Ben, list, You wrote: "But can the induction of characters and qualitative induction be understood as increasing only the breadth, not the depth?"
My understanding is that, since characters have to do with depth, not breadth, then it is not possible to understand the induction of characters and qualitative induction as increasing only the breadth, and not the depth. In fact, it is the other way around: They increase only the depth, and not the breadth. However, though that is my understanding, what Peirce actually says is more complicated. The following quote from "Upon Logical Comprehension and Extension", sixth section or paragraph, will help: "There is, therefore, this important difference between induction and hypothesis, that the former potentially increases the breadth of one term, and actually increases the depth of another, while the latter potentially increases the depth of one term, and actually increases the breadth of another." I tried to think this out, but it is a bit complicated to work out. If I recall correctly, at this point in time Peirce hasn't really adopted the icon and index point of view on propositions. Both terms are symbols, each of the terms contributing their own breadth and depth by necessity; which, as I understand it, has to do with the cases in which the term-symbol appears as predicate and as subject in other propositions. The term-symbol's appearance as a predicate will then increase its breadth, because it is applied to a new subject, while its appearance as a subject will increase its depth, because a new predicate has been applied to it. If one thinks about it in this way, the nuances of information theory and the role of inference is in ascription of modifiers to the increase, such as actual, potential, conceived, etc. It may be helpful to consider what he said preceding the statement quoted above: Induction requires more attention. Let us take the following example:-- > S', S'', S''', and Siv have been taken at random from among the M's; > S', S'', S''', and Siv are P: > any M is P. > > We have here, usually, an increase of information. M receives an increase > of depth, P of breadth. There is, however, a difference between these two > increases. A new predicate is actually added to M; one which may, it is > true, have been covertly predicated of it before, but which is now actually > brought to light. On the other hand, P is not yet found to apply to > anything but S', S'', S''', and Siv, but only to apply to whatever else may > hereafter be found to be contained under M. The induction itself does not > make known any such thing. Now take the following example of hypothesis:-- > > M is, for instance, P', P'', P''', and Piv; > S is P', P'', P''', and Piv: > S is all that M is. > > Here again there is an increase of information, if we suppose the premises > to represent the state of information before the inferences. S receives an > addition to its depth; but only a potential one, since there is nothing to > show that the M's have any common characters besides P', P'', P''', and > Piv. M, on the other hand, receives an actual increase of breadth in S, > although, perhaps, only a doubtful one. The part that you referenced with respect to generalization is potentially illuminating, as this may show the way to understanding the new place of abduction or hypothesis in the theory of information. Thank you for pointing out this material. It is a bit unclear to me why some of the changes in information didn't seem to correspond to one of the three inferences, and perhaps they are key to thinking more about abduction from an informational perspective. You're certainly giving me much to ponder over! With respect to your recent discussions on classifying basic inference modes, I haven't been following closely, and so couldn't comment. But understanding that reference helps me understand what you meant when you said that in the previous post. Franklin On Mon, Nov 2, 2015 at 9:35 AM, Benjamin Udell <[email protected]> wrote: > Found an error of thought in my post. Corrected below with 'DELETE' and > 'INSERT' tags. Sorry. - Best, Ben > > Franklin, list, > > You wrote: > > I'm somewhat curious about the last thing you said, "[f]or my part, > extension and comprehension seem more useful in exploring inference than in > defining basic modes of inference." Would you be willing to elaborate on > that a bit? I would suppose that in order to explore inferences in that > way, one would already have to know which inferences causes changes in > which quantity and how they change it. But perhaps this is not necessarily > the case; or even if it is, some or even most of the time we don't need to > know which inferences effect which changes, so long as we can appreciate > that changes in the information of a sign occurred. Maybe you think about > it in this way? > [End quote] > > I actually haven't been exploring comprehension and extension much lately, > but I notice when others do, Peirce in particular. In "Upon Logical > Comprehension and Extension" (1867), Peirce defined induction as increasing > the breadth (extension, denotation) while leaving the depth (comprehension) > unchanged, and defined generalization as increasing the breadth while > decreasing the depth such that the information (breadth × depth) unchanged. > But can the induction of characters and qualitative induction be understood > as [*DELETE*] keeping unchanged the product of breadth × depth? [END > DELETE] [*INSERT*] increasing only the breadth, not the depth? [END > INSERT] Anyway, more on generalization: In "A Guess at the Riddle" (1877–8 > draft, <http://www.iupui.edu/%7Earisbe/menu/library/bycsp/guess/guess.htm> > http://www.iupui.edu/%7Earisbe/menu/library/bycsp/guess/guess.htm and > Essential > Peirce 1:273), discussing evolution, he wrote, "The principle of the > elimination of unfavorable characters is the principle of generalization by > casting out of sporadic cases, corresponding particularly to the principle > of forgetfulness in the action of the nervous system." In 1903 in > "Syllabus", Essential Peirce 2:287, > <http://www.commens.org/dictionary/entry/quote-syllabus-syllabus-course-lectures-lowell-institute-beginning-1903-nov-23-some> > http://www.commens.org/dictionary/entry/quote-syllabus-syllabus-course-lectures-lowell-institute-beginning-1903-nov-23-some > , Peirce said that there is a kind of abduction that concludes in a _ > *generalization* _ from a surprising observation. This resembles > induction on the surface but one can see that it differs from induction by > originating an idea rather than testing an idea by examining a fair sample; > it also differs in that it adds something (breadth) beyond that in the > premisses but also omits something (some of the characters or depth) that > was in the premisses. This stuff is interesting but generally the > conceptions of inductive and particularly abductive inference get slippery, > as Houser noted about abduction in "The Scent of Truth" > http://www.academia.edu/611929/The_scent_of_truth . Anyway, I was > alluding to my discussing recently on peirce-l the idea of classifying > basic inference modes by entailment relations or, to the same effect, by > truth/falsity preservativeness (basically by compounding the > deductive/ampliative distinction with a repletive/attenuative distinction), > but the result is un-Peircean in defining four modes. > > Best, Ben > > > > ----------------------------- > 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 .
