On Aug 17, 2011, at 1:23 PM, John F. Sowa wrote:
>> Would you provide an example of different, modern day linguistic
>> frameworks that are "incommensurable"? Please stick to frameworks
>> that have a bearing on ontological engineering.
> When I commented on Richard's post, I ignored this point and discussed
> the question of using "Human Intelligence" to resolve such issues.
> I agree that the term 'incommensurable' requires some definition.
> But I suspect that people apply it to vague, confused, or missing
> definitions. For such things, I would apply the epithet by Alan Perlis:
> You can't translate informal specifications to formal specifications
> by any formal algorithm.
> For such things, I agree that no formal algorithm can do the mapping.
> But I would also say that human intelligence, by itself, can't do
> the mapping either. You would need some additional information
> that could be used to fill in the gaps, resolve ambiguities, and
> clarify vague points. (01)
But then "incommensurable" is surely a misnomer where "incomplete", "vague",
"incompatible", etc would be far more accurate. (I'm sure you agree.) (02)
> Another interpretation of the term 'incommensurable' might mean
> that you have two theories about the same subject for which there
> is no 1-to-1 of terms from one to the other. (03)
Right. And here two cases might be distinguished. (1) There are conservative
extensions T1' and T2' of T1 and T2 in which appropriate names and predicates
are added that render them "commensurable", i.e., such that T1' and T2'
basically "say the same thing" (in a sense that can be made precise in terms of
interpretability). (2) There aren't such extensions. An example of the latter
would be Quine's NF set theory and Zermelo-Fraenkel set theory. These two
theories embody different conceptions of "set". But again there is no need to
invoke the mysterious and evocative notion of incommensurability, as the
difference between the two can again be explained in terms of traditional
notions of interpretability, consistency, etc. And in this sort of case it
seems to me that the right thing to say is, not that the two theories have
incommensurable conceptions of X, but that they simply have different (though
perhaps related) conceptions of different things. There are NF-sets and
ZF-sets; they are similar in some respects and different in others, like
dachshunds and German shepherds. (04)
Bottom line for me is that I've yet to see an alleged case of
"incommensurability" that wasn't either trivially resolvable (e.g., the old
chestnut about how the Aleut conception of "snow" is incommensurable with ours)
or more clearly explicable in more traditional terms.* (05)
*Actually, the Pirahã language, as described in Dan Everett's fascinating work,
*might* provide some examples where the notion has some purchase. (07)
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