Jon, Yes, that is exactly it, thank you so much!
-- Franklin On Mon, Apr 20, 2015 at 8:30 PM, Jon Awbrey <jawb...@att.net> wrote: > Franklin, > > This looks like the post you had in mind: > > BU: > article.gmane.org/gmane.science.philosophy.peirce/15796/match=breadth+depth > > BU:http://permalink.gmane.org/gmane.science.philosophy.peirce/15796 > > Regards, > > Jon > > > On 4/20/2015 8:21 PM, Franklin Ransom wrote: > >> Jon, Ben, lists, >> >> Whoops! Sorry about that! I guess it just struck me as a "Jon" kind of >> thing to do, with the slow reads going on about Peirce's earlier logical >> works. I apologize for the mistake! >> >> -- Franklin >> >> On Mon, Apr 20, 2015 at 7:42 PM, Jon Awbrey <jawb...@att.net> wrote: >> >> Franklin, List, >>> >>> I think that was Ben Udell. >>> >>> Regards, >>> >>> Jon >>> >>> http://inquiryintoinquiry.com >>> >>> On Apr 20, 2015, at 7:30 PM, Franklin Ransom < >>> pragmaticist.lo...@gmail.com> >>> 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 <stj...@hum.ku.dk> >>> 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 < >>>> pragmaticist.lo...@gmail.com>: >>>> >>>> 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 <cl...@waikato.ac.nz> >>>> 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 >>>>> >>>>> > -- > > academia: http://independent.academia.edu/JonAwbrey > my word press blog: http://inquiryintoinquiry.com/ > inquiry list: http://stderr.org/pipermail/inquiry/ > isw: http://intersci.ss.uci.edu/wiki/index.php/JLA > oeiswiki: http://www.oeis.org/wiki/User:Jon_Awbrey > facebook page: https://www.facebook.com/JonnyCache >
----------------------------- PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the line "UNSubscribe PEIRCE-L" in the BODY of the message. More at http://www.cspeirce.com/peirce-l/peirce-l.htm .
