On Mar 16, 2007, at 2:27 PM, Duane Nickull wrote:
> On 3/16/07 12:20 PM, "Christopher Menzel" <cmenzel@xxxxxxxx> wrote:
>
>>> CM> if you are talking about the usual sort of first-order
>>> language in which predicates cannot also be arguments to other
>>> predicates, then of course there will be loss of expressivity.
>>>
>>> If one interpreted this as saying that there are no higher order
>>> properties, then surely that would be an ontological implication.
>>
>> Surely it would not; it would be a logical howler. From the
>> inability to say there are Xs nothing whatever follows about the
>> existence or nonexistence of Xs. (01)
> IMO - this discussion is rapidly reaching the "say something to
> prove you
> exist" challenge. Since several of the upper level ontology work
> defines
> forms of first order logic, can we at least frame this debate/
> conversation
> in some lexicon? Wouldn't it make infinite more sense than
> starting with a
> blank slate? (02)
I do not see the relevance of this comment to the exchange above. My
point was a simple logical one. Chris P claimed that inferring (03)
(1) There are no higher-order properties (04)
from (05)
(2) Traditional first-order language L is unable to express that
there are higher-order properties (06)
is an "ontological implication". My response is that there is no
implication of any sort here, there is simply a bad inference. (2)
does not *imply* (1), and so it would be a logical mistake to *infer*
(1) from (2). Nothing, once again, follows about the existence of Xs
from the fact that a given formalism cannot say anything about Xs. (07)
-chris (08)
ps: If you wish to pursue this matter, would you mind interleaving
comments instead of top-posting? (09)
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