Review Essay of John Leslie's The End of the World

(London: Routledge, 1996), pp. vii + 310.

Quentin Smith

Western Michigan University

1. The Anthropic Principle and Human Extinction

     The End of the World is the third of the books authored by Leslie and shares with the first two an originality and boldness of thought that make Leslie's work stand out from much other work being done today. In Value and Existence Leslie argued that the reason why the universe exists is that there is an ethical requirement for its existence. In Universes, Leslie argued that considerations based on the fine-tuning of the basic physical constants confirm the hypothesis that there are many universes or that God (or an "ethical requiredness") created the universe. Many theists have taken over Leslie's argument about the fine-tuning of the physical constants in the early universe and use it as the contemporary "argument from Design" that has replaced the pre-Darwinian argument of Paley and others. Leslie is also regarded by many philosophers and physicists as the leading exponent of the anthropic principle, which he extends in THE END OF THE WORLD.

  In The End of the World, Leslie uses the anthropic principle to show that there can be philosophical arguments about how long the human species will survive. There are various possible formulations of the anthropic principle and Leslie formulates it as follows: "observers can most expect to find themselves in the spatiotemporal regions where most of them are found" (p. 190). According to Hawking, intelligent observers may be emitted from a black hole and in a large enough collection of black holes observers would be emitted occasionally. But if almost all intelligent life in the universe is found on planets that orbit stars, then intelligent observers are more likely to find themselves on planets than on edges of black holes.

   Leslie applies this to the temporal position of humans; humans are most likely to find themselves living in the temporal span where most humans are found. If humans will exist for millions of more years, we occupy an exceptionally early position in human history. This gives some reason to think that humans will become extinct soon. "We ought to have some reluctance to believe that we are very exceptionally early, for instance in the earliest 0.0001 per cent, among all humans who will ever have lived. This would be some reason for thinking that humankind will not survive for many more centuries, let alone colonize the galaxy." (p. 1)

     The Doomsday argument, which is the principal philosophical feature of Leslie's book, will be evaluated below. First, I will discuss some of the ideas in the first half of his book, which is devoted to detailing the various risks or potential causes of human extinction. Leslie displays here an impressive erudition about the relevant scientific and historical literature; he mentions dozens of potential risks (e.g., biological warfare, a pollution crisis, ozone depletion, a greenhouse effect, vacuum metastability, the accidental spread of genetically engineered "contraceptive viruses", etc.), but I shall briefly discuss the three risks that seem to me the most likely causes of early human extinction.

2. Accidental Nuclear War

    Leslie believes there is a 30% chance the human species will be extinct by 500 years from now (p. 146).¹ He seems to think the main risk at present (even if not 500 years from now) is accidental nuclear war: "Probably, however, it has been accidental nuclear war between the United States and Russia which has represented the most immediate danger to humankind since Russia's development of the H-bomb". (p. 32).

   How should we evaluate this claim? Leslie writes about ". . . the dangers of nuclear war or of pollution [and other risks]. This book will make few claims to expertise about the details of such highly complex matters. What it will claim instead is that even non-experts can see that the risks aren't negligible." (p. 3)

   Leslie would certainly admit that if expert research is consulted, this could show that what non-experts believe is mistaken. I shall suggest that the research about nuclear war (part cited by Leslie and part from other sources) indicates the probability that an accidental Russia-America nuclear war will extinguish the human race is vanishingly small and is negligible.

  There are two probabilities we need to calculate. If there is an accidental nuclear war between the US and Russia, what is the likelihood that it will extinguish the human species? Second, what is the likelihood of an accidental nuclear war between these two countries?

   The bomb which destroyed Hiroshima was equivalent to 10,000 tons of TNT, but as early as 1961 the former Soviet Union had tested a bomb of 58 million tons of TNT (p. 26). (But Carl Sagan says the Hiroshima bomb was equivalent to 13,000 tons of TNT. [Carl Sagan, COSMOS. New York: Random House, 1980, p. 322]. Adding to Leslie's observations, I would note that the largest bomb recently in America's arsenal is equivalent to 9 million tons of TNT (Scientific American, October 1987, p. 26), even though the US tested a bomb equivalent to 15 million tons at Bikini in 1954 (Sagan, p. 322). In a full-scale nuclear war in the early 1980s (before arsenals were reduced), 10,000 megatons of explosives would be dropped; there would be 16, 160 distinct nuclear explosions. (See R. Turco et. al., "Nuclear Winter", Science 222, December 23, 1983, pp. 1283-1292, and R. Turco et. al. "The Climatic Effects of Nuclear War, Scientific American, August 1984.)

   In 1982 the World Health Organization estimated a global nuclear war would kill quickly half the human population (Leslie, p. 26). The blast waves, firestorms, and gamma rays and neutrons released in the first fractions of a second, would be the immediate causes of death from the 16,160 nuclear explosions (Sagan, p. 321). The debatable question relevant to human extinction is the later deaths that are expected. The later deaths would be from radiation and nuclear winter. Is there a non-negligible probability that these would kill all humans left after the initial heat and blast effects?

   Leslie suggests that the other half would die later due to the effects of radiation (cancers, weakened immune systems that let infectious diseases run riot and numerous birth defects) and loss of food from the hundreds of millions of tons of smoke and dust that would fill the air and block the sunlight. The death of microbes upon which human life is dependent is another possibility Leslie mentions (pp. 26-28), but he refers to Sagan's COSMOS, which mentions this as a mere epistemic possibility, not as a known probability: "Many microorganisms would be killed; we do not know which ones or how many, or what the consequences might be. The organisms killed might, for all we know, be at the base of a vast ecological pyramid at the top of which we totter." (Sagan, p. 322).

   I shall first discuss the most pertinent evidence we have about deaths from radiation. The evidence of the Chernoyble disaster have shown the dangers of radiation to have been greatly overestimated by previous studies. The explosion of the nuclear reactor at Chernoyble "was comparable to a medium-size nuclear strike", which is often defined as a 3,000 megaton war, in terms of radiation released. (See "Ten Years of the Chernoyble Era", by Yuri Shcherbak, Scientific American, April 1996, p. 45.) This does not include, of course, the immediate heat and blast effects of a bomb, but that is not the relevant issue here, which is the long term radiation effects. "The destroyed reactor liberated hundreds of times more radiation than was produced by the atomic bombings of Hiroshima and Nagasaki" (Yuri, p. 45). And yet the effects are considerably less than had normally been expected. Even Greenpeace Organization, which is politically inclined towards the worst case estimates, estimates only 32,000 deaths. (Yuri p. 46). A 1997 documentary indicated that animals, such as mice, are currently thriving next to the old reactor, contrary to expectations. The genes of the mice mutated, but the mice adapted and flourished. If there are only 32,000 deaths from long term radiation effects from an equivalent to a medium-sized nuclear strike of the US upon Russia, then we can effectively dismiss long term radiation as a potential cause of the extinction of the human species in a nuclear war.

    The main research on nuclear war indicates that the blast, heat and radiation deaths pose no realistic threat to human extinction. Rather, it is nuclear winter that poses the main threat. The question of human extinction from an accidental nuclear war between the US and Russia reduces to the question of the effects of nuclear winter on the Southern Hemisphere. Humans in the Northern Hemisphere, the site of the nuclear war, will probably all be killed, but before studies of nuclear winter it was thought that most people in the Southern Hemisphere would escape death.

   However, results of numerous studies, summarized in R. Turco et al, "The Climatic Effects of Nuclear War", Scientific American, August 1984, discuss the Southern Hemisphere issue. They consider a 5,000 megaton war, which corresponds more to the late 1990s arsenals than the 1980s arsenals, since significant arms reductions have occurred since the mid 1980s. In this war, there would be 10, 400 distinct nuclear explosions. 225 million tons of smoke and 65 million tons of dust would be injected into the stratosphere of the North Temperate Zone. This would block 95% of sunlight, causing subfreezing temperatures within a few days in the Northern Hemisphere. The subfreezing temperature would last for several months. This dust and smoke cloud would be reduced to half of its original strength within 4 months and would be negligible within a year. How would this affect the Southern Hemisphere?

     The air circulation patterns of the two hemispheres normally consist of distinct Hadley cells, each of which has independent wind patterns that circle the cell. One of the Hadley cells normally extends from 30 degrees North to the equator. This is separate from another cell that extends from the equator to 30 degrees South. The danger from nuclear war is that these two cells would no longer be separate, but merge into a single cell. The 10, 400 nuclear explosions would warm the troposphere, due to the absorption of sunlight by the smoke clouds and this would cause a single Hadley cell to extend from 30 degrees North to 30 degrees South, carrying the smoke and dust clouds that block the sunlight and cause lowering temperatures. Darkness and freezing temperatures would destroy food supplies and other items necessary for survival.

    However, this Hadley cell would not extend further than 30 degrees South.  The wind patterns would protect the southernmost parts of the earth from the dust and smoke clouds. The circulation pattern below 30 degrees south is governed by a distinct Hadley cell that circulates wind from 30 degrees South to 60 degrees South. This covers the southern halves of Australia, Argentina and Chili, and includes all of New Zealand. This is sufficient for the human race to survive. Survival may mean that there are left only 100,000 people on New Zealand or southern Chili, people who are reduced to living and reproducing in Stone Age conditions. Since this is the worst case scenario of an American-Russian war for which there is any evidence, the evidence indicates that it is highly improbable that a global nuclear war would cause the extinction of the human species. (100,000 is not a small figure, since there are now 100,000 apes [orangutans, chimpanzees and gorillas] on the earth and they are able to survive despite the various legal and illegal efforts of humans that threaten their survival.)

  The probability of human extinction from accidental nuclear war between the US and Russia becomes exponentially lower when we consider the other probability, the probability that there will be an accidental nuclear war.

  Some facts Leslie mentions are not relevant evidence. For instance, he mentions the case of the B-52 bomber that disintegrated and released two 24 million ton bombs over North Carolina in 1961. (p. 32) Five out of the six safety switches on one them had failed. If one more switch had failed, the explosive equivalent of about 50, 000 Hiroshima bombs would have exploded in North Carolina. Leslie certainly recognizes that isolated nuclear accidents of this sort are not very evidentially relevant to the hypothesis of an accidental global nuclear war that destroys the human species.

   It is faulty attack-detection systems that pose a relevant sort of risk. Leslie notes some evidence in this regard: Between January 1979 and June 1980, 147 serious false alarms in the US system alone were documented. For example a wargame tape had been accidentally allowed to control the main NORAD warning displays, leading to B-52 bombers being prepared for take-off and missile crews starting preliminary launch procedures, such as inserting launch keys (p. 33).

    Perhaps, however, such evidence disconfirms rather than confirms the hypothesis that there will be an accidental war. Consider further evidence of this sort (from B. Blair and H. Kendall, "Accidental Nuclear War", Scientific American, December 1990). Between 1979 and 1984 NORAD assessed about 2,600 warning indications of an attack. Each warning requires an assessment at a special conference among the command director at NORAD, the Strategic Air Command and the Pentagon. One hundred and thirty of these warnings appeared serious enough to require further assessment. Only one or two alarms a year proceeded to the more serious stage of a nuclear alert: bomber crews are scrambled, Minuteman launch crews remove authorization codes and launch keys from safes, and command aircraft are launched.

   If 2,600 false alarms occurred over a five year period, and each one was recognized to be false and thereby did not result in an accidental nuclear war, that provides very good evidence that defective computer chips, inaccurate data and other malfunctions that generate false alarms are highly unlikely to cause an accidental nuclear war. If we use these figures to average out the false alarms since the onset of the nuclear age in the 1940s until today, including both the US and Russia, then very approximately a total of 50,000 false alarms have occurred from the late 1940s to the late 1990s.

This is evidence that false alarms are highly likely to occur over the next 50 years. But it is also evidence that these false alarms are highly unlikely to lead to accidental nuclear war. Using very rough statistics, we may say the chance of nuclear war occurring during the first half of the next century, coming from any particular one false alarm, is less than 1/50,000.

   If we combine these figures with the unlikely odds that every single person below 30 degrees South would be killed by radiation or nuclear winter, then the odds that humans will become extinct by accidental nuclear war between US and Russia are negligible. The popular belief that a global nuclear war will kill of the human species is a myth based on ignorance of the scientific data.

   Given the continued improvement of military technology, it is fairly likely that nuclear weapons will be obsolete 100 years from now (perhaps there may be developed a computer-based laser system that reliably detects and destroys every threatening missile or bomb). "Extinction by nuclear war" would then be a possible threat for only 100 more years.

3. Disease

   I believe we are much more likely to become extinct from a lowly virus or bacterium than from humankind's most grandiose accomplishments in the area of military technology. Infectious diseases are caused by viruses (from the common cold to AIDS), bacteria (which causes smallpox, diphtheria, tuberculosis, etc), rickettsiae or parasites (e.g. the protozoa of malaria).

    An inductive examination of past actualities suggests that disease is the most likely cause of human extinction. In the 14th century plague, between 1/3 and 2/3 of Europe's population was killed by the plague. (Leslie cites from a source that says 30%.) The plague killed about 25 million people.

   The second biggest catastrophic disease was the Spanish Influenza virus, which between September 1918 and November 1918 killed 20 million people, twice as many as were killed in WWI. No cure was ever found for the Spanish Influenza; rather, the virus disappeared of its own accord. About 700 million people were seriously affected, which represented about 1/3 of all people then alive. Although Americans entered the army in 1917-1918 much more afraid of the Germans than of nature, many more American soldiers died from the flu than in battle. Not coincidentally, many more soldiers died from illness than from enemy fire in the American Civil War and many other wars. Even in highly technological battles, there are more causalities (killed, wounded, sick) caused by sickness than from enemy fire; for example, in the Battle for Moscow, November 27 1941 to March 31 1942, there were 376, 000 German causalities from enemy fire and over half a million German causalities from various illness. (Albert Seaton, The Battle For Moscow: New York, A Jove Book, 1983, p. 291.) Even in many situations where humans try to kill each other with their most advanced weapons of death, natural factors are ascendant as the main cause of causalities.

    The Black Plague and the Spanish Influenza epidemic are the nearest humans have ever come to being extinct. The germs for the bubonic plague and the Spanish Influenza have a "infection\death ratio" lower than some other diseases; for example, the Ebola virus kills 90% of its victims but the bubonic plague 50%. (Leslie, p. 77). It is a matter of chance or luck that bubonic plague and Spanish Influence did not have a 100% death rate; if the Spanish Influenza had infected everyone and had a 100% death rate, the human race would have become extinct in late 1918.

   AIDs has a 100% death rate, but recently some scientists suggest that the progression from being HIV positive to AIDS is slightly less than 100%. Leslie notes: " . . . it had been a matter just of biological chance that AIDS wasn't as highly contagious as the common cold." (p. 77). 750,000 Americans now have the virus and more than 350,000 have died; worldwide, 30 million people have HIV (S. O'Brien and M. Dean, "In Search of AIDS-Resistance Genes", Scientific American, September 1997, p. 44). N. Myers estimates that one-fifth of the earth's population, which means over one billion people, will eventually die from AIDS (Leslie, p. 80). Leslie dispels some popular misconceptions about HIV infection, e.g., he notes that 80% of those infected with HIV "have contracted it through heterosexual activity" (p. 79).

    Bacteria and viruses were the first life forms to evolve, about 3.5 billion years ago, and are the most long lasting or "fittest" forms of life. Humans (homo sapiens sapiens) evolved only 100,000 years ago (give or take a few thousand years) and are the species most susceptible to death through being affected by various environmental causes, e.g., invading viruses. It seems to me that the present and past evidence about lethal bacteria and viruses make an "inductive argument to death from disease" the best argument for human extinction. Given that we have antibiotics, but no comparable antiviral agents, the most likely cause of extinction is a virus.

   However, as in the case with nuclear war, the odds for complete extinction are exponentially lower than the odds for massive deaths or near extinction. Wind patterns and water patterns are insufficient to infect every person on earth and infection would have to be produced by human or animal contagion. This requires that each human habitat eventually be reached by carriers of the virus. The "worst case" scenario would be, in part, similar to the spread of the AIDS virus, where humans can travel for up to ten or fifteen years without any visible signs of illness. If we add to this long incubation period a virus that is as highly contagious as the Spanish Influenza, then we have a worst case scenario. In order to have human extinction, we need the added requirement that there are no pockets of human population that are isolated from outside visitors during the period of contagion, sickness and death. But there are many such populations, e.g., on various islands in the Pacific and Atlantic Oceans, however small they be, and these would survive the disease.  All that is needed for survival is, say, an isolated band of 10,000 people or so in the Northern Latitudes who are self-sufficient in their food supplies and are able to reproduce. Extinction from disease is the most likely threat to humans over the next few centuries, but the probabilities here are still so low that they are virtually negligible.

3. Comets and Asteroids

   If you are an American, what sort of natural disaster is most likely to kill you? A hurricane, flood, tornado, snow blizzard, forest fire, or famine? The answer according to NASA studies, The Economist and other sources is the impact of a comet or asteroid on earth. (Leslie, pp. 84-85). The most conservative estimate is that the chances are one in two million. The most liberal estimate is that there is a 1 in 200 chance that in a fifty-year life time a person would die from an extra large impact of a comet or asteroid, one killing at least 500 million people. But these figures are not about impacts that will wipe out the entire human race.

    There have been at least five mass extinctions in the Earth's biological history. The last mass extinction occurred 65 million years ago, saw the end of dinosaurs and enabled mammals to evolve and replace reptiles as the dominant life form. Tree shrews evolved into prosimians (the earliest forms of primates, one of the most developed forms of mammals), which lead to anthropoids (about 45 million years ago), hominoids (about 20 million years ago), hominids (about 5 million years ago), homo sapiens (150,00 years ago) and homo sapiens sapiens (about 100,000 years ago). (See Avers, Process and Pattern in Evolution. New York: Oxford University Press, 1989.) This last mass extinction, which made the prosimian/homo sapiens sapiens line possible, is now thought by many (as Leslie correctly points out) to be the result of an asteroid hitting the Yucatan peninsula in Mexico. It exploded with the energy of 100 million megatons of TNT, about ten thousand times the energy locked up in the world's nuclear arsenals when at their largest (Leslie, p. 82).

   Leslie picks the year 2000 as the year most likely for humans to become extinct, since he thinks computers will not adequately be able to handle the time change. No plausible evidence is provided for this claim. Leslie mentions that NASA postponed a flight that would straddle the year's end because of this problem (p. 96), but his suggestion that an accidental nuclear war may be started because military computers cannot handle the change of date is unsupported and primae facie implausible.²

   If one has to pick a year for extinction, the most likely year is 2126. At this time a comet (named the "Swift-Turtle"), which is the same weight (a trillion tons) as the asteroid that caused the mass extinction 65 million years ago, will pass the Earth's orbit at a point at which (if present calculations are right) the earth will be only two weeks distant. If the present calculations are wrong or if causal factors slightly affect the Swift-Turtle, the comet could crash into the earth, causing the 6th mass extinction.

    The greatest mass extinction occurred about 250 million years ago, wiping out between 75 and 96 per cent of all species. Several hypotheses have been formed about its causes. Some have claimed there is evidence of an asteroid crater, the same size as the Yucatan asteroid crater (300 kilometers across) in the southern part of Gondwanaland (a huge continent in which South America, Africa and Antarctica were joined).

    Some suggest that about once every thirty to one hundred million years the earth is hit by a comet or asteroid large enough to vaporize the oceans and cause mass extinction. (Leslie, p. 83)

    If Swift-Turtle in fact misses us, which it probably will naturally or else by our launching an explosive device to alter its course, the likelihood of extinct by comets or asteroids in the next few centuries is very close to zero. Once one recognizes that the probability of an accidental nuclear war or disease killing off the entire species is considerably lower than a war or disease killing off a very large segment of the population, then Leslie's subjective betting odds of 5% (his odds prior to taking into account the Doomsday argument) for extinction by 500 years does not seem warranted. The evidence suggests that the probability is exponentially lower than one per cent. In terms of complete extinction, there is nothing in sight that any reasonable person should worry about, even if we should worry that a new virus might kill off a major segment the human species some time in the next two centuries.

4. Evolving into Intelligent Robots

      Nuclear war, disease and asteroid/comet impacts seem to be the most likely causes of human extinction. But there is a completely different sense in which we may regard humans as extinct by 500 years; they may well voluntarily evolve into a different species, androids or computer intelligences.

   Leslie does not present the following predictions, but I believe they are reasonable:

       The probable next step of evolution will be unique in that it will be voluntary; humans will choose to transform

        themselves into computers.

   This will occur in three stages. The artificial heart invented and applied a few decades ago will eventually lead to the development of artificial organs of all sorts. The knowledge of the brain, presently extremely limited compared with knowledge of other organs, will increase to the extent that changes in parts of the brain will become possible. New sorts of surgery will become available that will enable DNA, neurons and neuronal circuits to be implanted or altered to rectify head injuries or cure illnesses ranging from Alzeihmer's disease to Downs syndrome to schizophrenia. A guess that is more conservative than any of those I have seen in the scientific and medical literature is that this will occur 150 to 250 years from now.

   The second stage is "normal" people deciding to improve their memory, intelligence, happiness, goodness, etc., by having large parts of their brains transplanted or altered. Eventually the limbic system as well as the cerebral cortex will be able to be manufactured and every organ of the human body could be built artificially. The knowledge enabling this to occur will involve knowing enough of the DNA structure to construct a human being; people will be able to choose the DNA of their (technologically "adopted") children. Eventually, all humans will become artificial humans, being the result of selected DNA or, more likely, of carriers of "genetic information" that are more long-lasting and impervious to damage than DNA molecules. A conservative guess is that we will have the technology to do this in about 500 years. The computer scientist Hans Moravec (MIND CHILDREN: Cambridge: Harvard University Press, 1988) says the entire human brain processes information at 10 teraflops. The general consensus of computer scientists is that a 1,000-teraflop range computer will be developed by 2002 (Henry Burkhardt, "Computing in Science", Science 256 (1992), p. 51.; at the time of Burkhardt's writing, there was the know-how to produce at most a 2 teraflop computer.)

    Humans have used every available technological discovery (surgical, medicinal, etc.) to improve their physical and mental states and it is highly unlikely this natural or innate propensity for technological self-improvement will somehow "vanish" from human nature once we have the technology to make intelligent organisms and completely remake our own brains. Most people now do not believe this will happen for religious reasons, but religious beliefs (and what counts as "religious beliefs") change with time, circumstance and culture. Homo sapiens sapiens will want to program these computer intelligences to include what we value, such as artistic appreciation and a meaningful life. One advantage of these computer intelligences is that they can be programmed to have religious or spiritual needs, or the need for a meaning to life, that are fulfilled by what established scientific knowledge discloses to be the "purpose" of life (viz., survival and reproduction) and the "purpose" or direction of the universe (viz., the universal tendency towards perfect thermodynamic equilibrium and maximal disorder). Religious belief or belief in a meaning to life and the universe will no longer be based on the tenuous, contentious, individually and culturally divergent, assumptions and arguments that homo sapiens sapiens currently rely upon, but will be based on universally verified and evidentially clear scientific facts. One may even say that the current "spiritual" goal of homo sapiens sapiens should be to become as like as possible to these future computer intelligences (compare with "as like as possible to Christ or the Bhudda").

   Leslie would reject such naturalism in ethics, but I believe a global, naturalist version of Thomas Hurka's theory of perfectionism (cf. Hurka's Perfectionism [Oxford University Press, 1993] can sustain such a theory. I developed such a version of Hurka's perfectionism in Ethical and Religious Thought in Analytical Philosophy of Language (Yale University Press, 1997). Leslie's argument against naturalism in ethics is based in part on a questionable representation of John Mackie's theory. Leslie says Mackie believes it is synthetically necessary that there are no nonnatural moral facts and Leslie responds that the belief that this is synthetically necessity is less plausible than the belief that it is synthetically necessary that there are such moral facts (pp. 165-166). But Mackie does not say this: he rejects the very idea of synthetic necessity as a "queer" idea and says it is an a posteriori, synthetic and contingent truth that there are no nonnatural moral facts. (John Mackie, Ethics [Penguin Books, 1977, p. 39])

 5. The Doomsday Argument

    Let us now turn to the main philosophical substance of the book, what some may consider a "paradox about inductive logic" and which is called the Doomsday argument.

   Leslie presents the Doomsday argument almost entirely in terms of analogies. This conforms to Leslie's belief that rigorous and technical arguments are a less epistemically reliable guide to truth than appeals to intuition and imagination. This is a common belief among postmodernists or continental philosophers, but it is an unusual position for an analytic philosopher to hold, especially for a person like Leslie who has a highly developed capacity for logically rigorous and scientifically technical thinking. The reliance on analogies makes it hard to decipher the logical structure of the Doomsday argument, which consequently make it an elusive target and hard to "refute" or "prove". In the following I shall present the argument in a non-analogical manner.

    First let us consider some population statistics that are relevant to the argument. 10,000 years ago there were more than 6 million humans. In A.D. 1, there were 300 million humans. (Levin, THE EARTH THROUGH TIME, fifth edition, Saunders College Publishing, 1996, p. 570).

    Leslie says that in 1800, there were about one billion humans; in 1900, two billion humans; in 1950, four billion humans. But Levin (p. 570) says in 1970 there were 3.6 billion humans.

     According to Leslie, in 1997 there are about six billion humans. According to Levin, in 2000 thee will be 7.5 billion humans and in 2010, more than 10 billion humans. Leslie's figures are that in 2030, there are expected to be 10 to 12.5 billion humans and that in 2100, there are expected to be 27 billion humans.

   Up to the present, there have existed about 70 billion humans. If there now exist 6 billion humans, then almost 10 percent of humans that have ever lived are now alive. If the human race becomes extinct in AD 2100 or 2150, adding tens of billions of more humans to the figure of 70 billion, then the present generation contains roughly between 5-8 percent of all humans that ever will live. But if humans last for millions of more years, then the present generation contains much less than .000000001 of all humans that will ever live. Since it is more probable that we should find ourselves among 5-8 per cent of all humans than among a generation that contains .0000000001 of all humans, this increases the likelihood that humans will become extinct in a century or so rather than in tens or hundreds of millions of years.

   Leslie states his argument about being among the earliest group of some duration. If we are among the earliest 10 percent of all humans that will ever live, then the total number of humans will be 700 billion. This figure may be reached in a few centuries, perhaps as earlier as 2300 or perhaps near 2500, depending on whether the population continues to increase exponentially or its increase gradually levels off.

    Leslie argues that if you think that there is merely 1 per cent chance that the human race will be extinct by AD 2150, then if you take into account your position in time and Bayes' theorem (and adopt the assumption that the world is not radically indeterministic), you will revise your estimate to thinking that there is slightly over 50% chance that humans will be extinct by AD 2150 (p. 201-02.)

    Bayes's theorem gives us four probabilities. (i) P(h/e) is the probability that h is true, given the evidence e. (ii) P(h) is the prior probability of h, the probability of the hypothesis h before the evidence e is taken into account. (iii) P(e/h) is the probability that e would be true if h were true. (iv) P(e) is the probability that the evidence e would obtain regardless of whether h or not-h is true. Bayes' theorem relates these probabilities as follows:

    P(h/e) = [P(h) P(e/h)] divided by [P(h) P(e/h) + P(not-h) P(e/not-h)]

Applying this to your belief that there is only a 1% probability that the human race will be extinct by 2150, we have the following assignments of values to the variables. For simplicity's sake, we suppose with Leslie there are only two alternatives, extinction by 2150 or surviving for thousands of centuries.

h = the human race will be extinct by 2150

e = a person finding herself alive in 2000

e/h=  a person finding herself alive in 2000, given the race will be extinct by 2150.

(not-h) = it is false that the human race will be extinct by 2150 (which we are taking as equivalent to the human race surviving for thousands of centuries)

e/not-h = a person finding herself alive in 2000, given that it is false that the race will be extinct by 2150 (and will survive for thousands of centuries).

Thus, for you

P(h) = 0.01

P(e/h) = 0.1

P(not-h) = 0.99

P(e/not-h) = 0.001

If we place these values in Bayes' theorem, we have:

P(h/e) = [0.01 x 0.1] divided by [0.01 x 0.1 + 0.99 x 0.001]

Calculations show that p(h/e) is approximately 0.5; thus, one's risk estimate shifts from 1% to about 50%. This enormous shift is for some the "shocking" import of the Doomsday argument. Furthermore, it can easily be seen from the calculations that the longer one expects the human species to survive, if it passes the year 2150 safely, the greater the probability one should assign to extinction before 2150. If one expects humans to colonize the galaxy and live for a long time after our sun explodes 5 billion years from now, then the probability of extinction before 2150 increases to over 99%. If we expect survival for hundreds of trillions of years or more, then we should believe there is over a 99.99% chance that the human species will be extinct in the next 10 seconds. This is indeed shocking.

   This argument certainly appears paradoxical or at least "controversial", as Leslie acknowledges. But Leslie finds no reason to disbelieve the argument (given the premise that the world is not radically indeterministic) and has argued at length that previous or possible attempts to refute the argument are unsuccessful.

6. Do Statistics Causally Influence our Extinction?

     Leslie gives as his reference class the set of all observers or intelligent beings that exist as a result of intelligent life on earth. This is taken to cover the computers into which humans may voluntarily "evolve". The earliest members are taken to be homo sapiens, who include Neanderthals, and which (by the classification Leslie uses) evolved about 600,000 year ago (p. 256).

   Leslie excludes Australopithicines, who evolved about 4.5 million years ago. Hominids first evolved 4.5 million years ago, their first representatives probably being Australopithecus ramidus (Levin, THE EARTH THROUGH TIME, p. 558) and the latest being homo sapiens sapiens, who evolved about 100,000 years ago. In determining what counts as a typical or atypical member of this class, we take into account only one's temporal position in human history. ("Human" is here used to refer to any member of this class, from a Neanderthal to the earth-originated computer intelligences.) This follows from the definition of the reference class: it is the class of all earth-originated intelligent beings that are ordered in terms of temporal position (in terms of the temporal place in human history the being occupies). Leslie suggests that "intelligence" implies the ability to form the concept of one's temporal position in human history. Given that the only variable feature that belongs to the definition of this class is temporal position, being exceptional and being unexceptional are definable only in terms of this property. Given this, people in the late 20th century are exceptionally early if humans will live for millions of more years. Since we ought to prefer theories that make us unexceptional if there is a plausible theory that makes us so, we ought to conclude that it is more probable than we otherwise thought that we will die within 500 years.

       I believe the structure of the Doomsday Argument can best be analyzed if we consider h to be the hypothesis that the human species will become extinct soon, and e the evidence of various risks, such as evidence for extinction through disease, asteroid impacts or nuclear war. If d is the doomsday argument, then p(h/e & d) > p(h/e). Suppose one thinks there is a 30% chance the human race will be extinct 500 years from now, that is, p(h/e & d) = 0.3 Why should this value be higher than p(h/e)? Leslie's argument is that it is improbable that we are very exceptionally earlier among all humans ever to live. This, in brief, is the argument "d" in p (h/e & d) > p (h/e).      

    We should separate d into two components, one being (o) our observed position in time and the second being a criterion (c) used to select among competing theories, such as the criteria of simplicity or explanatory power. The relevant criterion c is that "prima facie, we should prefer theories which make our observations fairly much to be expected, rather than highly extraordinary" (p. 187). Our observed position in time (o) involves the conditional that if the human species will last for thousands of more centuries, then we are among the earliest 0.001 per cent of humans, whereas if we became extinct in a century or so, we are among 0.1 of all humans who will ever have lived. We would expect to be among an ordinary position in the history of the human race, a position including ten percent of all humans who will ever have lived, rather than an extraordinary position, a position that includes only one thousand percent of all humans who will ever live. Combining the observation o and the theoretical criterion c, the Doomsday argument may be represented as the argument that p(h/e & o & c) > p(h/e), where h is the hypothesis that we will become extinct soon and e the causal factors that could extinguish the species.                          

   Naturally, it is not d (= o & c) that will cause our extinction; rather, the cause will be among the items in e, the risks to our survival. The role that d plays is to increase the likelihood that an item in e will cause our extinction.

   But how could d do that? An item in e is a possible physical cause of humans' extinction. For each of these items, there is a certain probability that it will actually cause our extinction. There is no problem with imagining certain physical changes on the earth or in our solar system that will make one of these possible causes c more likely to be actual than c otherwise would have been. But how can the argument d make c more likely to be actual?

How could the fact that "it is more probable that we are among the earliest 0.1 of humans than among the first 0.001" make it more likely than it otherwise would have been that the incoming comet Swift-Turtle--instead of missing the earth--will hit the earth and wipe out the human race in AD 2126? Statistical unusualness in a randomized reference class is not a physical cause or any other sort of cause that can affect the direction of a comet.        Perhaps there is nothing here that appears paradoxical. Imagine that the balls in an urn include only one ball that is white. It is easy to imagine other balls hitting this ball and knocking it into a position where it becomes more probable than it otherwise would have been of being the only ball to fall out of the urn when a latch is lifted. We also accept "the fact that there are only three balls in the urn makes it more likely that the white ball will fall out of the urn than it would have been if there had instead been one thousand other balls."

    But this urn analogy does not appear applicable, since the added information that there are only three white balls is information about the causal factors at work. The information is about the causally preventive factors, the factors that would operate in the relevant future situation (e.g., the turning of the urn) that would physically prevent the white ball from falling out of the urn. The information is that these preventive factors are considerably less numerous in the case where there are only three balls in the urn. However, "we are among the earliest ten percent of humans rather than among the earliest one thousand percent" does not give us more information about the causal factors at work in allowing or preventing humans' survival for thousands of years in the future.

   A defender of Leslie's argument might well call into question the premise, "x can increase the likelihood of possible causes becoming actual if and only if x causally influences the relevant situation". In particular, the defender might say that the probabilities we are discussing are subjective probabilities, not objective propensities, finite frequencies or limiting relative frequencies. Leslie does not say which theory of probability he is using, or which sort of probability he is discussing, but his argument is most plausibly stated in terms of subjective probabilities. (Leslie discusses probability on pages 243 and 150ff.) Accordingly, his argument would that my subjective probability or the "betting odds" I would accept relevant to the hypothesis that some possible extinction cause will become actual would be increased if I added to my stock of knowledge the doomsday argument d. If I take into account my position in time in the history of the human race, I would believe the odds are higher that some possible cause will become actual.

    But there still is a problem. If I consider myself as a statistically random member of the human species and as occupying an unusually early position in human history, can this statistical unusualness give me reason to believe that some potential cause has a greater likelihood of becoming actual than I would otherwise have believed? If so, I would have to believe that the fact that x occupies an improbable position in a statistically random sequence of items makes a large comet (for example) more likely to hit the earth in the next 200 years than if x occupied a probable position. But how could x's statistical position do this otherwise than by causally influencing the comet? Only a causal influence upon a physical system that is a potential cause of a certain effect can increase the likelihood that this system will be an actual cause of the effect.

  Indeed, the fact that we are merely considering the totality of all past, present and future humans as a randomized reference class shows that this randomized class is not a physical existent, but a concept. Statistical unusualness in this conceived class is itself a concept. But a concept cannot physically cause a comet to strike the earth or the Spanish Influenza to return in a more deadly form. (Leslie is not relying on the neoplatonic theory of his Value and Existence and Universes--that abstract objects can cause concrete objects-- to drive his Doomsday argument.)

7. Are Observed Regularities Evidence of Doom Soon?

      Leslie responds to the argument that our position in time is not a cause of our extinction in this way: "The doomsday argument is simply an argument for re-evaluating the risks associated with those [causal] mechanisms, on the basis of our observed position in time. Observations can suggest this or that future catastrophe without having to be potential causes of it. Movements of clock hands may be mere indications that a bomb is about to explode, rather than being parts of a triggering process". (p. 213) Leslie plausibly makes the point here that indications need not be causes of what they indicate. But is this point and the analogy he gives sufficient to ward off the objection that our statistical unusualness in a conceived class cannot increase the probability that potential causes of our extinction will become actual?

   Suppose I know that the triggering mechanisms of a bomb will cause it to explode at noon. If I look at my watch and to see to my surprise that it is later than I thought, that it is 11:58, then this observation will justify revising upwards my estimate of the probability that the bomb is about to explode. Why is this? Because of my past observations of causal regularities in nature; I know that in most cases bombs have gone off at the time they have been triggered to go off, and I know that in the past my watch has reliably indicated the correct time. The indication that the bomb will explode is based on causal regularities, even if it is not a cause of the bomb's explosion.

     Is there anything analogous in the Doomsday case? What are the past, observed, causal regularities that justify the revision of my subjective probability for the end of the human species? There are none. Millions of species of organisms have lived on the earth. In every observed case, there have been members of the species that have been among the earliest 0.01 per cent of that species. How could these observed regularities be evidence that our species does not have members that are among the earliest 0.01 per cent?

     One might well see how Leslie would respond to this "observed regularities objection". The issue is not, he might say, the probability that the human species has an earliest 0.01 per cent. The issue concerns the probability that we (all of us alive today) are among the earliest 0.01 per cent. It is more probable that we are among the earliest 0.1 percent of all the humans that will ever live than that we are among the earliest 0.01 percent, and this increases the subjective probability that the human species will become extinct in a century or so rather than thousands of years from now. Given this, the fact that there is an earliest 0.01 percent of other observed species is not relevant to Leslie's argument.

   If this is granted, then the bomb/clock analogy is not relevantly analogous to the doomsday scenario. The bomb/clock analogy relies on past, observed causal regularities to justify revising upwards my subjective probability based on the "indicating"; but the past, observed causal regularities (that  otehr species have an earliest 0.01 per cent) are not relevant to the sort of "indicating" (our position in a randomized reference class) that pertains to the Doomsday scenario.

  8. Urn Analogies and the Big Bang

   Leslie may not agree that causal facts and observed regularities play no role in his argument. For example, there may be another urn analogy that avoids the aforementioned problems about causality. An urn analogy may be used to ward off the objection that occupying any temporal position is equally unlikely as occupying any other temporal position and thus that the earliest temporal position is not special.

   We should prefer theories that make our observations fairly much to be expected, rather than highly extraordinary. Is the observation that we occupy the first 0.0001 per cent of human history an unexpected observation? Would it be unexpected to observe ourselves as occupying a period in human history when between 56.9999 and 57 percent of that history has elapsed? A critic of the Doomsday argument may say that any position drawn out to 4 decimal places is a highly unlikely place to find myself and each such position is equally unlikely. Accordingly, the theory we should adopt is that we should expect ourselves to occupy, with equal probability, any one of these temporal positions. Thus, there is no need to assume Doom Soon in order to have a theory that makes our observed temporal position something to be expected.

    Leslie appears to formulate and answer a similar objection in terms of an urn analogy. "'What's so special', it may be protested, 'about coming out as early as we did from the imaginary urn of all humans, past, present and future? How could earliness be anything special? Being drawn in the first ten would be no more special than being drawn somewhere among draws 767,421 to 767,430. The answer to any such protest is that your name coming from an urn in the first ten can be 'special' when you have some viable theory, for instance that there were only about fifteen or only about a hundred names in the urn, instead of a million, which makes being drawn in the first ten specially much to have been expected, or at least not very unlikely." (pp. 208-209).

    What is the logical structure of this "urn analogy"? Leslie seems to be supposing that when we make the first ten draws, we do not know how many names are in the urn. He says that my name coming from an urn in the first ten draws is "special" if there is a viable theory which makes it being drawn in the first ten draws probable or not very unlikely. It is probable if the "viable theory" is that there are fifteen names in the urn. Is there also a viable theory for the draw between 767,421 and 767,430? The viable theory is that the urn contains a set of million names and that I should expect to draw my name from one of the many subsets of names with 9 members, each of which by itself has an equally low probability of being drawn.

   Leslie might respond that the set of 10 names has the property of being likely to contain my name (if there are 15 names in the urn), and this is what "special" means, whereas the set of 9 names between 767,421 and 767,430 has the property of being unlikely to contain my name (if there are a million names in the urn), and thus is not "special".

    If h is the hypothesis that there are 15 names in the urn and e is the fact that I draw my name among the first 10 draws, then e increases the probability of h. p(h/e) > p(h). Is this a relevant analogy?

    Drawing my name among the first ten draws is an effect of a past causal factor, somebody placing 15 balls in the urn. The hypothesis h is equivalent to this causal hypothesis and the hypothesis h' is that a cause placed a million balls in the urn. The evidence e is for the existence of a past cause of a certain sort, viz., the one specified by h. The analogy for human extinction may be that h is the causal hypothesis that initial conditions at the big bang determined (we are here assuming a deterministic universe) human to become extinct in (say) 2150 A.D. and h' the hypothesis that these initial conditions determined humans to survive for millions of years beyond 2150 A.D. The evidence e is that our position in the randomized sequence of humans is  the late 20th century.

   Relating this to my analysis of the structure of the Doomsday argument in terms of the extinction hypothesis, observed risks, our observed position in time and the theoretical criterion that we should prefer theories that make our observations fairly much to be expected, we may say that the probability associated with the risks should be understood as built into the prior probabilities p(h) and p(h') of h and h', which are hypotheses that initial conditions at the big bang lead by a causal chain to the extinction of humans at a certain future time. We can see that our familiar problem returns, for p(h/e) cannot be greater than p(h), for our position in a conceptualized randomized reference class cannot affect the initial conditions at the big bang so as to increase the likelihood that they will led to our extinction in 2150 A.D. This is an instance of the more general principle that an abstract object (the concept of our position in a conceptually randomized reference class) cannot act upon a concrete object or situation and make certain of its causal powers more likely to be exercised and certain other of its causal powers less likely to be exercised.

9. Probabilistic Independence

   Problems with causality prevent the probabilistic independence that is required for the randomization of the class of all humans that is required to consider our position in history as random. Leslie wishes to consider late 20th century homo sapiens as random members of the reference class of homo sapiens and earth-originated intelligences. This implies that each member of the class is probabilistically independent of each other. Leslie does not explain his notion of randomness. It is not Von Mises' notion, Kolgoroff's, Earman's, Fine's or that of other philosophers. It seems to be the notion of randomness that statisticians employ when they discuss random sampling. According to this notion of statistical randomness, a random variable is a quantity X capable of taking on different numerical values; the statement that X lies in a certain interval of real numbers is assigned a certain probability. A random variable X is a function whose domain is the set of possibilities and whose values are real numbers. The set of possibilities is a set of mutually exclusive and exhaustive outcomes of some repeatable experimental procedure (this set is the "outcome space" of the experiment). For example, the outcome space would be the number of heads obtained in n tosses of an unbiased coin. A sample specified by n random variables X1, . . . Xn is random if the Xi are probabilistically independent and have the same probability distribution. Two hypotheses h1 and h2 are probabilistically independent if and only if p(h1 & h2) = P(h1)P(h2); if the probabilities are greater than zero, P(h1/h2) = P(h1) + P(h2/h1) = P(h2). The Xi have the same probability distribution if and only if the probability of Xi's taking any value is the same as Xj's.  

   However, the members of Leslie's reference class are not probabilistically independent. The probability that I exist in the late 20th century is not independent of the probability that my parents exist some time in the 20th century. Nor is the probability that homo sapiens sapiens evolved about 100,000 years ago probabilistically independent of the earlier evolution of homo sapiens. Suppose we write all the names of the members of Leslie's reference class on pieces of paper and put then in an urn. Are the slips of paper probabilistically independent? Even if they are, the only conclusion that demonstrably follows is that a slip of paper with my name drawn on it may be drawn unusually earlier. Leslie does not show there is a relevant analogy to this slip of paper and my actual existence in the late 20th century. In fact, there is a relevant disanalogy, namely, that the slips of paper are not born from other slips and are not causes or effects of other slips of paper. This disanalogy prevents the urn analogies from holding. This is all the more the case since the members of Leslie's reference class are (by definition) causes or effects of some other members of that class. It is essential to humans to be caused by other humans (except for the very first humans, which are effects of other hominids). This is true even of natural subclasses: the evolution of homo sapiens is a cause of the evolution of homo sapiens sapiens and the evolution of machine intelligences will be the effect of the technological work of homo sapiens sapiens.

    Leslie implies (pp. 221-222) that (for example) he is not considering his exact genes, memories of his 20th century parents, etc., but genes and memories of the general sort common in the 20th century. But this merely locates the probabilistic interdependencies among general rather than individually unique properties of the members of the reference class. John Leslie (qua possessing genes and memories of a 20th century sort) is dependent on the existence of parents of a 20th century (or late 19th century) sort.

   On page 247, Leslie discusses a "small room/large room" analogy and asserts that it is irrelevant whether the "large room people" are generated by the "small room people". Let us take this idea to an extreme and say there are no generative, causal dependencies among any of the people in the rooms. It follows that these are not really people or anything relevantly similar to people and thus that the "small room/large room" analogy is not a relevant analogy to human survival. The more probabilistic independence is built into the "analogies", the less relevantly analogous these "analogies" become to the actual situation of human history.

10. Conclusion

   The Doomsday argument might well outweigh in value the ideas of its various critics, including the ideas in this essay. My criticism is incompatible with Dieks' (in THE PHILOSOPHICAL QUARTERLY) and Erkhardt's (in MIND and JOURNAL OF PHILOSOPHY), and with the numerous other criticisms Leslie lists in his book. Each previous critic has presented his or her criticism as an expose of the "obvious" fallacy of the Doomsday argument. By now, I think, criticisms should be advanced with considerable more caution.  William Eckhardt says ". . . critiques that have not been snidely dismissive have tended to be as mystifying as the doomsday argument itself". ("A Shooting-Room View of Doomsday", JOURNAL OF PHILOSOPHY 94 [1997], p. 244.) In addition, it should be noted that some, such as Anthony Flew in his review of Leslie's book in PHILOSOPHY (January, 1997), have regarded Leslie's Doomsday argument as obviously sound. These facts suggest what may be the lasting value of Leslie's book, namely, a certain analogy with Zeno's work.

    Zeno's paradoxes are paradoxes about the application of mathematics to motion; likewise the Doomsday argument is a paradox about the application of Bayes' theorem to human survival. In both cases, the arguments appear intuitively plausible, the conclusion appears intuitively implausible, and the critics' many and varied counterarguments seem too difficult or complicated to be intuitively sure if they really are plausible or not. The Doomsday argument and responses to it show that our fundamental concepts of probability are unclear or at least that there is little consensus among experts in probability theory about the meaning of the main ideas ("randomness", etc.) or the truth of certain theses. For this reason alone, the paradox may well outlive all its critics.³

Notes.

1. This is the estimate Leslie gives in his book. In a private communication, he explained that his estimation of doom prior to taking into account the doomsday argument is 5%, and 30% is his estimation that takes into account Doomsday reasoning. The reason it is not higher than 30%, he says, is that he believes the universe may well be indeterminist to a significant extent and that this lowers his estimate of doom to 30%.

2. Leslie reports (private communication) that S. Reeve, J. Adams and J. Davison wrote in World Press Review, September 1996, p. 37, that "The most extreme forecasts are that 45,000 mainframe computers will crash, paralyzing whole societies. An American study suggests that preventing a global millennium meltdown may cost around $600 billion . . .  [In the US] the Defense Department has even warned of a potentially 'catastrophic' outcome in which the country would be unable to respond to military threats and some weapon systems could run out of control."

3. I wish to thank Arthur Falk for discussions of the Doomsday argument and John Leslie for providing many helpful criticisms of an earlier draft.

10. The Survival Argument

   If I consider myself as a member of Leslie's reference class, then I consider only what I have in common with all homo sapiens (Neanderthals, homo sapiens sapiens, etc.) and earth-originated intelligent machines. However, if I consider my membership in other reference classes, then we get "Survival Arguments".

   Suppose I consider myself to be an animate earthling. Using Leslie's reasoning, I would not expect myself to be exceptionally at the end or beginning of all animate earthling, but somewhere in or near the middle. Animate beings have lived on the Earth for at least 3.5 billion years. The sun will engulf the earth in about 5 billion years; this means the class of animate earthlings will exist at most 8.5 billion years. Considering myself to be 3.5 billion years later than the beginning and 5 billion years before the end of animate earthlings is very unexceptional and is the sort of observation to be expected. (If there are animate beings whose ancestors are earthlings but take up residence elsewhere in the Milky Way galaxy, they are animate but are not earthlings.) This Survival Argument suggests (by Leslie's own principles) that it is very unlikely that there will be an extinction of humans, and all other animate beings, in the next few centuries or even in the next few millions of years.

   A similar Survival Argument can be developed if I consider myself as a member of the reference class of all animals, or all veterbrae or of all mammals.

    If we assume Leslie's principles and take all the Survival and Doomsday arguments into account, they effectively cancel each other out and are overwhelmed by the probabilities pertaining to the potential causes of the demise of humans. All we need consider is p(h/e) in the probability p(h/e & o & c).

     Leslie objects to allowing the reference class to include all hominids, or all anthropoids, or all mammals, or all vertebrae, or all animals or all organisms. "Widenings of reference class can easily be taken too far. For example, we ought to think twice before accepting any widening which counted as 'observers' even more primitive forms of animal life. These might well not be conscious at all." (p. 260)

   It seems that Leslie is stipulating that being an observer or being conscious is necessary in order to be a member of the reference class. Why impose this restriction? Perhaps because we happen to be interested in the survival of intelligent beings? This may be our interest, but this is not a criterion for choosing the reference class. Rather, the procedure should be to include the beings in whom we are interested, which includes at a minimum homo sapiens sapiens, in all the reference classes that are relevant to determining their survival. It turns out, however, that all such reference classes share with homo sapiens sapiens the property of being liable to extinction by some of the causal factors that are potential causes of the extinction of homo sapiens sapiens. Certainly animals and even bacteria are liable to extinction by some of the potential causes of the extinction of homo sapiens sapiens. This fact suggests the Survival arguments are at least as equipotent as Doomsday arguments. It indicates an additional reason why the urn analogies Leslie uses are not relevantly analogous. In each analogy, Leslie calculates the probability based on sampling from one urn. However, this requires that homo sapiens sapiens be assigned to only reference class in calculating the probability of their extinction. In fact, there are assigned to many reference classes. A correct analogy would be to consider drawings of a ball of a certain color from many different urns that have different constituents (e.g., drawing a white ball from an urn with three white balls and one red ball, drawing a white ball from another urn with five white balls and one million green balls, etc.).

     The point now is not the one Leslie discusses, namely, that we can be interested in predicting the survival of animate earthlings rather than humans, and that his book is merely about the survival of humans. My point is rather that if we are to construct doomsday/survival arguments about humans, we need to take into account all relevant evidence, which includes evidence about animate earthlings. This additional evidence is not merely the evidence about risks obtained prior to considering the earthlings' position in time, but also the posterior evidence that includes the earthlings' position in time.

   But this sort of criticism of Leslie's argument, namely, that there are corresponding Survival arguments, is an "internal criticism" in the sense that it supposes that p(h/e) is not equal to p(h/e & o & c), i.e., that position in time in a conceptually randomized class can affect the probabilities of possible physical causes becoming actual. Since this assumption is false, the real criticism of the Doomsday argument is the "external criticism", namely, the criticism that statistical unusualness or usualness in a merely conceived, randomized reference class cannot affect the probabilities of possible causes becoming actual.

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7. Bayes Theorem and Doomsday

    If the "d" in p(h/e & d) is neither among the causes of our extinction, nor based on observed regularities in nature, then in what respect does it count as "evidence" on which to revise our probability estimates (based on e) about our future? What sort of evidence are we dealing with?

   The probability, p(h/ o & c), would suggest that it is much more likely that the human species will become extinct by five hundred years than survive for thousands of centuries and populate the galaxy. However, as Leslie emphasizes, the Doomsday argument is meant as information to revise upwards p(h/e), where e are the various risks (nuclear war, etc.) that may cause human extinction. The practical and emotional significance of the Doomsday argument depends on how much p(h/e) differs from p(h/ e & o & c). If it leas to an upward revision of merely one billionth of a percent, then it has no practical and emotional significance; but if the upward revision is by twenty-five percent, it is greatly significant.

   They also do not meet the second condition, namely that samples have the same probability distribution.

8. TYPICAL AND ATYPICAL FEATURES IN THE REFERENCE CLASS

   (A). The problem with this is that it may be that the machine intelligences may have the property of being indestrutible by most of the causes Leslie mentions, disease, war, famine, comet strikes, etc. This affects the hypothesis that the reference class may end by one of these causes at a time when these machine intelligences live. "Probable indestructability" is a variable feature of this reference class that is relevant to the hypothesis of doom soon, and if we abstract from it, we are abstracting from a realistic probability estimate.

    (B) But once we allow into cosideration properties relevant to doom, then we introduce all the properties of being liable to the wars, diseases, etc., Leslie mentions. These liabilities will swamp or eliminate the probabilities based on temporal position.

    This shows something has gone wrong with the use of Bayses theorem.

Combining the observation o and the theoretical criterion c, it seems plausible that p(h/e & o & c) > p(h/e), where h is the hypothesis that we will become extinct in about one hundred years and e the causal factors that could estinguish the species. We have different hypotheses h1. h2. etc., for each different century. Each hypothesis is of a form such as

h = the class of homo sapiens and earth-originated intelligent machines are extinct by one of the causal factors in e by the year 2,300

What is supposed to be typical or atypical is the class mentioned in each such hypotheses h is stated in the last phrase of h, which means the position in history of the intelligent beings. However, this cannot give us an adequate inductive argument about risk estimates unless all relevant evidence is taken into account. And there is relevant evidence about the causal connections between the risk factors and which beings--e,g, intelligent machness--are alive at which century. If this relevant evidence is ignored, we do not have an adequate inductive argument.

   If we grant to Leslie that this inductive argument is acceptable, then we will also have a Doomsday Argument that gives us different results. Leslie stipulated that "human" was to be used in his argument in the way I explained. If we instead include all hominids, we will have a Doomsday argument with different probability estimates.  Machine intelligences or androids are not hominids and if homo sapiens sapiesn evolve into them in 500 years, that is the extinction of all hominids. Given this, the hominids now alive--the 6 billion homo sapiens sapiens--occupy a fairly typical period. Even though hominids stretch back 4.5 million years, there population is comparatively insiginficant to the population figure that homo sapiens sapiens will have achieved by 500 years from now. This argument differs from Leslie in that it includes hominids that are not homo sapiens and in that it excludes machine or computer intelligences. The practical result is that the evolution to computer intelligences is a continueanto of Leslie's line of earth-originated intelligences, who face other sorts of possible dooms, such as a comet impact.

   What seems crucial to Leslie is the survival of some group, species or class to which humans in the late 20th century consider themselves as belonging to. This group belongs to a large number ofreference classes and in reference to some class we get Survival Arguments instead of Doomsday Argum,ents.    The fact that we can vary our reference class leads to more significant results, namely, we also have Survival Arguments. I now consider the reference class of verterbrates, which evolved about 600 million years ago during the Cambridge explosion in the seas. If verterbrates live for hundreds of thousands or millions of more years, then the verterbrare that live in the late 20th century do not occupy an exceptionally early position but a more or less typical one. We get another Suvival Argument if our reference class is mammals, who evolved about 450 million years ago.

   Suppose we consider ourselves as belonging to the reference class of  beings containing physical parts, ranked in temporal order. Suppose I think the universe began 15 billion years ago and will end in about 25 billion years. This is a typical position and thus gives me no reason to think that we will cease to exist in the next few centuries.

   Suppose I consider myself as belonging to the reference class of conscious beings ranked in temporal order in a universe with an infinite past and infinite future. I would expect to find myself in a temporal position that has an infinite past and future.

    We can multiply Doomsday and Survival Arguments more or less at will. Since they give mutually inconsistent results and there is no reason to prefer any one over the others, there results can safely be said to have no probabilistic relevance to our future.

    But this goes back to the question of whether position in time can increase the probabilities that potential causes will be actual causes. For suppose that homo sapiens sapiens in the late 20th century occupied an unusually early position in all reference classes, even the class of all organisms. This could be the case if all organisms grow in population and survived for tens of billions of years. Organisms living the late 20th centry would then be unusually early. However, this cannot increase the likelihhod of doom soon for all organisms unless one accepts the principle that statistical unusualness can increase the likelihood of possible causes becoming actual causes.

.............................

 But here again there is a causal relationship. The fact that there are 15 names in the urn is a cuasally contributing factor to my drawing my name in the first 10 draws. 14 names are less likely to prevent my name from being in the "draw position" than are one million names.   

    But then we may respond that the word "special" no longer is relevant to the property of being earlier. If the viable theory that there are 15 names in the urn is true, then my name does not occupy an early position. My position is special in that it is likely to be drawn, but it is not an early position. On the other hand, if my name is among the 9-group between 767,421 and 767,430 and the urn contains a millin names, than the position of my draw is also not early, and is not likely to be drawn. But now my viable theory includes the hypothesis that my name will be drawn randomonly from any one of the equally unlikely sets of 9 names. Each 9-set now has the property of being                    ..............................................

    There are no known cases where an individual (due to a psychological abberation) have caused a threat, false alarm or nuclear alert. There are too many individuals involved in the chaim of command for this to occur. In the US, a massive attack (unprovked by a "false alarm" or anything other than a psychologically distubed state of mind) requires the President to send launch orders to the National Military Command Center (or the underground or airborne command post). If the President has sufffered a mental breakdown, he will be prevented from giving launch orders from the retinue of officials that regularly accompany the President. Even if the President evades this, the several individuals at the National Military Command Center will recognize the mental breakdown and not pass on the launch orders to the submarines, bombers and ICBM crews. (The USSR chain of command involves many more inter-dependent decision-makers and thus is much safer in this regard than the US chain of command.)

Recall we are talking about a massive nuclear attack, which

    In a full-scale nuclear war in the early 1980s, 10,000 megatons of explosive would be dropped. There would be 16, 160 distinct nuclear explosions. (See R. Turco et. al., "Nuclear Winter", Science 222, December 23, 1983, pp. 1283-1292, and R. Turco et. al. SA). The immediate heat and blast would kill hundreds of millions. But the question is about the long term effects that would be required to kill all humans. These are either radiation or nuclear winter.

     Leslie says of radiation: "A more likely scenario [than survival of a few million in Stone Age conditions], however, wold be extinction through the effects of radiation. . " (p. 27) However,

  Leslie also discusses intentional nuclear war and his estimates for this are too high since they are based on some inaccurate information about leader's actions. The Cuban missle crisis is the main case in point here. For example, he says of the Cuban missle crisis: "What is more, an obviously available bargainig chip, unused even after the Soviet Union had drawn attention to it, had been to offer to remove US Jupiee missles from Turkey." 9P. 29). Release of auditory recordings of conversations and accounts given by particpants show this statement is inaccurate. It was precisely the secret agreement Kennedy made with Kruschchov to remove the Jupiter misssles in Turkey (6 months after the missles were removed from Cuba) that broke the impasse and enable Krushvev to reach agreement about withdrawing the missles.

   But in Leslie's favor, he notes that T. Sorenson reports Kennedy as saying he believed the risk of nuclear war with the Soviet Union at one point had rise to between 1/3 and 1/2. If so, this shows that (contray to received wisdom), Kennedy  satisfied a sufficient condition for acting irrationally and immorrally. For one thing, in 1962 it is was both true and obvious to the US and the USSR that the US had an enormous milatary superiority overthe USSR and would have won a nuclear war. The basic instinct of self-preservation could have been used to predict that the Soviets would have "backed down". The concept of parity, mutual assurred destruction, and an unwinnable nuclear war was not formed until years later. It also shows Kennedy behavored immorrally. Kennedy and his advisors had estimated the military danger of missles in Cuba as relatively insignificant and saw the issues as more one of political prestige. For the sake of his and "his nation's" political prestige, Kennedy was prepared to take 1/3 to 1/2 chances to destroy most of human civilization. The Cuban crisis, like the Korean and Vietnam war, were not based on perceived threats of the USSR destroying the US, but on perceived threats to America's global supremacy and prestige.

   But such considerations are less relevant now given the disintegration of the Soviet Union and the end of the cold war. In any case, a deliberate nuclear war would not estinguish the human species for the reasons given above.

    Further, the inevitable advance of military technology will probably render nuclear bombs obsolete within about 100 years. Computer based sensors connected to lasers could shoot down any missle or bomber that is determined to carry a nuclear bomb.

I will spell out the mathematical operations in painful detail, since I wish to show that Leslie's calculation of over 50% is not the accurate one (it is off by about 45%). Converting the above numbers into fractions, we have 1/100 x 1/10 = 10/1000 x 100/1000 = 1,000/1,000,000 = 1/1000. We divide this by 1/100 x 1/10 + 99/100 x 1/1000 = 10/1000 x 100/1000 + 990/1000 x 1/1000 = 1,000/1,000,000 + 990/1,000,000 = 1,990/1,000,000 = 199/100,000. Rounded off, this gives us 200/100,000 = 2/1000 = 1/500. This gives us 1/1000 divided by 2/1000 = 1/1000 divided by 20/10,000. Since the division of a fraction is carried out as multiplication by its reciprocal, we have 1/1000 divided by 20/10,000 = 1/1000 x 10,000/20 = 1/1000 x 1000/2 = 1/1000 x 500 = 500/1000 = 50/100. Thus p(h/e) = 1/2 = 0.5 = 5%.

....................

   A defender of Leslie might have two responses. First, we should choose the reference class that is maximally specific. Since this is a reference class to which all living humans belong, this class would seem to be that of homo sapiens sapiens. But then we are likely to become extinct 500 years from now by computer-based evolution, so we have this sort of "doom" already ahead of us. Even if this scenario is rejected, it does nothing to impugn Leslie's argument. If there are independent reasons for thinking homo sapiens sapiens will be replaced by machine intelligences in 500 years, Leslie's Doomsday argument would suggest the probability for this occuring should be revised upwards.

   Perhaps the maximally specific reference class is all civilized homo sapiens sapiens. Suppose we became civilized about 4,000 years ago. Perhaps the class is all technological humans; this would include all humans in England, France, Canada, United States, etc. and other countries since about 1800. The narrower the class, the more imminent our doom.

   Leslie would object to narrowing the reference class in this way. But if so, I can object to his narrowing of the class to homo sapiens and earth-originated intellegent machines. I can get Survivial arguments broadeningk the refernce class to mammals, vetrebra, animate beings, physical beings, etc.

   The probm, then is that an arbtrary choice of a reference class gets one a Doomsday argument or a Survival argument. Result; the argument form does not increase our knowledge.

   A second objection might be one Leslie makes:..................................     

............................. Because it considers only one urn, corrsesponding to one reference class. In fact I draw my name from countless reference classes (all civilized homo sapiens sapiens, homo sapiens sapien, homo spaiens, hominoids, anthropids, mammals, vetrbra, organisms, etc.); in some my name is drawn among an early group, others among a late group, and others among a typical or middle group. For this reason, the urn analogies, the main analogical evidence for the Doomsday Argument, do not support it.      

    But this cannot be the fundamental reason, since if the urn analogy failed only for this reason, we ..............................................................

   We shall eventually see that the significance of the Doomsday Argument is lessened by the fact that the "reference class" can be varied so. Leslie suggests (but is not wholly explict or clear on this subject) that the criterion for the reference class is the ability to form a concept of being at a particular place in the history of the human species (p.261)