It was in Sellars’ seminars that I came to sense the enormous, mysterious, gap between names and statements. For Sellars, as I remember him, this is the first thing we need to understand about language. For me, there is a mystery: I was puzzled then, and it is something that I still find very puzzling.
This post is not mainly about Sellars, one of my teachers and a fascinating person, but about what I find so puzzling.
Sellars’ guiding text here was a passage in Wittgenstein’s Tractatus (4.1432), “We must not say: ‘The complex sign ‘aRb’ says ‘a stands in relation R to b‘”. We must say instead “That ‘a’ stands in a certain relation to ‘b’ says that aRb.”
There are complex names, and to understand them we have to take into account what their parts are and how they are related to each other. We can say the very same thing about statements. But there must be a glaring difference beyond that similarity, for a statement is most certainly not a complex name. That glaring difference is there even if in English, or any natural language with its own peculiarities, we find ourselves looking at the very same overt expression.
Take “The deer run”. This can be used as a complex name, to denote something, similar to the expression “the dog run”, as in “The deer run, where we can admire their graceful prancing, is just at the edge of the forest”. Or it can be used as a sentence, as in “The deer run swiftly along the edge of the forest”. In both cases we have to understand their grammatical parts and to appreciate the relation between them, that is, their auditory or visual configuration. But what we do in this appreciation, or what it is that is appreciated, must be very different. For in the first use, the expression denotes, it designates something, it is a complex name. In the second use it asserts, it says that something is the case, it is a statement.
How the difference disappears
That illustration is striking precisely because it forces us to notice a difference between two identical appearances. In a fully disambiguated language, a logician’s dream, I could not give it. But perhaps that is exactly why in formal semantics, and more generally in some examples of mainstream philosophy of language, where the disambiguation is presupposed, the difference appears to disappears.
In formal semantics, for the usual sort of language studied in logic courses, a name denotes a thing, an element in a domain of discourse. Or in intensional logic, it denotes a function from worlds into elements of a domain or domains. In both cases, the ‘semantic value’ is a thing, whether concrete or abstract. Just right!
But a statement is something assertable, which a name is not. A predicate is something applicable to a thing, which a name is not. So why is it that in the formal semantics we teach and use, their semantic values are things as well?
For Carnap in Introduction to Semantics the denial at is explicit: he simply asks what a statement designates, and says that it is a proposition. A proposition is a thing. An abstract thing, but a thing nevertheless.
In more detailed accounts the semantic value of a statement — which Carnap said is a proposition — is a truth-value, or a function (from worlds into truth-values), or a set (of worlds). These are all things, abstract things. The semantic value of a predicate is a set (subset of a domain of discourse) or a function (from worlds into subsets of a domain or domains). These too are things, abstract things.
Thus in semantic analysis of language everything is reduced to things and relations among things. Things are not assertible, nor applicable. What has happened to real statements and predicates in use, after we start mentioning them and talking about them?
Retrenchment, possibly
The clue may be in my preceding sentence: once we mention, rather than use, a piece of language, we have literally reified it. Or replaced it by a simulacrum: rather than talk about the English statement that snow is white, we talk about the expression “Snow is white”, a sequence of concatenated letters, thus, a thing.
Peter Strawson insisted on distinguishing statements from sentences. Above I was careful to us “statement” throughout (although sometimes it felt more natural to use “sentence”). It seems to me that we are forced to go along with Strawson. Let us use “sentence” for an expression belonging to a certain syntactic category, and identified as an ordered concatenation of letters.
And then we can say that the sentence is a stand-in for the English statement. Sentences are things we use to represent statements. Thus, a sentence is not what we naturally, as speakers and hearers, take a statement to be. Instead, this stand-in, the sentence, is a complex name of a thing, more generally of some relational structure (thus, an abstract thing), namely its semantic value. What is the interest of this representational procedure? In formal semantics it is that they allow us to catalogue certain inference patterns in natural language.
Fine. We have worked enough in that vineyard that we’d have to feel acutely embarrassed to deny its value. But …
Is there any way for us, in philosophy of language, to get behind this representational procedure, and talk about the English statements and predicates themselves, directly, and not by proxy, not only by talking about the things which stand in proxy for them?
(Threat of paradox? To explain that proxy relation it seems we would have to be able to talk about the statements as well as about the sentences. So then we will find ourselves in quite a predicament if we can only talk about statements by talking about the sentences that are their proxies!)
This I find all very puzzling.
Appendix
For Sellars’ discussion see his “Naming and Saying”, in Philosophy of Science 1962, reprinted as Chapter 7 of his Science, Perception, and Reality. For a quick discussion and critique of this point in Carnap’s Introduction to Semantics see the review by Alonzo Church, The Philosophical Review 52 (1943): 298-304.
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