Jon wrote (091814-1) through (091814-3): First off, you appear to be confusing a category with (091814-1) a single composition triple of functions (f, g, h) such that h = f o g, and that is a serious confusion.
I know there are more complex compositions than involving three mappings, f, g and h, but for my purpose it is sufficient to use the simplest category. Is that a sign of confusion? Next, you confuse a sign relation, a subset of a (091814-2) cartesian product O x S x I, with a single triple (o, s, i) in a sign relation, and that is another serious confusion. What other possible sign relations do you have in mind other than the (o, s, i) triple defined by the Cartesian product O x S x I ? And also, what are the elements of the sets, O, S and I ? Functions are defined as mappings between sets, . . . (091814-3) But not all mappings may be functions which concept never appeared in my previous email to which you are responding. I need mappings, not functions which sounds too mathematical for my taste. My impression is that you may be trying too hard to apply mathematics to biosemiotics. Your criticism of my work reminds me of what Einstein said about mathematics in general: As far as the laws of mathematics refer to reality, they (091814-4) are not certain; and as far as they are certain, they do not refer to reality. This statement, called the Einsteins Uncertainty Thesis (EUT) in [1], may well apply to the debate between mathematicians/normative scientists and biologists/biosemioticians/physicists on these lists, leading me to suggest that As far as the laws of mathematics and normative science (091814-5) refer to biosemiosis, they are not certain; and as far as they are certain, they do not refer to biosemiosis. For convenience, we may refer to Statement (091814-5) as the Semiotic Uncertainty Principle (SUP). With all the best. Sung ____________________________________________________ Sungchul Ji, Ph.D. Associate Professor of Pharmacology and Toxicology Department of Pharmacology and Toxicology Ernest Mario School of Pharmacy Rutgers University Piscataway, N.J. 08855 732-445-4701 www.conformon.net Reference: [1] Ji, S. (2012). Molecular Theory of the Living Cell: Concepts, Molecular Mechanisms, and Biomedical Applications. Springer, New York. P. 139. > Thread: > GR: http://permalink.gmane.org/gmane.science.philosophy.peirce/14086 > JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14122 > GR: http://permalink.gmane.org/gmane.science.philosophy.peirce/14123 > JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14124 > JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14127 > GR: http://permalink.gmane.org/gmane.science.philosophy.peirce/14128 > JA: http://permalink.gmane.org/gmane.science.philosophy.peirce/14129 > SJ: http://permalink.gmane.org/gmane.science.philosophy.peirce/14133 > > Sung, > > In order to pursue these questions with any degree of seriousness a person > would > have to take the definition of a triadic sign relation and the definition > of a > mathematical category seriously, and so far you haven't been doing that. > > First off, you appear to be confusing a category with a single composition > triple of functions (f, g, h) such that h = f o g, and that is a serious > confusion. > > Next, you confuse a sign relation, a subset of a cartesian product O x S x > I, > with a single triple (o, s, i) in a sign relation, and that is another > serious > confusion. > > Finally, you propose what amounts to saying: > > f maps o to s > g maps s to i > h maps o to i, where h = f o g > > Functions are defined as mappings between sets, so we need to have names > for the > sets of objects, signs, and interpretant signs that are under > consideration in a > given discussion. Let's call those sets O, S, I, respectively. So what > you are > saying, more properly stated, amounts to this: > > f : O -> S > g : S -> I > h : O -> I, where h = f o g > > Functions are special cases of dyadic relations. So we have the > following: > > f is a subset of O x S > g is a subset of S x I > h is a subset of O x I, where h = f o g > > Right off the bat there is a problem. There is indeed a dyadic relation > between > objects and signs that can be "projected" out of a triadic relation, but > that > dyadic projection is not a function in general. Objects may have many > signs > that denote them, and signs may have general reference or plural > denotation, > just for instance. The same thing applies to all the other pairs of > domains. > > That is not the last of the problems, not by a long shot, but it's all I > have > time for right now. > > Regards, > > Jon > > -- > > 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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