I realized too late that I made Lowell 2.9 too short, so I'll make up for it this time with a longer excerpt, starting in the middle of 2.9:
Beginning then with the sign which consists in scribing together, or as we may term it, compounding, the definition of it in terms of permission will be 1st, predicating the definition of the definitum, if it is permitted to scribe on the sheet of assertion a replica of a compound graph, then it is permitted to scribe on the sheet of assertion a replica of either component. Or, stating this in terms of transformations: Any replica of a compound graph may on the sheet of assertion be transformed into a replica of either component. That is to say, under a more practical aspect, any partial graph on the sheet of assertion may be erased or cancelled. This shall head our list of alpha permissions[:] Permission No 1. Any graph on the sheet of assertion can be erased. 2nd, predicating the definitum of the definition: if it be permitted to scribe on the sheet of assertion a replica of which we please of two graphs then it is permitted to scribe the replica of the compound graph of which those two are the sole components. Or in terms of transformation, if it be permitted to transform the blank sheet into either we please of two graphs, it is permissible to transform it into the compound of the two. That is to say, under a more practical aspect, whatever might be scribed on the sheet of assertion were this blank, can be scribed regardless of what is already scribed. This shall be our second alpha permission. Permission No 2. Whatever is permissively scribable on the sheet of assertion is so regardless of what is already scribed. Let us now treat the scroll in the same way. First, the predication of the definition with the definitum as subject is that when it is permitted to scribe upon the sheet of assertion a scroll with two graph-replicas, x and y, in its outer and in its inner close, or on its bottom and on it[s] patch, respectively, then whenever it is permitted to put the graph x upon the sheet of assertion, it will likewise be permitted to put the graph y upon the sheet of assertion. Or in terms of transformation it will be permissible on the sheet of assertion to transform x by the insertion into it of y as a component of a compound graph xy. In order to put this into a more explicit shape, I will first call your attention to a corollary from it. A corollary to a proposition of Euclid is a necessary consequence drawn from it by some editor of Euclid's Elements and inserted by him, originally, I suppose, marked with a little crown in the margin. These additions are, for the most part, propositions that Euclid thought too obvious for special notice. Hence, any easily drawn necessary consequence of a proposition is termed a corollary. Here I will tell you a secret about necessary consequences. It is a very useful thing to know, although most logicians are entirely ignorant of it. It is that not even this simplest necessary consequence can be drawn except by the aid of Observation, namely the observation of some feature of something of the nature of a diagram, whether on paper or in the imagination. I draw a distinction between Corollarial consequences and Theorematic consequences. A corollarial consequence is one the truth of which will become evident simply upon attentive observation of a diagram constructed so as to represent the conditions stated in the conclusion. A theorematic consequence is one which only becomes evident after some experiment has been performed upon the diagram, such as the addition to it of parts not necessarily referred to in the statement of the conclusion. In the present case, I am going to draw a conclusion about a double enclosure, that is, two cuts one within the other and with the annular space between them blank like this The observation which I ask you to make is that in every such case there will be a graph of which one replica is in the outer close while another is on the sheet of assertion outside. Namely, that graph is the blank. And since the present principle permits us to transform [into] whatever x may be, it allows this transformation when x is the blank; so that we can transform into We may count this as our third permission, so that we have Permission No 3. A graph within a double enclosure on the sheet of assertion may be scribed on the sheet of assertion, unenclosed. The consideration of what further explicit permission is involved in the predication of the definition, the definitum being the subject, had better be postponed until we have considered the predication of the definitum the definition being the subject. This predication is that in case the permission to scribe on the sheet of assertion a replica of a graph, x, would carry with it in every case a permission to scribe on the sheet of assertion a replica of a graph, y, then it is permissible to scribe on the sheet of assertion a scroll containing in its outer close only a replica of x an in its inner close a replica of y. Or in terms of transformation, if it would be permissible to transform a graph, x, should it occur on the sheet of assertion, into a graph, y, then it is permissible to transform a blank on the sheet of assertion into a scroll having only x in its outer close and having y in its inner close. We may here draw a corollary analogous to [?], but much more obvious. Namely, To say that it is permissible to scribe any graph, y, on the sheet of assertion is to say that it is permissible to transform a replica of the blank into a replica of y. But this, according to this part of the definition of the scroll, permits us to place on the sheet of assertion the scroll Hence we have Permission No 4. If a graph could be permissively scribed on the sheet of assertion a double enclosure containing that graph may be placed on the sheet of assertion. 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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