draft of a paper submitted at "Context '99"
1 april 1999
2nd draft: April, 20, 1999
version .ps of the accepted paper
Objective and Cognitive context

Carlo Penco

Department of Philosophy - University of Genoa (Italy)
penco@unige.it

Abstract
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.

Keywords: Context, Cognitive, Indexicals, Defeasable reasoning

TWO CONCEPTS OF CONTEXTS

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, place, speaker,...>
and
(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
and
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 interpretations:

- "objective" or "metaphysical" (ontological) theory of context.
and
- "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 theories?

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 objective world).(1)

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 world.(3)
We might embed the theory of cognitive context inside the model-theoretical framework, using the most recent development of model theoretic semantics.(4) 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 theory) (5)
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 so on.


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.


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 contexts.
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
therefore:
(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)

in c2:
(2) a is kind to b
(3) a = husband of b

in c3:
(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)
revise c1
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 description.
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.

BIBLIOGRAPHY



FOOTNOTES

(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 precision)

(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)

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