Consider the concept 'Dog'. The knowledge about how the concept 'dog' is exactly represented in brain is ZERO.
Concept is sign. So, how is peircean triadic sign represented in Brain in a case 'DOG'. Is that sure that 'DOG' is triadic sign? kindly, markku Lähetetty laitteesta Windowsin sähköposti Lähettäjä: Jeffrey Brian Downard Lähetetty: tiistai, 27. tammikuuta 2015 21:08 Kopio: [email protected], [email protected] Hi Jon, Lists, I've been thinking about the way you are characterizing triadic relations in terms of ordered triples. For a while now, I've been wondering if there are limits to such an approach that might make it difficult to explain what is special about a genuinely triadic relation. Here are a few quick comments that I wanted to register--with the hope that we might, over time, compare Peirce's more algebraic and geometric approaches for setting up formal systems. In particular, I'm wondering if there might be limitations that come with the more algebraic approach when we turn from formal logic to semiotics and try to put those systems to work for the sake of philosophical analysis and explanation. So, here are two passages I wanted to put on the table: First, Peirce says the following in "The Logic of Mathematics, An Attempt to Develop My Categories from Within": "What is a triad? It is a three, But a three what? If we say it is three subjects, we take at the outset an incomplete view of it." (CP, 1.471) Second, he says the following in his discussion of the improvement of the gamma graphs: "For although I have always recognized that a possibility may be real, ... I have invariably recognized, as one great class of relations, the class of references, as I have called them, where one correlate is an existent, and another is a mere possibility; yet whenever I have undertaken to develop the logic of relations, I have always left these references out of account, notwithstanding their manifest importance, simply because the algebras or other forms of diagrammatization which I employed did not seem to afford me any means of representing them." (CP, 4.579) I don't yet have a clear way of stating many of the questions that have been puzzling me. Having said that, let me try to get one question out so that we might start a conversation about the limitations that might be involved in trying to analyze the phenomena associated with reasoning and then build philosophical explanations by relying too heavily on the idea of ordered triples and algebraic expressions of the relations between such triples. Here is the starting question: Doesn't the notion of an ordered triple require that we already have things sorted out in such a way that we are able to ascribe quantitative values to each subject that is a correlate of the triadic relation? Here are a few comments to put some flesh to the bare bones of what I'm trying to ask. It seems to me that one advantage of a more topological approach in setting up logical systems is that we can iconically represent relations between things that do not yet have such quantitative values. After all, there are many kinds of relations (e.g., those involved in relations of similarity between feelings) that may not have a determinate scale for the attribution of a quantity to it. That is one reason Peirce is so keen to point out in his discussion of quantity that the conception of a quanta is not grounded arithmetically. Rather, it is fundamentally a geometric notion. My hunch is that Peirce is trying to set things up so that he can explain what is necessary for establishing such ordered relations between things serving as signs, objects and interpretants in the growth of understanding. The second quote listed above from the essay on the improvement of the gamma graphs seems to suggest that Peirce saw limitations to more algebraic ways of trying to lay out the formal relations, and he couldn't find any way around the problem until he moved to more geometric (i.e., iconic) approaches in the existential graphs. --Jeff Jeff Downard Associate Professor Department of Philosophy NAU (o) 523-8354 ________________________________________ From: Jon Awbrey [[email protected]] Sent: Wednesday, December 17, 2014 9:12 PM To: Howard Pattee Cc: [email protected]; 'Peirce-L' Subject: [PEIRCE-L] Re: Triadic Relations Howard, At this point we can can distinguish two forms of decomposability or reducibility -- along with their corresponding negations, indecomposability or irreducibility -- that commonly arise. 1. Reducibility under relational composition P o Q. All triadic relations are irreducible in this sense. This is because relational compositions of monadic and dyadic relations can produce only more monadic and dyadic relations. 2. Reducibility under projections. For that we need some definitions: Every triadic relation, say L contained as a subset of the cartesian product X x Y x Z, determines three dyadic relations, namely, the projections of L on the "planes" X x Y, X x Y, and Y x Z. In particular: Every sign relation, say Q contained as a subset of the cartesian product O x S x I, those being the sets of objects, signs, and interpretant signs respectively under discussion, determines three dyadic relations, which we may notate as follows: * proj_{OS}(Q), the projection of Q on the O x S plane; * proj_{OI}(Q), the projection of Q on the O x I plane; * proj_{SI}(Q), the projection of Q on the S x I plane. To visualize the situation for sign relations, see the following paper: ☞ http://www.iupui.edu/~arisbe/menu/library/aboutcsp/awbrey/integrat.htm And contemplate the following figure: ☞ http://www.iupui.edu/~arisbe/menu/library/aboutcsp/awbrey/FIG3.gif Here is the critical point. The triadic relation always determines the three dyadic projections but the three dyadic projections may or may not determine the triadic relation. Thus we have two cases: 1. If the dyadic projections determine the triadic relation, that is, there is only one triadic relation that has those three projections, then the triadic relation is said to be "projectively reducible" to those three dyadic relations. 2. If the dyadic projections do not determine the triadic relation, that is, there is more than one triadic relation that has those same three projections, then the triadic relation is said to be "projectively irreducible". Regards, Jon Howard Pattee wrote: > At 12:12 AM 12/17/2014, Jon Awbrey wrote: > >> What do I see in a picture like this? >> >> ```````s`` >> ``````/``` >> o---<R```` >> ``````\``` >> ```````i`` >> >> The "R" brings to mind a triadic relation R, which collateral >> knowledge tells me is a set of 3-tuples. What sort of 3-tuples? The >> picture sets a place for them by means the place-names "o", "s", "i", >> in no particular order. Without loss of generality I can take them up >> in the ordered triple (o, s, i). All of this is just mnemonic >> machination meant to say that a typical element is (o, s, i) in R. >> It's up to me to remember that R is a subset of O x S x I, with o in >> O, s in S, and i in I. The diagram is just a mnemonic catalyst. You >> have to know the codebook to decode it. > > I can see that with the help of your words. But I also see dyadic > relations, which I agree are not to be confused as corresponding to > "parts of signs." I see no harm in recognizing their formal necessity, > as long as they are not misinterpreted. > > Howard > > -- 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
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