"The concept "fair", entails, in its entirety, that the coin will, in the long run, produce an equal number of heads and tails with no pattern."George will correct me and I defer to his greater knowledge of probability theory. I believe a fair coin the distribution of heads/tosses will have an expected value of 1/2. For a large number of tosses the probability of an equal number of heads and tails is vanishingly small.FrankOn Sun, May 24, 2020 at 8:25 PM Eric Charles <[hidden email]> wrote:Nick,I feel like this fast-forwarded some how. The first and most important thing Perice wants is for us to think clearly about our concepts, right?So, before we get going into this, the first thing we need to do is figure out whether we agree on the following:The concept "fair", entails, in its entirety, that the coin will, in the long run, produce an equal number of heads and tails with no pattern.That is, while we can hypothesize about whether the coin is fair based on all sorts of things - studying how it was made, measuring it's symmetry, etc. - we recognize that any such evidence would be irrelevant in the face of results from a very large number of flips.Phrased the other way around: The claim that a given coin is "fair", if we are thinking clearly, a claim about what result we will see if we flip the coin a very large number of times. Nothing more, nothing less. Though we expect the construction of a coin to impact whether or not it is "fair", we are definitely not asserting that it has any particular construction when we assert that it is fair.**** Note the connection with our prior discussion of psychological terms and human insides.
-----------Eric P. Charles, Ph.D.
Department of Justice - Personnel PsychologistAmerican University - Adjunct Instructor-- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ...On Sun, May 24, 2020 at 2:56 PM <[hidden email]> wrote:-- --- .-. . .-.. --- -.-. -.- ... -..-. .- .-. . -..-. - .... . -..-. . ... ... . -. - .. .- .-.. -..-. .-- --- .-. -.- . .-. ...All, particularly, George—
In an earlier larding, I argued that Peirce’s idea of truth is essentially a statistical one. So:
Is it true that the coin I hold in my hand is a fair coin?
Let the coin be flipped once, and it comes out heads, what do you think? No way of telling, right? OK. Flip it again. Heads again. Two heads in a row. P=0.25. Sure, I guess so. It could be fair. Flip it again. Hmmm. Three heads in a row………Five heads in a row. P= 03125. You know? I think that coin is probably not fair. “Fair” in this formulation means the infinite distribution of H and T coinflips is .5. “Probably not” means, the chances that this coin’s flips are drawn from a .5 distribution is less than 0.0312 and my threshold of dis belief is 0.05. Thus, when I say that the coin is not fair, that inference is in part a statement about me, and the truth of the matter, the limit of the distribution of flips, is prospective. But the notion that there can be some truths of some matters is absolutely essential to science. Why else would we flip the coin?
Now George: why am I bothering you about this. Three questions:
- Is this valid statistical logic? I ask because all psychologists are only amateur statisticians, and many of us bugger up the logic. In particular, we are known to confuse type I and type II error.
- Is this Peirce’s logic? If not, what is Peirce’s logic; and
- Is Peirce’s logic the ORIGIN of the logic of statistical inference that I was taught 60 years ago in graduate school**. If so, which among the famous statisticians, Pearson, Spearman, Fischer, etc., read Peirce?
[signed]
TLOLTT*
* The Little Old Lady Tasting Tea
** RIP, Rheem Jarrett
Nicholas Thompson
Emeritus Professor of Ethology and Psychology
Clark University
https://wordpress.clarku.edu/nthompson/
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