Gary F, List,
Following on the heels of your remark about transformations of graphs involving "insertion or erasure, iteration or deiteration", let me add the following. I place great weight on Peirce's suggestion that, ultimately, there are only three such permissions in the existential graphs that are needed to understand the nature of the illative transformation. Those are colligation, iteration and erasure. (CP, 5.579) My assumption is that he is making a point about any kind of illative transformation when he says this, and not just the transformations involved in deductive inferences. After all,his main point in this passage is that these three permissions are precisely what is needed in order to gain a deeper understanding of the self correcting character of any kind of inference--including inferences by induction and abduction. --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: [email protected] <[email protected]> Sent: Sunday, December 3, 2017 12:35:06 PM To: 'Peirce List' Subject: RE: [PEIRCE-L] Lowell Lecture 2: conclusion List, In wrapping up this serialization of Lowell Lecture 2, I’d like to reiterate a couple of key points about existential graphs. One is that their purpose, according to Peirce in this lecture (and elsewhere), is “to enable us to separate reasoning into its smallest steps so that each one may be examined by itself”; and each “step” is a transformation of one graph to another, according to the rules (conventions, permissions) outlined by Peirce. It follows that “a reasoning” is a process which can only be represented by a sequence of transformations. A single graph can represent a proposition but not an argument. The transformations of graphs can involve insertion or erasure, iteration or deiteration, and now extensions of ligatures — all of which operations can take place across cuts. Peirce’s example here is the Victoria-and-Edward sequence: from the premisses that Victoria is Edward’s mother and that any mother loves her sons, we deduce that Victoria loves Edward, and this reasoning takes five steps in EGs. The final set of graphs in Lowell 2 show the different effects that ligatures can have depending on which cuts they cross. This shows diagrammatically how spots can be connected to individual subjects, and thus connected to each other, across cuts — and thus how different areas or universes can be related to one another. This is a semiotically vital possibility, semiosis being the realm of the Third Universe: [[ The third Universe comprises everything whose Being consists in active power to establish connections between different objects, especially between objects in different Universes. Such is everything which is essentially a Sign,—not the mere body of the Sign, which is not essentially such, but, so to speak, the Sign's Soul, which has its Being in its power of serving as intermediary between its Object and a Mind. Such, too, is a living consciousness, and such the life, the power of growth, of a plant. Such is a living institution,— a daily newspaper, a great fortune, a social “movement.” ] EP2:435 ] This completes our rough sketch of alpha and beta parts of existential graphs; we will get to the gamma part, as Peirce says in closing, in a later lecture (4). But the next step in the Lowells is into the phenomenological “categories” or “elements.” I’ve already uploaded to my website the text of Lowell Lecture 3, http://www.gnusystems.ca/Lowell3.htm, and will start serial posting of it shortly, but we can still continue any unfinished conversations about Lowell 2, if anyone is so inclined. Gary f. From: [email protected] [mailto:[email protected]] Sent: 3-Dec-17 07:21 To: 'Peirce List' <[email protected]> Subject: [PEIRCE-L] Lowell Lecture 2: conclusion Continuing from Lowell Lecture 2.17, https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii/display/13629 This concludes Lowell Lecture 2. 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 [cid:[email protected]] 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.” Now the reformed rule of iteration and deiteration is, that any partial graph, detached or attached, may be iterated within the same or additional cuts provided every line or hook of the iterated graph be attached in the new replica to identically the same ligatures as in the primitive replica; and if a partial graph be already so iterated it can be deiterated by the erasure of one of the replicas which must be within every cut that the replica left standing is within. For example, suppose we have these premisses: [cid:[email protected]] We can iterate the two outside lines of identity within the outer cut, thus: [cid:[email protected]] Within one enclosure we can join the two lines on each side, thus: [cid:[email protected]] We can now deiterate “mother of”, thus: [cid:[email protected]] We can now erase the two cuts which have nothing between them but lines of identity, thus: [cid:[email protected]] We can now erase “mother of,” thus [cid:[email protected]] I now proceed to the new fourth rule. It runs as follows: The innermost effective ligature between two spots lies within every cut that encloses both those spots. In order to illustrate the meaning of this I take these [five] graphs: [cid:[email protected]] The first three of these mean, respectively, “Nobody loves anybody whom he does not respect,” “Somebody loves nobody whom he does not respect,” “Somebody is loved by nobody who does not respect him.” Those three propositions cannot be expressed, with the same degree of analysis, without the ligature the innermost of which is within the cut that encloses both spots. But the fourth, which means “There is somebody whom somebody does not love unless he respects him” will not have its meaning changed by breaking both ligatures, as in the fifth graph, so as to make it read “Either there is somebody who non-loves somebody or else somebody respects somebody” or “If everybody loves everybody somebody respects somebody.[”] The juncture protruding through two cuts could be cut without altering the meaning: [cid:[email protected]] By putting two cuts round the “loves” and retracting the junctures through two cuts we get the equivalent graph [cid:[email protected]] The third chapter of the exposition of existential graphs is by far the most important and interesting of the three. The whole gist of mathematical reasoning depends upon it. I shall have to remit it to another [lecture.] http://gnusystems.ca/Lowells.htm }{ Peirce’s Lowell Lectures of 1903 https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii
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