I was recently writing about in relation to the distinction between constructive and non-constructive thought (in P or not-P). In this post (on my other blog) I employed an image taken from Alain Connes to illustrate the constructive/non-constructive distinction such that the constructive perspective is like that of a mountain climber while the non-constructive perspective is like that of a visitor who flies over the summit of a mountain laboriously climbed by the other.

Any thorough investigation will want to make use of both perspectives in order to obtain the most comprehensive perspective possible — even though each perspective has its blind spots and its shadows that compromise our perspective on the whole. Indeed, it is precisely because each perspective incorporates deficits specific to the perspective that one will want to supplement any one perspective without another perspective with a different set of specific deficits. Between two or more fundamentally different perspectives on any one state-of-affairs there is the possibility of constructing the comprehensive conception that is excluded by any one perspective in isolation.

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 imagine 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.

This reflection gives us yet another perspective on utopianism, which I have many times tried to characterize in my attempts to show the near (not absolute) historical inevitability of utopian schemes transforming themselves upon their attempted implementation into dystopian nightmares — the utopian planner attempts to design from a purely non-constructive perspective without the benefit of a constructive perspective. This dooms the utopian plans to inevitable blindspots, shadows, and deficits. The oversights of a single perspective then, in the fullness of time, create the conditions for cascading catastrophic failure.

Historically speaking, it is not difficult to see how this comes about. After the astonishing planned cities of early antiquity, many from prehistoric societies that have left us little record except for their admirably regular and disciplined town plans, Europeans turned to a piecemeal, organic approach to urbanism. Once this approach was rapidly outgrown when cities began their burgeoning growth with the advent of the Industrial Revolution, it was a natural response on the part of Haussman-esque planners to view organic urbanism as a “failure” that necessitated replacement by another model that envisioned the already-built environment as a tabula rasa to be re-built according to rational standards. Cities henceforth were to be wholly planned to address to inadequacies of the medieval pattern of non-planning, which could not cope with cities with populations that now numbered in the millions.

I have observed elsewhere (in my Political Economy of Globalization) that many ancient prehistoric societies were essentially utopian constructions over which a god-king presided as a living god, present in the flesh among his people, and indeed some of the most striking examples of ancient town planning date from societies that exhibited (or seem to have exhibited) this now-vanished form of order. For only where a god-king is openly acknowledged as such can a social order based upon living and present divinity within the said social order be possible.

Nazca, however, does not seem to have been based on this social plan of a divinely-sanctioned social order which can bring utopian (and therefore likely non-constructive, top-down) planning into actual practice because of the physical presence of the god in the midst of his people. The book that I cited yesterday, The Ancient Civilizations of Peru by J. Alden Mason, has this to say of Nazca society:

“…the general picture seems to be one of a sedentary democratic people without marked class distinctions or authoritarianism, possibly without an established religion. There is less difference in the ‘richness’ or poverty of the graves, and women seem to be on an equality with men in this respect. The apparent absence of great public works, of extensive engineering features, and of temple pyramids implies a lack of authoritarian leadership. Instead, the leisure time of the people seems to have been spent in individual production, especially in the making of quantities of perfect, exquisite textiles and pottery vessels. This seems to indicate a strong cult of ancestor-worship. Cloths on which an incredible amount of labor was spent were made especially for funerary offerings and interred with the dead. The orientation seems to have been towards individualized religion rather than towards community participation, dictation, coercion, and aggression.”

J. Alden Mason, The Ancient Civilizations of Peru, Penguin Books, 1968, p. 85

Such egalitarian societies focused on the satisfaction of consumer demands were rare in the ancient world, but we should not be surprised that it was an egalitarian society, organized constructively from the bottom up, that produced the astonishing lines in the desert of the Nazca. Without an aerial perspective, the making of these lines was a thoroughly constructivistic undertaking, not even counter-balanced by a non-constructive perspective, which has only been obtained long after the Nazca civilization has disappeared, leaving only traces of itself in the dessicated sands of the desert.

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While I am posting this a couple of days after the fact, this entire account was written in longhand on the day here described.

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Grand Strategy Annex

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Epistemic Hubris

21 November 2010


The peacock is not a bird to hide its light under a bushel.

In More Evidence for the Copernican Principle I finished with this observation:

Now we know, and can demonstrate, that planetary systems are not unique to the Milky Way. From this stronger inductive position, we can with greater confidence extrapolate our existing knowledge to the furthest reaches of the universe.

The Copernican Principle tutors us in metaphysical modesty, but the growing evidence for the Copernican Principle, and the paucity of counter-examples, inspires us to metaphysical ambition. Scientific knowledge is the expression of this metaphysical ambition as much or more than it is an expression of metaphysical modesty.

As soon as I wrote this I realized that this is an idea that deserves its own independent exposition, as there is much that can be said on this head. I will touch on some of these issues here, though a full treatment would require a treatise, so I may need to return to this fascinating topic at a later date in order to refine and extrapolate my formulations as presented below.

I linked the above quoted idea to my post on Metaphysical Modesty, in which I discussed Jeffrey L. Kasser’s lectures on the philosophy of science published by The Teaching Company, and his exposition of the role of humility in scientific knowledge. There I wrote, “The Professor characterizes metaphysical modesty as, ‘The way the world is does not depend on what we think about it’.” And I added, “Now, this is simply an alternative formulation of realism, but Kasser has chosen to express realism as a moral virtue, and particularly as the moral virtue of metaphysical modesty.”

In recognizing the role of humility in scientific knowledge, and formulating it in moral terms, Kasser was not putting himself out on a limb, but on the contrary was staking out a classic position in the philosophy of science. Despite the contempt for philosophical ethics found in much early twentieth century positivist thought (and the formulation of doctrines like the emotivist theory of ethics), many of these scientifically-minded philosophers gave expositions of scientific knowledge saturated in moral significance.

While Bertrand Russell was never a positivist per se, nor simpliciter, he provides a wonderful example, perhaps even the locus classicus, of moralized scientific epistemology. Russell writes of the notion of good and evil being “extruded” from scientific philosophy. After an extensive explanation of how ethical preoccupations have compromised philosophical and scientific inquiry (in the last paragraphs of section I of “On Scientific Method in Philosophy”), Russell begins section II as follows:

“If the notion of the universe and the notion of good and evil are extruded from scientific philosophy, it may be asked what specific problems remain for the philosopher as opposed to the man of science?”

“On Scientific Method in Philosophy,” section II, collected in Mysticism and Logic

Russell’s criticism of the moral preoccupations of earlier philosophers is in the same paper:

“The ethical element which has been prominent in many of the most famous systems of philosophy is, in my opinion, one of the most serious obstacles to the victory of scientific method in the investigation of philosophical questions.”

For Russell, ethics is regulative of scientific thought, rather than constitutive of scientific thought, but that moral concerns are still present is unquestionable, as we see in his discussions of scientific humility:

“A truly scientific philosophy will be more humble, more piecemeal, more arduous, offering less glitter of outward mirage to flatter fallacious hopes, but more indifferent to fate, and more capable of accepting the world without the tyrannous imposition of our human and temporary demands.”

the last sentence of his “Mysticism and Logic” paper

And again:

“The concept of ‘truth’ as something dependent upon facts largely outside human control has been one of the ways in which philosophy hitherto has inculcated the necessary element of humility. When this check upon pride is removed, a further step is taken on the road towards which a certain kind of madness—the intoxication of power which invaded philosophy with Fichte, and to which modern men, whether philosophers or not, are prone. I am persuaded that this intoxication is the greatest danger of our time, and that any philosophy, which, however unintentionally, contributes to it is increasing the danger of vast social disaster.”

Bertrand Russell, A History of Western Philosophy, Chapter XXX, “John Dewey,” p. 828

And again:

“By the practice of methodological doubt, if it is genuine and prolonged, a certain humility as to our knowledge is induced: we become glad to know anything in philosophy, however seemingly trivial. Philosophy has suffered from the lack of this kind of modesty.”

Bertrand Russell, Our Knowledge of the External World, third from the last paragraph of the last chapter.

Would it be too much to say that scientific humility was a preoccupation of Russell’s? As I noted above, Russell is the locus classicus here, and Kasser was on firm ground following his lead.

Russell makes a persuasive case for the role of humility in science, but as I realized as I was writing about the further evidence we now have for the Copernican Principle, the role of ambition in science is no less central, and perhaps more interesting. As our patient methods of induction increase our level of certainty about an hypothesis, we rightly become more comfortable with its further generalization and extrapolation.

To make a sweeping generalization about a law of nature, as when Newton posited universal gravitation, is an act of epistemic hubris. That the mind can capture, in an act of thought, a truth that is as true immediately beneath our feet as it is on the other side of the universe, is nothing short of astonishing. Nevertheless, it can be expressed with cool detachment, as with Newton’s law of gravitation:

“Every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them.”

Newton here invokes “Every particle of matter in the universe” without qualification. It is this simplicity that gives general laws of nature such great power of prediction and theoretical unity, but it also must be recognized as a triumph of epistemic ambition, if not epistemic hubris. As it often commented in regard to Newton, he said that “I feign no hyptheses” (“Hypotheses non fingo”) even while formulating an unconditional and universal law of gravitation. If this isn’t an hypothesis, I don’t know what is.

To contemplate the possibility of metaphysical ambition co-equal with metaphysical modesty as one of the springs of science brings us to the locus classicus of ambition, MacBeth’s speech as he contemplates politically-motivated murder:

I haue no Spurre
To pricke the sides of my intent, but onely
Vaulting Ambition, which ore-leapes it selfe,
And falles on th’ other.

Shakespeare, William, 1564-1616. Macbeth (1623 First Folio Edition)

Shakespeare’s use of “Vaulting Ambition” in this speech has often been quoted. I cite it here because of what it implies: a leaping-over of all that intervenes into order to get directly to the object without recourse to the painstakingly slow method of creeping along the ground. This way of formulating Vaulting Ambition reveals it as a non-constructive strategy, and this makes it interesting.

If you have not studied philosophy, logic, or mathematics you are not likely to be consciously aware of the formal distinction between constructive and non-constructive methods, or, formulated metaphysically, between idealism and realism. Nevertheless, the distinction is fundamental, and even those who cannot distinguish a constructive proof from a non-constructive proof will be immediately familiar with the intuitive instantiations of these divergent attitudes, as in “seeing is believing” (a constructivist idea) or “there is more to the world than we can see” (a Platonic, and therefore a realist, non-constructive idea).

Vaulting ambition in science, as revealed in breathtaking leaps of deduction to striking and unexpected conclusions, is usually a non-constructive enterprise. Non-constructive proofs are fascinating, and show us things we would probably not otherwise even guess, but they have their weaknesses. Some non-constructive proofs prove things but do not show us how to find them, construct them, or otherwise submit them to immediate observation, inquiry, or further analysis. For example, we may “feel in our bones” that there is more to the world than meets the eye, but not be able to say exactly what it is that the world consists of but which cannot be seen.

By way of contrast, the humility in science, of the sort recommended by Bertrand Russell and Kasser (though formulated in the language of metaphysical realism), is usually a constructive enterprise, whereby we reach our conclusions by the most slow and painstaking methods, so that when we arrive at our conclusion we know exactly how we got there, what we found, and we can point to the result of our research so that others can inspect it for themselves.

Both humility and hubris are to be found in scientific thought, with now one, now the other, taking precedence in the way we understand the world, but even when one is in the ascendancy, the other is never absent.

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