Non-Implications

In a colloquium I recently attended this passage was cited from Peirce.

In another sense, honest people, when not joking, intend to make the meaning of their words determinate, so that there shall be no latitude of interpretation at all. That is to say, the character of their meaning consists in the implications and non-implications of their words; and they intend to fix what is implied and what is not implied. They believe that they succeed in doing so, and if their chat is about the theory of numbers, perhaps they may. But the further their topics are from such presciss, or "abstract," subjects, the less possibility is there of such precision of speech.  ["Issues in Pragmatism," The Monist, 1905]

What, however, are "non-implications"?

Apparently, non-implications can be looked at as just the negation of implication, in which case the non-implications would seem to refer to any exceptions to the implications.  That is, we would have certain implications or consequences by which a word or concept is generally understood, but to understand it clearly, we would also have to be aware of any exceptions to those inferences.  I'm not sure how must sense that makes, and it does seem a bit strict.  As Peirce says, "perhaps" we can do this with something like the theory of numbers but with other things it's not really feasible.

The speaker at the colloquium (Dave Beisecker of UNLV) approached this use of "non-implication" in terms of implications that would be "permitted" as opposed to those that would be "obligatory."  Diagrammatically, I find this proposal interesting.

For example, within the context of a roadmap inferences regarding distances and towns are obligatory but those regarding the shape of the roads or rivers drawn on it are not.  In general, some elements of any diagram (or concept) would seem to be functionally obligatory while others are not.

Or, in the case of Mark Twain becoming a steamboat pilot, he says:

Now when I had mastered the language of this water and had come to know every trifling feature that bordered the great river as familiarly as I knew the letters of the alphabet, I had made a valuable acquisition. But I had lost something, too. I had lost something which could never be restored to me while I lived. All the grace, the beauty, the poetry had gone out of the majestic river! [Chapter 9, Life on the Mississippi]

Is that really true?  Twain goes on to describe a memorable sunset in vivid and exquisite detail. Don't those permitted inferences continue within the diagrammatic functionality of obligatory inferences, giving some color and life to sterility of the diagram itself?  It would seem such experiences would still be possible, that they are still part of the concept.  Is that where the diagrams of our thinking go astray?  When our concepts are not coupled to a direct acquaintance with the thing itself and all those merely permitted implications that can come along with the strictly functional ones?