Negation and Difference

Abstract

Two theoretical orders have governed thought about negation. In the first, negation is construed as an activity of the mind in its capacity for "pure" thought or language. In the second order, negation is taken as grounded in experience and, so, as prior to, or at least exterior to, reflective thought and language. Within the first order, the task is to provide a proper semantic theory for some set of negative words or symbols. Within the second order, the task is to locate negation within the structure of experienced reality. The first is the order of Logic, the second of Ontology. The difference between the two orders is reflected in the symbolic notation each uses to signify the negative: "-A" for the logical order; "Nothingness" for the ontological. Each order must cope with an apparent asymmetry between negativity and positivity. No matter whether we consider them under the banner of Logic or Ontology, affirmative phenomena strike us as capable of "standing on their own" while negative phenomena are dependent on affirmative ones. Within the logical order, this asymmetry is reflected in the formal syntax for the negation operator. Negation occurs through the addition of the negation symbol and the corresponding action of the negation operation: IMAGE FORMULA3 Quine goes so far as to refer to this operation as "denial," explicitly naming negation as derivative upon an initial assertion.1 While there is debate over the extent to which negation in natural language is fully captured by the logical treatment of negation, linguists too are in agreement that negation is the "marked" case, i.e., the case that is formally more complex, morphologically more regular, and semantically less neutral.2 Within the Ontological order, the same asymmetrical relationship finds expression in the subordination of nothingness to being: There is more and not less, in the idea of an object conceived as "not existing" than in the idea of this same object conceived as "existing;" for the idea of the object "not existing" is necessarily the idea of the object "existing" with, in addition the representation of an exclusion of this object by the actual reality taken in block. (Bergson)3 It is Being, "the being present," that takes first place. In both the logical and ontological order, affirmation, as independent presence, stands opposed to negation as dependent absence. Within each order, the counter-view has struggled to find expression, striving to revoke the privilege granted to affirmation while at the same time explaining the appearance of affirmative precedence. Frege refused to allow that the syntactic markedness of negation corresponded to a subordinate status: "For every thought there is a contradictory (or opposite) thought; we acknowledge the falsity of a thought by admitting the truth of its contradictory. The sentence that expresses the contradictory thought is formed from the expression of the original thought by means of a negative word."4 For Frege, the co-emergence of a thought and its opposite indicates their logical equality. Negation indicates only a relative position. Hegel attempted something similar in his dialectical synthesis of Being and Nothingness. Being and Nothingness are shown to contain each other: "If when we view the whole world we can only say that everything is, and nothing more ... instead of absolute plenitude, we have absolute emptiness."5 Counter-charges immediately overshadow these attempts to flatten the distinction between the negative and the positive. For the need to specify a difference is keenly felt. As Merleau-Ponty reminds us, if Being and Nothingness are absolute opposites they are not defined by anything that would be proper to them. As soon as one is negated the other is there; each of them is only the exclusion of the other, and nothing prevents them, in the end from exchanging their roles.6 In other words, Hegel's formulation forgets the fundamental fact: "Being is and nothingness is not. …