[FOM] Fuzziness

[Patrik Eklund]

On 2016-07-21 00:08, Charlie wrote:
> Is there anything to the charge I’ve often heard that Fuzzy Logic is
> really probability theory requiring arbitrary assumptions?

This is a long-standing debate, that has so far never come to any sort 
of conclusion.

In

http://www.glioc.com/files_glioc/FuzzySetsAndSignatures.pdf

you will find an (not necessarily 'the' but 'one') explanation of the 
difference between probability, possibility and many-valued logic. This 
note is a summary of postings I had provided within the BISC mailing 
list over the last years before writing that note.

It has to be said that probability is not logical, and probability is 
untyped. Probability may be seen closer to look like a propositional 
logic, since probability leans on its "universe of samples", which is 
just a set, or a set of names, and "events" which are just sets as 
elements in a sigma-algebra. And so on. Probability then is capable of 
responding to "how many?" on a population (again a set) basis, but not 
capable of responding to "how?" which often is more like rule and 
sequence.

This is the dilemma of evidence-based medicine (EBM) where clinical 
trials are based on sampling and population, but "evidence" as to appear 
in clinical guidelines need to be designed so that they target 
individuals. Probability remains logically two-valued in the sense that 
belonging or not to a sample set is indeed bivalent, but in reality (in 
clinical trials) some samples are "better" than others. Exclusion 
criteria in sampling are also bivalent. Health is in my view an 
excellent playground for connecting theory and practice, even as related 
to foundational questions.

Best,

Patrik