2006/11/17

Nonreferring ontological terms: drop them.

Frege distinguished sense from reference. But what might a sense be, given that it is what is supposed to determine the reference (if any) of a term or sentence, and what kind of thing is it that "presents" bits of the world in one way or another? The mirror of the telescope stands in some relation between observed and heavenly body; yet we cannot allow the relation to be characterized as such since we will be led on a regress trying to explain the relation of the relation, mirror, body, and star, and so forth... The thought is that we refuse to trat predication terms as terms that have sense when taken alone... which is to say, things like 'red' in English do not refer, and this is because they present nothing at all--and the move in the other direction is to make 'function' do something (philosophically) unusual, as well. (If you have trouble reading this, get the code2000 font.)
...a sense is importantly like a function. It might just be a function, on the obvious understanding of how functions operate which consists in bringing objects into definite relations–‘bringing’ here abbreviating the process of our noticing such associations. The relevant notion is this: Some function following the form ⌜ƒxy⌝ is such that what we might substitute in for ⌜‘x’⌝ and ⌜‘y’⌝, say sets or ordered sequences or the members thereof, or numbers, or names, are necessarily in the background of any understanding of this function, so that function-ness cannot be explained without essential reference to arguments and values: we shall say it is incomplete. For example, where ‘ƒ′’ is interpreted as a standard addition function we must explain what it does using the notions of number; viz. something like ‘ƒ′xy: x + y = … ‘ where our ellipsis is filled by an appropriately defined successor-function-dependent syntactic relation. Keep in mind how handily the active “does” fits the function notion, as opposed to a more static “is.”

Things like sets, numbers, colors, categories, laws, natural kinds, these have all been taken more or less platonically across the history of philosophy, and it has only been relatively recently that reductionism has attempted to do away with the jungles of nonphysical odds and ends various theories generate. Even the most parsimonious, however, have often felt it useful to adopt at least sets, and usually numbers into their ontologies. Once one has sets in hand, functions are a short step to reach. I will now argue that “a sense” is not an abstract object in the usual (philosophical) understanding. And here is the question, to begin: what is “a function” to be?

I pose the problem this way in light of Donald Davidson’s posthumously published lectures on predication, in which he argues persuasively that any account of predication in which predicates standing alone are taken to denote cannot escape inherent vulnerability to third-man arguments. Say we see ⌜R(a,b)⌝, as usually understood. The expression ‘Rab’, for instance, appears to consist of three names, that is ‘a’, ‘b’, and the name of some relation ‘R’. But this is a result of losing sight of the fact that the relation-term, a two-place predicate, is supposed to do the work of unifying the other terms so as to form a sentence (here one thinks of Russell’s claim that every sentence requires a universal ). One cannot just stick these terms together (if they are names) as 〈R,a,b〉 or the like, for then one merely has three names to one another: something else is needed to make this collection of names into a (unified) sentence. , The same problem will happen with 〈Q,R,a,b〉, 〈P,Q,R,a,b〉 and so forth, in infinite regress. Davidson takes this ubiquitous failure to be a reductio of views of predicates holding them substantial. Since any function ‘ƒ′′(ϕ)=ψ’ can be recharacterized as Fϕψ, functions do not stand much chance as objects.

I have followed Joan Weiner’s exposition and called senses of sentences thoughts. Further, a thought is not what a sentence means: that is its truth-value, on the Sinn und Bedeutung view. ‘Concept’ I hereinafter reserve for those things associated with noun-phrase terms, which present objects in various modes. Words for concepts act like words for objects, insofar as we are able to discuss what concept words denote when used in oblique contexts. While to say ‘Superman = Clark Kent’ is to say something about an object and to say ‘‘Superman’ ≡ ‘Clark Kent’’ is to say something about terms (i.e. that their denotata are identical), to say ‘Superman ≡ Clark Kent’ is to say something about senses. One says in this example that an object is presented in two modes, while what one means is true. , But must an object be substantial? No: “an object” need not be substantial to fulfill the roles a quasi-Fregean semantic theory needs senses to fulfill.

In order to elucidate, we take a detour into terms for other nonphysical “entities.” According to the well-known “Slingshot” argument, which has been attributed to Frege, every true sentence denotes one thing, and every false sentence denotes another, if sentences denote. Sentences express thoughts that map them onto truth values. But truth and falsity are not objects. The truth of a sentence, for Frege, is derivative from the truth of its sense, for only thoughts are such that the question of truth “arises” for them. Thoughts are the intensional entities, then, and it is expressing a thought that connects sentences via reference to truth or falsity. But truth and falsity are not concepts (functions), either, on that view. They are not things, to borrow a figure, but not nothings. So the cognate terms of ‘truth’ and ‘falsity’ are serviceable even though properly speaking they are irreferential.

So far we have seen that predicate terms may be characterized as functions. (A one-place predicate is a degenerate case: it takes only an argument, and when it does it expresses a thought, which is true or false, but one may say that in predicating an atomic sentence consisting of a completed one-place predicate functions as a two-place predicate with truth or falsity as its value.) Thoughts are also, in a way, functions. So when we talk about them we may characterize them as such, e.g. a thought about a sum, as expressed by ⌜ƒ′′′(+,x,y,z) = V⌝ where V∈{T, ⊥}. Similarly, when we discuss senses in terms of functions like Fxy, we implicitly treat the senses as incomplete in the fashion that functions were said earlier to be incomplete. As objects or entities, this could be problematic. However, functions constituting senses (and thoughts, but let us leave that discussion for now) are not objects, as I have indicated, though we must needs use language in a way that assumes they are such. As a first approximation to the idea, contrast what one understands by ‘It is a red coat’ with ‘∃x(Rx∧Cx)’.
. The basic motivation for moving away from characterizing senses as objects is to avoid the regress problem with accounts of predication. If one wants senses, they just cannot be entities. If the predicate does not stand for an object, there may not need to be a relation between what it is predicated of and something further in order for predication to happen. More generally, if one avoids taking terms’ concepts to be objects (in that ordinary sense) one may avoid similar third-man difficulties arising from relating senses to objects and utterances. Another motivation, for those who like it, though not justifcatory, is ontological parsimony. Further, the obscure nature of these entities, concepts and thoughts, can make them seem like stop-gaps rather than important and central features of a semantic theory.

Indeed, it seems to be the obscurity of Frege’s intensional entities that led Davidson to reject the idea that predication consists in anything further than satisfaction, which is taken to rest upon the simple notion of truth. Whether or not his view is correct I cannot say, but I have adopted some of this method, a sort of “deflation” of certain intensional entities. One needs an “aboutness” relation, in order to connect parts of the world: what’s “in the head,” what’s said, and the bits of the world answering to them, if any. Terms that act like names, such as predicates taken in isolation, would seem to be about something. Each meaningful term in an expression, predicates and names , would contribute to the sentence what it was about and the structure (or something) would unite these pieces into an expression of a thought, with a truth value. Here follows an example (failing) account of senses by which they are not entities.

To avoid the regression problem, predicates must be meaningless when taken in isolation—or to be more precise, concepts must be insubstantial. Though things may be red, there is no “color red.” ‘R’ does nothing by itself, but ‘Rx’ is useful, e.g. in ‘◊∃xRx ∧ ~∃y(Cy)’. So our senses occur in predication, that is, when something is predicated of something, the noun phrase or sentence thereby created has a sense (under normal circumstances). A term, for instance a complex term like the noun phrase ‘the black cat on the mat in the den of my uncle Charlie’s cottage’ presents a particular object(s) in a certain way, but it associates the cat also with other objects which are presented along with it. The phrase will be satisfied if certain circumstances appear, otherwise not. If one wanted the phrase to stand by itself as a sentence, one could insert the copula between ‘cat’ and ‘on’, and the truth-conditions of the resulting sentence would be the satisfaction conditions of the presentational phrase. The thought expressed by ‘The cat is on the mat’ functions to give some truth condition or other through the utterance. Which one is a matter best explored elsewhere. The upshot is that presentation of an object, e.g. by predication, just is the function—a presentation through concepts.

(Now some bold conjectures.) A predication is a syntactic activity, a singular event whose effects may persist, but only through the syntactic act does the semantic value of a syntactic object appear. Ostention is a primitive syntactic and semantic activity: the object and the term appearing together serves to introduce, roughly, satisfaction conditions for terms while establishing the syntactic identity of terms. (Homonyms and synonyms being complications of natural, which is to say non-ideal, languages.) Saying “‘Black’ ‘cat’” gets one nowhere, nor does “Black, cat,” as these are again mere concatenations of names (or name-like terms). Saying something along the lines of “That cat is Black” or “Black(Tabby)” is predication. The predicative act does not occur in the mind, as on Russell’s sometime view. Predication occurs in the linguistic act (on the model presented above, whole sentences could be treated as multiplace predicates per impossibile). The act expresses a thought, which is related as mentioned above to ideas one has; the ideas are “in the head” but the thought is not. A thought expressed by a sentence has to be “somewhere” however. I say it is in the world. A thought expressed by a sentence is some arrangements of spatiotemporal and abstract objects (like numbers). What is expressed, on this view, is not the ideas in the head but parts of the world itself. Expression and presentation are the same. Grasping the meaning of a sentence is not taking hold of an extraphysical object (usually ), but rather it is contacting the world through language. One can see through language to the world behind it. And this is because language names (presents) parts of the world.
Now for a moment imagine that all physical objects (including events) are labeled and put in sequence. Then primitive sensory information could counterfactually tell one about (the (indirect) effects of) those objects, whereby satisfaction of any utterable sentence could be ascertained. Since the whole world is sequenced, the sequence either satisfies a sentence or it doesn’t. Every satisfied sequence, on the familiar Tarskian model, is true if and only if satisfied. A sentence is about, on ordinary conceptions, regions of the world; but here we see that sentences are about the world in so far as they are satisfied by it, which is to say in so far as they are true. So if sentences are about anything, they are true or false. (On this view, however, we have not so far said that sentences mean truth or falsity.)

On the example view just expounded*, senses occur in physical locations, supervening on expressive utterances, and the senses are the onstention-based connections between syntactically developed names of objects and objects via presentation (“here is how one finds out whether the world satisfies the sentence… ”). This amounts, apparently, to a functional competence. There are sentences which are terms arranged in such a way that they express a thought, and the thought is some purported region of the world. This of course begs the question how it comes to be a unity, but apparently merely existing as an expression is enough to make it so. There are thoughts expressed by the sentences, as it turns out they to are physically located.

That view is unsatisfactory for any number of reasons, but let me mention two straw parts. First, the explanation that the very act (or event) of predication creates the intensional state is opaque as far as explanatory potential goes. Second, it is not clear what it would mean to express part of the world.

...and so forth.


*In order to show that it is possible for someone to hold a view with the desired consequences, and also to make clear which moves a subsequent positive view won't make.

(Those who care can email us for bibliographical information.)

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