Arthur C Clarke

Arthur C. Clarke is best remembered for this science fiction stories, but many of his dicta and aphorisms have become common currency and are quoted and repeated to the point that their connection to their source is sometimes lost. (Clarke’s thought ranged widely and, interestingly, Clarke identified himself as a logical positivist.) Recently I quoted one of Clarke’s well-known sayings in Happy Birthday Nicolaus Copernicus!, as follows:

“Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.”

quoted in Visions: How Science Will Revolutionize the Twenty-First Century (1999) by Michio Kaku, p. 295

In so saying, Clarke asserted a particular case of what is known as the logical law (or principle) of the excluded middle, which is also known as tertium non datur: the idea that, given a proposition and its negation, either one or the other of them must be true. This is also expressed in propositional logic as “P or not-P” (“P v ~P”). The principle of tertium non datur is not to be confused with the principle of non-contradiction, which can be formulated as “~(P & ~P).”

Even stating tertium non datur is controversial, because there are narrowly logical formulations as well as ontological formulations of potentially much greater breadth. This, of course, is what makes the principle fascinating and gives it its philosophical depth. Moreover, the principle of the excluded middle is subtly distinct from the principle of bivalence, though the two usually work in conjunction. Whereas the law of the excluded middle states that of a proposition and its negation, one of the other must be true, the principle of bivalence states that there are only two propositional truth values: true and false.

To get started, here is the principle of the excluded middle as formulated in The Cambridge Dictionary of Philosophy edited by Robert Audi:

principle of excluded middle, the principle that the disjunction of any (significant) statement with its negation is always true; e.g., ‘Either there is a tree over 500 feet tall or it is not the case that there is such a tree’. The principle is often confused with the principle of bivalence.

THE CAMBRIDGE DICTIONARY OF PHILOSOPHY second edition, General Editor Robert Audi, 1999, p. 738

And to continue the Oxbridge axis, here is the formulation from Simon Blackburn’s The Oxford Dictionary of Philosophy:

excluded middle, principle (or law) of The logical law asserting that either p or not-p. It excludes middle cases such as propositions being half correct or more or less right. The principle directly asserting that each proposition is either true or false is properly called the law of bivalence.

The Oxford Dictionary of Philosophy, Simon Blackburn, Oxford University Press, 1996, p. 129

For more partisan formulations, we turn to other sources. Mario Bunge formulated a narrowly syntactical conception of the law of the excluded middle in his Dictionary of Philosophy, which is intended to embody a scientistic approach to philosophy:

EXCLUDED MIDDLE A logical truth or tautology in ordinary (classical) logic: For every proposition p, p v ~p.

Dictionary of Philosophy, Mario Bunge, Prometheus Books, 1999, p. 89

By way of contrast, in D. Q. McInerny’s Being Logical: A Guide to Good Thinking we find a strikingly ontological formulation of the law of the excluded middle:

“Between being and nonbeing there is no middle state. Something either exists or it does not exist; there is no halfway point between the two.”

D. Q. McInerny, Being Logical: A Guide to Good Thinking, Part Two, The Basic Principles of Logic, 1. First Principles, p. 26

What these diverse formulations bring out for us is the difficulty of separating logical laws of how formal systems are to be constructed from ontological laws about how the world is constructed, and in so bringing out this difficulty, they show us the relation between the law of the excluded middle and the principle of bivalence, since the logical intuition that there are only two possible truth values of any one proposition — true or false — is so closely tied to our logical intuition that, of these two values, one or the other (but not both, which qualification is the principle of non-contradiction) must hold for any given (meaningful) proposition.

The powerful thing about Clarke’s observation is that it appeals to this admixture of logical intuitions and empirical intuitions, and in so doing seems to say something very compelling. Indeed, since I am myself a realist, and I think it can be shown that there is a fact of the matter that makes propositions true or false, I think that Clarke not only said something powerful, he also said something true: either there are extraterrestrial intelligences or there are not. It is humbling to contemplate either possibility: ourselves utterly alone in a vast universe with no other intelligent species or civilizations, or some other alien intelligence out there somewhere, unknown to us at present, but waiting to be discovered — or to discover us.

alien excluded middle 2

Although these logical intuitions are powerful, and have shaped human thought from its earliest times to the present day, the law of the excluded middle has not gone unquestioned, and indeed Clarke’s formulation gives us a wonderful opportunity to explore the consequences of the difference between constructive and non-constructive reasoning in terms of a concrete example.

To formulate the existence or non-existence of extraterrestrials in the form of a logical law like the law of the excluded middle makes the implicit realism of Clarke’s formulation obvious as soon as we think of it in these terms. In imagining the possibilities of our cosmic isolation or an unknown alien presence our terror rests on our intuitive, visceral feeling of realism, which is as immediate to us as the intuitions rooted in our own experiences as bodies.

The constructivist (at least, most species of constructivist, but not necessarily all) must deny the validity of the teritum non datur formulation of the presence of extraterrestrials, and in so doing the constructivist must pretend that our visceral feelings of realism are misleading or false, or must simply deny that these feelings exist. None of these are encouraging strategies, especially if one is committed to understanding the world by getting to the bottom of things rather than denying that they exist. Not only I am a realist, but I also believe strongly in the attempt to do justice to our intuitions, something that I have described in two related posts, Doing Justice to Our Intuitions and How to Formulate a Philosophical Argument on Gut Instinct.

In P or not-P (as well as in subsequent posts concerned with constructivism, What is the relationship between constructive and non-constructive mathematics? Intuitively Clear Slippery Concepts, and Kantian Non-constructivism) I surveyed constructivist and non-constructivist views of tertium non datur and suggested that constructivists and non-constructivists need each other, as each represents a distinct point of view on formal thought. Formal thought is enriched by these diverse perspectives.

But whereas non-constructive thought, which is largely comprised of classical realism, can accept both the constructivist and non-constructivist point of view, the many varieties of constructivism usually explicitly deny the validity of non-constructive methods and seek to systematically limit themselves to constructive methods and constructive principles. Most famously, L. E. J. Brouwer (whom I have previously discussed in Saying, Showing, Constructing and One Hundred Years of Intuitionism and Formalism) formulated the philosophy of mathematics we now know as intuitionism, which is predicated upon the explicit denial of the law of the excluded middle. Brouwer, and those following him such as Heyting, sought to formulate mathematical and logic reasoning without the use of tertium non datur.

Brouwer and the intuitionists (at least as I interpret them) were primarily concerned to combat the growing influence of Cantor and his set theory in mathematics, which seemed to them to license forms of mathematical reasoning that had gone off the rails. Cantor had gone too far, and the intuitionists wanted to reign him in. They were concerned about making judgments about infinite totalities (in this case, sets with an infinite number of members), which the law of the excluded middle, when applied to the infinite, allows one to do. This seems to give us the power to make deductions about matters we cannot either conceive or even (as it is sometimes said) survey. “Surveyability” became a buzz word in the philosophy of mathematics after Wittgenstein began using it in his posthumously published Remarks on the Foundations of Mathematics. Although Wittgenstein was not himself an intuitionist sensu stricto, his work set the tone for constructivist philosophy of mathematics.

Given the intuitionist rejection of the law of the excluded middle, it is not correct to say that there either is intelligent alien life in the universe or there is not intelligent alien life in the universe; to meaningfully make this statement, one would need to actually observe (inspect, survey) all possible locations where such alien intelligence might reside, and only after seeing it for oneself can one legitimately claim that there is or is not alien intelligence in the universe. For am example closer to home, it has been said that an intuitionist will deny the truth of the statement “either it is raining or it is not raining” without looking out the window to check and see. This can strike one as merely perverse, but we must take the position seriously, as I will try to show with the next example.

The day before the Battle of Salamis, Aristotle might have said that there would be a sea battle tomorrow or there would not be a sea battle tomorrow, and in this case the first would have been true; on other days, the second would have been true.

The day before the Battle of Salamis, Aristotle might have said that there would be a sea battle tomorrow or there would not be a sea battle tomorrow, and in this case the first would have been true; on other days, the second would have been true.

Already in classical antiquity, Aristotle brought out a striking feature of the law of the excluded middle, in a puzzle sometimes known as the “sea battle tomorrow.” The idea is simple: either there will be a sea battle tomorrow, or there will not be a sea battle tomorrow. We may not know anything about this battle, and as of today we do not even know if it will take place, but we can nevertheless confidently assert that either it will take place or it will not take place. This is the law of the excluded middle as applied to future contingents.

One way to think of this odd consequence of the law of the excluded middle is that when it is projected beyond the immediate circumstances of our ability to ascertain its truth by observation it becomes problematic. This is why the intuitionists reject it. Aristotle extrapolated the law of the excluded middle to the future, but we could just as well extrapolate it into the past. Historians do this all the time (either Alexander cut the Gordian Knot or Alexander did not cut the Gordian Knot), but because of our strong intuitive sense of historical realism this does not feel as odd as asserting that something that hasn’t happened yet either will happen or will not happen.

In terms of Clarke’s dichotomy, we could reformulate Aristotle’s puzzle about the sea battle tomorrow in terms of the discovery of alien intelligence tomorrow: either we will receive an alien radio broadcast tomorrow, or we will not receive an alien broadcast tomorrow. There is no third possibility. One way or another, the realist says, one of these propositions is true, and one of them is false. We do not know, today, which one of them is true and which one of them is false, but that does not mean that they do no possess definite truth values. The intuitionist says that the assertion today that we will or will not receive an alien radio broadcast is meaningless until tomorrow comes and we turn on our radio receivers to listen.

The intuitionists thus have an answer to this puzzling paradox that remains a problem for the realist. This is definitely a philosophical virtue for intuitionism, but, like all virtues, it comes at a price. It is not a price I am willing to pay. This path can also lead us to determinism — assuming that all future contingents have a definite truth value implies that they are set in stone — but I am also not a determinist (as I discussed in The Denial of Freedom as a Philosophical Problem), and so this intersection of my realism with my libertarian free willist orientation leaves me with a problem that I am not yet prepared to resolve. But that’s what makes life interesting.

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Grand Strategy Annex

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Today we celebrate the 540th anniversary of the birth of Nicolaus Copernicus. The great astronomer was born 19 February 1473 in Toruń, now part of Poland. The name of Copernicus belongs with the short list of thinkers who not only changed the direction of civilization, but also the nature and character of Western civilization. Copernicus as the distinction of having a cosmology named in his honor.

We would do well to recall how radically our understanding of the world has changed in relatively recent years. Up until the advent of modern science, several ancient traditions of Western civilization had come together in a comfortingly stable picture of the world in which all of Western society was deeply invested. The Aristotelian systematization of Christian theology carried out by Thomas Aquinas was especially influential. Questioning this framework was not welcome. But science was an idea whose time had come, and, as we all know, nothing can stop the progress of an idea whose time had come.

Copernicus began questioning this cosmology by putting the sun in the center of the universe; Galileo pointed his telescope into the heavens and showed that the sun has spots, the moon has mountains, and that Jupiter had moons of its own, the center of its own miniature planetary system. Others took up the mantle and went even farther: Tycho Brahe, Johannes Kepler, and eventually Newton and then Einstein.

Copernicus was a polymath, but essentially a theoretician. One must wonder if Copernicus ever read William of Ockham, since it was Ockham along with Copernicus who initiated the unraveling of the scholastic synthesis, out of which the modern world would rise like a Phoenix from the ashes of the medieval world. Ockham provided the theoretical justification for the sweeping simplification of cosmology that Copernicus effected; it is not outside the realm of possibility that the later theoretician read the work of the earlier.

Today, when our knowledge of cosmology is expanding at breathtaking speed, Copernicus is more relevant than ever. We find ourselves forced to consider and to reconsider the central Copernican idea from every possible angle. The Fermi Paradox and the Great Filter force us to seek new insights into Copernicanism. I quite literally think about Copernicanism every day, making Copernicus a living influence on my thought.

As our civilization grows in sophistication, the question “Are we alone?” becomes more and more pressing. Arthur C. Clarke wrote, “Two possibilities exist: either we are alone in the Universe or we are not. Both are equally terrifying.” This insight is profound in its simplicity. Thus we search for peer civilizations and peer life in the universe. That is to say, we look for other civilizations like ours, and for life that resembles us.

SETI must be considered a process of elimination, which I take to already have eliminated “near by” exocivilizations, although we cannot rule out the possibility that we currency find ourselves within the “halo” of a vanished cosmological civilization.

A peer civilization only slightly advanced over our own (say 100-500 years more industrial development), if it is in fact a peer and not incomprehensibly alien, would also be asking themselves “Are we alone?” They, too, would be equally terrified at being alone in the cosmos or at having another peer civilization present. Because we know that we exist as an industrial-technological civilization, and we know the extent to which we can eliminate peer civilizations in the immediate neighborhood of our own star, we can assume that a more advanced peer civilization would have an even more extensive sphere of SETI elimination. They would home in on us as incredibly interesting, as an exception to the rule of the eerie silence, in the same way that we seek out others like ourselves. That is to say, they would have found us, not least because they would be actively seeking us. So this may be considered an alternative formulation of the Fermi paradox.

Despite the growing tally of planets discovered in the habitable zones of stars, including nearby examples at Tau Ceti which lies within our SETI exclusion zone (which excludes only civilizations producing EM spectrum signals), there is no evidence that there are other peer civilizations, and advanced peer civilizations would already have found us — and they would be as excited by discovering us as we would be excited in discovering a peer civilization. There are none close, which we know from the SETI zone of exclusion; we must look further afield. Other peer civilizations would also likely have to look further afield. In looking further afield they would find us.

I don’t believe that any of this contradicts the Copernican principle in spirit. I think it is just a matter of random chance that our civilization happens to be the first industrial-technological civilization to emerge in the Milky Way, and possibly also the first in the local cluster of galaxies. We are, after all, an accidental world. However, it will take considerable refinement of this idea to show exactly how the uniqueness of human civilization (if it is in fact locally unique) is consistent with Copernicanism — and this keeps Copernicus in my thoughts.

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Grand Strategy Annex

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Do you notice any symmetries between these poster images?

Do you notice any symmetries between these poster images?

The popularity of science fiction in contemporary culture provides important insights into the nature of the world today. These insights are more significant than the silly pulp science fiction images that featured on the film advertisement posters. The covers of pulp science fiction novels were equally absurd and equally unrelated to the content of the story.

To watch and to understand a contemporary production of science fiction (and this holds as well for reading science fiction) requires mastering a certain set of background assumptions. It requires moreover an initial flexibility of interpretation, as when one is initially exposed to a new science fiction universe one does not yet know the possibilities and limits of the technologies that shape the stories. For example, there is an important structural difference between stories that assume faster than light travel is possible (in some form or another), so that heroes, heroines, and villains can go from planet to planet more or less effortlessly, and stories in which it is assumed that interstellar travel and commerce is a long-term proposition. And there are, of course, degrees between these possibilities, and some plots that have these possibilities overlap.

It would be easy to write all day long about the relationship between technological speculation and the structure of science fiction stories, but that isn’t what I want to pursue today. Recently I wrote Themes from The Tempest after watching the science fiction classic Forbidden Planet for the umpteenth time. In that post I mentioned in particular two other science fiction films, The Day the Earth Stood Still and This Island Earth. Now I have just watched This Island Earth again and this has led me to rethink some of my earlier interpretations of both films.

I was always bothered by the ham-handed injection of religion into Forbidden Planet and This Island Earth. Now having seen both again recently, I have a little different take on what I always assumed was an uptight 1950s McCarthy-era theological jingoism — sort of like the absurdity of “I am an American Day” except in a science fiction context this becomes, “I am a Christian Day” — an exercise in profound existential insecurity. (Recall that it was 1957 that “In God we trust” was added to US currency.) Well, the scenes I have in mind may be all that after all, but they represent other cultural developments as well.

Science fiction can be understood as the contemporary incarnation of the fairy tale, simply giving incomprehensible technological explanations to account for things that in previous ages would have been credited to magic — the deus ex machina with the deus naturalized. This is essentially the position of Arthur C. Clark and his much repeated Third Law: Any sufficiently advanced technology is indistinguishable from magic.

However, the corollary of Clark’s Third Law is that magic is indistinguishable from any sufficiently advanced technology (and “sufficiently” must be understood to be culturally relative). Clark’s Third Law and its corollary together might be called the principle of equivalence for magic and technology. Given the equivalence, it is a matter of perspective whether we regard magic as primary and technology as imitating magic, or we regard technology as primary and magic as imitating technology. But the difference of perspective is important, because different people with different perspectives will see things in different ways.

Arthur C. Clark was primarily a story teller, and his “laws” are formulated poetically. For Clark, a science fiction story was a fairy tale updated for the modern world, and technology imitated magic. But no genre can be confined to the views of one man, however influential. It is more or less inevitable that there will be others who see the principle of equivalence for magic and technology in terms such that a fairy tale was nascent science fiction that was trying to do what could not yet be done with man’s technological resources, and that magic is a pale imitation of technology. We shall call the first view represented by Clark the poetic conception, and we will call the second view the naturalistic conception, since it assumes a naturalistic world view.

I think that science fiction is becoming progressively more naturalistic, and that signs of this shift away from fairy tales to stories, in which science fiction is simply another setting for a story and not a fantastic setting, is already apparent in Forbidden Planet. The religious intrusion that bothered me in Forbidden Planet can be interpreted in this way. The scene occurs near the end of the film, at the climax, when Dr. Morbius (Walter Pidgeon) is struggling with Commander Adams (Leslie Nielsen), who shouts at Morbius: “We’re all part monsters in our subconscious! — So we have laws and religion.” (Near the beginning of the film there is also the line, “The Lord sure makes some beautiful worlds.” This, however, is noticeably less obtrusive, and does not feel out of place in the dialogue.)

As irritatingly obtrusive as this line is, here religion is presented in an essentially naturalistic way as a social control, a mechanism to prevent the destructive subconscious drives of the id from wreaking havoc. Forbidden Planet is well-known for its Freudian themes, and this too can be considered an application of Freud’s point of view in The Future of an Illusion and Civilization and its Discontents. Religion and civilization impose limits on the fulfillment of instinctual gratification, and they do so because it is preferable to the alternative of barbarism and savagery.

This Island Earth is rather less sophisticated, and it cannot be assimilated to this interpretation. The religious intrusion in this film, as in Forbidden Planet, occurs near the end, hence near the climax of the action (not unlike the simple-minded condemnation of philosophers who have denied the gods at the climax of Aristophanes’ The Clouds). When Dr. Ruth Adams (Faith Domergue) and Dr. Cal Meacham (Rex Reason) are introduced to the Monitor of Metaluna (Douglas Spencer), and the plan to colonize earth and to place human beings in an inferior position is revealed, the Monitor states in a matter-of-fact way, “It is indeed typical that you Earth people refuse to believe in the superiority of any world but your own. Children looking into a magnifying glass, imagining the image you see is the image of your true size.” To which Meacham replies, “Our true size is the size of our God.”

Of the three films I previously mentioned, The Day the Earth Stood Still is perhaps the most sophisticated, and it has no intrusion insisting upon either the value or veracity of religious doctrines. There is only one mention of religion in the screenplay, and this is not in the dialogue:

INTERCUT with the above are group and individual shots of
the people in the meeting. They are the cream of Earth’s
intellectuals — scientists, churchmen, educators, leaders
of social and political thought. There are several women
among them. There are turbaned Indians, Chinese, Japanese,
several Negroes. All religions are represented. Every
important world power is represented.

The very diversity of the scene represented demonstrates a secular and international perspective that precludes the kind of outbursts detailed above. In both of the scenes I mentioned above the religious intrusion struck me as forced, artificial, and out of place — essentially as absurd and as unrelated to the story as the illustrations on the film posters shown above. I have to wonder if similar religious intrusions were suggested for the script of The Day the Earth Stood Still but were abandoned as simply too forced and artificial. But this is mere speculation on my part.

Given the distinction I drew above between the poetic conception and the naturalistic conception of science fiction, I am inclined to classify The Day the Earth Stood Still and Forbidden Planet as embodying the naturalistic conception, while This Island Earth embodies the poetic conception. In other words, This Island Earth is a fairy tale whereas the other two films are not. This may seem like an odd assertion, given that This Island Earth was based on a novel from 1952 whereas Forbidden Planet was (loosely) based on Shakespeare’s The Tempest. But I think it is a fair division. The more I think about it, the more I see how This Island Earth could be rewritten as, say, a tale from the Arabian Nights, while the contemporary elements, which include central plot devices, of The Day the Earth Stood Still and Forbidden Planet would not translate well into an earlier, pre-science ficiton idiom.

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Grand Strategy Annex

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