Continuing from Lowell 2.3, https://www.fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903 -lowell-lecture-ii/display/13602:
The most immediately useful information is that which is conveyed in conditional propositions, "If you find that this is true, then you may know that that is true." Now in ordinary language the conditional form is employed to express a variety of relations between one possibility and another. Very frequently when we say "If A is true, then B is true," we have in mind a whole range of possibilities, and we assert that among all possible cases, every one of those in which A is true will turn out to be a case in which B is true also. But in order to obtain a way of expressing that sort of conditional proposition, we must begin by getting a way of expressing a simpler kind, which does not often occur in ordinary speech but which has great importance in logic. The sort of conditional proposition I mean is one in which no range of possibilities is contemplated, which speaks only of the actual state of things. "If A is true then B is true," in this sense is called a conditional proposition de inesse. In case A is not true, it makes no assertion at all and therefore involves no falsity. And since every proposition is either true or false, if the antecedent, A, is not true, the conditional de inesse is true, no matter how it may be with B. In case the consequent, B, is true, all that the conditional de inesse asserts is true, and therefore it is true, no matter how it may be with A. If however the antecedent, A, is true, while the consequent, B, is false, then, and then only is the conditional proposition de inesse false. This sort of conditional says nothing at all about any real connection between antecedent and consequent; but limits itself to saying "If you should find that A is true, then you may know that B is true," never mind the why or wherefore. http://gnusystems.ca/Lowell2.htm }{ Peirce's Lowell Lectures of 1903 https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low ell-lecture-ii
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