Thinking about Contradictions by Venanzio Raspa

Author:Venanzio Raspa
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

In this formulation, which substantially corresponds to the formulation of the principle of contradiction in An. post. i 11 (see Sect. 4.​1), contradictory objects are not given in our world, and from this arises the necessity to postulate an imaginary world for a logic devoid of the law of contradiction.

As to negation, Vasil’ev defines it in a manner that mirrors (1):

(4) “negation is that which is incompatible with affirmation.”24

Vasil’ev aims in fact to show that the law of contradiction is already included in such a definition and therefore his strategy consists in working out a different concept of negation, one in which elements of both a logical and ontological order are fused.

In this case too, Vasil’ev develops his idea by taking Sigwart ’s Logik as his point of departure. Sigwart — as is evidenced in the essay “On Particular Judgments, the Triangle of Oppositions, and the Law of Excluded Fourth” — had taken negation to be “a judgment concerning a positive judgment that has been essayed or passed [ein Urteil über ein versuchtes oder vollzogenes positives Urteil],”25 that is, as an act which the subject makes against an affirmation, or at least against the idea of an affirmation, where one asserts its falsity. It follows that the negative judgment is incompatible with the affirmative judgment, but does not have the same value: to the contrary, it is subordinate to it, in so far as it is understood only in relation to the affirmation, without which it could not even exist.26 All this has an ontological foundation, namely that neither sensations nor representations are given of negative ‘things.’ Consequently, Vasil’ev takes affirmation to be a judgment on objects or facts, one grounded in sensations, perceptions or representations of such objects or facts, which are as positive as their respective sensations and perceptions.

If, however, only positive facts and objects exist, for which there are corresponding equally positive sensations, perceptions or representations, and if therefore, only the affirmative judgment is directly grounded on the sensation and perception of facts and objects, the negation, to which nothing real corresponds, cannot be, from a logical point of view, anything other than the ‘refusal’ by the subject of something positive. Thus, negation is invariably deduced, or simply asserts the incompatibility between predicates (in a sense that will be immediately clarified).

With regard to definition (4), Vasil’ev specifies that negation is given if there is, in effect, an incompatibility between predicates: it is not given if there is a simple difference between them, or where a predicate is lacking. In the first case, he explains that the negation of blue cannot be something like dry, which is not incompatible with blue, but rather something that falls under the non-blue, in other words, red, white, orange and so on. This clearly recalls to mind the conception in Husik, who restricted the meaning of negation to its region (see Sect. 4.​2).

If dry is a negation of blue — Vasil’ev argues —, then any statement ‘dry can be blue’ will be a breach of the law of contradiction, a coincidence of affirmation and negation.

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