Hi Gary F, List,
Colligation is a move by which separate propositions are brought together in a single premiss. As such, we might have: If anything is a man, then it is mortal. Socrates is a man. By colligation, we get: If anything is a man then it is mortal, and Socrates is a man. In terms of the EG, we bring two propositions together on the same sheet of assertion. This is easy to do if we thing of one as assertion A and another as assertion B. As such, we just scribe A B next to one another on the sheet. Given the fact that the first premiss of the argument above is couched in the form of a conditional, we'll need a scroll to express it in the EG. In order to bring the first and second premisses together by colligation, we'll need lines of identity between predicates forming a ligature crossing the scroll. As such, colligation in this case is more than just writing two assertions next to one another. It is an operation by which what were once two separate graphs are combined into one graph. --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 2:59:46 PM To: 'Peirce List' Subject: RE: [PEIRCE-L] Lowell Lecture 2: conclusion Jeff, list, I think your addition is a good fit. Colligation is a term (adopted from Whewell) that Peirce doesn’t seem to use much after the turn of the century, but it is etymologically related to ligature, the root concept being connection, and I can see how ligatures in graphs can do some of the colligation work. I agree that “illative transformations” are involved in all forms of inference; in the Lowell Lectures, I think Peirce took up deduction (“necessary reasoning”) first because he really thought it was the simplest form of inference (partly because it is strictly two-valued), and the most “elementary” to reasoning in general. (Even a digital machine can do it!) He left induction and abduction for the last two of the Lowell Lectures — which I haven’t read yet, so we’ll see later on whether this conjecture is borne out. Gary f. From: Jeffrey Brian Downard [mailto:[email protected]] Sent: 3-Dec-17 15:11 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
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