This essay was written in mid-2016!

**Introduction**

The Doomsday argument is a probabilistic argument that attempts to predict the impending doom of human civilisation, surprisingly, based on non-inductive premises; namely, the seemingly random birth rank of individuals during our time period. Though mathematical in nature, the argument has frightening philosophical implications and thus, ought to be evaluated as such.

In §2 of this paper I shall detail the necessary assumptions of Leslie and Bostrom’s doomsday argument, making use of popular analogies, when appropriate, to further understand it. §3 shall evaluate Richard Gott’s method of probabilistic lifespan prediction, which I shall then use in tandem with Leslie and Bostrom’s doomsday argument to perform my own calculation of the doomsday hypothesis. In §4, I shall provide rebuttal to the doomsday argument, and with each, I shall show their failure to properly refute its statistical method. In conclusion, §5 shall postulate the legitimacy of the doomsday argument.

**The Doomsday argument**

Fundamentally, the doomsday argument is an extension of Brandon Carter’s weak anthropic principle, which was later developed in John Leslie’s famously influential essay ‘Is the End of the World Nigh?’, and further researched by Nick Bostrom in a series of articles expounding the anthropic principle (Leslie, 1990). In §2 of his essay, John Leslie describes the fundamental principle which the doomsday argument relies on – the self-sampling assumption, stating that “one should, all else being equal, take one’s position to be fairly typical rather than very untypical” (Leslie, 1990, p.66). The meaning of this passage is best perhaps explained in Nick Bostrom’s cubicle analogy (Bostrom, 2012).

**2a. Bostrom’s cubicle analogy**

In the analogy, it is supposed that there exists a universe solely comprised of 100 cubicles, such as one those would find in an office building (Bostrom, 2012). Ninety of the hundred cubicles are painted blue on the outside, while the other ten are painted red, and none allow those on the inside of the cubicle to know their colour without first exiting the cubicle. Suppose now that someone finds themselves in a cubicle. As Bostrom points out, accepting the self-sampling assumption and considering oneself to be fairly typical will garner a 90% success rate in guessing the cubicle colour, while rejecting the assumption invokes a 50% chance of guessing correctly. Therefore, Bostrom argues, it is rational to accept the self-sampling assumption, and that you are typical rather than atypical.

Suppose now that we modify the analogy to include, rather the cubicles being painted blue or red, their representation in numerical order (Bostrom, 2012). Given that we have 100 cubicles, Bostrom supposes that a fair coin is flipped which, conditional on the toss, determines whether a person is placed in every cubicle (heads) or in only the first ten (tails). Finding oneself in a cubicle without knowledge of its exterior, one can hypothesise with 50% accuracy that the coin flip fell heads (as there is no point of reference by which a more accurate calculation can be performed).

Now suppose that, upon opening the door, one sees that they reside in cubical 5. Given this knowledge, the probability of hypothesis tails being the case greatly increases to approximately 9/10 (Bostrom, 2012). If hypothesis heads were the case, the probability of finding oneself in one of the first ten cubicles would be a mere 1/10 as opposed to hypothesis tails, which garners the probability of one (it accounts only for those in cubicles one to ten). Thus, given, the knowledge of our cubicle number, we can calculate with a 10% margin for error that hypothesis tails is the case – that only the first ten cubicles are populated.

**2b. An application of this method**

Given our calculation in the preceding paragraph, it seems clear that one can, with knowledge of their place in an order, make a calculation to approximate the lifespan of that order. If this is so, then if would follow that the human race (an order) can receive a lifespan approximation based on the knowledge of our place in that order. Given, this method of calculation does not provide us with exact numerical values, it does however allow us to compare the likelihood of two rival hypotheses to produce an approximation, and can be done through the following.

Consider these two rival hypotheses – doom early and doom late (Bostrom, 2010). Much like hypothesis tails in the cubicle analogy, doom early predicts that humankind will fall extinct at approximately 200 billion humans to have ever existed. And corresponding to hypothesis heads, doom late predicts that humankind will fall extinct at approximately 200 trillion humans to have ever existed.

Suppose that, much like the cubicle number, one has knowledge of their birth-rank which is, incidentally, 100 billion. Knowing this, we can calculate that it is statistically more likely for doom early to be the case, given that our birth-rank is a random sample from the pool of humans who have ever lived. As Bostrom points out, “the posterior probability of Doom Soon will be very close to one”, for, without using numerical values to assign probability, we know that it is more likely that we are a typical human than an extremely abnormal human, at the very brink of humankind’s flourishing.

**Lifespan calculation and the self-sampling assumption**

**3a. Richard Gott and the Copernican principle**

In 1969, standing upon the Berlin Wall, Richard Gott somewhat stumbled upon a newfound application of the Copernican Principle (Gott, 2002). Rather than addressing the unimportance of human civilisation in the cosmos, as the principle had been originally intended for, Gott found that it may also apply to time. Suppose, Gott postulates, that the period of time we live in is not unique or privileged, as it may intuitively seem. Assuming that the point in time one estimates from is a random point in their lives, we can use that information to perform a probabilistic prediction, calculating the remaining duration of their lifespan.

According to Gott’s method of calculation, the degree of accuracy one can garner in their prediction corresponds almost entirely to the range that they are willing calculate within (Gott, 2002). In lifespan prediction, let us suppose that, say, Jones is 35 years old and that he is not in the first or last 10% of his life. We may then calculate within these constants to produce an estimate of Jones’ hypothetical longevity. 35 divided by 0.9 equals 39 (≈), and 35 divided by 0.1 equals 350. Therefore, given that the period at which Jones estimates from is not special (insofar that it is not in the first or last 10% of his life), we can reasonably predict that Jones will die at some point aged between 39 and 350 years. Given a more liberal estimate such as 20%, the accuracy of the prediction increases to be between 44 (≈) and 175 years of age, though so too does the margin for error, for the prediction will then (theoretically) be wrong 20% of the time.

Though there are fairly obvious shortcomings to using this method, such as its dependence on being a truly random point in one’s life, with no further evidence to support knowing an entities lifespan but their position in time, this method produces surprisingly accurate empirical predictions.

**3b. A doomsday calculation**

Given the nature of this calculation, it is worth emphasising the role of the self-sampling assumption, which we shall use to justify our position as a random sample of the human population (Bostrom, 2012). In the previous calculation, we did not need to justify ourselves in this regard as we had prior knowledge of human longevity. The following calculation, however, concerns something of which we have no experience with, and thus, no inductive knowledge to guide us in our prediction. To create a reference point by which we base our calculations on, we must reason as if we are a randomly selected human from the pool of existent humans – in other words – accept the self-sampling assumption.

According to the most recent analysis on world population, conducted by the world Population Reference Bureau in 2011, the total number of humans to have ever lived is approximately 107.6 billion (Haub, 2011). For the purposes of a sound calculation, we shall pretend that the year is 2011. Given this estimate, and using Gott’s method of lifespan prediction, we can calculate with a relatively conservative margin of error of one percent that the human race will cease to exist at some point in between 108,700,000,000 (≈) and 10,760,000,000,000 humans to have ever existed (approximately one hundred and eight billion humans to eleven trillion humans).

Unlike Bostrom’s method of calculation, we now have numerical values which, conditional upon the soundness of Gott’s calculations, accurately represent the lifespan of humankind. However, by incorporating Bostrom’s method of calculation, we have the tools to produce a doomsday argument that more accurately represents the state of humankind.

Let us suppose that doom early, in this case, represents the hypothesis that humankind will become extinct at approximately 1 trillion humans to have ever existed. In this case I am transposing the probability of 1/10 from Bostrom’s cubicle analogy and, moreover, we have strong empirical reasons to think that humankind is not on the brink of extinction. Contrarily, we shall assign doom late the hypothesis of approximately ten trillion, given the one tenth removal of eleven trillion, our initial limitation. As was discussed in §2 of this paper, it seems as if doom early is more probable, though unlike §2, these hypotheses contain actual empirical data which makes its predictions both more contemporarily applicable and accurately depicting of humankind.

**Criticisms of the argument**

While many have attempted to refute the doomsday argument, most apparent refutations are on second glance mere misinterpretations of the argument, insofar as they might attack certain non-relevant features of its constitution, ignoring the legitimacy of its statistical method. For example, many claim that this argument does not work because no matter how many times it can be used throughout history, doom late always seems to be the case; why should we trust it now? This objection, however, relies on the lesser form of inductive reasoning, that because it may have failed in the past then it must too fail in the present. Furthermore, the doomsday argument does recognise the potential for error – this does not distract us from the legitimacy of its statistical method. The only plausible method of refuting the argument, I believe, is in suggesting a more viable alternative to the self-sampling assumption, which the argument relies on to function.

The self-indication assumption as expounded by Nick Bostrom in ‘Anthropic Bias’ (2010) states that rather than viewing yourself as a random sample of a population, one ought to consider the possibility of their existence as being dependent upon the pool of humans that will ever exist. It claims that, given two hypotheses, you ought to accept the one that offers a higher number; in this case – doom late – for a higher number of humans to have ever existed seems to entail a higher possibility of you existing.

Shortly after postulating this, Bostrom realized its faults. He imagines a fair coin toss, where “Heads would lead to the creation of a million observers”. Due to the nature of the self-indication assumption, “[Y]ou would have to be virtually certain that the coin fell heads (P=99.9999%) without knowing anything directly about the outcome” (Bostrom, 2010, p.122-127). Even with knowledge of the prior probability of heads, the self-indication assumption fails to produce a satisfactory answer and, thus, is not sufficient to refute the doomsday argument.

**Conclusion**

In conclusion, I have examined Richard Gott’s method of lifespan prediction, transposing empirical data concerning humankind to the position as developed by Leslie and Bostrom. Though the statistical method inherent in the doomsday argument may seem intuitively incorrect, we have yet to develop a satisfactory refutation and thus, we ought to accept it for the time being.

**Bibliography**

Bostrom, N., (1998), ‘The Doomsday Argument: A Literature Review’, *Anthropic Bias*, Accessed 04/06/16, <http://www.anthropic-principle.com/preprints/lit/>

Bostrom, N., (2010), *Anthropic Bias: Observation Selection Effects in Science and Philosophy (Studies in Philosophy)*, New York: Routledge

Bostrom, N., (2012), ‘A Primer on the Doomsday Argument’, *Anthropic Bias*, Accessed 03/06/16, <http://www.anthropic-principle.com/?q=anthropic_principle/doomsday_argument>

Carter, B., McCrea, W., (1983), ‘The Anthropic Principle and its Implications for Biological Evolution [and Discussion]’, *Philosophical Transactions of the Royal Society of London*, vol. 310, no. 1512, pp. 347-363)

Gott, R., (2002), *Time Travel in Einstein’s Universe*, New York: Mariner Books

Haub, Carl., (2011), ‘How Many People Have Ever Lived on Earth?’, *Population Reference Bureau*, Accessed 07/06/16, <http://www.prb.org/Publications/Articles/2002/HowManyPeopleHaveEverLivedonEarth.aspx>

Leslie, J., (1990), ‘Is the End of the World Nigh?’, *The Philosophical Quarterly*, vo. 40, no. 158, pp. 65-72.