As a of the laughing Santa vocabulary, the task of the automaton is to produce only writer licit strings of that vocabulary, by a process that can produce any and all such strings. It begins in its initial state, State 1, and emits an (its only available move), changing to State 2. In this ‘h’ state, it can produce either an or an selects one at random—and goes into State 3. In ‘a’ ‘o’—it this state, it can either tack on an exclamation point, and move into its final state, State 4, finishing the process, or emit another and return to State 2 to repeat the process. In any case, ‘h’ whenever it reaches State 4 and halts, the string it has constructed will be a member of the laughing Santa vocabulary. I hope this brief rehearsal makes it clear how the constellation of nodes and arrows that makes up this directed graph represents the abilities to read and write (recognize and produce arbitrary strings of) the laughing Santa vocabulary. What it represents is abilities that are to that vocabulary—that is, read and write it, in the attenuated sense appropriate deploy to this purely syntactic case. And the digraph representation is itself a that is vocabulary to those vocabulary-deploying abilities. That is, the digraph representation of specify this finite-state automaton is a for the laughing Santa vocabulary. pragmatic metavocabulary The relation between the digraph vocabulary and the laughing Santa vocabulary is, then, a now but between vocabularies. pragmatically mediated—not semantic, syntactic—relation It may seem that I am stretching things by calling the digraph form of representation a It will be useful, as a way of introducing my final point in the vicinity, to consider ‘vocabulary’. a different form of pragmatic metavocabulary for the laughing Santa vocabulary. Besides the digraph representation of a finite-state automaton, we can also use a representation. state-table For the laughing Santa automaton this is: State 1 State 2 State 3
As a writer of the laughing Santa vocabulary, the task of the automaton is to produce only licit strings of that vocabulary, by a process that can produce any and all such strings. It begins in its initial state, State 1, and emits an ‘h’ (its only available move), changing to State 2. In this state, it can produce either an ‘a’ or an ‘o’—it selects one at random—and goes into State 3. In this state, it can either tack on an exclamation point, and move into its final state, State 4, finishing the process, or emit another ‘h’ and return to State 2 to repeat the process. In any case, whenever it reaches State 4 and halts, the string it has constructed will be a member of the laughing Santa vocabulary. I hope this brief rehearsal makes it clear how the constellation of nodes and arrows that makes up this directed graph represents the abilities to read and write (recognize and produce arbitrary strings of) the laughing Santa vocabulary. What it represents is abilities that are to deploy that vocabulary—that is, read and write it, in the attenuated sense appropriate to this purely syntactic case. And the digraph representation is itself a vocabulary that is to specify those vocabulary-deploying abilities. That is, the digraph representation of this finite-state automaton is a pragmatic metavocabulary for the laughing Santa vocabulary. The relation between the digraph vocabulary and the laughing Santa vocabulary is, then, a pragmatically mediated—not now semantic, but syntactic—relation between vocabularies. It may seem that I am stretching things by calling the digraph form of representation a ‘vocabulary’. It will be useful, as a way of introducing my final point in the vicinity, to consider a different form of pragmatic metavocabulary for the laughing Santa vocabulary. Besides the digraph representation of a finite-state automaton, we can also use a state-table representation. For the laughing Santa automaton this is: State 1 State 2 State 3
Analytic%20Pragmatism%20Expressivism%20and%20Modality%2014-10-2%20a.docx