Continuing from Lowell 2.16, https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-low ell-lecture-ii/display/13626
Lines of identity bring only one new rule of illative transformation. (Illative transformation, by the way, is transformation of the nature of necessary inference.) But lines of identity require some slight changes to be made in the three primary rules already given. Under the rule of omission and insertion, it is to be noted that a line of identity may be broken within an even number of cuts or on the sheet of assertion, while two lines may be joined within an odd number of cuts. We also have the curious fact that as far as this rule is concerned a point on a cut is to be treated as being within the cut, although in other respects it is to be treated as being outside the cut. The cause of this is that we take it for granted that something exists. How this cause produces this effect I shall leave it for you to make out. The rule about the double enclosure receives an extension since not only are two cuts of no effect when no graph is between them, but they are equally so when nothing is between them except lines of identity that traverse the space between the two cuts. The rule of iteration and deiteration takes a form which cannot easily be expressed without defining a new term, ligature. Namely, a line of identity is, as I have said, a graph and as such it cannot be part on one side of a cut and part on the other side. In the graph there are two lines of identity. But their having a common point on the cut identifies the individuals they denote. By a ligature is meant a line of identity together with all other lines of identity that have points in common with it. For example means any man loves himself. It has four lines of identity, one attached to the monad spot "is a man," two attached to the dyad spot loves and one joining the triple point to the inner cut. But all those make a single "ligature." 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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