.The principle of the excluded middle is incomplete, in my view, and we miss a principle of the fourth excluded, replacing it. The formulation of this new principle should be: a thing or a quality is something or is not something, or is both fields (be something and not be something), simultaneously, and there is no place to the fourth hypothesis. In fact, the principle of excluded middle, immensely useful in determining the dialectical law of principal contrariety - marxists call it principal contradiction, for example, Allied against the Axis in 1939-1945 - seems insufficient on considering intermediate states. The excluded middle postulates: a thing or quality belongs to group A or group not A, not having the third hypothesis.
This commitement finds difficulties. For example, the hermaphrodite does not belong neither to the group male nor to the group female, whether he has a rudimentary male sexual organ and an incipient female sexual organ. He belongs to both groups. The principle of the excluded middle does not include simultaneous something belonging to both grups.The chessboard simultaneously belongs to genus white and not white: white in diagonal white squares and non-white, black in this case, in the diagonals black squares.
With this principle of the fourth excluded, the reality of the triad (the contraries and the intermediate) fits the dyad (A, not A), invades somehow this one, instead of constituting a separate intermediate range. The three stays within the two rather than constituting one segment apart. It should be noted that Aristotle, the great master of logic, argued that only contraries have intermediate - example: every human being is an intermediate between love and hate - and that the contradictories have no middle term between them - i.e., any entity is Dog or not Dog, without intermediate state. I suppose I could say that if it is true that the contradictories have no intermediate term, they can have an intra-mediate term, I mean, a term that is common to both and is within them, simultaneously, not in a neutral zone boundary. It would therefore, constitute an internal synthesis and not an external synthesis.
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© (Direitos de autor para Francisco Limpo de Faria Queiroz)
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