Antonio Calonego

Notes on negation and contradiction

 

[1] In the propositional calculus of Logic, given a proposition "p", it is always allowed to construe a new proposition "~p" just placing the symbol of negation "~" before it. As it is well known, the symbol of negation turns the true of "p" into the falsity of "~p" and viceversa, i. e. it excludes that the two propositions can be both true and false together and, so working, it gives rise to an extreme case, which occurs when the two propositions are linked each other by a logical conjunction.
A logical contradiction ("p AND ~p") presupposes this role played by the symbol "~" and, therefor, a very strong concept of negation as it was a sort of external force, so to say, which turns upside down the previously assigned true-value of a given proposition any time it applies to it.

[2] In everyday language the role of negation doesn’t identify with the one we sketched above.
One can oppose someone else who claims. "This is white", by saying: "No, this is not white". But it is wrong to consider the stated answer as if it could only be an instance of "~p" and had to match so strong a sense of negation as the logical one. There’s no reason, in principle, to shut out that "No, this is not white" could be interpreted as "No, it is not-white", meaning, for instance, it is black. The negative proposition, then, would certainly exclude its opponent can be true if it is true, but it would not exclude the falsity of the two both.
Moreover, to someone saying: "It is sweet" I could reply "No, it is bitter", giving for granted it can’t be nor sweet nor bitter (the two propositions can’t be both false), but not excluding it may be either sweet either bitter (the two propositions can be both true).
In everyday language the role of negation is context sensitive: it depends on circumstances and can’t be fixed once forever.

[3] For a proposition like "~ this is white" to be a negation, in the strong sense, of "this is white", the term "white" has to maintain the same sense in both cases. But the "permanence of meaning", which can be properly achieved only by a scientific discourse, is, in everyday language, rather problematic.
Suppose "~ this is white" is now a genuine negation, in the strong sense, of "this is white".
In everyday language, the sheer presence of a strong sense of negation is not sufficient to conclude that a contradiction is there. As long as the two "parties" fighting each other are thought as excluding alternatives (as aut … aut) there isn’t any contradiction: we feel we must share one position, because it is true, and oppose the other because it is false; we don’t feel entrapped in any contradiction.
It is when we begin to view our experience as from a distance and take it as a whole (as if an AND now linked what was formerly separated by an aut) that a contradiction appear.

[4] A contradiction is based on a very peculiar use of negation and it seems to be there no universal reason to assign to it a primary position, as far as everyday language is concerned.
Those who take up everyday language as a paradigm and think it can represent the last word in Philosophy, will conclude that also at level where theories are built up, it is wrong to assign to "contradiction" a primary position.
On the contrary, those who assume that the very task of intellectual research is to construe or find out an order, fixing concepts and drawing up hierarchies of meanings where the everyday man can’t see but a disperse plurality, will not agree to shut out, at least in principle, a determinate theory which, for instance, would explain society saying that its basic and relevant conflicts are contradictions – though they will likely ask it to define "relevant" and provide evidence and reasons. (We won’t say, then: "The relevant conflicts of this society are contradictions"; we'll say: "Given this theory so and so grounded, the relevant conflicts of this society are contradictions").
But, in both cases, "contradictions" are not a natural law of human life nor the dynamic core of a living Totality (for which the asking for evidence would be senseless).