EVANDRO AGAZZI

C A N K N O W L E D G E BE A C Q U I R E D

T H R O U G H C O N T R A D I C T I O N ?

1. Contradiction, at least in Western thought, has always been con- sidered as the first enemy of knowledge, in the sense that the discovery of a contradiction is the surest evidence of error, but error is the exact contrary of knowledge (Parmenides, Aristotle, etc.).

2. Why is this so? Because the principle of 'non-contradiction' is actually the principle of 'diction', i.e., one cannot claim anything without making a definite claim, and this means without distinguishing it from what it is not. Indeed claiming something and the negation of it amounts to claiming nothing at all (hence, as Aristotle says, one would be reduced to silence, one would become "like a tree").

3. All this means that knowledge cannot consist in contradiction, but does not exclude that it may be acquired through contradiction, provided this claim be correctly understood, i.e., in the sense that it is often through the discovery and subsequent removal of contradiction that knowledge is acquired. This was already clear with Parmenides.

4. In order to see this role of contradiction more clearly one has to distinguish at least two different ways in which discovery and elimina- tion of contradiction occur and play the role of the elimination of error: (i) contradiction within discourse, and (ii) contradiction between dis- course and 'reality'.

5. Contradiction within discourse may surface in different ways, but its being inadmissible is based on the fact that one cannot think anything without thinking something definite (see point 2 above). Hence if our discourse leads us to say contradictory things, there is no thought that could be expressed by that discourse, so that it becomes meaning- less. Of course it is possible to utter (verbally) contradictions, but this does not mean that we can attach a meaning to these utterances (Aristotle said that "not all that one says, one also thinks"). Note that all this regards the semantic logos, i.e., the level of meaning, and not yet the apophantic logos, or level of 'affirming and denying'. In Fregean terms, no Sinn can correspond to a contradictory concept (such as a

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206 EVANDRO AGAZZI

'square circle'), nor to a contradictory statement (which cannot express any Gedanke).

6. Logical consistency is a particular way of treating the above sketched requirement, in the sense that it forbids admitting a formal system in which contradictions of the kind (A and non-A) may be deduced. However here the question is rather complicated, since we have at least two possibilities:

(i) The contradiction emerges because it was implicit in the pre- mises (i.e., in the 'non-logical' axioms), and was brought to light by means of a set of 'correct' logical rules.

(ii) The contradiction was not implicit in the premises as such, but was produced by a particular logical calculus used in the deduction.

From (ii) follows the problem of characterizing logical contradiction, e.g., in terms of 'non-triviality', or of rejecting the possibility of deduc- ing formulae of the kind (A and non-A). However, it must be noted that the above aspects are interrelated, since it cannot be said whether certain premises are 'consistent in themselves' or not if we do not implicitly admit that they are such with reference to an 'ideal' correct logic to be used in deducing their consequences.

7. The case of contradiction between discourse and reality is much more complex, since it means that something which can be said in a consistent way (and hence be thought) may come into collision with something which is outside the discourse. How is this possible? One answer could be that reality 'has its own discourse', which is or may be at variance with ours; but this pictorial solution is actually no solution at all. The contradiction may emerge only if we are able to 'translate' the alleged discourse of reality into ours, so that this translation leads to a statepaent S of our discourse equivalent to a negation of some other statement A of our discourse, with the result that admitting S would amount to admitting A and non-A within our discourse.

8. But so what? Is it not possible that two discourses be mutually incompatible while both being internally consistent? Moreover, why should we worry about that inconsistency, if we do not know whether the other discourse is itself consistent? But even in this case, are we entitled to presuppose that the consistency of non-contradiction we accept for our discourse is the same as the consistency of the other? In other words, claiming that we must remove contradiction between our

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discourse and reality might mean either that we want to impose on reality our criteria of consistency, or that we accept that reality imposes its criteria of consistency on us.

9. These remarks show that the so-called 'contradiction between discourse and reality' is of a really new kind: indeed it imposes the transition from meaning to reference and installs the level of the apophantic discourse proper. The transition from the one to the other might be expressed as follows: in the same way that it was recognized that 'not whatever can be said can also be thought', it must now be recognized that 'not whatever can be thought must be real'.

10. The last statement can be understood in two different ways, leading to two opposite outlooks. According to the first, it means that it is not the case -- to put it briefly -- that 'the laws of thought and the laws of reality are the same'. According to the second, it means that, in spite of these laws being basically the same, they do not fully determine the 'content' of statements concerning reality. The first position leads to scepticism and solipsism the second to a programme of rational investi- gation of reality. There is of course also a third position, claiming that 'whatever can be (correctly) thought is also real', and this is idealism.

11. The second position mentioned is that already advocated by Parmenides, and which may be called the idea of 'non-contradictoriness of reality', based on the ontological principle that nothing can at the same time and in the same respect be and not be (this is the so-called ontological formulation of the principle of non-contradiction). This position enables us to claim that whatever is contradictory cannot be real, while still admitting the possibility that something which is not contradictory in itself might fail to be real (but be only 'possible').

12. Within this position it is no longer necessary to use the pictorial image of the 'discourse of reality'. The discourse is always ours, but when it is referential it speaks of reality (and this leaves open many complex ontological precisions). It follows that whenever we find contradictions between referential sentences of our discourse and other sentences already admitted in it, we must remove the contradiction, if we intend our discourse to remain referential (i.e. to be about reality, and not simply about possibilia). The contradiction may be removed not by saying that reality might perhaps be inconsistent (this would amount basically to admitting the unintelligibility of reality), but either

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(i) by checking whether reality was correctly represented in our referential sentences or (ii) by modifying the body of already admitted sentences in order to make it consistent with the new referential ones.

13. From what has been said it is possible to see how contradiction may contribute to the acquisition of knowledge. The discovery of a contradiction is indeed the discovery of an error, both in the case of purely logical contradictions, and in that of contradictions 'between discourse and reality', and the elimination of the contradiction corre- sponds to the elimination of an error. This is already an acquisition of knowledge.

14. But more can be said if we ask how it was possible to believe the error before discovering that it was an error. The answer is that the erroneous statement was in itself meaningful and as such not contradic- tory. Hence it corresponded at least to some possible state of affairs and (in most cases) it fitted well a certain state of affairs. The discovery of the contradictions has therefore the meaning of uncovering the partiality of the claim contained in the error. This corresponds well to the fact that 'men learn through errors' and that knowledge in general (including scientific knowledge) advances through errors as well. The fruitfulness of errors consists in their being not so much destructive as rather corrective (perhaps contrary to Popper's falsificationism): they show limits much more than plain falsities.

15. This is possible because contradiction, though formally ex- pressed through (A and non-A), never comes about as a mere negation (which 'infinitizes' and as such is not informative), but as a determined negation (which is informative), and demands an overstepping of levels in which it must be possible to account for both partial aspects. This after all is the correct claim of the dialectic way of thinking.

SOminaire de Philosophie, Universit~ de Fribourg, CH-1700 Fribourg, SWITZERLAND