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This Subsection highlights an issue of ''style'' that arises in describing a formal language. In broad terms, I use the word ''style'' to refer to a loosely specified class of formal systems, typically ones that have a set of distinctive features in common. For instance, a style of proof system usually dictates one or more rules of inference that are acknowledged as conforming to that style. In the present context, the word ''style'' is a natural choice to characterize the varieties of formal grammars, or any other sorts of formal systems that can be contemplated for deriving the sentences of a formal language.
In looking at what seems like an incidental issue, the discussion arrives at a critical point. The question is: What decides the issue of style? Taking a given language as the object of discussion, what factors enter into and determine the choice of a style for its presentation, that is, a particular way of arranging and selecting the materials that come to be involved in a description, a grammar, or a theory of the language? To what degree is the determination accidental, empirical, pragmatic, rhetorical, or stylistic, and to what extent is the choice essential, logical, and necessary? For that matter, what determines the order of signs in a word, a sentence, a text, or a discussion? All of the corresponding parallel questions about the character of this choice can be posed with regard to the constituent part as well as with regard to the main constitution of the formal language.
a formal language. In broad terms, I use the word "style" to refer to a
of distinctive features in common. For instance, a style of proof system
In looking at what seems like an incidental issue, the discussion arrives
In order to answer this sort of question, at any level of articulation, one has to inquire into the type of distinction that it invokes, between arrangements and orders that are essential, logical, and necessary and orders and arrangements that are accidental, rhetorical, and stylistic. As a rough guide to its comprehension, a ''logical order'', if it resides in the subject at all, can be approached by considering all of the ways of saying the same things, in all of the languages that are capable of saying roughly the same things about that subject. Of course, the ''all'' that appears in this rule of thumb has to be interpreted as a fittingly qualified sort of universal. For all practical purposes, it simply means ''all of the ways that a person can think of'' and ''all of the languages that a person can conceive of'', with all things being relative to the particular moment of investigation. For all of these reasons, the rule must stand as little more than a rough idea of how to approach its object.
at a critical point. The question is: What decides the issue of style?
into and determine the choice of a style for its presentation, that is,
rhetorical, or stylistic, and to what extent is the choice essential,
logical, and necessary? For that matter, what determines the order
of signs in a word, a sentence, a text, or a discussion? All of
the corresponding parallel questions about the character of this
If it is demonstrated that a given formal language can be presented in any one of several styles of formal grammar, then the choice of a format is accidental, optional, and stylistic to the very extent that it is free. But if it can be shown that a particular language cannot be successfully presented in a particular style of grammar, then the issue of style is no longer free and rhetorical, but becomes to that very degree essential, necessary, and obligatory, in other words, a question of the objective logical order that can be found to reside in the object language.
of saying the same things, in all of the languages that are capable of
that a person can conceive of", with all things being relative to the
As a rough illustration of the difference between logical and rhetorical orders, consider the kinds of order that are expressed and exhibited in the following conjunction of implications:
: <math>X \Rightarrow Y\ \operatorname{and}\ Y \Rightarrow Z.</math>
<pre>
Here, there is a happy conformity between the logical content and the
Here, there is a happy conformity between the logical content and the
rhetorical form, indeed, to such a degree that one hardly notices the
rhetorical form, indeed, to such a degree that one hardly notices the
of sentences in the two implications and the order of implications
of sentences in the two implications and the order of implications
in the conjunction. The logical content is given by the order of
in the conjunction. The logical content is given by the order of
propositions in the extended implicational sequence:
X =< Y =< Z.
X =< Y =< Z.