Malcolm Fraser

Contradiction is a relation existing between two terms or two proposals of which one (E) affirms what the other denies - has and non-A are contradictory, the sentences “All the men are bearded” and “Some men are not bearded” are contradictory -.

We will name “principle of contradiction” this law which wants that one cannot affirm and deny the same term or the same proposal: " It is impossible that the same attribute belongs and does not belong at the same time and under the same report/ratio to same a chose" (Aristote, Metaphysics, 1005 B 19-20). Undoubtedly, a thing can be white today or of another color tomorrow. In the same way, this thing is larger or smaller than another at a given time. But, it is impossible that these determinations appear simultaneously and apply same point of view to this thing. Impossible thus that at the same time a thing either and is not.

Need for the principle of contradiction?

The principle of contradiction is a Axiome

Aristote poses the principle of contradiction like a peremptory necessity. It is a Axiome, i.e.: it is a truth first which contributes to show the other truths, but itself cannot be deduced under the terms of its simplicity and of its character first. What is it to say more precisely?

In the first time, it acts of the character " performatif" principle. Whoever is not limited to silence but agrees to say something of judicious, since it starts to speak, known as something of given and implicitly excludes the reference to another thing: to say has, it is to exclude to hear all that is not has, or which is non-a. This “monstration” of the principle ensures of it the infallibility simply because the principle of contradiction will be the prerequisite of very thought and of any speech. “ the principle is not to require of the adversary to say that something is or is not, but to at least say something which presents a significance for itself and for others . ” (Metaphysical Aristote, , 1006 has 18-21) Toujours already, we give feel so that we name. the decision of the direction constitutes, for B. Cassin and Mr. Narcy, the significance and the essential stake of the principle of contradiction. The proscription of contradiction becomes an obviousness first and indémontrable, since it conditions until the possibility of saying something.

In the second time, the non-contradiction did not arise only with the speech. It possible, and is perhaps required, to seek the base in the plan of it to be it itself. Logical impossibility to affirm and deny at the same time the predicate of the subject is based on the ontological impossibility of the coexistence of the opposites. Consequently, more than one fault of speech, contradiction becomes the measurement even of the unthinkable one. It is an inconsistency revealed in all its nonsense by the seven arguments exposed at the end of the 4th chapter of the Book Gamma of metaphysics. For example, if reality is contradictory, then, Aristote concludes, there is no more distinction between a man and a boat - cf in particular Métaphysique 1007 B 20 -. In addition, the contradiction which the movement implies - what exchange contradictorily becomes what it is not - is only one appearance. It would be “ignorance, indeed,” to have forgotten the principles exposed in the Physique .

The principle of contradiction is an ethical need

In its work, Of the principle of contradiction at Aristote , Jan Łukasiewicz comments on and critical the company aristotelician. According to him, Aristote fails in the task which it set: it cannot justify the absolute need for a principle of contradiction. However, if the argumentation of Aristote is defective, its principle does not remain less essential about it. In another optics however: no longer like an ontological or logical law but like practical need. An anthropological fact orders and imposes a principle of contradiction. It is our only weapon against the lie and the Relativisme of the Sophistes.

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