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Re: [ontolog-forum] Anthropology of Colour

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Christopher Menzel <cmenzel@xxxxxxxx>
Date: Mon, 17 Mar 2008 18:03:58 -0500
Message-id: <47DEF8DE.2050800@xxxxxxxx>
Ed Barkmeyer wrote:
> I wrote:
>>> That is the point I thought should not be lost: Formalization turns
>>> adjectives, including colour attribution, into predicates ("verbs").
> Pat Hayes wrote:
>> I wouldn't say for a second that predicates in FOL have any clear
>> connection with verbs in English.
> Upon reflection, I have to agree.  Logical predicates seem to
> represent nouns, adjectives, verbs and adverbs without prejudice.    (01)

Not adverbs, typically.  In a standard logical language, sentences like    (02)

(1) John buttered the toast    (03)

and    (04)

(2) John buttered the toast slowly    (05)

would have to be represented using completely different predicates, one
for "buttered" and another for "slowly buttered", e.g., "Bjt" and "Sjt"
or "Buttered(john,thetoast)" and "SlowlyButtered(john,thetoast)".  This
is very unsatisfactory, however, as sentence (1) obviously follows from
(2), whereas "Bjt" obviously does not follow from "Sjt".    (06)

This observation was Davidson's motivation for arguing that the logical
form of "action sentences" like (1) and (2) involved quantification over
events.  Thus, if we represent the logical form of (1) and (2) as    (07)

(1')  (Ex)(Event(e) & Buttering(e) & Agent(e,j))    (08)

and    (09)

(2')  (Ex)(Event(e) & Buttering(e) & Agent(e,j) & Slow(e))    (010)

respectively, it is obvious that (1') now follows from (2') by simple
predicate logic.    (011)

Others (e.g., Harman) have argued that Davidson's logical forms for
sentences like (1) and (2) are too remote from their surface grammatical
forms to serve as satisfying logical forms.  Rather, adverbs seem to
function much more as operators on predicates.  Capturing the logical
forms of action sentences like (1) and (2) on this approach thus require
augmenting the usual apparatus of first-order logic with formal
predicate operators and the addition of new logical principles to govern
their behavior, e.g., for operator S and unary predicate P, that S[P](x)
entails P(x).    (012)

The two options here nicely illustrate a frequent trade-off in the
semantics of natural language: Increase ontological commitments and keep
the necessary logical apparatus simple (Davidson) or avoid the
ontological commitments and make the logical apparatus more complex
(Harman).    (013)

Chris Menzel    (014)

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