Samples and Logical Form
M. G. Yoes
Standard logic, the classical logic of truth-functions, quantifiers and identity, enjoys a measure of authority. It is not unchallenged, but by dint of its simplicity, power, and length of time in the curriculum its authority thrives. So examples of sentences whose logical form resists recasting in standard logic are often tantalizing. Who knows what revolution in logic lurks in an example?
This one has been folklore for several decades though the source is unknown to me:
Let `Jones talked' be an atomic sentence and represent it by `A'. Why not let
do the work? And then
comes in for similar treatment as
And so on. Obviously this is faulty, one hears, because (2) and (2') are logically equivalent to each other and each is logically equivalent to A. This would have standard logic saying not only that (1) and (2) are logically equivalent but also that (1) and (2) are logically equivalent to
There is, then, a logical difference at a fundamental level to which standard logic is insensitive. So much for standard logic.
Logical form is deep structure. Those following Russell's principle that grammatical form is no sure guide to logical form might look below the surface in this case somewhat as follows. What appears to be a conjunction of singular sentences is actually no conjunction at all but at bottom a singular predication of some predicate of Jones: Jones was being loquacious (or some such)! With a single one-place predicate the form of (1) is represented by
(3), then, being of the form Tj, is seen not to be logically equivalent to (4). Two atomic sentences each with different predicates are not logically equivalent. If (1) and (1') may be regarded as instances of the same predicate, they are logically equivalent; otherwise not. Perhaps this situation indicates an underlying ambiguity. (1) and (1') say similar things. But do they say the same thing? Have it your way.
Whatever the predicate, one result is needed: both (1) and (1') should yield (3). He talked, but he was not loquacious. But he can't be loquacious, or whatever the predicate is, without talking. Jones was loquacious, so he talked. If (1) and (1') are at bottom singular sentences, then how are any implicants they may have established? For each such predicate, we could introduce a set of axioms governing it and designed to produce just the consequences wanted. (∀x)(Tx → Lx) and Tj would give (4), for example. This would mean a new set of axioms for each new predicate. If one decides that the underlying predicate in (1) and (1') are different and that further sentences with more conjuncts are different, then more axioms would be needed. Alternatively, such implicates could be left to some sort of analytic implication. Is this the best that can be done? No doubt the problems of this example are merely illustrative. There must be many such sentences.
One important way a symbol may function is as a sample; it may exemplify something. On Goodman's account, a sample is a symbol of some property it has; it exemplifies that property. (See .) Of course a sample does not symbolize all its properties. The salesperson's sample stands for its color and texture, say, but not the property of having been carried around in this sample case all day or its specific gravity. Since sentences are symbols, they too can function as samples, as exemplifiers of some of their own properties. Such sentences as (1) give information, but some of that information is by way of its being a sample.
(1) makes a statement, but it also exemplifies a property of the scene. (1) does not merely say that Jones talked, but it also exemplifies how he talked and by doing so conveys information not conveyed in what is said. There is more to conveying, more to talking, than saying. Let us recognize, then, that there are two symbol systems here, that they overlap, and that they operate together on the same symbol. Logical form is one thing, conveying by exemplifying is another, not wholly distinct, thing.
The talked and talked case is just such a case. The illusion of nonlogical equivalence here is fostered by the fact that the sentences have different exemplifications! This also explains why the question of equivalence becomes intuitively uncertain as the number of clauses grows: two different such sentences each with many but a different number of conjuncts such as (2) and (2') can exemplify the same vague predicate. Intuitions may differ as the number of conjuncts increases. It is clear enough that these do not pose questions of logical equivalence.
Anything can be a symbol, and nothing is intrinsically one. That is, anything can function as a symbol, but nothing intrinsically so functions. At a minimum something functions as a symbol if it stands for something, refers to something, though of course this is at best a reasonable first approximation if not a truism. How a symbol functions depends on the symbol system of which it is a part and which is operative at the time. A sign reading «No Parking Here» may function as a command in one symbol system, a symbol for Mars in an impromptu explanation of the solar system, or as a sample of an imperative in an English lesson.
What a symbol system is, how it determines or contributes to the function of symbols within it, and how to tell whether a given symbol system is in play -- these are questions which in one form or another have exercised philosophers. In recent years further important questions have been raised. When does a symbol function as a sample? When does a symbol express something? When does it represent?
These and related questions lead, or perhaps should lead, to a symbolic turn off the linguistic turn. A fixation on language, natural or formal, carries with it a blindness to the way symbols function in general and to a lack of appreciation of language as one symbol system among many. A subtle effect of this fixation seems to be the assumption that given a symbol and its system in operation there can be no other symbol system overlapping it. A symbol plays in only one language game at a time. The simple case before us demonstrates otherwise.
What further consequence are there of this observation? Does it corrupt counterexample-making by making counterexamples radically uncertain? Is this a basis for explaining conversational implicature, a basis quite distinct from Grice's intentional account? Does it go any way toward clarifying the function of figurative symbols?