Wednesday, November 30, 2011

Remarks 48 & 49

Communication, meaning

In these Remarks, W emphasizes the dependence of meaning on context - the specific language game being played. This is an important concept in the technical area of communication theory. I find interpreting these Remarks from that perspective helpful. Perhaps others will as well, or at least find it interesting.

There is some overlap between the vocabulary used in discussing the example language of Remark 48 and the vocabulary of comm theory, but unfortunately the same word may be used in both vocabularies but refer to entities that are not analogs. In the following, I use W's vocabulary when discussing language and the comm theory vocabulary when discussing comm theory. Hopefully, doing so doesn't add to the inevitable confusion.

In Remark 48, 3X3 matrices of squares - each either red, green, black, or white - are to be described in a language the words of which are "R", "G", "B", and "W" (corresponding in the obvious way to the colors of individual squares) and the sentences of which are sequences of nine words, eg, RRBGGGRWW. The analogous entities in communication and coding theory are a set of symbols (an alphabet) sequences of which are called codewords. So, here the sequence RRBGGGRWW could be a codeword nine symbols long.

In talking about language, the transmission medium is usually taken for granted as being either vocal utterance or writing/printing. So, W's "words" might be transmitted by vocalizing the corresponding letters in some language. It will be useful to consider in slightly more detail how the symbols of a communication codeword are transmitted from sender to receiver. In general, any way that the sender can take one of a set of actions distinguishable by the receiver will work. Examples are sending electrical signals on different frequencies, holding a flag in different positions, raising different monochrome flash cards, or lighting different numbers of latterns. Thus, the symbols of a quatenary alphabet can be sent over a quatenary channel which comprises four distinguishable actions. However, an important alternative medium for conveying symbols is to use a binary channel and to convey each symbol using the appropriate number of binary digits. Eg, a member of the quatenary symbol set {R,G,B,W} can be conveyed by sending one of the two binary digit sequences 00, 01, 10, or 11.

W notes that in response to the question "What are the simples?", the answer "the individual squares" seems as good as any for the example language game, but adds that one can imagine that other language games - ie, other contexts - might dictate considering other entities as simples. Similarly, consider transmitting quatenary symbols over a binary channel as two binary digits so that each nine symbol codeword is sent as a sequence of 18 binary digits. Now the question "What are the simples?" can be interpreted as asking how the receiver should interpret each codeword: as 18 binary digits, nine quatenary digits, six 8-ary digits, or even as a mix of those? Or equivalently, "Where do the commas demarcating the symbols go?" (Just as one hearing a language they don't know well often asks "Where are the pauses between words?") The answer is that this must be established by prior agreement between sender and receiver. Ie, it depends on the total context.

I interpret the somewhat cryptic comment in Remark 49 - "a sign 'R' ... may sometimes be a word and sometimes a sentence" - as addressing this issue. If A is just learning to associate "R" with a color, "R" is merely a word (or symbol) but has not yet acquired a role in a language game; ie, A has yet to fit the word into a context. But if, for example, A has to describe complexes of colored squares to B and learns to use the 'R' by itself to indicate that all nine squares are red, then we can say that "R" is a sentence since it is then a description and has therefore acquired meaning.

We see that language - and communication in general - require a great deal of prior agreement between participants. In the example language game of Remark 49, there must be agreement between speaker and hearer on the correspondence between squares in the matrix and position in a sentence, on the correspondence of color to word, and that a sentence is to be interpreted as a description of the appearance of a 3X3 matrix of colored squares. In the case of a communication system, sender and receiver must agree on numerous procedural details (the so-called "communication protocols"). In both cases, the parties must futhermore agree on how the receiver is to act in response to the information received. Thus, Frege's claim that a word has meaning only in the context of a sentence seems right, but the "context of a sentence" should be understood as often quite involved.

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