Re: Extramathematical Notions and the Continuum Hypothesis

Phyllis,

I don't know how long ago the terminology was established,
but it's common usage in probability and statistics these
days to draw a distinction between occurrences and events.
An "occurrence" is a single element of the sample space,
while an "event" is a subset of the sample space, one
to which a measure of its probability can be assigned.

Regards,

Jon


Phyllis Chiasson wrote:
> Something about this reminds me of Peirce's statement about the difference between a fact and an occurrence. The only place I've seen the passage is in Sandra Rosenthal's book, Peirce's Pragmatic Pluralism (pp. 5-6) Google books.
> 
> Jon Awbrey <[email protected]> wrote:
> 
>> Re: http://www.cs.nyu.edu/pipermail/fom/2013-January/016954.html
>> In: http://www.cs.nyu.edu/pipermail/fom/2013-January/thread.html#16929
>>
>> FOM List,
>>
>> This brings us round again to a recurring question about the
>> domain of scientific knowledge and a more lately entertained
>> question sbout its relationship to the domain of computation.
>>
>> Aristotle laid down the law that scientific knowledge is limited
>> to universals, that there can be no knowledge, properly speaking,
>> of haecceities, hapax phenomena, individuals, unique occurrences.
>>
>> We recognize this doctrine today in our awareness that science
>> is a matter of results reproducible indefinitely in principle.
>> I have forgotten the name for this, but I remember that it
>> entails a definite species of periodicity or symmetry in
>> the potential observations of observers distributed in
>> space and time.
>>
>> Another dim memory I have is that computable functions are
>> “ultimately periodic” or something like that, but I'm sure
>> someone here can correct me on that if I remember it wrong.
>>
>> At any rate, it strikes me that these two limitations are
>> very much alike, perhaps even identical in the long run.
>>
>> Regards,
>>
>> Jon Awbrey
>> http://inquiryintoinquiry.com/
>>
>> cc: Arisbe, Inquiry, Peirce List

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