The paradox
If the doomsday argument's lifetime is governed by the principle of indifference and the Copernican principle then based on the length of its current existence, and assuming that it is randomly drawn from a reference class of probabilistic speculations it is 95% certain that it will be refuted before the year 2500.
If the doomsday argument is not itself subject to these principles then its assumption that the human race's survival-time can be modeled using them appears to be a paradox (to Lansberg & Dewynne).
Alternatively, if the doomsday argument is subject to these presumptions, then as it is expected to expire (be refuted) earlier that its own prediction for the likely survival time of humanity there is a second paradox: The predictions of a theory concerning events to occur after it has been refuted (such as human extinction) are not logically meaningful. Conversely, if the doomsday argument survives until the end of human civilization (in the year 5000, say) then it will have dramatically beaten the odds against the expectations of the Copernican principle. This can create a paradox for an argument based on probability, as shown if future scenarios are broken into three groups:
- Human extinction occurs before the year 2,500 AD.
- Human extinction occurs after the year 2,500 AD and the doomsday argument is never refuted.
- Human extinction occurs after the year 2,500 AD but not before the doomsday argument is refuted.
The "quick extinction" in possibility 1 is considered fairly likely in those doomsday arguments using the number of births as a reference class, but comparing like-for-like we should compare the length of time the doomsday argument survives before refutation with the length of time the human race survives before extinction. Therefore, J. Richard Gott's (temporal) doomsday argument is used to calculate the probabilities of the three scenarios above:
- According to Gott's doomsday argument it is extremely unlikely that the human race will become extinct before the year 2,500 AD, as this would make us extremely special observers; applying the indifference principle to the duration of the human race makes the odds around 400:1 against (0.25% chance).
- If the Copernican principle applies to the lifetime of theories as well as species (depending on the reference class evidence says it does) then the chance of the (relatively young) doomsday argument surviving sustained critical analysis for the next 500 years = 22/500 = 4.4%
- By eliminating the other two outcomes we are left with the third, that the human race will survive to see the doomsday argument refuted. The chance of this = 100 - (4.4 + 0.25) = 95.35%
Paradoxical conclusion
If the doomsday argument can apply to itself it can be simultaneously right (as a probabilistic argument) and probably wrong (as a prediction).
Therefore, Landsberg and Dewynne argue that it is more likely that the doomsday argument is wrong (even if its logic is correct) than that the human race will become extinct in 9,000 years (which the doomsday argument calculates at around 95% likely). The interesting paradox is that the Doomsday argument is probably wrong even assuming it to be completely right (in its 95% estimate).
The anthropic principle, also known as the observation selection effect, is the hypothesis, first proposed in 1957 by Robert Dicke, that the range of possible observations that could be made about the universe is limited by the fact that observations could happen only in a universe capable of developing intelligent life. As Steven Weinberg puts it: "Where else could we be, except on a planet that can sustain life?" Proponents of the anthropic principle argue that it explains why the universe has the age and the fundamental physical constants necessary to accommodate conscious life, since if either had been different, no one would have been around to make observations. Anthropic reasoning is often used to deal with the idea that the universe seems to be finely tuned for the existence of life.
In physical cosmology, the Copernican principle states that humans, on the Earth or in the Solar System, are not privileged observers of the universe, that observations from the Earth are representative of observations from the average position in the universe. Named for Copernican heliocentrism, it is a working assumption that arises from a modified cosmological extension of Copernicus' argument of a moving Earth.
Falsifiability is a deductive standard of evaluation of scientific theories and hypotheses, introduced by the philosopher of science Karl Popper in his book The Logic of Scientific Discovery (1934). A theory or hypothesis is falsifiable if it can be logically contradicted by an empirical test.
Sir Karl Raimund Popper was an Austrian–British philosopher, academic and social commentator. One of the 20th century's most influential philosophers of science, Popper is known for his rejection of the classical inductivist views on the scientific method in favour of empirical falsification. According to Popper, a theory in the empirical sciences can never be proven, but it can be falsified, meaning that it can be scrutinised with decisive experiments. Popper was opposed to the classical justificationist account of knowledge, which he replaced with critical rationalism, namely "the first non-justificational philosophy of criticism in the history of philosophy".
The problem of induction is a philosophical problem that questions the rationality of predictions about unobserved things based on previous observations. These inferences from the observed to the unobserved are known as "inductive inferences". David Hume, who first formulated the problem in 1739, argued that there is no non-circular way to justify inductive inferences, while acknowledging that everyone does and must make such inferences.
A scientific theory is an explanation of an aspect of the natural world and universe that can be repeatedly tested and corroborated in accordance with the scientific method, using accepted protocols of observation, measurement, and evaluation of results. Where possible, some theories are tested under controlled conditions in an experiment. In circumstances not amenable to experimental testing, theories are evaluated through principles of abductive reasoning. Established scientific theories have withstood rigorous scrutiny and embody scientific knowledge.
In philosophy of science, confirmation holism, also called epistemological holism, is the view that no individual statement can be confirmed or disconfirmed by an empirical test, but rather that only a set of statements can be so. It is attributed to Willard Van Orman Quine who motivated his holism through extending Pierre Duhem's problem of underdetermination in physical theory to all knowledge claims.
The mediocrity principle is the philosophical notion that "if an item is drawn at random from one of several sets or categories, it's more likely to come from the most numerous category than from any one of the less numerous categories". The principle has been taken to suggest that there is nothing very unusual about the evolution of the Solar System, Earth's history, the evolution of biological complexity, human evolution, or any one nation. It is a heuristic in the vein of the Copernican principle, and is sometimes used as a philosophical statement about the place of humanity. The idea is to assume mediocrity, rather than starting with the assumption that a phenomenon is special, privileged, exceptional, or even superior.
Critical rationalism is an epistemological philosophy advanced by Karl Popper on the basis that, if a statement cannot be logically deduced, it might nevertheless be possible to logically falsify it. Following Hume, Popper rejected any inductive logic that is ampliative, i.e., any logic that can provide more knowledge than deductive logic. This led Popper to his falsifiability criterion.
The doomsday argument (DA), or Carter catastrophe, is a probabilistic argument that claims to predict the future population of the human species based on an estimation of the number of humans born to date. The doomsday argument was originally proposed by the astrophysicist Brandon Carter in 1983, leading to the initial name of the Carter catastrophe. The argument was subsequently championed by the philosopher John A. Leslie and has since been independently conceived by J. Richard Gott and Holger Bech Nielsen. Similar principles of eschatology were proposed earlier by Heinz von Foerster, among others. A more general form was given earlier in the Lindy effect, which proposes that for certain phenomena, the future life expectancy is proportional to the current age and is based on a decreasing mortality rate over time.
Human extinction is the hypothetical end of the human species, either by population decline due to extraneous natural causes, such as an asteroid impact or large-scale volcanism, or via anthropogenic destruction (self-extinction), for example by sub-replacement fertility.
John Richard Gott III is a professor of astrophysical sciences at Princeton University. He is known for his work on time travel and the Doomsday argument.
The self-indication assumption doomsday argument rebuttal is an objection to the doomsday argument by arguing that the chance of being born is not one, but is an increasing function of the number of people who will be born.
Originally, fallibilism is the philosophical principle that propositions can be accepted even though they cannot be conclusively proven or justified, or that neither knowledge nor belief is certain. The term was coined in the late nineteenth century by the American philosopher Charles Sanders Peirce, as a response to foundationalism. Theorists, following Austrian-British philosopher Karl Popper, may also refer to fallibilism as the notion that knowledge might turn out to be false. Furthermore, fallibilism is said to imply corrigibilism, the principle that propositions are open to revision. Fallibilism is often juxtaposed with infallibilism.
Models of scientific inquiry have two functions: first, to provide a descriptive account of how scientific inquiry is carried out in practice, and second, to provide an explanatory account of why scientific inquiry succeeds as well as it appears to do in arriving at genuine knowledge. The philosopher Wesley C. Salmon described scientific inquiry:
The search for scientific knowledge ends far back into antiquity. At some point in the past, at least by the time of Aristotle, philosophers recognized that a fundamental distinction should be drawn between two kinds of scientific knowledge—roughly, knowledge that and knowledge why. It is one thing to know that each planet periodically reverses the direction of its motion with respect to the background of fixed stars; it is quite a different matter to know why. Knowledge of the former type is descriptive; knowledge of the latter type is explanatory. It is explanatory knowledge that provides scientific understanding of the world.
A self-refuting idea or self-defeating idea is an idea or statement whose falsehood is a logical consequence of the act or situation of holding them to be true. Many ideas are called self-refuting by their detractors, and such accusations are therefore almost always controversial, with defenders stating that the idea is being misunderstood or that the argument is invalid. For these reasons, none of the ideas below are unambiguously or incontrovertibly self-refuting. These ideas are often used as axioms, which are definitions taken to be true, and cannot be used to test themselves, for doing so would lead to only two consequences: consistency or exception (self-contradiction).
John Andrew Leslie is a Canadian philosopher and writer.
Bold hypothesis or bold conjecture is a concept in the philosophy of science of Karl Popper, first explained in his debut The Logic of Scientific Discovery (1935) and subsequently elaborated in writings such as Conjectures and Refutations: The Growth of Scientific Knowledge (1963). The concept is nowadays widely used in the philosophy of science and in the philosophy of knowledge. It is also used in the social and behavioural sciences.
The Lindy effect is a theorized phenomenon by which the future life expectancy of some non-perishable things, like a technology or an idea, is proportional to their current age. Thus, the Lindy effect proposes the longer a period something has survived to exist or be used in the present, the longer its remaining life expectancy. Longevity implies a resistance to change, obsolescence, or competition, and greater odds of continued existence into the future. Where the Lindy effect applies, mortality rate decreases with time. Mathematically, the Lindy effect corresponds to lifetimes following a Pareto probability distribution.
