Re: Issues about contexts and quantifiers

Jim Fulton <>
Date: Thu, 8 Apr 93 11:42:18 -0700
From: Jim Fulton <>
Message-id: <>
To:, interlingua@ISI.EDU,,
Subject: Re:  Issues about contexts and quantifiers
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.

Jim Fulton