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REDUCTIO AD ABSURDUM exposes a statement ("The bug is dead") and its
negation ("The bug is alive") as consequences of the same set of
postulates. The respective theory is an inconsistency, and some
philosophers of science hold that the inconsistency deserves "the
lowest degree of verisimilitude" (without referring to Divine Albert's
Divine Theory of course):

W. H. Newton-Smith, The rationality of science, Routledge, London,
1981, p. 229: "A theory ought to be internally consistent. The grounds
for including this factor are a priori. For given a realist construal
of theories, our concern is with verisimilitude, and if a theory is
inconsistent it will contain every sentence of the language, as the
following simple argument shows. Let 'q' be an arbitrary sentence of
the language and suppose that the theory is inconsistent. This means
that we can derive the sentence 'p and not-p'. From this 'p' follows.
And from 'p' it follows that 'p or q' (if 'p' is true then 'p or q'
will be true no matter whether 'q' is true or not). Equally, it
follows from 'p and not-p' that 'not-p'. But 'not-p' together with 'p
or q' entails 'q'. Thus once we admit an inconsistency into our theory
we have to admit everything. And no theory of verisimilitude would be
acceptable that did not give the lowest degree of verisimilitude to a
theory which contained each sentence of the theory's language and its
negation."

Other philosophers of science find the inconsistency fruitful:
"Pursuing inconsistent systems is sometimes the only way to obtain new
information":

http://homepage.mac.com/otaviobueno/.Public/InconsistenNotHell.pdf
Why Inconsistency Is Not Hell
Making Room for Inconsistency in Science
Otavio Bueno
"On most accounts of belief change, inconsistent belief systems are an
"epistemic hell" to be avoided at all costs (see, e.g., Gärdenfors
1988, p. 51). From a normative point of view, we can perhaps
understand why this is the case. The underlying logic of most theories
of belief change is classical, and classical logic is explosive, that
is, everything follows from a contradic-tion. And a belief system from
which everything follows should definitely be avoided. It is certainly
of not much use if one wants to determine what one should believe and
what one should do.....I argue that Levi's own approach to belief
change could become stronger by making room for inconsistency, without
giving up the crucial features of his pragmatism. The crucial move is
to change the underlying logic to a paraconsistent one, which, in
consistent contexts, yields exactly the same results as the classical
approach (see, e.g.,da Costa and Bueno 1998). Once there is room for
inconsistency, there is also room for informativeness in inconsistent
belief systems.....Pursuing inconsistent systems is sometimes the only
way to obtain new information, particularly information that conflicts
with deeply entrenched theories (see Lakatos 1978 and Feyerabend
1988).....The considerations above indicate that, properly
conceptualized, inconsistent belief systems, whether about empirical
or nonempirical domains, can provide invaluable information. Even
though an inconsistent system may only be a first, but important, step
toward a consistent successor, the point still remains that such a
system is significant.....Suppose, however, that the only way of
obtaining certain bits of information is by deliberately expanding
into inconsistency. Bohr's case discussed above illustrates this
situation - as well as the earlier formulations of the calculus and
the conjunction of quantum mechanics and relativity theory. To obtain
the relevant information, in each of these cases, it looks as though
one is forced to expand into inconsistency. Now, as long as the
underlying logic is paraconsistent, there need not be anything
unacceptable here."

Who is right: Newton-Smith or Otavio Bueno?

Pentcho Valev wrote:

Deductive systems establish a procedure whereby one passes from a
premise or premises to a conclusion. The derivations are usually
presented as a sequence of numbered lines. For instance:

(1) Premise A
(2) Premise B
(3) Conclusion C 1,2
(4) Conclusion D 2,3
(5) ....................

The entry to the right of line (4) shows that that line was obtained
from the second and third lines, that is, that Conclusion D was
deduced from Premise B and Conclusion C.

This particular presentation of the derivations as a sequence of
numbered lines seems practical and yet it has never been and will
never be used by Einsteiniana's highest priests. The reason is easy to
see if one first considers the bug-rivet story:

http://hyperphysics.phy-astr.gsu.edu/Hbase/Relativ/bugrivet.html
"The bug-rivet paradox is a variation on the twin paradox and is
similar to the pole-barn paradox.....The end of the rivet hits the
bottom of the hole before the head of the rivet hits the wall. So it
looks like the bug is squashed.....All this is nonsense from the bug's
point of view. The rivet head hits the wall when the rivet end is just
0.35 cm down in the hole! The rivet doesn't get close to the
bug....The paradox is not resolved."

and then tries to imagine the following sequence of numbered lines
published in both the journal Nature and the journal Science:

(1) Premise: The principle of relativity
(2) Premise: Einstein's 1905 light postulate
(3) Conclusion: Time dilation 1,2
(4) Conclusion: Length contraction 2,3
(5) Conclusion: The bug is dead 4
(6) Conclusion: The bug is alive 4

In the era of Postscientism REDUCTIO AD ABSURDUM is universally called
"paradox", that is, there is camouflage that misleads everybody, and
yet Einsteiniana's highest priests wholeheartedly avoid the
presentation of the derivations as a sequence of numbered lines.

Pentcho Valev
pvalev@yahoo.com