Helmut,
The information “that it is cold because it hails” is not “lost” because it was never implied by the scroll in the first place. Remember the scroll expresses a conditional de inesse, not a causal relation. So all we know (about this wholly imaginary universe) is that If it hails, it is cold, or no hail without cold, as Jon A. put it; we don’t know why. (Actually, in what we call empirical reality — which has nothing to do with “necessary reasoning” — hail usually occurs in summer, when it is not cold!)
Gary f.
From: Helmut Raulien [mailto:[email protected]]
Sent: 12-Nov-17 14:21
To: [email protected]
Cc: 'Peirce List' <[email protected]>
Subject: Aw: [PEIRCE-L] Lowell Lecture 2.11
List,
I understand, that "it hails, and if it hails it is cold" implies that "it hails and it is cold". But is both the same? I think, that information is lost: That it is cold because it hails, and that it does hail not because it is cold, but because in this sheet of assertion it just hails.
Best,
Helmut
Sonntag, 12. November 2017 um 16:21 Uhr
[email protected]
Continuing from Lowell 2.10,
By combining the two parts of the definition of the scroll we get the highly useful graphical form of the principle of contraposition. Namely, suppose that a replica of the graph x, were it scribed on the sheet of assertion, would be permissively transformable into a replica of the graph, y, and suppose that the scroll
were permissively placed on the sheet of assertion. Then, by the predication of the definition concerning the definitum, y, if scribed on the sheet of assertion, would be transformable into z. So x being transformable into y and y in its turn into z, it follows that x would on the sheet of assertion be transformable into z. Hence by the predication of the definitum concerning the definition, it would be permitted to place on the sheet of assertion the scroll
That is to say, the permissibility of the transformation on the sheet of assertion of x into y, carries with it the permissibility of the transformation on the bottom of a cut placed on the sheet of assertion, of the reverse transformation of y into x. Here is a principle which involves many permissions.
Permission No 5
The Principle of Contraposition.
Of whatever transformation is permissible on the sheet of assertion, the reverse transformation is permissible within a single cut.
Thus if
and so on indefinitely. In short, whatever transformation is permissible on the sheet of assertion is permissible within any even number of cuts while the reverse transformation is permissible within any odd number of cuts. For example, since any graph can be erased on the sheet of assertion any graph can be erased within any even number of cuts while any graph can be inserted within any add number of cuts. Since any graph already scribed on the sheet of assertion can by Permission No 2 be iterated on the sheet of assertion, that can have another replica of it placed on the sheet; it follows that if one replica of a graph is on the sheet of assertion and another replica of the same graph is oddly enclosed, the latter can be erased. Thus,
can be transformed into
and thence by Permission No 3 into x y, and thence by Permission No 1 into y. Thus what the logic books call the modus ponens
gives successively
it is cold.
The fact that our system breaks this up into three steps goes to show that our main purpose, that of dissecting reasoning into its simplest elements, has been, in some measure, at least, attained.
It still remains to treat the blank and the blot in the same manner.
http://gnusystems.ca/Lowell2.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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