Coordinating the transfer of information

John Collier University of KwaZulu Natal

and

Konrad Talmont-KaminskiMarie Curie-Sklodowska University

Standard formalist view of language

• Primary function of language is representation.• Language encodes thoughts of the transmitter into

words that are decoded by the receiver, giving a shared representation.

• Signal “carries” the relevant meaning; the meaning is “in” the signal.

• Most terms are generals, not context dependent• Pragmatics restricted to indexicals and ambiguous

terms and usages• Contexts disambiguate utterances

Standard view as an idealization

• Modeled on formal languages– Each symbol has a unique interpretation, and can

be applied generally.– Well-formed formulas each have a unique

propositional correlate with an unambiguous reference, or meaning.

• Formal languages are maximally precise idealizations of imprecise natural language.

Situation semantics(Barwise and Perry)

• Utterances primary; generals are abstractions• Utterances are situations that carry information

about situations. • All situations are particulars in the world; meaning

is in the world• Interpretation is situation dependent:– Generals associated with instances by regular use

(conventions), sometimes situation dependent– Context disambiguates indexicals and ambiguous terms

Significance of situation semantics

• Logic of situations is nonstandard (Mates)?– However, we can recover standard logic– But this depends on A and B being commensurate.

• Reception of situation semantics concentrated mostly on the semantics, and left most of the rest in the classical form.

• We are not so interested in the semantics as in– Primacy of utterances over generals– Utterances are situations– Information transfer– Context as part of the situation

Information transfer

• Components are transmitter, receiver, channel and message.

• Noise entering the channel can introduce ambiguity, but this can be reduced through redundancy in the message. Reliable channels are highly redundant.

• Eliminating noise is not always desirable: noise can be promoted to information with novel possibilities (e.g., mutations, creative misunderstandings)

Messages

• Messages are determined by a disambiguation of the set of possible messages that can be transmitted through a channel (Shannon 1949, Deacon at his talk here, Perry)

• Perry (PAPA Presidential Address 1994) showed a set of children’s blocks of different shapes, with each shape a different colour. “Pillar”, in the context, would select a pillar. However, all pillars are red, so “red” would serve the same purpose of disambiguation in an appropriate language game (compare Wittgenstein).

• So disambiguation is not sufficient for content: “pillar” and “red” do not mean the same, and are not even the same grammatical category.

Information channels

• Shannon did not give us a theory of channels; this had to wait for Barwise and Seligman (1997).

• Current status of the logic of channels is not integrated with transmission in Shannon’s sense. Devlin, Seligman, Gorenson and others are working on this.

• The fundamental concept of an information channel is an infomorphism, which is a relation between classifications, a classification being a set of tokens arranged under a set of types.

Classifications (types)

• Mathematics and theories deal with types (i.e. classes, or categories or other abstract kinds).

• For example, if we consider the information that two dice were rolled, then we might consider the probability of getting a seven (a type of outcome).

• This is the outcome which has six possible forms, and the probability is 1/6. The information that a seven was rolled therefore is 1/6log26, or about .43 bits.

Classifications (types and tokens)

• Information is carried by particulars, or tokens. • A classification A is an ordered triple <A, A,╞A> of a set

A of objects to be classified (the tokens of A), a set of objects used for classification and binary relation between the two A, that tells which tokens are classified as which type, ╞A.

• For the dice example, the classification is made up of the total of each possible roll from two to twelve, the particular rolls, and the assignment of each roll to a number.

Classifications and constraints

• The classification ╞A constrains the assignment of tokens through constraints if and only if the classification assigns some token a in the set of interest A to a type α within a set of types A in the classification. The complete set of constraints is called the theory of the classification, ΘA.

• Interestingly, types and tokens are duals, so tokens can serve as types, and vice versa.

• For example, a system might sort signals or objects into different “locations”. The part that sorts objects of type A is an A-filter, and is a token of type A. This allows a physicalist account of information flow.

Infomorphism

f

fA C

A C

╞C╞A

Fundamental property of infomophisms

• An infomorphism is a pair f of functions ‹f, f› between two classifications A and C, one from the set of objects used to classify C to the set of objects used to classify A, and the other from A to C, such that the biconditional relating the second function to the inverse of the first function holds for all tokens c of C and all types of A, f(c) ╞A α if and only if c╞C f( α).

• The biconditional is called the fundamental property of infomorphisms.

Channel definition

• An information channel for a distributed system is an indexed family of infomorphisms with a common core codomain C. The infomorphisms allow information to be carried from one part of the system to another.

• In the simplest case we have only one infomorphism making a channel.

Simple example• For example, in a flashlight, the components might be a bulb,

battery, switch and case. The channel is basically a connected series of infomorphisms from switch to bulb through the mediation of battery and case. A channel does not need to be sequential as a whole, but various parts do, e.g., the switch sends information to allow the flow of electricity through the case to the bulb, so that the bulb has information about the state of the switch.

• Note that infomorphisms may be directed (hold between classifications in one direction, but not the other). In the flashlight case, if the channel is functioning the switch also has information about the bulb, but this sort of converse relationship need not hold.

Channels can be directed

• Channels are typically directed. For example a thermometer varies with the temperature of the air, but changing the thermometer reading will not change the air temperature.

• The logic of directed channels (and the logic of information flow in general) is nonstandard (Barwise and Seligman).

• To recover standard logic in situation semantics we need further constraints on information flow.

Interpretation of infomorphisms

• Some classifications are natural; others are artificial, or constructed.

• Infomorphisms between natural classifications can be satisfied by natural types and tokens, allowing a natural interpretation.

• Infomorphisms between natural kinds and mental classifications imply either general knowledge or very good luck.

Meaning

• It is natural to talk of tokens of C being about tokens in A when classification C is artificial, perhaps when C is selected (Deacon).

• However, the A and C classifications need not be the same, or even commensurate in general. Satisfying the channel conditions in a given case is sufficient for information flow (recall Perry’s blocks).

• Classifications can be the ground of meaning, but we need further constraints for a theory of meaning in communication.

• In selection there is a tuning of genes and traits with the environment so that the classifications correspond in general. We need something similar for linguistic communication.

Our view (Pragmatist pragmatics)

• Unlike the standard view, in which contexts disambiguate utterances, on our view utterances disambiguate contexts.

• Pragmatics extends to all interpretation, and context includes all factors but the transmitted utterance.

• Classifications are a result of context.• Overlapping contexts are required for common

propositions.

Components of context

• general semantic conventions • local semantic conventions • ongoing perceptions and possible perceptions of the

environment• background knowledge, explicit and tacit • context specific knowledge • syntactic rules (including parts of speech) – innate and

otherwise • intentions and purpose (the “game” being played)• inferences and anticipated inferences• just about anything else

Example 1

I go into a coffee shop in China and say “latte”. I receive a latte and hand over more than I think it will cost and receive change.

• Note that I need not speak the language; we need only a common word and a common context. “Latte” disambiguates the context. Not necessarily needed given a local convention.

• This would not work in a taxi.• Function is not representation but request

Example 2

In a restaurant the manager says to a waiter, “The roast beef wants a glass of water.”

• This could be a new innovation, referring to the diner eating roast beef by their meal.

• But it could also be a convention established by repetition of similar usages.

• Original use must have been a perhaps playful innovation; conventional usage retained due to its practical value in the context.

Example 3

Two hunters A and B are hunting deer:A: “Over there,” pointing casually towards the

woodsB: acts confusedA: nods upwards towards the sky over the

woodsB: sees agitated birds over woods, says, “Oh.”

Information is not enough for common representation/interpretation

• Perry game: information can be transferred with no common representation.

• Latte case: common language is not necessary for communication (in restricted contexts); pointing would be enough in some cases, or regular practices

• Kuhnian situations: incommensurability results from incompatible classifications. Information is transferred between paradigms, but no common interpretation. Result: miscommunication

Coordinating representations

• Hunter case: heavy reliance on context and common expectations to establish that a common representation is accepted by both that is sufficient for their purposes

• Coordinating representations requires transfer of information, but also coordinating classifications enough for common interpretation of the situation.

• Coordination uses utterances as well as copious background explicit and tacit knowledge, as well as situational circumstances.

• Hypothesis: coordination cannot typically be done by through language alone.

Recovering traditional semantics

• Once representational meaning is determined, it can be fit more or less well into the idealized structure of traditional semantics.

• This allows us to use traditional logic to analyze meanings and relations of meanings.

• There will be limits to formalization because communication often needs only sufficient overlap in meaning for the circumstances, and need not be fully precise.

• At least part of the appeal of traditional formal methods comes from the possibility of this sort of post facto formalization.

Summary• Utterances reduce ambiguity of contexts. • Contexts can be made up of a variety of factors including linguistic

conventions (global and local), background knowledge, occurring perceptions, intentions, and many other things that can be exploited.

• Common reference requires coordination of classifications, though information transfer does not.

• Only enough clarity for current purposes is required.• Language does not stand on its own, but is located in the world, and is

impossible without context.• Novel usages can spawn new conventions.• Traditional semantics and logic can be recovered (within limits) after

meaning is established, explaining its appeal.

Thank you for your attention

If you want to see more:"Reference as a pragmatic achievement", Pragmatics and Cognition

(under review)"Pragmatist Pragmatics: The functional context of utterances",

Philosophica 75 (2005), pp. 61-88“Information, causation and computation” in Information and

Computation: Essays on Scientific and Philosophical Understanding of Foundations of Information and computation (World Scientific Series in Information Studies) Ed by Gordana Dodig Crnkovic and Mark Burgin, Singapore: World Scientific 2010.

Can be found at www.ukzn.ac.za/undphil/collier/papers