Cathy, Jeff, lists, Jeff has taken an interesting approach to trying to meet the issue, but I will try my own take here.
Cathy, I note that you specify quantifying the information in a proposition, although this is not the point of the OLEC--that paper has to do with the information of a symbol, which is something quite different. Yes, Peirce says that we can also apply information to propositions and to arguments. But information will not apply to propositions and arguments in the same way that it does to symbols. (Moreover, I'm not sure it's right to think of the information as being "in" a symbol, proposition, or argument.) In the case of the symbol, the information has to do with the sum of propositions in which it appears as either subject or predicate. It's true that quantifying every exact instance can be tedious. But in a scientific inquiry, in which one is conducting experiments and publishing a report of the results, one should hope that this quantifying is exactly what is being accomplished and communicated to future inquiry. As for your objection to applying a metric that brings in a linear scale from less to more information: Peirce is attempting to do away with the thinking that the logical quantities are always inversely proportioned, and proposes instead that a symbol can grow in overall determination. If this were not possible, we can not talk about learning and the development of symbols in inquiry. When we treat of the growth of the symbol, this growth can be viewed both in terms of the objects to which it applies and in terms of the qualities or characters that apply to it. One or the other increases. We don't have some outside point of view to decide how close we are to a perfect state of information, or what Peirce refers to as the substantial depth and breadth of a symbol. But we can still count the objects, and we can still enumerate and weigh the characters, and the amount of objects might increase, and the characters which are deemed applicable might increase too. I confess I do not see why you find this objectionable just because we can't quantify in a way that tells just how close we are to total information. I notice that your quotes show that counting logical depth doesn't work out, because qualities or characters (or possibilities, which are what qualities as Firsts are from the modal point of view) can't be counted. I myself said this in previous posting on this thread. But Peirce supposes that they can be weighed instead, which means there is some kind of measuring of depth as a quantity. -- Franklin On Wed, Apr 22, 2015 at 8:01 AM, Catherine Legg <cl...@waikato.ac.nz> wrote: > Hi Franklin, > > Thanks for your reply. I was not objecting to *comparisons* being made > between the breadth and depth of various scientific terms, of the richness > you so ably describe. My objection was to applying a *metric* to that, > which effectively puts it on a linear scale of more or less > information. For that, it seems one must require some way of > quantifying the information in a proposition, say, between zero (no > information) and 1 (total information). And I can't see how that could be > done. > > The claim that propositions themselves can't be counted I took > from Peirce. I just had a look through the CP but couldn't locate it, but I > did find the quotes below which are related. > > You also asked: "Even an artifically generated term such as 'red' and > 'cow' will still partake of the surprisingness of 'cow' and 'red' taken on > their own." What does surprisingness have to do with what we're discussing? > > Just the fact of continued inquiry that you were talking about, which runs > on abduction, which runs on surprise. > > Cheers, Cathy > > 2.706: If I am permitted the extended sense which I have given to the word > > "induction," this argument is simply an induction respecting qualities > instead of > > respecting things. In point of fact *P*', *P*'', *P*''', etc., constitute > a random sample of the > > characters of *M*, and the ratio *r *of them being found to belong to *S*, > the same ratio of > > all the characters of *M *are concluded to belong to *S*. This kind of > argument, however, > > as it actually occurs, differs very much from induction, owing to the > impossibility of > > simply counting qualities as individual things are counted. Characters > have to be > > weighed rather than counted. Thus, antimony is bluish-gray: that is a > character. > > Bismuth is a sort of rose-gray; it is decidedly different from antimony in > color, and > > yet not so very different as gold, silver, copper, and tin are. > > > also in 5.169 he says: > > "mere possibilities are not capable of being counted" > > >
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