the meaning of 'relevant' used in linguistic explanations

Question

Maybe someone who is well-versed in semantics could help me.

The word relevant turns up at places in the following paragraph. While I know the fundamental meaning of it — pertinent, germane, there seems to be more to it when used in linguistic explanations. Could anyone please help me with its nuance, connotation, subtlety etc.? (I'm not a native speaker of English, by the way. If you would put your help in plain English as much as possible, it would be really appreciated)

(14) # While in Santiago, Bill broke his foot and was rushed to the big hospital.

Here, the hearer is licensed to assume that the modifier is relevant (in accordance with the maxim of Relation (Grice 1975)). However, the modifier in (14) could only be relevant if it distinguishes this hospital from others, in which case the hospital in question is no longer undifferentiable and, in the absence of unique identifiability, the conditions for the felicitous use of the definite have not been met. Hence, infelicity results. To put it another way, since the modifier is presumed to be relevant, it must be the case that it matters which hospital, or at least what type of hospital, is under discussion -- i.e., that it is big. Thus, the condition of not being relevantly differentiable is not met, and the hearer must assume that the other condition for the felicitous use of the definite applies -- i.e., that the hospital be uniquely identifiable. In the absence of a uniquely identifiable hospital, the utterance in (14) is simply infelicitous.

Uniqueness, Familiarity, and the Definite Article in English by Betty Birner and Gregory Ward, Berkeley Linguistics Society, 1994, via eLanguage

Answer 1

The sense of Relevance in Birner and Ward 1994 is identified as that of Grice's Maxim of Relation.

This maxim is one of those specified in Grice's 1967 William James lectures at Harvard, later
published as "The Logic of Conversation" in 1975, and developed in many other works. Grice was a philopher and was concerned with the underlying assumptions behind human communication.

He proposed that that principle was Cooperation. From the Wikipedia article:

As phrased by Paul Grice, who introduced it, it states, "Make your contribution such as it is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged." Though phrased as a prescriptive command, the principle is intended as a description of how people normally behave in conversation.

Unpacking that principle led to what have come to be called Grice's Maxims, which are now standard classroom material in philosophy of language, linguistic pragmatics, conversational analysis, artificial intelligence, user interface design, and cognitive studies, among many other disciplines.

The list is short enough to post in full:

• Maxims of Quantity

  1. Make your contribution as informative as is required.
  2. Do not make your contribution more informative than is required.

• Maxims of Quality

  1. Do not say what you believe to be false.
  2. Do not say that for which you lack adequate evidence.

• Maxims of Manner

  1. Avoid obscurity of expression.
  2. Avoid ambiguity.
  3. Be brief.
  4. Be orderly.

And, finally, the one maxim that is not under the speaker's control:

• Maxim of Relation
  
  1. Be relevant.

The relevance of a conversational contribution depends on how it is interpreted -- or intrepretable -- by addressees. Addressees do certainly -- constantly, and expertly -- interpret and evaluate everything that speakers say (assuming they are paying attention, of course; but this is philosophy, and philosophers always assume their addressees are paying attention).

That's the point that Birner and Ward are addressing in the quotation.
If one encounters sentence (14) (boldface added):

• While in Santiago, Bill broke his foot and was rushed to the big hospital.

one must, in order to understand the definite article, assume that

Santiago is a place where there are at least two hospitals, of which only one is large.

Otherwise the big hospital is ungrammatical. The addressee assumes it's not ungrammatical (a cooperative assumption) and then figures out the context, again assuming the speaker is being relevant.

This is quite a lot of specific meaning to load on one unstressed word, and of course it's not what the means -- the doesn't mean anything. But it's what's required to make it relevant, and listeners will absorb that information along with the news about Bill.

Thus non sequiturs do not occur often in conversation; no matter what you say, somebody will figure out a way to make it relevant to what they understand as the point of the discourse. It's hard to make a non sequitur.

And the fact that Relevance is the one thing the speaker isn't in charge of -- but can manipulate -- has led to further theoretical expansion along these lines; see, for instance, Relevance Theory.