John and all, (01)
Thank you for the link. I have followed it and have some comments:
>
>As useful background, I often cite the following tutorial
>by the philosopher Norman Swartz:
>
> http://www.sfu.ca/philosophy/swartz/definitions.htm
> (02)
I found it not quite satisfactory for the purposes of this forum. IMHO - it
lacks interdisciplinary connections in defining the terms which are equally
important to other fields besides philosophy and linguistics. I doubt that this
tutorial will answer the need for suitable common reference as asked repeatedly
by the participants here. (03)
For example, following explanation:
"The extension of a term or phrase is understood to be the timeless class of
all things which properly 'fall under' or are described by that phrase."
This may be workable for linguist, but not for computer scientists or
mathematician (although I am not one of them). (04)
Here is quite different definition of the same term in
http://en.wikipedia.org/wiki/Extension_(predicate_logic)
"The extension of a predicate ? a truth-valued function ? is the set of tuples
of values that, used as arguments, satisfy the predicate. Such a set of tuples
is a relation."
In this case at least there a link to alternative definition from another
field, and even suggestion that definitions should be merged. However, no one
so far had attempted to that publicly. (05)
I recall several discussion on this forum that attempted to connect the terms
"intension", "extension", "class", "predicate" etc. into coherent framework,
but IMO failed to do so for the very same reason - lack of interdisciplinary
definition that would satisfy the need of constructive discussion. (06)
Unfortunately, I can not offer any better alternative. However I do believe
that it is possible. May be we should attempt this relatively humble objective
before trying to develop yet another FO or repository of such. I think step one
in that direction would be to accept the absence of common definitions, which
should be apparent from following discussion over a long period of time (as I
did). (07)
If anyone agrees with me I would suggest to begin with notions of "intention"
and "extension" as it relates to notions of "model" and "theory". (08)
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