My opponent says Yes; I return a negative answer. This entry continues the discussion in earlier theological posts, but leaves the simple God out of it, the better to dig down to the bare logical bones of the matter. Theologians do not have proprietary rights in the Inexpressible and the Ineffable.
The opponent offers a reductio ad absurdum:
a. It is not the case that everything is an object. (Assumption for reductio)
b. Something is not an object. (From (a) by Quantifier Negation.)
c. 'Something' means some thing, some object.
d. Some object is not an object. Contradiction!
e. Everything is an object. (By reductio ad absurdum)
The argument could also be put as follows. An object is anything that comes within the range of a logical quantifier. So someone who denies that everything is an object must be affirming that something is not an object, which is tantamount to saying that some item that comes within the range of a quantifier -- 'some' in this instance -- does not come with the range of a quantifier. Contradiction. Therefore, everything is an object!
First, two subarguments for premises in my main argument against.
Every declarative sentence contains at least one predicate.
No predicate functioning as a predicate is a name.
No declarative sentence consists of names only.
For example, 'Hillary is crooked' cannot be parsed as a concatenation of three names. A sentence is not a list of names. And the unity of a proposition expressed by a sentence is not the unity of a collection of objects. A proposition attracts a truth-value, but no collection of objects attracts a truth-value. The mereological sum Hillary + instantiation + crookedness is neither true nor false. But Hillary is crooked is true.
Adding a further object will not transform the sum into a proposition for well-known Bradleyan reasons.
So what makes the difference between a mereological sum of sub-propositional (but proposition-appropriate) items and a proposition? A noncompound proposition is clearly more than its sub-propositional constituents. The proposition a is F is more than the sum a + F-ness. The former is either true or false; the latter is neither. (Bivalence is assumed.) What does this 'more' consist in? The 'more' is not nothing since it grounds the difference between sum and proposition. The 'more' is evidently not objectifiable or reifiable.
The ancient problem of the unity of the sentence/proposition was already sighted by the 'divine' Plato near the beginning of our tradition. The problem points us beyond the realm of objects.
The paradox, of course, is that I cannot say what I mean, or am 'pointing to.' For if I say: 'Something lies beyond the realm of objects,' then I say in effect: 'Some object is not an object.' But I am getting ahead of myself.
Names refer to objects and predicate expressions refer to concepts.
Anything that can be quantified over can in principle be named.
Concepts cannot be named.
Concepts cannot be quantified over.
In support of the second premise: 'Some horse is hungry' cannot be true unless there is a particular horse in the domain over which the existential/particular quantifier ranges, and this horse must in principle be nameable as, say, 'Harry' or 'Secretariat.' There needn't be a name for the critter in question; but it must be possible that there be a name.
Now for the main argument contra:
A. There are declarative sentences.
B. No declarative sentence consists of names only; predicative expressions are also required. (Conclusion of subargument I)
C. Predicates refer to concepts, not objects.
D. Concepts cannot be quantified over. (Conclusion of Subargment II)
E. Concepts are real ingredients of propositions but they are not objects.
F. Not everything real is an object among objects.
The unity of the sentence/proposition is one of several problems that point us beyond what I have been calling the Discursive Framework (DF). These problems, properly understood, show the inadequacy of this framework and refute its claim to unrestricted applicability. The unity of the sentence/proposition needs accounting. (There is also the unity of concrete truth-making facts or states of affairs that cries out for explanation.)
Now we should try to account for sentential/propositional unity as parsimoniously as possible. We shouldn't bring in any queer posits if we can avoid them, a point on which my opponent will insist, and in those very terms. Unfortunately, we cannot eke by with objects alone. To repeat: a sentence is not a list; a proposition is not a collection of objects. So we need to bring in some queer entities,whether Fregean unsaturated concepts, or Strawsonian nonrelational ties, or relational tropes, or some odd-ball Bergmannian nexus, even my very own Unifier. (See A Paradigm Theory of Existence, Kluwer, 2002.)
The problem, of course, is that these queer items entangle us in contradictions when we try to state the theories in which they figure. The contradictions give aid and comfort to the Opponent who takes them as justifying his claim that the DF is unrestricted in its applicability.
Frege's paradox of the horse illustrates this very well. Frege notoriously asserted, "The concept horse is not a concept." Why not? Because 'the concept horse' names an object, and no object is a concept. An application of existential/particular generalizattion to Frege's paradoxical sentence yields: Some concepts are not concepts. But that's a contradiction, as is the original sentence.
But Frege was no 'stoner' to use an expression of the Opponent. His contradiction is, shall we say, motivated. Indeed, it is rationally motivated by the noble attempt to understand the nature of the proposition and the nature of logic itself.
Why can't concepts be named? Suppose we try to name the concept involved in 'Hillary is crooked.' The name would have to be something like 'crookedness.' The transformation of the predicate into an abstract substantive loses the verbal chararacter, the characterizing character of the predicate '___ is crooked' functioning as a predicate. If 'crookedness' has a referent, then that referent is an object. But as I said, the proposition Hillary is crooked is not the mereological sum Hillary + crookedness. The former attracts a truth-value; the latter doesn't.
The unity of a proposition, without which it cannot be either true or false, is not the unity of an object or a collection of objects, which is just a higher-order object. This peculiar truth-value attractive unity cannot be accounted for in terms of any object or collection of objects. And yet it is real. So not everything real is an object.
We seem to be in an aporetic bind. We need to bring in some queer elements to solve various problems that are plainly genuine and not pseudo. But the queer items generate paradoxes which, from within the DF, are indistinguishable from bare-faced contradictions. The paradoxes/contradictions arise when we attempt to state the theories in which the queer entities figure. They arise when we attempt to talk about and theorize about the pre-objective or non-objectifiable. I cannot state that no concept is an object, for example, without treating concepts as objects. But doing so drains the concept of its predicative nature. I cannot say what I mean. I can't eff the ineffable.
One move the Opponent can make is to flatly deny that there is the Inexpressible, thereby defying the author of Tractatus 6.522. Das Mystische does not exist, and, not existing, it cannot show itself (sich zeigen).
If the Opponent is a theist, then his god must be a being among beings, a highest being, a most distinguished denizen of the Discursive Framework, but not ipsum esse subsistens.
How might the Opponent deal with the problem of the unity of the sentence/proposition? Perhaps he will say that a noncompound proposition is a partially but not wholly analyzable unity of sense, but that the 'more' that makes the proposition more than the sum of its constituents has no Deep Meaning, it does not 'point' us anywhere, and certainly not into Cloud Cuckoo Land but is merely a curious factum brutum for which there is no accounting, no philosophical explanation.
I don't think this would be a good answer, but this entry is already too long.
At the moment I would happy if I could get the Opponent to make a minimal concession, namely, that I have mounted a strong, though not compelling, rational case for the thesis that reality is not exhausted by objects, and that I have not "destroyed all of logic" in so doing.
But I am undermining the claim of the DF to have universal applicability. This undermining takes place within the DF by reflection of something essential to the DF, namely, propositions. As long as I refrain from making positive assertions about the Transdiscursive, I avoid contradiction.