Jerry R, list,
Lowell 2.4 introduces the “conditional de inesse,” as Peirce calls it, as the most simple and basic logical form that needs to be represented in the system of existential graphs. It was not obvious to me at first why Peirce chose this particular form as the place to start; so in the presentation of Lowell 2 on my website, I inserted as a sidenote a section from one of his 1898 Cambridge Lectures that explains in more detail what the logical issue is and why the “conditional de inesse” is so important for the Peircean approach to formal logic in the Lowells. And of course, you have to understand the part formal logic and existential graphs play in Peirce’s whole philosophy in order to see the point of what he’s doing in Lowell 2. So if you weren’t following Lowell 1 very closely, you probably won’t follow Lowell 2 very closely either. That may mean you have to set aside your own pet theories and predilections to get on board with Peirce’s train of thought. Here’s the 1898 excerpt that explains the importance of the “conditional de inesse” (R441, RLT 125-6, NEM4 169-70): Cicero informs us that in his time there was a famous controversy between two logicians, Philo and Diodorus, as to the signification of conditional propositions. Philo held that the proposition “if it is lightening it will thunder” was true if it is not lightening or if it will thunder and was only false if it is lightening but will not thunder. Diodorus objected to this. Either the ancient reporters or he himself failed to make out precisely what was in his mind, and though there have been many virtual Diodorans since, none of them have been able to state their position clearly without making it too foolish. Most of the strong logicians have been Philonians, and most of the weak ones have been Diodorans. For my part, I am a Philonian; but I do not think that justice has ever been done to the Diodoran side of the question. The Diodoran vaguely feels that there is something wrong about the statement that the proposition “If it is lightening it will thunder” can be made true merely by its not lightening. Duns Scotus, who was a Philonian , as a matter of course, threw considerable light upon the matter by distinguishing between an ordinary consequentia, or conditional proposition, and a consequentia simplex de inesse. A consequentia simplex de inesse relates to no range of possibilities at all, but merely to what happens, or is true, hic et nunc. But the ordinary conditional proposition asserts not merely that here and now either the antecedent is false or the consequent is true, but that in each possible state of things throughout a certain well-understood range of possibility either the antecedent is false or the consequent true. So understood the proposition “If it lightens it will thunder” means that on each occasion which could arise consistently with the regular course of nature, either it would not lighten or thunder would shortly follow. Now this much may be conceded to the Diodoran, in order that we may fit him out with a better defence than he has ever been able to construct for himself, namely, that in our ordinary use of language we always understand the range of possibility in such a sense that in some possible case the antecedent shall be true. Consider, for example, the following conditional proposition: If I were to take up that lampstand by its shaft and go brandishing the lamp about in the faces of my auditors it would not occasion the slightest surprise to anybody. Everybody will say that is false; and were I to reply that it was true because under no possible circumstances should I behave in that outrageous manner, you would feel that I was violating the usages of speech. I would respectfully and kindly suggest to the Diodoran that this way of defending his position is better than his ordinary stammerings. Still, should he accept my suggestion I shall with pain be obliged to add that the argument is the merest ignoratio elenchi which ought not to deceive a tyro in logic. For it is quite beside the question what ordinary language means. The very idea of formal logic is, that certain canonical forms of expression shall be provided, the meanings of which forms are governed by inflexible rules; and if the forms of speech are borrowed to be used as canonical forms of logic it is merely for the mnemonic aid they afford, and they are always to be understood in logic in strict technical senses. These forms of expression are to be defined, just as zoologists and botanists define the terms which they invent, that is to say, without the slightest regard for usage but so as to correspond to natural classifications. That is why I entitled one of the first papers I published, “On the Natural Classification of Arguments.” And by a natural classification, we mean the most pregnant classification, pregnant that is to say with implications concerning what is important from a strictly logical point of view. Now I have worked out in MS. the whole of syllogistic in a perfectly thoroughgoing manner both from the Philonian and from the Diodoran point of view. But although my exposition is far more favorable to the Diodoran system even than that of DeMorgan in his Syllabus of Logic, which is much the best presentation of the Diodoran case ever made by an adherent of it, yet I find that the Philonian system is far the simpler,— almost incomparably so. You would not wish me to take you through all those details. This general statement is all that is appropriate for this brief course of lectures. Be it understood, then, that in logic we are to understand the form “If A, then B” to mean “Either A is impossible or in every possible case in which it is true, B is true likewise,” or in other words it means “In each possible case, either A is false or B is true.” From: Jerry Rhee [mailto:[email protected]] Sent: 23-Oct-17 18:51 Gary f, list: Thank you for that posting. I must assert though, I am surprised that if A is true, B is true, for I thought: if A were true, C would be a matter of course. Does B and not C surprise you? http://www.iupui.edu/~arisbe/menu/library/bycsp/L75/ver1/l75v1-04.htm Best, Jerry Rhee On Mon, Oct 23, 2017 at 9:36 AM, <[email protected] <mailto:[email protected]> > wrote: Continuing from Lowell 2.3, https://www.fromthepage.com/jeffdown1/c-s-peirce-manuscripts/ms-455-456-1903-lowell-lecture-ii/display/13602: The most immediately useful information is that which is conveyed in conditional propositions, “If you find that this is true, then you may know that that is true.” Now in ordinary language the conditional form is employed to express a variety of relations between one possibility and another. Very frequently when we say “If A is true, then B is true,” we have in mind a whole range of possibilities, and we assert that among all possible cases, every one of those in which A is true will turn out to be a case in which B is true also. But in order to obtain a way of expressing that sort of conditional proposition, we must begin by getting a way of expressing a simpler kind, which does not often occur in ordinary speech but which has great importance in logic. The sort of conditional proposition I mean is one in which no range of possibilities is contemplated, which speaks only of the actual state of things. “If A is true then B is true,” in this sense is called a conditional proposition de inesse. In case A is not true, it makes no assertion at all and therefore involves no falsity. And since every proposition is either true or false, if the antecedent, A, is not true, the conditional de inesse is true, no matter how it may be with B. In case the consequent, B, is true, all that the conditional de inesse asserts is true, and therefore it is true, no matter how it may be with A. If however the antecedent, A, is true, while the consequent, B, is false, then, and then only is the conditional proposition de inesse false. This sort of conditional says nothing at all about any real connection between antecedent and consequent; but limits itself to saying “If you should find that A is true, then you may know that B is true,” never mind the why or wherefore. 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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