Helmut, lists, Since I've been a little out of the loop, for now I'll only add a couple of things..
1st, in consideration of the categorial path (vectorial movement) of the three inference patterns as given in the famous bean example (3ns being 'rule', 2ns being 'case', 1ns being 'qualitative result': Deduction: rule (3ns) -> case (2ns) -> qualitative result (1ns) All the beans from this bag are exactly1/2 black, 1/2 white; these beans are from this bag; therefore, these beans will necessarily be exactly1/2 black and 1/2 white. Induction: case (2ns) -> quality (1ns) -> rule (3ns) These beans are from this bag, they turn out to be (approximately) 1/2 black and 1/2 white, so, beans from this back will tend to be (approximately) 1/2 black and 1/2 white. Abduction (retroduction == inference from result to case): rule (3ns) -> quality (1ns) -> case (2ns). One may hypothesize that if these beans found on the table are1/2 black and 1/2 white that they might well be from this bag, these beans turn out to be 1/2 black and 1/2 white; so beans taken from this bag may well be from this bag. Also, in terms of inquiry as well as biological evolution, Peirce argues that the vectorial progress is from 1ns through 3ns to 2ns (note: therefore NOT following the Hegelian order of 1ns -> 2ns -> 3ns). So: Biological evolution: Chance sporting (1ns) -> new habit taking (3ns) -> evolutionary change--say, structural change (2ns). vectorially like: Inquiry: Abduction, or, hypothesis formation (1ns) -> Deduction, or, what would necessarily follow (for the purpose of devising tests) should the hypothesis be valid (3ns) -> Induction, the actual testing of the hypothesis to see the extent to which the hypothesis conforms with reality. There are, of course, 5 other paths through the categories, all of which Peirce exploits. Best, Gary *Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* *C 745* *718 482-5690 <718%20482-5690>* On Thu, Aug 21, 2014 at 5:40 PM, Helmut Raulien <[email protected]> wrote: > > 2nd supplement: I think, between the two kinds of induction I mentioned ( > false and real, I would replace with abductive and deductive ), there is a > third kind, that is, when you know , that the number of elements in the > object set is limited, but you dont know the number. That would be > inductive induction. Is this weird? I am wondering, why the thread stops, > just when it is getting interesting. Or is there something wrong with my > style of communication, I mean am I rude? Dilettantic? Hard to understand? > Too easy to understand, but missing the point? Believe me, i dont have an > idea. > > Supplement: So, maybe my example was a "false", or "pseudo"- induction, > which in fact is an abduction. Maybe a "real" induction is only given, if > one knows the set, the extension of the dynamical object, which knowledge > makes able to tell the value of teh probability, and whith that to tell it > from possibility. > Hi! I am sure, that deduction "is" thirdness, because it is obviously > an argument. Can induction be an argument too? No, because it has indexical > object relation, eg: "I have seen 342 white swans in my life, no swan of > other colour, so probably all swans are white": The 342 swans I have seen > are a subset of all swans there are in the universe. A subset relation is > an index, like spotted smoke is a subset of all smoking fires there are. > But a sign with an indexical object relation can not be an argument. It is > not even an argument about probability, because a premise is missing, that > is the number of existing swans. Without this premise you cannot even > distinguish probability from possibility, because what distiguishes both, > is the value of the probability. > Best, Helmut > > > *Von:* "Sungchul Ji" <[email protected]> > > (If Figure 1 is distorted, see the attached.) > > Stan, Mary, John, and list, > > We are dealing with three sets of three concepts distributed over a > diagram constrained by the mathematical concept of a category: > > 1) Possibility, Probability, Pattern. > 2) Firstness, Secondness, Thirdness, > 3) Abduction, Induction, Deduction. > > f g > A ------> B ------> C => T > | ^ > | | > |______________________| > h > > Figure 1. The ur-category defined as a set of three nodes (A, B, & C) and > three edges (f, g & h) connected in such a manner as to satisfy the > composition condition, f x g = h, resulting in a function or a goal > achieved (to be designated as T from teleonomy). The symbol "=>" reads > "is associated with" or "leading to". > > The specific realizations of A, B, C, f, g, and h may be variable, > dependent on the nature of T. In other words, depending on T, one or more > of the following POSSIBILITIES or choices may be realized: > > I = f, g, - h (i.e., clockwise motion, - h being the reversal of h) > II = f, - h, -g > III = g, -h, f > IV = g, -f, h > V = -h, f, g > VI = h, -g, -f > > The degree of realizing any of the above 6 possibilities (which are > discrete or ’quantized’ ?) can be expressed in terms of PROBBILITIES > continuously changing from 0 to 1. Here is something not usually > discussed: Even within a given possibility with an average probability, > there can be many different PATTERNS of probability distributions (e.g., > Poisson, Gaussian, ex-Gaussian, Gamma, etc) , each distribution being > associated with a specific function, a goal, or a meaning. > > It seems to me that there is no problem with the assignment of the first > two triads of concepts to the ur-category (i.e., A = Possibility = > Firstness; B = Probability = Secondness; C = Pattern = Thirdness) but > there are at least two different opinions on how to assign the third > triad (i.e., Abduction, Deduction, and Induction) to the ur-category: > > Sung: Choice I, i.e., A = Abduction; B =Induction; (6467-1) > C = Deduction > > John & Mary: Choice VI, i.e., A = Abduction; (6467-2) > B =Deduction; C = Induction > > Both these possibilities assume that Abduction is Firstness but differ in > the assignments of Induction and Deduction to Peircean categories of > Secondness and Thirdness: > > Sung: Induction = Secondness; Deduction = Thirdness (6467-3) > > John & Marty: Deduction = Secondness; Induction = Thirdness (6467-4) > > Can both (6467-3) and (6467-4) be right depending on T ? > > Can Peirce shed some light on this question ? > > Some of the above 6 possibilities may not be allowed (or may be forbidden) > by the laws of physics, chemistry, and/or biology. > > With all the best. > > Sung > > > > Mary -- Why is it necessary to place a starting point? Semiosis, as a > > natural process (as in BIOsemiotics), is 'all at once'. In my view it is > > best seen as a developmental cycle that cannot 'begin' at some point > > without starting up the whole thing, spontaneously (given the energy > > source). > > > > STAN > > > > > > On Tue, Aug 19, 2014 at 9:53 AM, Libertin, Mary <[email protected]> wrote: > > > >> Dear John, list, > >> > >> I agree with your suggested order below. The order would not be the > >> previously suggested A-I-D (abduction, induction, deduction) but A-D-I > >> based on Peirce’s writings. I will need more time to gather together > >> all of the evidence, but Peirce’s essay, “A Neglected Argument for > >> the Reality of God,â€� presents the three stages. Deely’s explanation > >> of the three stages makes sense as a sequence (A-D-I). A-D-I makes > sense: > >> getting an idea in the first place, developing the consequences of an > >> idea, experimentally testing those consequences and, if necessary, > >> deciding how to reformulate the hypothesis (found in the original > >> abduction). I am rushed with the start of the semester and apologize for > >> my haste. > >> > >> Cheers! > >> Mary Libertin > >> > >> From: <Deely>, "John N." <[email protected]> > >> Reply-To: "[email protected]" <[email protected]> > >> Date: Monday, August 18, 2014 at 3:31 PM > >> To: "[email protected]" <[email protected]> > >> Subject: [biosemiotics:6463] Re: Possibility, probability and pattern > >> > >> Abduction is getting an idea in the first place (also mis-called by > >> Peirce retroduction); deduction is developing the consequences of an > >> idea; > >> induction (ill-called by Peirce, better termed retroduction) is the > >> experimental testing of the consequences of an idea. > >> > >> > >> > >> *From:* Helmut Raulien [mailto:[email protected] <[email protected]>] > >> *Sent:* Monday, August 18, 2014 14:00 > >> *To:* [email protected] > >> *Subject:* [biosemiotics:6462] Re: Possibility, probability and pattern > >> > >> > >> > >> > >> > >> Dear Sung, List, > >> > >> Maybe in the posts below you were right, and I was wrong (Sorry!): > >> Perhaps > >> Peirce has not definitely written, that abduction, induction, deduction > >> are > >> caterorically 1-2-3. Now I have written a chapter, in which I have tried > >> to > >> show that they are. But Im afraid I first had to mor or less > >> hypothetically > >> reformulate the categories (in the other chapters), with which I think, > >> not > >> everybody would agree. See: www.signs-in-time.de , "English version", > >> "Abduction, induction, deduction". I hope, I have not mixed up the beans > >> from the bag in my example. > >> > >> Very best, > >> > >> Helmut > >> > >> > >> > >> Hi Sung, > >> > >> no, that was not me, it was Peirce himself, with the example about the > >> beans in a bag, I think. Whose own writings I have read less than > >> receptions: The assignment to the categories I think I have gotten from > >> secondary literature by eg. Nina Ort "Reflexionslogische Semiotik" > >> (logic-of-reflection-semiotics?), Winfried Nöth, Helmut Pape,... But > >> thank > >> you for your (mis-) estimation! > >> > >> Very best, > >> > >> Helmut > >> > >> *Gesendet:* Sonntag, 17. August 2014 um 01:24 Uhr > >> *Von:* "Sungchul Ji" <[email protected]> > >> *An:* [email protected] > >> *Betreff:* [biosemiotics:6458] Re: Possibility, probability and pattern > >> may > >> > >> Hi Helmut, > >> > >> If you can demonstrate that the triad of abduction (A), induction (I) > >> and > >> deduction (D) constitutes a mathematical category, you will have a new > >> category which may be referred to as the AID category. > >> > >> As you indicated, A, I and D indeed seem to correspond to Firsrtness > >> (F), > >> Secondness (S), and Thridness (T), and, since the triad of F, S and T is > >> a > >> mathemtical category (as I see it), you my have 'discovered' a new > >> mathemtical category -- the AID category ! > >> > >> With all the best. > >> > >> Sung > >> > >> > >> > >> > Supplement: Abduction and induction are selections too, abduction is > >> > tentative or hypothetic selection, induction is reasonable selection, > >> > and deduction is definitely justified selection. Or something > >> > overprecise like that. But mathematically, I assume, because > >> > mathematics is exact science, selection is only done, if completely > >> > justified, therefore deduction, or total induction, but that is > >> > deduction, because completion is a new premise, that turns induction > >> > into deduction Hi Sung, the brain I dont have much of an idea of, > >> > but I agree with your classification, because possibility, probability > >> > and pattern for me seem to be the grounds for abduction, induction and > >> > deduction, which are categorically 1-2-3 either. To me it seems, that > >> > "pattern" fits better than "selection", because > >> > "pattern" is the ground or reason of the inference, just > >> like > >> > "possibility" and "probability" are, while > >> > "selection" is the inference (deduction) itself. Best, > >> > Helmut > >> > Von: "Sungchul Ji" > >> > An: [email protected] > >> > Betreff: [biosemiotics:6454] Possibility, probability and pattern may > >> > form a mathematical category (If Figure 1 is distorted, see the > >> > attached.) > >> > > >> > Hi, > >> > > >> > While jogging along the Carnegie Lake in Princeton one morning > >> recently, > >> > a > >> > set of three concepts kept recurring in my mind – Possibility, > >> > Probability, and Selection -- which seemed to fit the Peircean > >> categories > >> > of Firstness, Secondness and Thirdness, except perhaps the last > >> category. > >> > But when I tried to represent this triad as a mathematical category, a > >> > new > >> > triad emerged wherein Selection is replaced by Pattern which I think > >> fits > >> > the Peircean Thirdness better than Selection. For convenience, I will > >> > refer to this triad as the PPP category, which evidently satisfies the > >> > composition condition, f x g = h: > >> > f g > >> > Possibility --------> Probability --------> Pattern > >> > (Firstness) (Secondness) (Thirdness) > >> > | ^ > >> > | | > >> > |____________________________________________| > >> > h > >> > > >> > Figure 1. The PPP-category. f = actualization; g = selection; h = > >> > validation, control or information flow. > >> > > >> > Out of many examples I have, let me present juts two that fit the PPP > >> > category: > >> > > >> > (1) There are several regions in the human brain (e.g., post and > >> anterior > >> > cingulated cortexes, ventral prefrontal cortex, hippocampus, and DMN, > >> > default mode network), each occupying an average volume of 50 -60 mm^3 > >> or > >> > 1x10^6 mm^3, that exhibit fMRI signal changes (reflecting neuronal > >> > firing/metabolic activity changes) upon a venous infusion of the > >> > psychedelic drug, psilocybin. Thus, since the fMRI (functional > >> magnetic > >> > resonance imaging) technique allows neuroscientists to monitor the > >> > neuronal firing activities non-invasively from live brain volumes of > >> > about > >> > 10 mm^3 called “voxels” (volume elements), the fMRI > >> technique > >> > can monitor > >> > the neuronal firing activities of about 10^5 voxels in these brain > >> > regions. Carhart-Harris and his coworkers [1] recently found that the > >> > psilocybin infusion caused an increase in the variety (or entropy) of > >> the > >> > fMRI signals measured from DMN regions of human subject (see Figure 1 > >> a) > >> > and b) attached). Psilocybin promotes unconstrained thinking > >> (“My > >> > thoughts wandered freely”) and decreases cerebral blood flow. > >> The > >> > term > >> > entropy used here simply means a quantitative measure of the variety > >> of > >> > the fMRI signals measured from a given brain regions calculated as the > >> > variety of the distances of the local signals from the mean signal of > >> the > >> > brain region under investigation. > >> > Based on a visual inspection of Figures 1a) and b) attached [2], the > >> > following conclusions can be made: > >> > > >> > (a) Possibility = the number of voxels in a brain region, i.e., ~ 10^5 > >> > voxels. > >> > (b) Probability = the probability of a given voxel exhibiting a fMRI > >> > signal that is 0.1 unit away from the group mean is about 0.1 > >> > pre-psilocybin and 0 post-psilocybin. Likewise, the probability of a > >> > given voxel’s fMRI signal deviating from the group mean by 0.4 > >> > units is > >> > 0.15 pre-psilocybin and 0.2 post-psilocybin, etc. > >> > (c) Pattern = the fMRI signal distance frequency distribution fits the > >> > Planckian distribution function reasonably well (see Figure 1a) and > >> b). > >> > Therefore, I conclude that the neurophysiology of the DMN (default > >> mode > >> > network) of the > >> > human brain can be represented as a mathematical category. > >> > > >> > (2) When DNA is fragmented into short segments, called n-mers, where n > >> is > >> > the number of nucleotides in them, the maximum number of n-mers is > >> given > >> > by 4^n since there are 4 different nucleotides, G, C, A and T. Zhou > >> and > >> > Mishra [3] studied the frequency distributions of 11-mers. Not all > >> > 11-mers occurred equally – some (as distinguished by their > >> > nucleotide > >> > sequences) occurred only once, some occurred not at all, while still > >> > others occurred more than hundred times. From Figure 1c), we can see > >> > that the number of the 11-mers that occurred only once in the genome > >> is > >> > about 0.002 x 4,194,304 = 8,329, while the number of the 11-mers that > >> > occurred about 20 times in the genome numbered 0.025 x 4,194,304 = > >> > 104,858. As evident in Figure 1 c), the 11-mer frequency distribution > >> in > >> > the primitive unicellular organism, Pyrococcus abyssi, fits the > >> > Planckian distribution with a great precision and hence, the genome of > >> > this organism can be considered as an example of the PPP category, > >> since > >> > (a) Possibility = 4^11 = 4,194,304 possible 11-mers > >> > > >> > (b) Probability = the probability of the 11-mers occurring only once > >> in > >> > the genome is about 0.002, while the probability of the 11-mers that > >> > occur > >> > 20 times in 0.0025. > >> > > >> > (c) Pattern = the11-mer frequency distribution fits the Planckian > >> > distribution function. > >> > > >> > It seems clear that the PPP category introduced above for the first > >> time > >> > is an example of the ur-category described in [biosemiotics:6360]. > >> > > >> > 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] Carhart-Harris, R. L. et al. (2014). The entropic brain: a theory > >> > of conscious states informed by neuroimaging research with psychedelic > >> > drugs. Frontiers in Human Neuroscience 8(Article 20): 1-22. > >> > [2] Ji, S. (2014). Planckian and Gaussian distributions in Molecular > >> > Machines and Living Cells: Evidence of Free Energy Quantization in > >> > Biology. Computational and Structural Biotechnology Journal (to > >> > appear). > >> > [3] Zhou, Y. and Mishra, B. (2004). Models of Genome Evolution. In: > >> > Modeling in Molecular Biology (Ciobanu G, Rozenberg G, eds), Springer, > >> > Berlin. Pp. 287-304. > >> > > >> > > >> > >> > > > > >
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