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Abhava, Millnong project, abstraction: descriptions and negation

In the Square of Oppositions conference last month in Lebanon, Mihir Chakraborty considered absence to understand negation and as a positive concept. The idea is central to the notion of abhava in Indian logic. Then there are objects and absences of objects over which, supposedly, once could quantify. I asked him how close Abhava was from a Meinongian theory of objects. His first reaction was to say that to think of the absence of something as an object was not a Meinongian move. In fact, it could seem that one can refer to absences using the original objects - and not descriptions - allowing them to have a modally open horizon of life (as I defined previously in this blog (for example, http://anarchai.blogspot.com.br/2011/06/open-horizon-of-life-and-absolute-other.html and http://anarchai.blogspot.com.br/2011/06/challenges-for-millnong-project.html). The name of an absence would be designed through the name of the lacking object. If this were so, I thought absences could be a way to implement the Millnong project - the project of combining Meinong and Mill by considering non-existing objects as independent from descriptions.

However, this individualization procedure would fail precisely because in this case there is no concretude: the absence of a book on the table is also the absence of a pad on the table unless I describe it one way or another. Nothing can then come and upset my modal tales about how the absence of the book would be if something else were the case. The absence of the book would be necessarily such absence - no modally open horizon. Absence of objects are like mathematical objects - utterly Meinongian in the sense of fully dependent on descriptions. No trace of the independent life that concretude can provide.

Interestingly, Juan Manuel Benitez had discussed, minutes earlier, Buridan´s octagon of oppositions. From a nominalist point of view, predicates should also not be devoid of the modally open horizon of life: they are not associated to descriptions and, viewing them as concrete universals, one could quantify over them. So if being mortal is an object, one can quantify over it and say, for example, being some mortal or being every mortal. (Then, clearly, instead of an A proposition, s is P, we have at least two, s is all P and s is some P.) However negation introduces abstraction and makes it impossible for something to carry on enjoying the modally open horizon: when we say s is no P, we would be close to the notion of absence. And, unless absence can be thought somehow not in purely Meinongian terms (which would amount to the Millnong project), descriptions would have to be fully brought in. It seems that a theory of descriptions is a chapter of a theory of negation.

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