PS In the previous 'bean' example, abduction is not given as felicitously as it might be. But this is a tricky matter which I'll try to get back to ed at a later date. GR
*Gary Richmond* *Philosophy and Critical Thinking* *Communication Studies* *LaGuardia College of the City University of New York* *C 745* *718 482-5690* On Thu, Aug 21, 2014 at 11:21 PM, Gary Richmond <[email protected]> wrote: > 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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