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I have claimed that since the inferential relations between the relevant feature-placing

sentences are based on the meanings of the complex predicates or feature-expressions of the

language, they cannot be purely formal and the feature-placing sentences do not have the

requisite logical form necessary for having any meaning at all. But suppose one abandons the

proposal given by Hawthorne and Cortens to build complex predicates by introducing

adverbial modifiers in the feature-placing language and instead, focuses on the way complex

predicates are built by predicate-forming functors of the kind featured in the Quanean

predicate-functorese language.

The predicate-functor language features truth-functional predicate functors such as “&”

and “~”. From a stock of simple predicates or feature-expressions such as ˹is A-ing˺ and ˹is B- ing˺, together with these truth-functional functors one can build complex feature-expressions such as ˹is A & B˺-ing. Attaching the sentence-forming functor ∆, one can then place the complex feature and make an assertion about its instantiation “It is (A & B)-ing” thus becomes

˹∆ (A&B)-ing˺. So one can infer the corresponding sentence ˹∆ (A)˺, i.e. “It is A-ing.” Even though Turner, for example, would consider the inference a reflection of the interrelations

between the meanings of the feature expressions “(A & B)-ing” and “A-ing”, this need not exclude treating the semantic structure encoded in the complex predicate, which supports the

inference in question, as also logical in some important sense. After all, the complex predicate

is built from the application of a truth-functional predicate functor and one need not know the

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assume that “logical form” can apply to the kind of mereological structure that complex feature-expressions seem to exhibit and treat the corresponding inferences underwritten by

such semantic, mereological structure as formal in nature?43

In effect, this proposal to extend the notions of logical form and purely formal inference

in this way amounts to the rejection of a basic distinction between those inferences that depend

essentially on the meanings of subsentential expressions, i.e. material inferences, and those

inferences that depend merely on the logical form of sentences, i.e. formal inferences. After

all, feature-placing expressions, simple or complex, are subsentential expressions or they have

to be treated in that way to preserve a basic distinction between sentences and other elements

of a language, which, presumably, any language should have. These expressions need to have

a sentence-forming functor attached to them to form sentences of the language. So if the

feature-expressions of the language are the bearers of “logical form” and their content also

serves to underwrite purely formal inferences, then there is no distinction to be made between

formal and material inferences. In this case, for an inference to be valid essentially in virtue of

the meanings of the subsentential expressions contained in the sentences that stand in the

relation of premises to consequences is for it to be valid essentially in virtue of logical form.

This is because here “logical form” really stands for the semantic structure of the values of feature-expressions and has nothing to do with the sentence-forming functor of the language,

∆, and its contribution to the structure of the sentence. “Logical form” will here apply to subsentential expressions and not sentential ones.

43 _{I owe this objection to Alan Nelson.}

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But such a mix of positions is unstable and ultimately incoherent. We want to say that

when inferences are formally valid in virtue of logical form, we are presupposing that logical

form applies to sentential symbols for it is sentences that stand in inferential relations of the

requisite kind, not their subsentential expressions. Put in a different way, it seems like it is a

basic conceptual point about “formal inference” to say that the bearers of formal inferential relations are the same kinds of things whose logical form is what makes these inferences

possible, namely sentences. Certainly, one might insist that the words of a language can also

stand in inferential relations or, rather, that the concepts that they express can do so, just as

some inferentialist views of the meaning of subsentential expressions would have it. But the

sense in which words or the concepts they express can stand in such relations can only be

derivative. Only in virtue of our prior understanding of what it is for sentences to stand in

inferential relations can we can we say that, for example, a word of the language stands in

inferential relations to another one in virtue of featuring within sentences that are

systematically inferentially related. So, we are committed to saying that the primary bearers of

inferential relations, formal or material, are also the bearers of logical form, which is what

makes such relations possible. The proponent of feature-placing languages, in effect, rejects

this point.

As long as one grants the basic distinction between sentences and subsentential

expressions, as one must, there seems to be room for the traditional distinction between validity

in virtue of the meaning of subsentential expressions and validity in virtue of logical form. The

objector’s de facto rejection of the latter distinction comes at the price of rejecting certain basic conceptual points about what we understand by “inference” and “formal inference” as attaching primarily to sentences. It is a rejection that brings the proponent of feature-placing

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languages to the point where he or she removes the common notions we can use to

meaningfully evaluate the proposal that we are dealing with a genuine language. For, after all,

these conceptual points are all we have to go on in the evaluation of this proposal. If we remove

them, all we have is just a proposal to mean something different by “inference” and “logical form” which is really to mean something different by “language.” I doubt that this is what the ontological nihilist is up to.

If the conclusion of the last few paragraph stands, then we have no good reason to think

that the atomic sentences of the feature-placing language can stand in systematic formal

entailment relations. They do not exhibit sufficient logical structure and hence fail to “hang

together” in the right way for us to preserve the initial assumption that we are dealing with genuine meaning-bearers. I do not think this should be surprising. By eliminating the basic

distinction between subject and predicate, the proponents of feature-placing languages have

actually eliminated the logical structure that makes possible purely formal relations at the level

of atomic sentences. They are thus naturally forced to resort to the meanings of feature-

expressions to show how the sentences of these languages can be inferentially related at all.

But there is no way we can make sense of the idea of a language whose sentences are

inferentially related only in virtue of the meanings of their subsentential expressions. It will

not help the nihilist to show that his or her preferred language houses purely formal rules of

inference, those articulated by the propositional calculus, for example. For even if there are

truth-functionally complex sentences that are related in a purely formal way, this achievement

comes only later, i.e. only under the condition that there are syntactic strings the propositional

calculus can treat as sentences, i.e. as meaning-bearers. But that condition cannot be met, as I

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