Hi Gary F, List,
Gary F: "The implication is that the form of the “scroll” is in some way appropriate to its object, instead of being arbitrarily assigned to that object." The guiding idea for developing each sort of figure in the EG, such as the scroll, is to construct a diagram in which the parts of the figure stand in the same sorts of formal relations as the things we are trying to represent--such as the relation of antecedent and consequent in the conditional de inesse. As such, we need to carefully analyze the relations between the parts of propositions that express such a conditional, and then we need to see if the figure we are using as a diagram has the same sorts of relations--no more and no less. In order to make that comparison, we will need to arrive at a clear understanding of what kinds of relations are elemental in our experience generally--and then we will need to draw on that account of the relations that are elemental for the sake of examining how those elemental relations figure into (a) the assertion of a conditional proposition and (b) in the construction of such a diagrammatic figure. As far as I can tell, the same procedure is being applied to the construction of blot as an iconic representation of logical absurdity. In this case, we need to see that the same relations holds through the topological transformation of the diagrammatic figure as it is made to disappear. As such, it might look like a sleight of hand, but the question is whether or not such a continuous transformation is possible. That is, does the continuous transformation of the blot so that it disappears preserve or destroy the kinds of relations that we were trying to represent in the first place? --Jeff Jeffrey Downard Associate Professor Department of Philosophy Northern Arizona University (o) 928 523-8354 ________________________________ From: g...@gnusystems.ca <g...@gnusystems.ca> Sent: Saturday, October 28, 2017 1:34:57 PM To: peirce-l@list.iupui.edu Subject: RE: [PEIRCE-L] Lowell Lecture 2.6 List, I hope Jon soon finds time to unpack that post, but in the meantime I’ll make my own attempt to answer the questions provoked by Lowell 2.6. I should perhaps mention first that I’m posting all these things in HTML format, and anyone who’s trying to read them with a mail app that doesn’t handle HTML will not be able to see the “blackboard” diagrams that Peirce is referring to throughout. To see them, you’ll need to either change the settings in your email reader or read the version of Lowell 2 on my website instead. In 2.6, the point of the “experiment” is “to get an insight into how the scroll represents” this kind of conditional. The implication is that the form of the “scroll” is in some way appropriate to its object, instead of being arbitrarily assigned to that object. For this experiment we need some “means of expressing an absurdity.” Why do we need that? I guess it’s because we are dealing with necessary reasoning here, which means we have to assume (without any reason for believing it) that the given premisses are true — unless they are logically absurd; so absurdity is the only way for a statement to be necessarily false. And it seems we need a graph for falsity. As an example of absurdity, Peirce chooses the assertion “everything is true” — and even gives a reason for his choice. But now he wants it so serve as the consequent in a scroll, and instead of simply writing the words in the inner close, he represents it as a “blot” which fills up the area enclosed by the inner cut. It makes a kind of sense, graphically, that if the blank area is the place of assertion, the blotted (completely filled) area is the place of absurdity or necessary falseness. At this point the “experiment” resorts to a kind of magic trick: Peirce makes the blot disappear (gradually but completely) — yet falsity remains, like the grin of the Cheshire Cat. According to Peirce, “This suggests that the relation which the cut asserts between the universe of discourse and what is scribed within it is simply that what is scribed within is false of the universe of discourse.” I guess we are to assume that this is true of any cut, no matter how deeply nested within other cuts: the place of that cut is a universe of discourse, and whatever is scribed on the area inside the cut is false of the universe outside that cut. So we are being asked to believe that (1) the area of a cut on the sheet of assertion represents a “universe of supposition” (as Peirce said awhile back) AND that any graph written on it is false of the universe represented by the sheet of assertion; and (2) the area of the cut inside that cut bears that same relation to the area of the cut within which it is placed — and so on, all the way down. Intuitively, this is not easy to swallow, at least for me; this interpretation seems to be arrived at by sleight of hand on Peirce’s part. But apparently Peirce’s argument follows the actual course of development of EGs in his imagination: The meaning of the cut is derived from the meaning of the double cut, i.e. the scroll. Roberts has a footnote which reads: In Ms 650, p. 20, Peirce says “Before I had the concept of a cut, I had that of two cuts, which I drew at one continuous movement” (as a scroll). That, I presume, is why we started this exposition with the conditional de inesse. Anyway, I’m still trying to see this feature of EGs as naturally “iconic.” Gary f. From: g...@gnusystems.ca [mailto:g...@gnusystems.ca] Sent: 28-Oct-17 04:38 To: peirce-l@list.iupui.edu Subject: [PEIRCE-L] Lowell Lecture 2.6 Continuing from Lowell 2.5: https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii/display/13608 15 (C. S. Peirce Manuscripts, MS 455-456 (1903) - Lowell Lecture II) | FromThePage<https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii/display/13608> fromthepage.com 15 (C. S. Peirce Manuscripts, MS 455-456 (1903) - Lowell Lecture II) - page overview. 12 experimental research. At present Thus far, we have no means of expressing an absurdity. Let us invent a sign which shall assert that... In order to get an insight into how the scroll represents the conditional proposition de inesse, we must make a little experimental research. Thus far, we have no means of expressing an absurdity. Let us invent a sign which shall assert that everything is true. Nothing could be more illogical than that statement, inasmuch as it would render logic false as well as needless. Were every graph asserted to be true, there would be nothing that could be added to that assertion. Accordingly, our expression for it may very appropriately consist in completely filling up the area on which it is asserted. Such filling up of an area, may be termed a blot. Take the conditional proposition de inesse, “If it rains then everything is true[”:] [cid:image001.jpg@01D34FE8.185C8580] That amounts to denying that it rains. But there is no need of making the inner cut so large. Let us write [cid:image002.jpg@01D34FE8.185C8580] or even [cid:image003.jpg@01D34FE8.185C8580] This suggests that the relation which the cut asserts between the universe of discourse and what is scribed within it is simply that what is scribed within is false of the universe of discourse. Then we may interpret [cid:image004.jpg@01D34FE8.185C8580] as meaning “It is false that it rains and that a pear is not ripe.” But we have already seen that this is precisely the whole meaning of the conditional de inesse; namely that it is false that the antecedent is true while the consequent is false. Thus, that which the cut asserts is precisely that that which is on its bottom is not, as a whole, true. 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 MS 455-456 (1903) - Lowell Lecture II (C. S. Peirce Manuscripts) | FromThePage<https://fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii> fromthepage.com MS 455-456 (1903) - Lowell Lecture II (C. S. Peirce Manuscripts) - read work.
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