Re: Issues about contexts and quantifiersJim Fulton <email@example.com>
Date: Thu, 8 Apr 93 11:42:18 -0700
From: Jim Fulton <firstname.lastname@example.org>
To: email@example.com, interlingua@ISI.EDU, firstname.lastname@example.org,
Subject: Re: Issues about contexts and quantifiers
Cc: email@example.com, firstname.lastname@example.org
John & Mike,
I just read your note on your discussion about quantifying into contexts.
My funding does not allow me to spend much time in responding, and perhaps
that is well, since a lot of contemporary philosophy has addressed just
that issue. So let me make some brief observations:
1. Formally, the questions you are asking about quantification are the
subject matter of modal logic, regardless of whether you accept a Kripke-
like semantics for that logic. I therefore do not quite understand your
reluctance to use that work as input to the process of answering these
2. Secondly, although Tarski couched his semantics using the language of
set theory, it would be a mistake to interpret his sets as mere data
structures. The extension of the predicate 'dog' is the set of all dogs;
the extension of 'Fido' is a particular dog; the sentence 'Fido is a dog'
is true because the particular object, referred to in this case by the
word 'Fido', belongs to a particular class, referred to in this case by
the word 'dog'. The set-theoretical extensions to the natural language
used in the meta-language, in which we do formal semantics, are used to
refer to real objects and real classes in a precise way, not to refer to
data structures except those whose meaning we are analyzing.
3. Thirdly, any attempt to analyze belief as some kind of relationship
among "internal" or "mental" surrogates seems doomed to failure. Every
attempt to offer any kind of explanation of these so-called objects has
failed to provide an adequate criterion for identity or recognition.
How can we possibly know whether Tom's belief state involves that
particular surrogate rather than another for which he uses the same name.
It seems clear to me that Tom can correctly be said to believe a fact with
respect to an object, i.e., Tom can believe block A to be on block B,
without there being episode in which Tom is in a belief state with respect
to some respective surrogates for block A, block B, and "on-ness". Belief
and most other psychological attitudes seems to be dispositional. Among
the dispositions is to describe the belief using sentences like "Block A
is on Block B". Another disposition is that if Tom uses that sentence,
he will take other sentences using "Block A" to be about Block A. On
the other hand, if Tom uses "George is on Foundation" to answer the
instruction "Describe those things", when issued pointing to Block A and
Block B, then one would expect him to use the word "George" in talking
about Block A.
This is a long-winded way of saying that our beliefs (and other psychological
attitudes are about things in the physical world (I should say the "real"
world, because many of our beliefs are about real, non-physical things.
Actually we have many beliefs about unreal things too.) The formal
problem is to come up with accurate principles of reasoning that apply to
statements about belief (and other attitudes). A formal epistemology
must take sentences such as the following as a given:
(a) Tom is believed by both George and Betty to be the next President.
(b) The next President is not believed by both George and Betty to be Tom.
(c) Tom is not believed by both George and Betty to be Winston.
(d) Winston is the next President.
All these sentences might be true. What it means is that 'the next
President' as it appears in (a) is not in a position that admits substitution
of identicals, and therefore MIGHT not admit quantification. Questions
like these are not going to be answered within the FOPC. I don't think
they can be answered by syntactic analysis at all. Each psychological
modality, i.e., our verbal and non-verbal reasoning about each modalities,
has to be explored specifically to determine the appropriate semantics,
i.e., what we mean by the words, and hence what we can infer from sentences
using those words. That reasoning will likely be non-monotonic, but that
does mean that current theories of non-monotonic reasoning will be of much
help. That reasoning will be intensional, but that only gives us a framework
in which to describe the questions; it doesn't answer them.
Sorry, I got on a soapbox. I'll get off and give you your turn.