Re: [PEIRCE-L] Lowell Lecture 2.4

Wed, 25 Oct 2017 17:05:34 -0700

Hi Jeff,


Thank you. The Bellucci reference is excellent and timely. I found a PDF online at http://www.academia.edu/download/41369857/Bellucci_CSP_consequences.pdf; some of the Abelard quotes are translated at http://johnmacfarlane.net/abelard.pdf.


Best, Mike


On 10/25/2017 6:18 PM, Jeffrey Brian Downard wrote:

Franklin, Gary F, List,


In Reading Peirce Reading, Richard Smyth suggests that many logicians, such as Quine, make the error of   making assignments to the truth table for the conditional in a rather arbitrary fashion. Peirce, on the other hand, is developing a logical theory that seeks to explain why some inferences that we take to be good or bad really are valid or invalid. As such, he is setting up a semantic assignment of values to the truth table that is not arbitrary.


Here, in the second lecture, he trying to show us how to set up mathematical system of logic that will enable us to analyze examples of reasoning more carefully and exactly. As such, he is trying to avoid the temptation of developing a logical system that prejudges the questions we're trying to answer in the normative theory of logic. 


For background on the relation between these different accounts of the conditional, it might be worth looking atFrancesco Bellucci's "Charles S. Peirce and the Medieval Doctrine of consequentiae".


In this article, he provides a historical reconstruction of what Peirce was drawing from in the medieval doctrine, and how this account of the conditional shape his understanding of the relation of implication.


--Jeff


Jeffrey Downard
Associate Professor
Department of Philosophy
Northern Arizona University
(o) 928 523-8354
From: Franklin Ransom <[email protected]>
Sent: Wednesday, October 25, 2017 1:51:13 PM
To: [email protected] 1
Subject: RE: [PEIRCE-L] Lowell Lecture 2.4
 
Gary F,

If I try to picture the Philonian and Diodoran interpretations in terms of truth value tables, they essentially correspond to material and strict implication, respectively. But I'm not sure how the distinction between ordinary consequence and simplex de inesse fits in. Would that have more to do with modal logic (possible vs...actual?), which the gamma graphs aim to treat of, and which you are suggesting is where the Philonian or material approach becomes problematic?

-- Franklin


On Oct 25, 2017 4:22 PM, <[email protected]> wrote:

Franklin, list,

 

The distinction between the conditional “simplex de inesse” and other if-then propositions is that the “simplex” is indeed simpler, and absolutely exact from a logical point of view, which removes all possible ambiguity from the interpretation of it. It asserts no connection at all between the truth of the antecedent and the truth of the consequent except that when the former is true, the latter is true, “never mind the why or wherefore.” This means that there is no way to falsify the conditional proposition as a whole except to observe that the antecedent is true and the consequent is false. The proposition as a whole — contrary to the “ordinary language” usage and the Diodoran point of view — remains perfectly true if both antecedent and consequent are in themselves false.

 

The significance of this distinction should become more clear as Peirce proceeds to define the “scroll” as the diagram representing the conditional de inesse. The reading of the scroll follows from the stipulation “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 this Peirce will derive the meaning of the cut as negation of what is inside the cut. It seems to me, in hindsight, that right here on the ground level of the whole EG system lies a design feature that will later become problematic for the gamma part of EGs, i.e. for modal logic. That’s why I’m trying to understand why Peirce felt compelled to design them in the way he did.

 

The significance of the distinction becomes amplified, I think, as soon as we take a step beyond exact logic into metaphysics. But we’re not ready to talk about that yet. Or at least I’m not, I’m still trying to clarify exactly how EGs are supposed to work, so that their meanings become more directly visible to me.

 

Gary f.

 

From: Franklin Ransom [mailto:pragmaticist.logos@gmail.com]
Sent: 25-Oct-17 14:32
Cc: [email protected] 1 <[email protected]>
Subject: Re: [PEIRCE-L] Lowell Lecture 2.4

 

Gary F,

 

Do you understand the significance of the distinction between regular consequentia and consequentia simplex de inesse to the conditional debate? That is not clear to me in what was stated in the excerpt from RLT, given what Peirce says in the excerpt from the second Lowell lecture.

 

-- Franklin

 

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.”

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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