The "Fermi Paradox," an argument that extraterrestrial intelligence cannot exist because it has not yet been observed, is a logical fallacy. This "paradox" is a formally invalid inference. both because it requires modal operators lying outside the first-order propositional calculus and because it is unsupported by the observational record. © 1985 Academic Press. Inc.
Renewed activity in the field of Search for Extraterrestrial Intelligence (SETI) has stimulated interest in an old argument purporting to show that ETI cannot exist. Known as the "Where Are They?" question or the "Fermi Paradox," this sophism posits that in time an intelligent extraterrestrial species must achieve high technology, exploring and colonizing first its planetary system, and later the Galaxy, as humanity has explored and colonized the Earth. These beings should have been able to travel to Earth, but we see no evidence of such visitations, hence ETI cannot exist. Proponents of the "paradox" (e.g., Hart, 1975; Tipler, 1980; Hart and Zuckerman, 1982) admit that it is incomplete in the loose form outlined above, but argue that alternatives purporting to explain the paradox (e.g., Ball, 1973; Sagan and Newman, 1983) are invalid or lead to contradiction or impossibility. This position has been weakly challenged (Cox, 1976; Schwartzman, 1977; Papagiannis, 1980; Stephenson, 1982), but the debate continues.
Logical Fallacy
It is surprising that the formal invalidity of the paradox, which cannot be cast in acceptable syllogistic form, has gone unmentioned in previous discussions. For instance, where A = ETI exist, B = ETI are here, and C = ETI are observed, the inference
Not-C
Therefore not-B
Therefore not-A
is both syntactically and semantically invalid because "probably" (also "ought to be," "should be," "might be," "believe to be," "hoped to be," "likely ... .. reasonably") is a modal truth functional operator outside the scope of the first-order propositional calculus. Even recast in the syntactically correct form
Not-(probably C)
Therefore not-(probably B)
Therefore not-A,
the inference is semantically valid if and only if it is possible to assert that not-(probably C) is true. But the truth value of not(probably C) is indeterminate, so S2 is, classically, semantically invalid. The embedded uncertainty cannot be removed from the primary and secondary subjunctives because neither A ® B nor B®C is certainly true; not-C cannot imply not-A because C is a subset of B and B is a subset of A (Fig. 1). Hence the Fermi Paradox line of reasoning has no formal probative value whatsoever.
The calculus of probability or probable inference (Keynes, 1921; Carnap, 1962), conditional probabilistic logic (Nute, 1980), statistical inference, and like methods cannot remedy the paradox. There are no statistical data on ETI, so probability assignments for A, B, and C are necessarily a priori and cannot serve as the basis of truth tests in formal assertoric logic. This problem persists even in fuzzy logic systems (Zadeh, 1983) where A, B, and C are conditional, qualified propositions or fuzzy predicates conjoined by a fuzzy probability or quantifier.
Probably can also be treated using modal first-order predicate calculi (Snyder, 1971; Bowen, 1979). Modal epistemic logics dealing in a limited way with what is known and with what is believed, credible, plausible (Rescher, 1964, 1974), or probable have been studied but show only weak transitivity because something being possible or probable is not incompatible with its not being so. To insist otherwise is to claim that whatever is probably so necessarily is so and that what is not so can have no probability of being so, demonstrably erroneous positions (White, 1975).
Evidentiary Flaw
An additional fundamental flaw in the paradox (Freitas, 1983a; Hibbs, 1993) is the extraordinary weakness of the evidence for not C. Not C is not certainly true on the basis of available evidence. Neither can C presently be shown to be true, but the non-truth of not C is sufficient to destroy any inference.
For example, an appropriate observational search limit for extraterrestrial messenger probe size is 1-10 m (Freitas, 1983b). Atrans-Plutonian spherical solar system boundary encloses 260,000 AU3 and 1011 km2 of planetary and asteroidal surface area. The continuous visible sky search limit is perhaps +14 mag by amateurs, plus intermittent coverage to +21 mag with the Palomar Schmidt and +24 mag for the best ground-based telescopes. Thus current surveys could not have detected even a 1- to 10-m probe more than 0.01-1 AU from Earth, so heliocentric orbital space is at least 99.999% unexplored for 1- to 10-m artifacts. The space telescope cannot materially improve this situation because of narrow field and a tight schedule. IRAS data establish new IR search limits about as good as in the visible; microwave limits remain far poorer.
Less than 10% of the Earth's surface, 1% of the Moon, 0.1% of Mars, and 10-7% of Venus (total 5 x 107 km2) has been surveyed to 1- to 10-m visible resolution. This leaves 99.96% of Solar System surface area (1.3 x 1011 km2) unexamined for likely artifacts. Interplanetary spacecraft and ground-based telescopes have photographed portions of some planets and asteroids down to 20-km resolution, plus a few tracts on some outer planet moons to 1-10 km. Objects buried or submerged are undetectable with current instrumentation. Large artificial habitats in the asteroid belt (Papagiannis, 1978) would appear visually indistinguishable from natural objects, especially since the belt population itself is poorly cataloged. The assertion that a resident artifact would alert us to its presence is an unwarranted, unsupportable, and untenable assumption.
There have been few serious searches (Freitas and Valdes, 1980; Valdes and Freitas, 1983) even for the most likely classes of oberservable artifacts, and none for less-likely classes. An active Search for Extraterrestrial Artifacts (SETA) program (Freitas, 1983a,b) would help fill this enormous and critical gap in the observational record.
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