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José M. Méndez 
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transdiciplinary, logic, semantics, critical theory
 German Widerspruch

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J.M. Díaz Nafría (20/07/2009)
[This entry is also provided in Spanish version]

Relationship between an affirmation and a negation having the same subject and predicate. It was traditionally studied under the “law of non-contradiction” and initially formulated and studied by Aristotle as a supreme principle of beings and thinking. It can be formulated as: 

“the same attribute cannot at the same time belong and not belong to the same subject and in the same respect.” (Aristotle, Metaph. B.IV, §3)

It has adopted a twofold interpretation distinguished by either a logical or an ontological sense, even erecting as an ontological principle, i.e. as expression of the constituting structure of reality. However, its fall as unquestionable principle can be found in Hegel’s regard of contradiction  as a basis of reality’s internal movement (though generally the philosopher refers more to opposing realities than contradicting ones) (Hegel 1841). Within the dialectic tradition of Hegelian roots, Adorno judges that there exists a link between the ontological and logical aspects (Adorno 1966). According to such link the “repressive structure of reality” and the coercive character of survival as well are reflected in the logical principle of contradiction (1956). Regarding Adorno’s negative dialectics, the possibility of transcending both the law of non-contradiction and the law of identity accounts for the capacity to overcome social contradictions. Generally according to dialectical schools, the consideration of the logical law is just subordinate to the need of overcoming contradictions of reality.

This –so to speak– utilitarian regard (genetic, following Adorno’s interpretation) of the law of non-contradiction can also be found in some of the information theories based on self-referential systems (autopoiesis). For instance, from a cybernetic perspective, the logical law of non-contradiction can be considered as being a part of the regulation mechanism under normal conditions, whereas the overcoming of such law corresponds to the need of re-adapting the mentioned regulation to changing circumstances (s. positive and negative feedbackcybernetics).

Although the law of non-contradiction might be easily refuted in its most brief expression (removing the italic text in the above formulation, without which it might be exposed to a large number of paradoxes), it must be pointed out that the remark of “at the same time and under the same respect” makes it less vulnerable. This remark also introduces a necessary contextualization of the statements (to which we have referred to in the →context article) for a correct analysis of the consistency of the semantic content of information, such as the approaches of Bar-Hillel and Carnap (1953), Dretske (1982) and Situation Theory (Barwise 1997) propose –though only the last ones consider context as a key issue– (→Situational logic).

In any case, the claim to consistency in what is considered →informational content means that contradictions have no place in informational context and, consequently, the probability of receiving self-contradicting information would be zero (according to a naturalistic approach on information, such as the one of Dretske, the ontological version of the law of non-contradiction states that contradictory information cannot emanate from reality, since reality itself rejects contradiction). Therefore, in case of considering the semantic content of an informative statement as inversely related to its probability –under Barwise’s inverse relationship principle (1997)–, the following paradox might arise: a contradiction provides a maximum amount of information, which Floridi (2005c) labels as the Bar-Hillel-Carnap Paradox. Circumventing this paradox, most of semantic approaches get somehow rid of contradictions.

Nevertheless, if a dialectical point of view is adopted (for instance, in critical theory) contradictions will not be something for turning a deaf ear, but, on the contrary, the possibility of updating the view of reality with fewer contradictions. That is, contradictions might somehow announce –so to speak- a new world, a new Weltanschaung. If it could be achieved, a new state of affairs could be seen, whereas much of what was previously seen would dissolve with the smoke of past errors. For instance, the superseding of classical physics due to accretion of contradictions of different nature –optical, electrical, astronomical, etc– can be regarded as one of these cases (Pointcaré 1904). However, it must be remarked, on the one hand, that rarely the so-called contradictions follow the clause of “at the same time and in the same respect”, on the other hand, that in normal situations –or what Kuhn (1962) called, concerning research work, “normal science”– the contradictions serve to detect false information, wrong interpretations, etc. Thus the law of non-contradiction becomes an essential tool to receive information in normal situations, as well as for its incorporation into knowledge systems.


  • Aristotle (350 BC), Metaphisics (translated by W. D. Ross). [online] Internet Classics Archive by Daniel C. Stevenson, Web Atomics <> [accessed: 12/12/2009]
  • Hegel, G.W.F. (1841). Wissenschaft der Logik. Erster Teil. Die objektive Logik. Berlin: Henning. [online] Guttemberg Project (ed. 2004) < > [accessed: 12/12/2009]
  • Adorno, T.W. (1956). Zur Metakritik der Erkenntnisstheorie. tudien über Husserl und die phänomenologischen Antinomien. Stuttgart: Kohlhammer.
  • Adorno, T.W. (1966). Negative Dialectics, (trans. E. B. Ashton, 1973). New York: Seabury Press.
  • Bar-Hillel, Y. & Carnap, R. (1953). Semantic information. British Journal of Science, 4, 147-157.
  • Dretske, F.I. (1981), Knowledge and the flow of information. Cambridge, MA: MIT Press.
  • Barwise, Jon (1997). Information and Impossibilities. Notre Dame J. Formal Logic, 38(4), 488-515.
  • Floridi, L. (2005c). Semantic Conceptions of Information. In E. N. Zahlta (ed.) Stanford Encyclopedia of Philisophy. Stanford: The Metaphysics Research Lab [online] <> [accessed: 12/11/09]
  • Kuhn, T.S. (1962). The Structure of Scientific Revolutions. Chicago: Univ. of Chicago Press.
  • Poincaré, H. (1904). The principles of Mathematical Physics. in P.L.. Williams (ed., 1968). Relativity Theory. New York: J. Wiley, pp. 39-49.

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