I put this question as to what Peirce himself meant by "non-implication" on Peirce-L. A couple of responses there focused on the diversity, and sometimes disparity, of consequences that can implicatively follow from a term or concept. "Non-implications" seems taken as referring to what are still implications but are ones not meant, not noticed, unexpected or unintended consequences of the term or concept. In one of the posts, Eugene Halton modifies the passage from Peirce's to say:
In another sense, honest people, when joking, intend to make the meaning of their words multi-determinate, so that there shall be latitude of interpretation. That is to say, the character of their meaning consists in the implications and non-implications of their words; and they intend to ambiguate what is implied and what is not implied.
This semantic ambiguity is not only the basis of humor, but also of art. And I would argue it is the basis for trapping, tricking, and taking advantage of all sorts of unthinking animals, unsuspecting humans, and various situations.
Further still though, it is these different, and even contrary, consequences that drive us back into our understanding of a term or concept itself. Cathy Legg noted:
Plato was also brilliant at 'speaking doubly' for purposes of awakening philosophical insight …
Thus, for example, the disparity of the use-value and exchange-value as consequences of the concept of "commodity," that can be taken advantage of on a practical level, can also propel us to look at the diagrammatic structure of that concept, its applications and consequences, such that it does produce, rightly or wrongly, these contrary consequences.
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