Gary F, Jeff, Mike, Thanks for the reference, Jeff.
I thought that the question of consequentiae might be more complicated than being able to relate it to the terms of formal symbolic logic, but I wanted to see what your thoughts were on it, and so I do. The confirmation is much appreciated. -- Franklin On Oct 25, 2017 8:05 PM, "Mike Bergman" <[email protected]> wrote: > 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 > <http://www.tandfonline.com/author/Bellucci%2C+Francesco>'s "Charles S. > Peirce and the Medieval Doctrine of *consequentiae".* > See: http://www.tandfonline.com/doi/full/10.1080/01445340. > 2015.1118338?scroll=top&needAccess=true& > > > 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 <(928)%20523-8354> > ------------------------------ > *From:* Franklin Ransom <[email protected]> > <[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:[email protected]] > *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 <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 > > > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > > > > > ----------------------------- > PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON > PEIRCE-L to this message. PEIRCE-L posts should go to > [email protected] . To UNSUBSCRIBE, send a message not to PEIRCE-L > but to [email protected] with the line "UNSubscribe PEIRCE-L" in the > BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm > . > > > > > >
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