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<mailto: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<mailto: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 ----------------------------- 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<mailto:peirce-L@list.iupui.edu> . To UNSUBSCRIBE, send a message not to PEIRCE-L but tol...@list.iupui.edu<mailto: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 .
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