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Aristotle's
Principle of Non-Contradiction
Jean-Louis Hudry
Institute of Philosophy
University of Neuchâtel, Switzerland
In Metaphysics
Gamma, Aristotle understands the principle of non-contradiction
(PNC) as the most certain principle of all such that it is impossible
to be mistaken about it. Yet, Aristotle is also concerned
with the fact that some people may reject this principle. In that
respect, he constructs arguments aiming to defend PNC as a true
opinion. There is then a difficult contrast to explain: on the one
hand, PNC is a necessary principle of the highest importance; on the
other, it is merely justified as a true opinion against those who
challenge it. So the essential question is as follows: if PNC is
postulated as the most certain principle of all, why does Aristotle feel the need to
speak of it as a mere opinion?
Many have
been puzzled by this contrast. Łukasiewicz (1910)
concludes about Aristotle: “he may himself have felt the weakness of his
arguments; and that may have led him to present his Law as an ultimate axiom—an
unassailable dogma” (p. 62, original emphases). Others have used Aristotle’s
weak and problematic arguments as a way to illustrate the failure of PNC (Priest,
2006).
These
reactions show that Aristotle’s defence of PNC is, at worst, not
understood or,
at best, not taken seriously. The aim of this tutorial will be to
answer this concern by
accounting for Aristotle’s method. We shall explain why PNC is
defendable only
as a true opinion, even though it is said to be the most certain
principle of
all, and we shall conclude that Aristotle’s weak defence of PNC is
perfectly compatible with the postulate of PNC as a strong axiom.
Everybody is welcome to join, and there are no specific prerequisites. The
tutorial will be divided into three sessions.
I.
Aristotle’s PNC and Łukasiewicz’s formulations
A
first session will focus on Aristotle’s definition of PNC, as it is
exclusively based on predicates and requires two conditions, namely
simultaneity and similarity. PNC is also to be distinguished from two
derived principles, namely the excluded middle and bivalence. Finally,
contradiction is more than mere contrariness, in so far as two
contraries are contradictory, if and only if one is true and the other
false. We shall then compare Aristotle’s PNC with Łukasiewicz’s
(1910) interpretations of it through an ontological, a logical,
and a psychological formulation. Influenced by Frege's logical
formalism, Łukasiewicz then accuses Aristotle of “logicism in
psychology”.
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II. An Aristotelian contextualization of PNC
In a second session, we
shall analyze the context in which Aristotle’s PNC takes place. Metaphysics Gamma
introduces a hierarchy of sciences: philosophy is the universal
science, which
includes the particular sciences of physics and mathematics. Aristotle
assesses PNC with respect to philosophy, in so far as PNC is a
necessary principle
only for those who know about the general nature of things, and which
goes beyond any specific mathematical or physical nature. It is within
this epistemic context that Aristotle’s PNC has to be understood,
meaning
that non-philosophers express an opinion about it, without being
knowledgeable about its necessity. As such, the definition of
Aristotle’s PNC is inseparable from the way PNC is either intrinsically
cognized or merely believed.
III. Aristotle on the rejection of PNC
A
third session will study why Aristotle explicitly admits the
possibility of rejecting PNC.
Indeed, he has to convince all non-philosophers that PNC should not be
regarded as a false
opinion. According to him, there are two ways of challenging PNC. One
is for physicists to assume that things are endlessly changing,
making their meanings indefinite and thereby irrelevant to PNC.
Aristotle’s reply is that physical motion cannot be used against the
postulate that things have definite meanings. The other objection is
that any proof of PNC already uses PNC in the premises of
the proof. Aristotle acknowledges this petitio principii,
and then concludes
to the absence of a direct proof. Nevertheless, he suggests an indirect
refutation to this objection, aiming to show that it is impossible not
to use PNC in language; thus, even the rejection of PNC will have to rely on the
use of PNC.
Bibliography
Barnes,
J. ‘The Law of Contradiction’, Philosophical
Quarterly
19,
302-09, 1969.
Cohen,
S. M. ‘Aristotle on the Principle of Non-Contradiction’,
Canadian Journal of Philosophy 16,
359-70, 1986.
Hudry,
J.-L. ‘Aristotle on Meaning’, Archiv
für Geschichte der
Philosophie 93, 253-80, 2011.
Hudry,
J.-L. ‘Aristotle on Deduction and Inferential Necessity’,
Review of Metaphysics 67, 3-30,
2013.
Hudry,
J.-L. ‘Aristotle on Modality and Predicative Necessity’,
International Philosophical Quarterly
53, 5-21, 2013.
Hudry,
J.-L. ‘Aristotle on Non-Contradiction: Philosophers vs.
Non-Philosophers’, Journal of
Ancient Philosophy 7, 51-74, 2013.
Kirwan,
C. Aristotle’s Metaphysics: Books
Gamma, Delta, and
Epsilon. Clarendon Press, 1993.
Łukasiewicz,
J. ‘Aristotle on the Law of Contradiction’ In Articles on
Aristotle: Metaphysics.
Barnes, Schofield, and Sorabji (eds.).
Duckworth, 1910/1979.
Priest,
G. Doubt Truth to be a Liar.
Oxford University Press, 2006.
Wedin,
M. ‘Some Logical Problems in Metaphysics Gamma’, Oxford
Studies in Ancient Philosophy
19, 113-62, 2000.
Wians,
W. ‘The Philosopher’s Knowledge of Non-Contradiction’,
Ancient Philosophy 26, 333-53, 2006.
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