""Extreme credences" here should likely be "infi..."


by Dewi Morgan Sep 25 2018

On the log\-odds line, credences range from $~$-\\infty$~$ to $~$+\\infty,$~$ with the infinite extremes corresponding to probability $~$0$~$ and $~$1$~$ which can thereby be seen as "infinite credences"\. That's not to say that $~$0$~$ and $~$1$~$ probabilities should never be used\. For an ideal reasoner, the probability $~$\\mathbb P(X) + \\mathbb P(\\lnot X)$~$ should be 1 \(where $~$\\lnot X$~$ is the logical negation of $~$X$~$\)\.3 Nevertheless, these infinite credences of 0 and 1 behave like 'special objects' with a qualitatively different behavior from the ordinary credence spectrum\. Statements like "After seeing a piece of strong evidence, my belief should never be exactly what it was previously" are false for extreme credences, just as statements like "subtracting 1 from a number produces a lower number" are false if you insist on regarding $~$\\aleph\_0$~$ infinity as a number\.

"Extreme credences" here should likely be "infinite credences".

Even so, previous page made the exact counterpoint:

While strong evidence may not change your view of things, things, extreme evidence absolutely should make you revisit your estimate of even an infinite credence level.