Could the peak at the right red mark and the leveling to its right be the soil where a Kuhnian paradigm shift is planted? — WISDOMfromPO-MO
The graph could reflect the process of evidence gathering rather than observers' marginal confidence in the evidence. — WISDOMfromPO-MO
Kind of like assembling a jigsaw puzzle. As more pieces are placed in their home the process of identifying the home of pieces accelerates and then peaks. — WISDOMfromPO-MO
The percentage of the puzzle completed would be linear to each piece placed. — Srap Tasmaner
I worried after I posted that maybe it should be flattened a bit, instead of being so dramatic, but I wonder if the dramatic shift isn't better after all ... — Srap Tasmaner
There's still something odd about that zone in the middle. Any thoughts? — Srap Tasmaner
There's still something odd about that zone in the middle. Any thoughts? — Srap Tasmaner
Did you mention that exactly halfway is where the rate of increase peaks, so is also exactly where the rate of decrease first starts? — apokrisis
max at the saddle point — Srap Tasmaner
single grains do start to make a clear difference at the critical threshold of any such phase change — apokrisis
But there’s another issue. The value of an individual grain of sand is noticeably larger between the two red marks. Our intuition is that one grain of sand more or less is always a small and uniform change. And similarly for observations supporting an inductive inference or a theory. — Srap Tasmaner
I didn't know this is called a "logistic function." — Srap Tasmaner
And the reason is simply that there is no sharp and precise fact of the matter to be located here. The "paradox" comes from the tension between the demand, urged by the framing of the problem and prompted by our familiarity with analysis, for a precise numerical solution - and the intuitive realization that no such solution will be satisfactory. — SophistiCat
But when the question is no longer about ticking off this or that checkbox on a clipboard and summing up results - when it is something as messy, ambiguous and fluid as a "belief" - why would you expect the answer to be in this definite numeric form? — SophistiCat
Sorites
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I think it's noticeably less controversial if you imagine this representing a population rather than an individual. — Srap Tasmaner
As above, we could graph her uncertainty about her answer instead, and we'd expect a normal distribution, wouldn't we? — Srap Tasmaner
One thing this curve could represent is an individual striving for consistency under conditions of irreducible uncertainty. — Srap Tasmaner
I'm just interested in how partial belief works, and I keep finding reasons to expect individuals and populations to be homologous. — Srap Tasmaner
If the middle section is where people are genuinely uncertain about their choice, the actual distribution of answers may break down into random noise. — SophistiCat
When you blow up a detail of a curve and ask about its physical meaning, always keep in mind the possibility that it may not have one: it may just be a modeling artefact. — SophistiCat
Well, one reason for that may just be that the curve, assuming it is the error function, is closely related to the normal distribution, which is ubiquitous whenever you deal with (or assume) random variables. — SophistiCat
Does the statistics (if there is in fact a consistent statistics) of individual choice represent one's degree of confidence/uncertainty? If we define it behaviorally, as you say later, then it does so, by definition. But then reporting observed behavior as the degree of uncertainty is merely tautological: despite the use of an ostensibly psychological term, this does not shed any light on our inner world. — SophistiCat
This may also serve to explain away the problem of induction — SophistiCat
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