[Top] [All Lists]

Re: [ontolog-forum] Editor COE view of a new list of categories

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Kathryn Blackmond Laskey <klaskey@xxxxxxx>
Date: Tue, 17 Jul 2007 09:48:46 -0400
Message-id: <p0611042dc2c276496f80@[]>
>  > But more seriously, HOW does one 'derive' axioms from a model?
>By induction (introducing universal quantifiers and implications),
>abduction (guessing, which may introduce any logical operators
>that seem "reasonable"), and further testing of any predictions
>derivable by deduction.
>This procedure provides a way to guarantee that the axioms are
>consistent:  just check that every hypothesis derived by induction
>or abduction is consistent with the observational reports (i.e.,
>those that describe a suitable model).    (01)

Typically, especially in recent years, the hypotheses are 
statistical. Furthermore, the issue typically is not whether the 
axioms of the theory are consistent with the data.  The logical 
constraints in statistical theories are extremely weak, admitting 
wildly improbable data. (E.g., a sequence of 20,000 tosses of a fair 
coin, all coming up heads, is consistent with the logical axioms of 
the statistical theory that the coin is fair.) In a good statistical 
theory, the data will not be EXACTLY consistent with the statistical 
axioms.   That is, the actual frequencies will not conform to the 
predicted frequencies under the statistical theory. (For example, we 
would not expect EXACTLY 5000 out of 10,000 tosses of a fair coin to 
come up heads.  In fact, people think Mendel fudged his data because 
the frequencies are too good.)  Statistical tests evaluate the degree 
to which the observations are a "typical" realization of the 
hypothesized data-generating process.    (02)

K    (03)

Message Archives: http://ontolog.cim3.net/forum/ontolog-forum/  
Subscribe/Config: http://ontolog.cim3.net/mailman/listinfo/ontolog-forum/  
Unsubscribe: mailto:ontolog-forum-leave@xxxxxxxxxxxxxxxx
Shared Files: http://ontolog.cim3.net/file/
Community Wiki: http://ontolog.cim3.net/wiki/ 
To Post: mailto:ontolog-forum@xxxxxxxxxxxxxxxx    (04)

<Prev in Thread] Current Thread [Next in Thread>