Franklin, List, I think that was Ben Udell.
Regards, Jon http://inquiryintoinquiry.com > On Apr 20, 2015, at 7:30 PM, Franklin Ransom <[email protected]> > wrote: > > Cathy, Frederik, lists, > > Yes, Frederik, that makes sense to me. As I mentioned in my previous post, > counting qualities or characters doesn't seem to be helpful. Although it > should be possible to enumerate them, to a point, for the purpose of some > inquiry. > > As I recall, Jon Awbrey in the last month or two referenced a text from > Peirce about the multiplication of breadth and depth using symbols like 1, 0, > and the infinity loop, to distinguish cases such as essential depth and > breadth, substantial depth and breadth, the idea of nothing, the idea of > being, etc. If infinity was indeed used then, Peirce had certainly > contemplated infinite depth and infinite breadth, although perhaps not simply > in the sense of counting with no end, but in the direct sense of being that > which is without limit, so depth without limit or breadth without limit. > > -- Franklin > >> On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt <[email protected]> >> wrote: >> Dear Franklin, Cathy, Lists - >> >> A small clarification: Peirce's BxD=A idea, I think, should not be taken a >> device for the arithmetic calculation of exact information size - it is >> rather the proposal of a general law relating Breadth and Depth. His idea >> comes from the simple idea that when intension is zero, there is no >> information, while when extension is zero, there is also no information - >> and that is the relation of the two factors in a product. (It is a bit like >> his first Boole-inspired definition of universal quantification as a product >> - he defines truth as 1, falsity as 0, then, in order to be true, each >> single case of a universal proposition should be true - if any single one of >> them is false, the total product of them all will be zero.) >> The BXD=A idea allows him to investigate what happens if intension or >> extension are in- or decreased, etc. - even if not being able to express >> that in precise numbers. >> >> Best >> F >> >> >>> Den 20/04/2015 kl. 01.14 skrev Franklin Ransom >>> <[email protected]>: >>> >>> Cathy, lists, >>> >>> Well, look at this way: It is possible for there to be objects in the >>> senses which are yet not perceived, because we do not yet have any idea of >>> what it is to which we are looking. It takes a hypothesis to introduce a >>> new idea to us to explain what it is, which hypothesis we can then put to >>> the test. In order to do so, we must determine what kinds of characters to >>> look for (deduction helps here) and then look for existent objects >>> (induction) to learn whether the purported relations between characters >>> obtain in fact, and in this way we come to understand the thing which we >>> are experiencing. It is of course induction which gives us more >>> information; abduction simply gives us the idea which needs to become >>> informed, and deduction is merely explicative, based on relating the idea >>> to other ideas and previously gathered information regarding those ideas. >>> >>> Obviously, we cannot conduct induction without end, because that is a >>> practical impossibility. Our 'sum', as you put it, far from being always an >>> infinity, will very likely never be an infinity in practice, in whatever >>> sense you mean to understand the application of infinity to a 'sum' of >>> information. Of course, as an ideal, where science, the community of >>> inquiry as such, continues to investigate, it is possible for the >>> information of an idea to reach a much greater 'sum' than would otherwise >>> be possible for individuals such as you or me. But it is a commonplace of >>> science that ideas that work and continue to work are understood more >>> thoroughly in their relations to other ideas over the course on inquiry. >>> This means of course that not only the breadth, but also the depth of the >>> idea continues to grow. As a result, typically, rather than tending to make >>> comparisons moot, we start to see a hierarchy of ideas and related sciences >>> appear. >>> >>> Consider this passage: "The former [Cows] is a natural class, the latter >>> [Red Cows] is not. Now one predicate more may be attached to Red Cows than >>> to Cows; hence Mr. Mill's attempts to analyze the difference between >>> natural and artificial classes is seen to be a failure. For, according to >>> him, the difference is that a real kind is distinguished by unknown >>> multitudes of properties while an artificial class has only a few >>> determinate ones. Again there is an unusual degree of accordance among >>> naturalists in making Vertebrates a natural class. Yet the number of >>> predicates proper to it is comparatively small" (NP, p.238, quoting >>> Peirce). We can see here that further simplifications are introduced, so >>> taking what is learned about various vertebrates, a new idea, that of >>> vertebrates, appears which simplifies the characters involved. Conversely, >>> species under vertebrates will become much more determinate in terms of >>> their characters, but be simplified with respect to their extension. >>> >>> You said above: "Under synechism every real object has an infinite number >>> of attributes, and every meaningful predicate or general term effectively >>> has an infinite number of aspects, so a simple multiplication of B x D is >>> pointless." And yet natural kinds appear, in which certain attributes, >>> predicates, or aspects appear significant, and others do not. It is >>> precisely the work of abduction to simplify what is observed so that what >>> is essential is grasped, and not simply a never-ending multitude of >>> characters. Such simplification is always with respect to a purpose. With >>> respect to natural kinds, such purpose, or telos, is objective, and we see >>> nature all around us selecting certain characters over others as more >>> significant. If this were not true, natural science would be impossible. As >>> to real objects, yes they have an infinite number, but not all of them are >>> relevant to the purpose of interaction with the real object. Certain >>> meaningful attributes are selected for in attention in order to aid conduct >>> with respect to some purpose at hand. Information relevant to that purpose >>> is what is sought for. >>> >>> I do have a couple of questions for you: >>> >>> For one, would you explain the idea that propositions can't be counted? I >>> would suppose that when conducting an experiment, the number of times a >>> fact is determined relates to developing a frequency ratio, which means >>> that propositions can be counted in this case, when they are instances of >>> the same kind or type, or close enough. But if we are talking about >>> propositions which are all different from each other, than I can see the >>> point, because that is like trying to count qualities, which isn't very >>> helpful for comparison. But of course, that's not the same thing as having >>> so many propositions that they go to infinity and thus can't be counted for >>> that reason. Is this what is meant, that there are supposed to be so many >>> propositions that they go to infinity? Perhaps it would be helpful if you >>> referenced the text where Peirce mentions this. >>> >>> For two, you said "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? >>> >>> >>> -- Franklin >>> >>> >>>> On Sun, Apr 19, 2015 at 4:42 PM, Catherine Legg <[email protected]> >>>> wrote: >>>> Hi Franklin, >>>> >>>> Sorry for taking so long to reply. Thanks for setting me straight on >>>> Peirce still using the idea of breadth x depth later on in his career. I >>>> have to say though that I don't understand how such a metric might work in >>>> the later semiotic, just because it seems to me that the result of such a >>>> 'sum' will *always* be an infinity of an extremely high order, so any >>>> comparisons seem moot. As Peirce notes, propositions can't be counted. >>>> Even an artifically generated term such as 'red' and 'cow' will still >>>> partake of the surprisingness of 'cow' and 'red' taken on their own. >>>> >>>> Best regards, >>>> Cathy >>> >>> >>> ----------------------------- >>> 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 [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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