There Is No Fermi Paradox
Xenology Research Institute. 8256 Scottsdale Drive Sacramento,
Icarus 62:518-520 (1985)
Received June 25, 1984: revised March 18, 1985
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.
Note: This web version is derived from an earlier draft of the paper
and may possibly differ in some substantial aspects from the final published
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;
Stephenson, 1982), but
the debate continues.
LOGICAL FALLACYIt 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
S1: If A, then probably B
If B, then probably C
Therefore not-Ais 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
S2: If A. then (probably B)
If (probably B), then (probably C)
Therefore not-(probably B)
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.
Fig. 1. Euler Diagram of the "Fermi Paradox." For A = (ETI
exist), B = (ETI are here). and C (ETI are observed), since
A ? ~C ®f then ~C®A (f = null set; U =
universe of possibilities: ? = set intersection operator).
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).
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). A trans-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
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
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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Last Modified: June 13, 1999
Editor: Robert J. Bradbury