4.9—
Four Modalities for Counters
The four conventional modalities are also applicable to counters. Returning to the optometrist examples, suppose that the optometrist's instrument is adjusted so that Jones can see more than one symbol at a time. Suppose, moreover, that what he sees is the following image:
p & q
Jones has just come from his logic class, and so, when asked what he sees, says "p and q ." The optometrist, however, is ignorant of the conventions of logic. To him, this is just a line of three characters: the letter p , an ampersand, and the letter q . As the doctor sees it, the symbols on the eyechart are not related to one another syntactically, because the "eyechart game" does not bare any syntactic rules .
Once again, both Jones and the doctor are partially right, and in much the same ways they were each partially right in the original examples. Jones has a point in that the figures he sees are interpretable as markers of familiar types (and are in this case intended to be of the types that Jones guesses), and he is furthermore right in seeing that they are arranged in a fashion that is interpretable, under the conventions he has been taught for the propositional calculus, as having a certain syntactic form in the propositional calculus. Yet the optometrist has a point as well: the chart at which Jones is looking was designed as an eyechart. (We may, if we like, assume once again that the doctor drew the chart himself, and knows quite well what he meant to draw.) It was not intended to contain formulas in the notation employed in propositional logic, and the fact that some symbols in the eyechart are interpretable as forming such a formula is quite accidental. Similarly, if a diagonal sequence of letters should be interpretable as a sentence in Martian, that fact would be quite accidental. When the author of the eyechart drew it, Martian language played no role in his activity, and neither did the propositional calculus. To use terminology developed earlier, syntactic relationships did not form part of the authoring intention with which the
Figure 6
chart was created, and so the symbols in question would not rightly be said to have been intended to have a particular syntactic form.
It is, of course, possible that someone should devise an eyechart or some other display of symbols with more than one symbol game in mind. Someone who believed in subliminal suggestion, for example, might devise a display of symbols so that parts of it were interpretable under standard English conventions in a fashion that was not supposed to be consciously recognized by the reader. Thus a greedy optometrist might try to sell extra pairs of glasses by designing his eyechart like that shown in figure 6. In this case, the figures on the chart can be interpreted in two ways: (1) as characters on an eyechart, and (2) as letters forming English words that make up the sentence "Buy an extra pair now." As they are employed in the "eyechart game," the markers on the display do not enter into syntactic relationships, because syntactic relationships are always relative to a system with syntactic rules, and the "eyechart game" has no syntactic rules. As markers used in the formation of an English sentence token, however, they are counters having syntactic properties, because the English language does have syntactic rules. In this example, moreover, the markers on the chart are not only (a ) interpretable as syntactically unstructured tokens in the eyechart game and (b ) interpretable as syntactically structured tokens in a written English sentence, they are also (c ) intended as syntactically unstructured tokens in the eyechart game and (d ) intended as syntactically structured tokens in a written English sentence. Both "games" are intended by the author of the chart in this case—unlike the earlier case, in which the optometrist did not intend the line of symbols p-&-q to count as a formula structured by the rules of propositional logic, even though the line of symbols was nonetheless interpretable as such.
In that example, moreover, the line of symbols was also interpreted (by Jones) as a formula in propositional calculus notation, and was interpreted in such a fashion that Jones imputed to it a certain syntactic structure that is provided for by propositional logic. This interpretation is not affected in the least by the fact that the eyechart was not designed with it in mind, or even by the fact that the author of the chart was unfamiliar with propositional logic. Finally, as in the case of markers and signifiers, there is infinite latitude in the ways a display of markers could, in principle, be interpreted as counters of various sorts, because any given marker type can be employed in an indefinite number of systems characterizable by syntactic rules. For any arrangement of markers, one could, as Haugeland says, "imagine any number of (strange and boring) games in which they would be perfectly legal moves" (Haugeland 1981: 25).
It is now possible to provide definitions for the four ways of being a counter. These definitions will not be employed directly in the argumentation that follows, but are provided for the sake of exactitude and balance in the development of semiotic terminology. They may safely be skimmed over by the reader who is not interested in the definitions for their own sake, but only in their contribution to the main line of argument.
(C1) An object X may be said to be interpretable as a counter of type C iff
(1) X is interpretable as a marker of type T ,
(2) the marker type T is employed in some language game G practiced by a linguistic community L ,
(3) G is subject to syntactic analysis,
(4) there is a class C of markers employed in G sharing some set F of syntactic properties, and
(5) the conventions of G are such that tokens of type T fall under class C .
(C2) An object X may be said to be intended (by S) as a counter of type C iff
(1) there is a language user S who is able to apply the conventions of a language game G ,
(2) the marker type T is employed in G ,
(3) G is subject to syntactic analysis,
(4) there is a class C of markers employed in G sharing some set F of syntactic properties,
(5) the conventions of G are such that tokens of type T fall under class C ,
(6) S intended X to be a marker of type T ,
(7) S intended X to count as a move in an instance of language game G , and
(8) S intended X to fall under class C .
(C3) An object X may be said to be interpreted (by H) as a counter of type C iff
(1) some language user H apprehended X ,
(2) H interpreted X as a token of type T ,
(3) H is able to apply the conventions of language game G ,
(4) the marker type T is employed in G ,
(5) G is subject to syntactic analysis,
(6) there is a class C of markers employed in G sharing some set F of syntactic properties,
(7) the conventions of G are such that tokens of type T fall under class C ,
(8) H interpreted X as counting as a move in an instance of G , and
(9) H interpreted X as falling under class C in game G .
(C4) An object X may be said to be interpretable-in-principle as a counter of type C iff
(1) X is interpretable-in-principle as a token of marker type T ,
(2) there could be a language game G employing markers of type T ,
(3) that game G would be subject to syntactic analysis,
(4) these conventions would be such that there would be a class C of markers employed in G sharing some set F of syntactic properties, and
(5) the conventions of G would be such that tokens of type T would fall under class C .