Page 46 - Žagar, Igor Ž. 2021. Four Critical Essays on Argumentation. Ljubljana: Pedagoški inštitut.
P. 46
four critical essays on argumentation
Begging the question [Petitio Principii, circular reasoning] fits in the
same category; already J. S. Mill (in his System of Logic, 1843) claims that all
valid reasoning commits this fallacy. While Cohen and Nagel affirm:
There is a sense in which all science is circular, for all proof rests
upon assumptions which are not derived from others but are jus-
tified by the set of consequences which are deduced from them
... But there is a difference between a circle consisting of a small
number of propositions, from which we can escape by denying
them all, or setting up their contradictories, and the circle of the-
oretical science and human observation, which is so wide that
we cannot set up any alternative to it. (Cohen, Nagel 1934: 379, in
Hamblin ibid.: 35)
A possible conclusion we could draw from this observation: on the mi-
cro level, we can fuss about small things, everyday conversation and every-
day reasoning, and pass our time in inventing numerous fallacies, but when
it comes to the macro level, to big things (the big picture), fallacies are not
objectionable any more—because there is no alternative. A problem that is
very similar to Gödel’s incompleteness theorem:
Any effectively generated theory capable of expressing elementary
arithmetic cannot be both consistent and complete. In particular,
for any consistent, effectively generated formal theory that proves
certain basic arithmetic truths, there is an arithmetical statement
that is true, but not provable in the theory. (Kleene 1967: 250)
This theorem was designed to prove inherent limitations (incomplete-
ness) for axiomatic systems for mathematics, but what Cohen and Nagel are
claiming is, mutatis mutandis, an application of Gödel’s (first) incomplete-
ness theorem to possible theories of fallacies. Graphically, we could repre-
sent this dialectical dynamics between macro and micro level like this:
46
Begging the question [Petitio Principii, circular reasoning] fits in the
same category; already J. S. Mill (in his System of Logic, 1843) claims that all
valid reasoning commits this fallacy. While Cohen and Nagel affirm:
There is a sense in which all science is circular, for all proof rests
upon assumptions which are not derived from others but are jus-
tified by the set of consequences which are deduced from them
... But there is a difference between a circle consisting of a small
number of propositions, from which we can escape by denying
them all, or setting up their contradictories, and the circle of the-
oretical science and human observation, which is so wide that
we cannot set up any alternative to it. (Cohen, Nagel 1934: 379, in
Hamblin ibid.: 35)
A possible conclusion we could draw from this observation: on the mi-
cro level, we can fuss about small things, everyday conversation and every-
day reasoning, and pass our time in inventing numerous fallacies, but when
it comes to the macro level, to big things (the big picture), fallacies are not
objectionable any more—because there is no alternative. A problem that is
very similar to Gödel’s incompleteness theorem:
Any effectively generated theory capable of expressing elementary
arithmetic cannot be both consistent and complete. In particular,
for any consistent, effectively generated formal theory that proves
certain basic arithmetic truths, there is an arithmetical statement
that is true, but not provable in the theory. (Kleene 1967: 250)
This theorem was designed to prove inherent limitations (incomplete-
ness) for axiomatic systems for mathematics, but what Cohen and Nagel are
claiming is, mutatis mutandis, an application of Gödel’s (first) incomplete-
ness theorem to possible theories of fallacies. Graphically, we could repre-
sent this dialectical dynamics between macro and micro level like this:
46
