Just a small correction: When you say the Method of Least Squares was a better fit than the Bell Curve
it should be noted that the method of least squares is the bell curve-that is, the Gaussian distribution. What CSP is distinguishing the method of least squares from is rather the notion that there should be a definite threshold ("limen") between perceived and not perceived, or between same and different. For CSP (and for us psychophysicists today) it's all probabilistic and a matter of more or less, and not of a definite threshold. The most recent incarnation of CSP's view is Signal Detection Theory, q.v. Jay Dowling From: Dennis Leri [mailto:dl...@earthlink.net] Sent: Tuesday, September 16, 2014 5:52 PM To: Peirce List Cc: biosemiot...@lists.ut.ee Subject: Re: [PEIRCE-L] Re: [biosemiotics:6834] Re: Natural Propositions, Chapter 2 Lists, On page 29, note 22 Frederick cites Gustav Fechner's Psychophysik. In his experiments with Jastrow, Peirce contributed three things central to the nascent science of Psycho-Physics after Fechner: 1) a better mathematical tool; 2) a recognition of sub-threshold awareness and hence bringing into question the usefulness of the idea of a threshold, a just noticeable difference (jnd); and 3) a new line of research, the application of mathematics to not just sensory differentiation but also to reasoning under uncertainty. Peirce followed a line of reasoning different from Fechner: ... the errors of our judgments in comparing our sensations seem sufficiently accounted for by the slow and doubtless complicated process by which the impression is conveyed from the periphery to the brain; for this must be liable to more or less accidental derangement at every step of its progress. According to Peirce, the Method of Least Squares was a better fit than the Bell Curve. Peirce: Accordingly we find that the frequencies of errors of different magnitudes follow the probability curve, which is the law of an effect brought about by the sum of an infinite number of infinitesimal causes. This theory, however, does not admit of an Unterschiedsschwelle [difference limen or threshold-DL]. On the contrary, it leads to the method of least squares, according to which the multiplication of observations will indefinitely reduce the error of their mean, so that if, of two excitations, one were ever so little the more intense, in the long run it would be judged to be the more intense the majority of times... But what about the just noticeable difference? For Peirce the math should not only conform to experience but be predictive as well: If there be a least perceptible difference, then when two excitations differing by less than this are presented to us, and we are asked to judge which is the greater, we ought to answer wrong as often as right in the long run. Whereas, if the theory of least squares is correct, we not only ought to answer right oftener than wrong, but we ought to do so in a predictable ratio of cases. (Quotes from: Peirce, Charles Sanders & Jastrow, Joseph. "On Small Differences in Sensation" [1885], in Memoirs of the National Academy of Sciences 3: 73-83) And Peirce's research showed that under uncertain conditions, when differences seemed to have disappeared or alternately to have not appeared, subjects did indeed choose correctly within a band or range of differences close to the jnd but definitely below it. What Peirce is saying is that we can and do as human beings make accurate judgments that are based upon differences that are not conscious, that are below threshold. And, not only do we do that to a degree of accuracy greater than chance but that a methodology predicated upon the Method of Least Squares says it must be the case. Differences that make a difference need not be conscious. Dennis
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