Wednesday


Addendum on Civilization and the Technium

in regard to human, animal, and alien technology


One of the virtues of taking the trouble to formulate one’s ideas in an explicit form is that, once so stated, all kinds assumptions one was making become obvious as well as all kinds of problems that one didn’t see when the idea was just floating around in one’s consciousness, as a kind of intellectual jeu d’esprit, as it were.

Bertrand Russell wrote about this, or, at least, about a closely related experience in one of his well-known early essays, in which he discussed the importance not only making our formulations explicit, but of doing so by way of putting some distance between our thoughts and the kind of facile self-evidence that can distract us from the real business at hand:

“It is not easy for the lay mind to realise the importance of symbolism in discussing the foundations of mathematics, and the explanation may perhaps seem strangely paradoxical. The fact is that symbolism is useful because it makes things difficult. (This is not true of the advanced parts of mathematics, but only of the beginnings.) What we wish to know is, what can be deduced from what. Now, in the beginnings, everything is self-evident; and it is very hard to see whether one self-evident proposition follows from another or not. Obviousness is always the enemy to correctness. Hence we invent some new and difficult symbolism, in which nothing seems obvious. Then we set up certain rules for operating on the symbols, and the whole thing becomes mechanical. In this way we find out what must be taken as premiss and what can be demonstrated or defined. For instance, the whole of Arithmetic and Algebra has been shown to require three indefinable notions and five indemonstrable propositions. But without a symbolism it would have been very hard to find this out. It is so obvious that two and two are four, that we can hardly make ourselves sufficiently skeptical to doubt whether it can be proved. And the same holds in other cases where self-evident things are to be proved.”

Bertrand Russell, Mysticism and Logic, “Mathematics and the Metaphysicians”

Russell’s foundationalist program in the philosophical of mathematics closely followed the method that he outlined so lucidly in the passage above. Principia Mathematica makes the earliest stages of mathematics notoriously difficult, but does so in service to the foundationalist ideal of revealing hidden presuppositions and incorporating them into the theory in an explicit form.

Another way that Russell sought to overcome self-evidence is through the systematic pursuit of the highest degree of generality, which drives us to formulate concepts that are alien to common sense:

“It is a principle, in all formal reasoning, to generalize to the utmost, since we thereby secure that a given process of deduction shall have more widely applicable results…”

Bertrand Russell, An Introduction to Mathematical Philosophy, Chapter XVIII, “Mathematics and Logic”

These are two philosophical principles — the explication of ultimate simples (foundations) and the pursuit of generality — that I have very much taken to heart and attempted to put into practice in my own philosophical work. Russell’s foundationalist method shows us what can be deduced from what, and gives to these deductions the most widely applicable results. To these philosophical imperatives of Russell I have myself added another, parallel to his pursuit of generality, and that is the simultaneous pursuit of formality: it is (or ought to be) a principle in all theoretical reasoning to formalize to the utmost…

Russell also observed the imperative of formalization, though he himself did not systematically distinguish between generalization and formalization, and it is a tough problem; I’ve been working on it for about twenty years and haven’t yet arrived at definitive formulations. As far as provisional formulations go, generalization gives us the highly comprehensive conceptions like astrobiology and civilization and the technium that allow us to unify a vast body of knowledge that must be studied by inter-disciplinary means, while formalization gives us the distinctions we must carefully observe within our concepts, so that generalization does not simply give us the night in which all cows are black (to borrow a phrase that Hegel used to ridicule Schelling’s conception of the Absolute).

Foundationalism as a philosophical movement is very much out of fashion now, although the foundations of mathematics, pursued eo ipso, remains an active and highly technical branch of logico-mathematical research, and today looks a lot different from what it was when it was first formulated as a philosophical research program a hundred years ago by Frege, Peano, Russell, Whitehead, Wittgenstein, and others. Nevertheless, I continue to derive much philosophical clarification from the early philosophical stages of foundationalism, especially in regard to theories that have not (yet) been reduced to formal systems, as is the case with theories of history or theories of civilization.

I am still a long way from reducing my ideas about history or civilization to first principles, much less to symbolism, but I feel like I am making progress, and the discovery of assumptions and problems is a sure sign of progress; in this sense, my post on Civilization and the Technium marked a stage of progress in my thinking, because of the inadequacy of my formulations that it revealed.

In my Civilization and the Technium I compared the extent of civilization — a familiar idea that has not yet received anything like an adequate definition — with the extent of the technium — a recent and hence unfamiliar idea for which there is an explicit formulation, but since it is new its full scope remains untested and untried, and therefore it presents problems that the idea of civilization does not present. I formulated concepts of the technium parallel to formulations of astrobiology and astrocivilization, as follows:

● Eotechnium the origins of the technium, wherever and whenever it occurs, terrestrial or otherwise

● Esotechnium our terrestrial technium

● Exotechnium any extraterrestrial technium exclusive of the terrestrial technium

● Astrotechnium the totality of technology in the universe, our terrestrial and any extraterrestrial technium taken together in their cosmological context

I realize now that when I did this I was making slightly different assumptions for civilization and the technium. The intuitive basis of this was that I assumed, in regard to the technium, that the technium I was describing was all due to human activity (a clear case of anthropic bias), so that the distinction between the exotechnium and the exotechnium was the distinction between terrestrial human technology and extraterrestrial human technology.

When, on the other hand, I formulated the parallel concepts for civilization, I assumed that esocivilization was terrestrial human civilization and that exocivilization would be alien civilizations not derived from the human eocivilization source.

Another way to put this is that I assumed the validity of the terrestrial eotechnium thesis even while I also assumed that the terrestrial eocivilization thesis did not hold. Is that too much technical terminology? In other words, I assumed the uniqueness of the human technium but I did not assume the uniqueness of human industrial-technological civilization.

This points to a further articulation (and therefore a further formalization) of the concepts employed: one must keep the conception of eocivlization (the origins of civilization) clearly in mind, and distinguish between terrestrial civilization that expands into extraterrestrial space and therefore becomes exocivilization from its eocivilization source on the one hand, and on the other hand a xeno-eocivilization source that constitutes exocivilization by virtue of its xenomorphic origins. If one is going to distinguish between esocivilization and exocivilization, one must identify the eocivilization source, or all is for naught.

All of this holds, mutatis mutandis, for the eotechnium, esotechnium, exotechnium, and astrotechnium, although I ought to point that my formulations in Civilization and the Technium, and repeated above, were accurate because they were formulated in Russellian generality. It was in my following exposition that I failed to observe all the requisite distinctions. But there’s more. I’ve since realized that further distinctions can be made.

As I thought about the possibility of a xenotechnium, i.e., a technium produced by a sentient alien species, I realized that there is a xenotechnium right here on Earth (a terrestrial xenotechnium, or non-hominid technium), in the form of tool use and other forms of technology by non-human species. We are all familiar with famous examples like the chimpanzees who will strip the leaves off a branch and then use the branch to extract termites from a termite mound. Yesterday I alluded to the fact that otters use rocks to break open shells. There are many other examples. Apart from tool use, beaver damns and the nests of birds, while not constructed with tools, certainly represent a kind of technology.

The nest of a weaver bird is a form of non-human technology.

If we take all instances of animal technology together they constitute a terrestrial non-human technium. If we take all instances of technology known to us, human and non-human together, we have a still more comprehensive conception of the technium that is more general that the concept of the human-specific technium and therefore less subject to anthropic bias (the latter concept due to Nick Bostrum, who also formulated existential risk). This latter, more comprehensive conception of the technium would seem to be favored by Russell’s imperative of generalization to the utmost, although we must continue to make the finer distinctions within the concept for the formalization of the conception of the technium to keep pace with its generalization.

There is a systematic relationship between terrestrial biology and the terrestrial technium, both hominid and non-hominid. Eobiology facilitates the emergence of a terrestrial eotechnium, of which all instances of technology, hominid and non-hominid alike, can be considered expressions. This is already explicit in Kevin Kelly’s book, What Technology Wants, as one of his arguments is that the emergence and growth of the technium is continuous with the emergence of growth of biological organization and complexity. He cites John Maynard Smith and Eors Szathmary as defining the following thresholds of biological organization (p. 46):

One replicating molecule -» Interacting population of replicating molecules
Replicating molecules -» Replicating molecules strung into chromosome
Chromosome of RNA enzymes -» DNA proteins
Cell without nucleus -» Cell with nucleus
Asexual reproduction (cloning) -» Sexual recombination
Single-cell organism -* Multicell organism
Solitary individual -» Colonies and superorganisms
Primate societies -» Language-based societies

He then suggests the following sequence of thresholds within the growth of the technium (p. 47):

Primate communication -» Language
Oral lore -> Writing/mathematical notation
Scripts -» Printing
Book knowledge -» Scientific method
Artisan production -» Mass production
Industrial culture -» Ubiquitous global communication

And then he connects the two sequences:

The trajectory of increasing order in the technium follows the same path that it does in life. Within both life and the technium, the thickening of interconnections at one level weaves the new level of organization above it. And it’s important to note that the major transitions in the technium begin at the level where the major transitions in biology left off: Primate societies give rise to language. The invention of language marks the last major transformation in the natural world and also the first transformation in the manufactured world. Words, ideas, and concepts are the most complex things social animals (like us) make, and also the simplest foundation for any type of technology. (p. 48)

Thus the genealogy of the technium is continuous with the genealogy of life.

Considering this in relation to the possibility of a xenotechnium, one would expect the same to be the case: I would expect a systematic relationship to hold between xenobiology and a xenotechnium, such that an alien eobiology would facilitate the emergence of an alien eotechnium. And, extending this naturalistic line of thought, that assumes similar patterns of development to hold for peer industrial-technological civilizations, I would further assume that a xenotechnium would not always coincide with the xenocivilization with which it is associated. If there is a “first contact” between terrestrial civilization and a xenocivilization, it is likely that it will be rather a contact between the expanding terrestrial technium (which is, technically, no longer terrestrial precisely because it is expanding extraterrestrially) and an expanding xenotechnium.

There remains much conceptual work to be done here, as the reader will have realized. I’ll continue to work on these formulations, keeping in mind the imperatives of generality and formality, and perhaps someday converging on a foundationalist account of biology, civilization, and the technium that is at once both fully comprehensive and fully articulated.

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Tuesday


Aristotle as portrayed by Raphael

Aristotle claimed that mathematics has no ethos (Metaphysics, Book III, Chap. 2, 996a). Aristotle, of course, was more interested in the empirical sciences than his master Plato, whose Academy presumed and demanded familiarity with geometry — and we must understand that for the ancients, long before the emergence of analytical geometry in the work of Descartes (allowing us to formulate geometry algebraically, hence arithmetically), that geometry was always axiomatic thought, rigorously conceived in terms of demonstration. For the Greeks, this was the model and exemplar of all rigorous thought, and for Aristotle this was a mode of thought that lacked an ethos.

Euclid provided the model of formal thought with his axiomatization of geometry. Legend has it that there was a sign over the door of Plato's Academy stating, 'Let no one enter here who has not studied geometry.'

In this, I think, Aristotle was wrong, and I think that Plato would have agree on this point. But the intuition behind Aristotle’s denial of a mathematical ethos is, I think, a common one. And indeed it has even become a rhetorical trope to appeal to rigorous mathematics as an objective standard free from axiological accretions.

In his famous story within a story about the Grand Inquisitor, Dostoyevsky has the Grand Inquisitor explain how “miracles, mystery, and authority” are used to addle the wits of others.

In his famous story within a story about the Grand Inquisitor, Dostoyevsky has the Grand Inquisitor explain how “miracles, mystery, and authority” are used to addle the wits of others.

Our human, all-too-human faculties conspire to confuse us, to addle our wits, when we begin talking about morality, so that the purity and rigor of mathematical and logical thought seem to be called into question if we acknowledge that there is an ethos of formal thought. We easily confuse ourselves with religious, mystical, and ethical ideas, and since the great monument of mathematical thought has been mostly free of this particular species of confusion, to deny an ethos of formal thought can be understood as a strategy to protect and defend of the honor of mathematics and logic by preserving it from the morass that envelops most human attempts to think clearly, however heroically undertaken.

Kant famously said that he had to limit knowledge to make room for faith.

Kant famously stated in the Critique of Pure Reason that, “I have found it necessary to deny knowledge in order to make room for faith.” I should rather limit faith to make room for rigorous reasoning. Indeed, I would squeeze out faith altogether, and find myself among the most rigorous of the intuitionists, one of whom has said: “The aim of this program is to banish faith from the foundations of mathematics, faith being defined as any violation of the law of sufficient reason (for sentences). This law is defined as the identification (by definition) of truth with the result of a (present or feasible) proof…”

Western asceticism can be portrayed as demonic torment or as divine illumination; the same diversity of interpretation can be given to ascetic forms of reason.

Though here again, with intuitionism (and various species of constructivism generally), we have rigor, denial, asceticism — intuitionistic logic is no joyful wisdom. (An ethos of formal thought need not be an inspiring and edifying ethos.) It is logic with a frown, disapproving, censorious — a bitter medicine justified only because it offers hope of curing the disease of contradiction, contracted when mathematics was shown to be reducible to set theory, and the latter shown to be infected with paradox (as if the infinite hubris of set theory were not alone enough for its condemnation). Is the intuitionist’s hope justified? In so far as it is hope — i.e., hope and not proof, the expectation that things will go better for the intuitionistic program than for logicism — it is not justified.

Dummett has said that intuitionistic logic and mathematics are to wear their justification on their face:

“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

The hope that contradiction will not arise from intuitionistic methods clearly is no such evident justification. As a matter of fact, empirically and historically verifiable, we know that intuitionism has resulted in no contradictions, but this could change tomorrow. Intuitionism stands in need of a consistency proof even more than formalism. There is, in its approach, a faith invested in the assumption that infinite totalities caused the paradoxes, and once we have disallowed reference to them all will go well. This is a perfectly reasonable assumption, but one, in so far as it is an article of faith, which is at variance with the aims and methods of intuitionism.

And what is a feasible proof, which our ultra-intuitionist would allow? Have we not with “feasible proof” abandoned proof altogether in favor of probability? Again, we will allow them their inconsistencies and meet them on their own ground. But we shall note that the critics of the logicist paradigm fix their gaze only upon consistency, and in so doing reveal again their stingy, miserly conception of the whole enterprise.

“The Ultra-Intuitionistic Criticism and the Antitraditional program for the foundations of Mathematics” by A. S. Yessenin-Volpin (who was arguing for intellectual freedom in the Soviet Union at the same time that he was arguing for a censorious conception of reason), in Intuitionism and Proof Theory, quoted briefly above, is worth quoting more fully:

The aim of this program is to banish faith from the foundations of mathematics, faith being defined as any violation of the law of sufficient reason (for sentences). This law is defined as the identification (by definition) of truth with the result of a (present or feasible) proof, in spite of the traditional incompleteness theorem, which deals only with a very narrow kinds [sic] of proofs (which I call ‘formal proofs’). I define proof as any fair way of making a sentence incontestable. Of course this explication is related to ethics — the notion fair means ‘free from any coercion or fraud’ — and to the theory of disputes, indicating the cases in which a sentence is to be considered as incontestable. Of course the methods of traditional mathematical logic are not sufficient for this program: and I have to enlarge the domain of means explicitly studied in logic. I shall work in a domain wherein are to be found only special notions of proof satisfying the mentioned explication. In this domain I shall allow as a means of proof only the strict following of definitions and other rules or principles of using signs.

Intuitionism and proof theory: Proceedings of the summer conference at Buffalo, N.Y., 1968, p. 3

What is coercion or fraud in argumentation? We find something of an illustration of this in Gregory Vlastos’ portrait of Socrates: “Plato’s Socrates is not persuasive at all. He wins every argument, but never manages to win over an opponent. He has to fight every inch of the way for any assent he gets, and gets it, so to speak, at the point of a dagger.” (The Philosophy of Socrates, Ed. by Gregory Vlastos, page 2)

According to Gregory Vlastos, Socrates used the kind of 'coercive' argumentation that the intuitionists abhor.

What appeal to logic does not invoke logical compulsion? Is logical compulsion unique to non-constructive mathematical thought? Is there not an element of logical compulsion present also in constructivism? Might it not indeed be the more coercive form of compulsion that is recognized alike by constructivists and non-constructivists?

The breadth of the conception outlined by Yessenin-Volpin is impressive, but the essay goes on to stipulate the harshest measures of finitude and constructivism. One can imagine these Goldwaterite logicians proclaiming: “Extremism in the defense of intuition is no vice, and moderation in the pursuit of constructivist rigor is no virtue.” Brouwer, the spiritual father of intuitionism, even appeals to the Law-and-Order mentality, saying that a criminal who has not been caught is still a criminal. Logic and mathematics, it seems, must be brought into line. They verge on criminality, deviancy, perversion.

Quine was no intuitionist by a long shot, but as a logician he brought a quasi-disciplinary attitude to reason and adopted a tone of disapproval not unlike Brouwer.

The same righteous, narrow, anathamatizing attitude is at work among the defenders of what is sometimes called the “first-order thesis” in logic. Quine sees a similar deviancy in modal logic (which can be shown to be equivalent to intuitionistic logic), which he says was “conceived in sin” — the sin of confusing use and mention. These accusations do little to help us understand logic. We would do well to adopt Foucault’s attitude on these matters: “leave it to our bureaucrats and our police to see that our papers are in order. At least spare us their morality when we write.” (The Archaeology of Knowledge, p. 17)

Foucault had little patience for the kind of philosophical reason that seemed to be asking if our papers are in order, a function he thought best left to the police.

The philosophical legacy of intuitionism has been profound yet mixed; its influence has been deeply ambiguous. (Far from the intuitive certainty, immediacy, clarity, and evident justification that it would like to propagate.) There is in inuitionism much in harmony with contemporary philosophy of mathematics and its emphasis on practices, the demand for finite constructivity, its anti-philosophical tenor, its opposition to platonism. The Father of Intuitionism, Brouwer, was, like many philosophers, anti-philosophical even while propounding a philosophy. No doubt his quasi-Kantianism put his conscience at rest in the Kantian tradition of decrying metaphysics while practicing it, and his mysticism gave a comforting halo (which softens and obscures the hard edges of intuitionist rigor in proof theory) to mathematics which some have found in the excesses of platonism.

L. E. J. Brouwer: philosopher of mathematics, mystic, and pessimistic social theorist

In any case, few followers of Brouwer followed him in his Kantianism and mysticism. The constructivist tradition which grew from intuitionism has proved to be philosophically rich, begetting a variety of constructive techniques and as many justifications for them. Even if few mathematicians actually do intuitionistic mathematics, controversies over the significance of constructivism have a great deal of currency in philosophy. And Dummett is explicit about the place of philosophy in intuitionistic logic and mathematics.

The light of reason serves as an inspiration to us as it shines down from above, and it remains an inspiration even when we are not equal to all that it might ideally demand of us.

Intuitionism and constructivism command our respect in the same way that Euclidean geometry commanded the respect of the ancients: we might not demand that all reasoning conform to this model, but it is valuable to know that rigorous standards can be formulated, as an ideal to which we might aspire if nothing else. And and ideal of reason is itself an ethos of reason, a norm to which formal thought aspires, and which it hopes to approximate even if it cannot always live up the the most exacting standard that it can recognize for itself.

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Studies in Formalism

1. The Ethos of Formal Thought

2. Epistemic Hubris

3. Parsimonious Formulations

4. Foucault’s Formalism

5. Cartesian Formalism

6. Doing Justice to Our Intuitions: A 10 Step Method

7. The Church-Turing Thesis and the Asymmetry of Intuition

8. Unpacking an Einstein Aphorism

9. Methodological and Ontological Parsimony (in preparation)

10. The Spirit of Formalism (in preparation)

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