Department of Philosophy - University of Genoa (Italy)
In what follows I consider the apparent contrast between two kinds of theories
of context: a theory of objective context - exemplified in the works of Kaplan
and Lewis - and a theory of subjective context -exemplified in the works of McCarthy and Giunchiglia. I consider then some difficulties for the objective theory. I don't give any formalization; instead I give some theoretical points
about the problem. A possible result could be the abandon of the double
indexing for a development a multi-context theory (I give an example of a
case). However other results could be possible and a challenge is posed to
solve problems using the best results from each tradition of research.
Contexts are not something we find in Nature; context is a concept
very used by philosophers and scientists, but with many different
definitions, such that it would be better to speak of many different concepts,
or at least a family-resemblance concept. Since Dummett we speak of "context
principle" in Frege and Wittgenstein; we speak of "context of utterance" in
pragmatics; we speak of "context sensitive" grammars in linguistics, and we
speak also of "linguistic context" and "non linguistic context"
Studying the many attempts to have a better grasp of what kind of concept a
context is, it is easy to find a strong counterposition between an objective
and a subjective view of context. Two paradigmatic positions representing
these alternative views are the model theoretical tradition developed in the
works of Kaplan, Lewis,... and the artificial intelligence tradition
developed in the works of McCarthy, Giunchiglia,....Both traditions give
formal settings to treat contexts; if I were a logician I would try to see
whether the concept of context envisaged by one formalism could be expressed
by the other. Not being a logician, I will restrict myself to some conceptual
analysis. The two different conception can be summarized as follows:
(a) context is a set of features of the world, we can express as: <time,
(b) set of assumptions on the world we can express as: <axioms, rules>
let us see some relevant quotation.
On (a): "context is a package of whatever parameters
are needed to determine the referent ... of the directly referential expressions";
"each parameter has an interpretation as a natural feature of a certain
region of the world" (Kaplan 1989);
on (b) "context is a group of assertions closed (under entailment) about
which something can be said"
(McCarthy 1993); context is "a theory of the world which encodes an
individual's perspective about it" (Giunchiglia 1993)
In "Afterthoughts" Kaplan speaks explicitly of the metaphysical point
of view in describing contexts, while in "Notes on formalizing
contexts" McCarthy uses a notion of context which is leading towards the idea
of "microtheory" (Guha) or towards the idea of a subjective point of view on
the world (Giunchiglia). Given these differences, I will call the two different
conceptions of contexts as:
a) context as an objective, metaphysical state of affair
b) context as a subjective, cognitive representation of the world.
However, in doing this distinction we are presupposing already a basic
choice. Giving two different names we think as we had two radically different
concepts. But in what sense are these two concepts different? We might be in a
situation similar to the concept of probability, where - with Carnap - it was
possible to distinguish probability1 and probability2 (subjective and
objective probability) as two different concepts linked by the common
obedience to Kolmogoroff's axioms. In this case we should have two concepts
strictly correlated, for which it is possible to have a unique formal
framework but different interpretation and therefore, also from an historical
point of view, different theories. We may suggest the following. We have two
different interpretations of what a context is: features of the world or
representations of features of the world; we might call the two different
- "objective" or "metaphysical" (ontological) theory of context.
- "subjective" or "cognitive" (epistemic) theory of context.
However we are in a different situation than the one characterizing
the concept of probability after Kolmogoroff's axioms. As far as the concepts
of context are concerned, we have different formal standards and
axiomatisations. We have two related questions:
- shall we look for some higher theoretical and formal setting on which to
place the two concepts of context?
- shall we be content of having two different concepts and two different
It is apparent that we need to have some distinction between
representation and what is represented. However we have at least two problems:
(a) Davidson has warned us of the perils to build a theory on a too easy
contrast between content and conceptual scheme. Shall we extend his warning
to the relation between represented content and means of representation? It is
apparent that means of representation affects the represented content: when I
see something as a bunch of leaves and a trunk I do not see a tree; when I
see something as a number of trees, I do not see a wood.
(b) Notwithstanding the clear cut of the two above mentioned theories of
context, the line of demarcation is not so easy to pose. I will not elaborate
on the point (a), but I will concentrate on this second point. As soon as
Lewis accepted Kaplan's theory of double indexing (an index for possible
words and an index for contexts), he held to his strategy to put inside the
index for contexts relevant subjective information, as the speakers' beliefs
or background knowledge, plugging in the "objective" context a subjective
content. A concept born to represent the objective features of the world seems
then to have a natural tendency to become subjective (somebody might also say
that the background knowledge or the speaker's beliefs still belong to the
On the other hand the subjective context has to deal with
objective states of affair, and also with the reference of "I" and "you" when
uttered in some specific situation - and with the objective reference of any
element of the cognitive context. If context is intended as a set of
assertion, certainly these assertions will be - or would like to be - about
something objective; therefore they have to give a representation not only of
points of view, but also of what is represented by them.
If we cannot "reduce" the concept of objective features of the world
to the concept of representation of them, we still have the problem of the
possible reduction of the correlated theories. We have two theories and we
have to check (2)
which of the two has more expressive power, which is better suited to help us
in understanding the working of our language and of our relations with the
We might embed the theory of cognitive context inside the
model-theoretical framework, using the most recent development of model
I do not have enough logical ability to show neither this strategy nor the alternative strategy of reducing the theories of objective context to a theory of
cognitive context (e.g. in term of reduction of modal logic to multi-context
Therefore I will give just
some intuitive and sketchy doubts and hints towards the possibility of this
reduction at the level of conceptual frameworks. In fact, besides the
development of formalism, we need conceptual clarification. And if we do not
attain clarification at a conceptual level, our formalisms might not help us to
reach a unifying theoretical framework.
PROBLEMS ABOUT A THEORY OF OBJECTIVE CONTEXT
We may distinguish two basic aspects in Kaplan's theory: (a)
the distinction between content and character, which is absolutely helpful to
distinguish the evaluation of indexical at different worlds and the way in
which this evaluation is performed. (b) the distinction between context of
utterance and circumstance (possible world plus time). I am very prone to
accept a development of the first distinction, while casting some doubt of
the viability of the second. Certainly in Kaplan the two ideas are strongly
dependent one another, being the distinction of character and content defined
in term of context (character being defined as a function from context to
contents). However the character-content distinction can be considered as a
general distinction concerning different levels of meaning, which could be
developed and generalized in many different ways. It can be viewed, for
instance, as an heir of Carnap's intensional isomorphism, which tries to give
more fine grained distinctions in meaning that just intension can give (for
hyperintensional contexts), and has been developed by Cresswell(6)
. Or it could be developed in an
inferential framework: if meaning is defined in inferential terms, we might
define the difference between character and content through the different
kinds of inferences which are available or permitted to the speaker or the
hearer. Take the cases of Perry on the use of "I" and "he" when the content of
the two indexicals is the same ("he is attacked by a bear", "I am attacked by a
bear"...); we may distinguish the inferences available from the point of view
of somebody not knowing the identity of "I" and "he", and the inferences
available to somebody who acknowledges the identity. These two points of view
can be considered two different cognitive contexts, two theories with some
relation of accessibility.
Leaving aside the first distinction, let us focus then of Kaplan's
basic distinction of (objective) context and circumstance. This distinction
can be considered as an attempt to devise a contrast between conceptual
elements and non conceptual ones inside a proposition. The conceptual elements
are expressed by predicates and definite descriptions and are evaluated at
every circumstance; the non conceptual element, the causal or contextual one,
is expressed by indexicals. Indexicals are the linguistic items which connect
us directly to the external world. Therefore we need a special account for
extracting information from indexicals: information on indexicals as "I" or
"now" has to be derived directly from the (physical) context of utterance. We
need therefore to plug in our formalism a new index, referring to the physical
features of the world, such as time and location of utterance or speaker, and
Doubts on direct reference
However what is it the direct connection to the world which is
supposedly given by the use of indexicals? The direct connection to the world
is given by the use of symbols for referring; therefore any use of any symbols
for referring gives a connection with the world. The logic of Demonstrative
should become a logic of demontration, of the use of linguistic items for
demontrative purposes. However, as Robert Brandom has widely shown, there are doubts about the foundation of "connection with the world" in the demontration and use of tokens; any use of linguistic items as demonstration has a reason to occur in language only because it is possible to embed the linguistic item in an anaphoric chain, as anaphoric initiator. There is no use of demonstration without anaphora; but with anaphora we build a conceptual link around our terms and use them always inside a kind of theory (right or wrong) about what it is happening.
"Physical" parameters are always given inside
The conclusion given before can be said in other terminology: an
evaluation of the Logic of Demonstratives gives the referent of the indexical
(of "now" for instance) depending on the information about the time, on the
accessibility of this information. We represent the actual and possible worlds
always inside a cognitive context, inside a point of view. An objective
indefeasible metaphysical point of view is not expressible by us (may be it is
not expressible at all); a formal system will represent the point of view of
the kind of information and rules embedded in the system. Every system cannot
but represent a point of view among others; therefore it belongs to a
cognitive context (let us say the context of the semantic of classical modal
Any point of view purports to represent objective reality, but no
point of view can be taken to be "the" representation of the objective reality.
Even the most abstract levels of representation of objective reality gives
different and possibly contrasting representations: a fragment of classical
logic represents a different point of view in respect of a fragment of
intuitionistic logic. Applying to indexicals: when a system evaluates an
indexical such as "you" or "I" at a time and location of utterance, it is
always bound to be criticized and my evaluation can be rejected as mistaken
(for instance: depending on the accessibility of time and location; or on the
existence of ambiguity between lexical items - as "we" and "I" or "you"
and "you" - in a language) . Any theory of system of representation (be it an
individual, a logical system, a society) is always a defeasable representation
Doubts on double indexing
The idea of the double indexing means that we need an index for
referring to possible words, where different conceptual possibilities arise,
and an index for referring to physical features of the actual (or possible)
world at which to evaluate indexicals or demonstratives.
Does the above criticism imply an abandon of double indexing? This
sounds unfair to this wonderful novelty in logic, but we might always check
whether some other trick can do the job. Actually it is not question of
tricks, but of theory: we need an overall view of the working of our language and of our (formal and not formal) representations of the world.
Every representation purports to represent the objective state of
affair; however no representation can be said absolutely certain and
indefeasible beyond any doubt; therefore we may only give cognitive or "marked"
representations of the world. My suggestion is that we could obtain the same
richness of double indexing with a work made on the operations among cognitive
contexts: objective contexts are given by some of the many possible
description of the world, always collocated - explicitly or implicitly -
inside a cognitive context. It performs the role of objective context for us
if we use it as such! But we have to be always ready to revise our assumption
in front of new contrasting information, to reach a better level of
WHAT AN OBJECTIVE THEORY OF CONTEXT CANNOT DO
A theory is better than another if it can solve the problems solved by
the previous one and still has some advantages. I list hereafter some cases
which seem to be a problem for the Logic of Demonstratives and seem to be solvable
in a multi-context theory. To give a proof of such a claim goes beyond the
limitation of the paper; here it can be considered - at least- a challenge to
be posed to both theories.
cases of ambiguity going beyond indexicals:
tomorrow every man (in this room) will be wearing a tie
(where every man who is currently in the room will wear a tie or every man who
will be tomorrow in the room will wear a tie);
cases of different inferences permitted by different indexicals:
"He is pouring sugar" and "I am pouring sugar"
permit different practical inferences, while Logic of Demonstratives can only
give the relevant evaluation of the indexicals;
possibility of false utterances with indexicals:
"Now I am here" said to somebody who believes (and I know she does) I
amelsewhere (it might be said that what I say is strictly true; however, from a
conversational point of view, what I say is an intentional lie, and a lie is
supposed to tell the false)
vagueness and dependence on cognitive context of the meaning
"I am here" may mean many different things. Certainly location is objective
and it can be define more and more precisely; however the kind of precision is
given by the cognitive context (I am in Italy, in Trento, in this room, on
this chair); and other kinds of use of "here" seem to go beyond this problem
of definition of the physical space (I am reading this passage on the text; I
am with you; "now I an mot here" said in front of a video representing the
place where you are at the moment).
cases where the partition of the world does not mean a physical
"All dogs are sleeping" referring to our dogs put here and there, while other
dogs are barking; we have the double problem of quantifying on a subset of dogs
(belonging to our domain) and locating dogs which are not in a same
location. On this second problem, it is always possible that "the criteria of
partition of the world is not space-time organized... how is it possible to
divide the world in portions without thinking of a cognitive intervention of
an agent, who "cuts" reality following his aims,
interests, beliefs...?."(Bouquet 1998)
ambiguities between speaker's reference and semantic reference
Given the limitation of time and location, I will expand only this last
THE KIND HUSBAND
Before trying to give a reduction of an objective theory of context to a
cognitive theory of context we might try a possible integration of the two
different perspective. I take a philosophical example from Kripke's
distinction of speaker's reference and semantic reference. Kripke 1975 debates
the problems which arise from the possibility to use a literally wrong
description of somebody to refer to him; take the following example invented
by Kneale and discussed by Donellan and Kripke:
John says: "her husband is kind to her"
The person referred to by John is not the husband, but John uses this
description with the intention to refer to the person which is in the scene.
Actually we could say that this case is a case of demonstration, where the
definite description, even if it were false, is used as a proxy for an
indexical; or we could use the term forming operator"..., who is F", in this
case "he, who is her husband". Instead of saying just "he", the speaker says
something more specific with the intention to help the audience to pick up the
right person (and with the wrong presupposition that, being kind, the person is
a husband) .
The objective, metaphysical context is a set of parameters where we
might put: . This set of parameters picks up the only person which is the
speaker's referent, beyond his wrong belief about the status of the person who
he referred to.
The alliance between the two theories here would help: a metaphysical
theory of context gives the existence of a unique individual referred to in
the objective context, individual which is the same in all possible worlds;
cognitive context explains the misunderstandings which arise in misplacing
some description in the actual demonstration. There are however some
problems which are not clearly answered in a theory of the metaphysical
context, dealing with identity and identification.
The metaphysical context postulates the existence, in an absolute way, of a
unique object referred to by the demonstrative; the individual referred by
"he, who is her husband" must be the same in all possible worlds. Therefore,
the parameters, giving the real situation, must be supplemented with the
possibility of re-identifying the object referred at any world. Can the
metaphysical theory of context be used to decide these identities? There is no
hint as to get to that.
Notwithstanding the misunderstandings, a logic of demonstrative should
be able to pick up the unique individual referred to. But how? We need the "how"
if we want to explain the possibility of misunderstanding. We need to express
the set of assumptions which represents information shared in the relevant
community; e.g. we may to rely on some data-base which contain information
about the marital status of all the person belonging to the community and
check the name of the lady's husband; then we may compare this name with the
name of the referred person and verify whether they match or not. If they
match, speaker's reference and semantic reference coincide; if they do not,
speaker's reference and semantic reference are to be distinguished. This seems
to be an empirical matter and to go beyond o theory of metaphysical context.
Is it really only an empirical matter? The flaws of a theory of
objective context can be partially answered by a theory of cognitive context
(actually theories of cognitive context have been built with these kinds of
problems in mind). The point is whether we may attain a general explanation of
the working of language and reasoning using only a theory of cognitive
context, whether the work done with the interplay between metaphysical and
cognitive theories of context can be given using only the concept of cognitive
context. Having the concept of a representation of reality from some point of
view, we apparently have the concept of represented thing; however we do not
start from a list of parameters giving the "real" and "objective" elements of
reality, but we start with different points of view about what is real or not,
and reach the idea of objectivity at the end of the interplay among cognitive
Let us maintain the previous example and see how the interplay among
contexts brings about a view on objectivity. I will not use any of the
different formalizations of multi-context theories, but I will really on an
intuitive assessment which can be coherent with most of them. In this case I
run the risk of hiding the most peculiar feature of multi-context theories,
that is the different kinds of rules of lifting and entering and exiting
contexts. However I rely on the simplicity of the example and the easy way of
translating it into some formal treatment. I assume also that each context
shares the same inference rules and has the minimum information required for
interpreting the sentence " his husband is kind to her" (the expression "in contex Cn" means that the sentences following are true in that context).
in context c1 (beliefs of reporter, normal observer)
(1) John says, looking at a, that her husband is kind to her
(2) John believes that a is kind to her (her=b)
(3) John believes that a is husband of b
From these reports the reporter himself, or any person listening to the report, may form a belief about John's point of view; therefore (2) and (3) mlay be re-written, taking care of cognitive contexts, as:
in context c2 (beliefs of John)
(2) a is kind to b
(3) a = husband of b
in context c3 (typically shared knowledge [or belief held by Kneale and possibly "us"])
(4) c = husband of b
(5) a is not husband of b
Context c1 and context c2 have two contrasting information. How to choose between one or the other? How to define the correct identities? We need some relation between contexts, a relation of reliability, which helps us to decide which context gives the right representation of the reality:
in context c4 (competent observer)
(2) a is kind to b
(3) a = husband of b
(5) a is not husband of b
c3 more reliable than c2
Here, given these assumptions, an inference engine should give the following operations:
discard (3), keep (2) and (5)
assert: (2) and (5)
This may also help us to verify some implicit assumption in the discussion of
the example. The supposition the relevant person is the lover and not the
husband is what we (or Kripke, Donellan and Kneale) say. However we may be
making a mistake. The relevant person could have been really the husband. Who knows? We need not only justification but also possibility of doubt. We may be ready to accept the introduction of other points of view which could be able to discard the objectivity we had reached with some difficulty. We may be
informed that "he" is the husband in disguise, pretending to be the lover.
Given the right "testimony" a new context may arise with this new piece of
information with evidence for it to decide for the reliability of what is
expressed in context 1 (even if based on chance and not on knowledge; e.g. on
the person revealing with highly reliable means this identity). We need in this
case another context c5 which could verify the validity of the conclusion in c4
and eventually accept of reject the conclusion in c4.
This sketchy presentation is intended just to give an idea of how we
may always explicit the cognitive context to which we adhere; the
objective context is nothing more than the context we recognize as objective.
To postulate an objective context as such, independent of a cognitive one, has
no use. Objectivity is always a result of our interaction, not a datum. We
know that there is some objective reality - and that we might get it wrong.
But any attempt to define it in an absolute way is misleading, because it
takes a description - given always inside some theory or cognitive context -as
an objective unrevisable description. To use an objective context is like to
decide that there is an outmost context. But there is no outmost context.
Objects are always described through some frame of mind, there is no neutral
The idea is the following: in any situation of collaboration or dialog
among many agents we may elaborate an outer context which has some mastery of
each of the other contexts; all terms and predicates can be lifted into the
outer context which serves as a paradigm of de-contextualisation. But
the de-contextualization is always relative (we must therefore speak,
as McCarthy suggests, of de-contextualisatrion). We cannot
assume to have reached the definitive representation of the structure of the
reality; there is no ultimate outer context, but it is always possible to
transcend the context in which we are. This gives rise to the possibility of
an infinite regress, but it seem that this infinite regress is harmless, and
represents our condition of limited humans. To stop the regress we simply
choose to use a cognitive context as objective.
This picture contrasts with the idea of a metaphysical context, which
give the "real" features of the reality. The general suggestion is that a
multicontext theory might perform what a logic of demontratives performs and
abandon the idea of metaphysical context, relying only on relative
de-contextualizations. That may appear an idealistic step, but it does not
follow. Speaking of relativity of contexts is just a reminder to the fact that
the world is given to us only inside a net of inferences and we cannot speak
of things in the world a part from some perspective, some point of view - more
or less reliable.
After this general comment on some of McCarthy's ideas, I still doubt
whether all I have said is irrelevant to the point. Is the example I have
chosen misleading? The problem is to have parameters of time, place and
speaker. The example compelled us to reason on speaker's reference, never
doubting of the speaker, the time and location, therefore, never posing doubts
on the parameters of metaphysical context. But the point is more relevant
than it appears. We may doubt of speaker, time and location; still the example
is understandable. Why? Because many of the reasoning processes we make
abstract of time and location. We may miss time, location and speaker, and only
another better cognitive context can help us to get them right.
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(1) Lewis 1970 thinks that it is needed to put many
parameters in the index, enclosing the background knowledge of the speaker. In the postcript (1981) he stresses that the package of features of context
should be enlarged. However he realizes that, besides the choice to build
richer and richer indexes, we have the choice to leave implicit most of the
aspects and at the same time to enlarge the double indexing (restricted by
Kaplan to possible world and time) also to location and standard of
(2) The problems are apparently at two different levels:
- from a semantic point of view: whether we need to use model theoretical
semantics (possible worlds semantics) or we may use another kind of formalism,
as inferential semantics (where the meaning of a sentence is not a function
from p.w. to truth values, but a set of inferences).
- from a syntactic point of view: whether we have to use a modal logic with
belief operators on propositions (and with the necessity to go on the second
order theories like the traditional one by Montague) or we may use a logic
with names for sentences, having - instead of operators -predicates with names
of sentences, names on which it is possible to quantify. Both theories have
their flaws and difficulties (see. Frixione1994).
My sensation is that, after the great amount of research in model theoretic
semantic, there is space for developing some theory of the inferential kind at
level of meaning. Which syntax this semantics should have is really a
difficult point to decide. The possibility to have an hybrid composing some
kind of inferential semantics with model theoretical semantics is still a
possible answer. Woods 1980 has suggested something similar speaking of the
connection between procedural semantics and model theoretical semantics.
(3) More expressive power is always linker to danger of a) inconsistency,
b) undecidability, c) computational intractability . An example of very
expressive systems is given by strong syntactic approaches, where the objects
of prepositional attitudes are represented as terms in a predicate language.
Therefore it is possible to quantify over the objects of prepositional
attitudes (something which is not allowed in modal logic, unless with the
passage to second order logic). However, as said before, syntactic approaches
may run the risk of inconsistency (see Thomason 1980; Frixione 1994,
pp.221-223; Penco-Palladino 1997).
(4) There are probably many possibilities from
preferential logics to the logics of explicit and implicit belief (Levesque).
Most of the attempts are framed inside some extension of modal logic;
traditional examples are for instance the works by Fagin and Halpern 1983, who extend the logic of implicit and explicit belief and use the concept of "frame of mind", applying a metaphor from Minsky's "society of minds".
(5) Attempts have been made by Giunchiglia-Serafini;
Giunchiglia-Serafini-Frixione 1993...An intermediate approach is the
"syntactic" approach by Konolige 1986, with a modal logic where the belief
operator is interpreted on a set of sentences.
(6) This does not mean that Cresswell's work can be interpreted as a development of the character-content distinction; it is however a different direction of thought stemming from the same carnapian roots, with the common aim to give more fine grained distinctions than intension alone)