Response to Objection 2:

The second objection may be somewhat harder to defuse. The objector could just grant

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is additional structure, which is ineffable for us. Let us then work on the assumption that there

is additional structure. I think we will eventually see that this objection is unsustainable too.

What is the relationship between the effable for us subject-predicate or relational structure and

the additional ineffable structure? There are three options here.

i. They can be conjoined, disjoined, etc.

ii. The effable structure can embed the ineffable structure

a. The subject-predicate structure can embed the ineffable structure

b. The relational structure can embed the ineffable structure

iii. The effable subject-predicate or relational structure can be embedded within a larger

ineffable structure

Recall that we are here excluding Boolean structure. So the two structures cannot just

be conjoined or disjoined, etc. So, we can dismiss (i) above. Notice also that the effable

structure cannot be embedded within universally generalized structure since this would be

effable for us, and I am excluding ineffable quantificational structure from consideration in the

paper. It also does not make sense to suppose that the subject-predicate structure of the alien

formula embeds further structure. At least, if we are to maintain our understanding of what

subject-predicate is, we cannot coherently maintain that they can embed further structure. So,

if the alien formula has a subject-predicate structure, it must be embedded in further

propositional structure. So, we can also dismiss (ii.a) above. So, we have two possibilities left,

(iii) and (ii.b). Showing that adopting (iii) cannot allow us to sustain the assumption that there

is additional ineffable structure will also show that (ii.b) cannot work. So, I will deal with the

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Now, the effable structure in the alien formula is presumably standing in some kind of

non-Boolean relation either to some other contents with different structures or to some familiar

kind of term, singular or general term. Consider the first possibility, namely that the effable

structure stands in some relation to a propositionally complex thing, i.e. another propositional

content. So, we know one of the relata within the overall propositional structure, namely

something of the form Fx or aRb. But now the other relatum in this additional propositional

structure must presumably still feature or bind together, so to speak, the same kinds of terms

that our familiar structures bind since we are working under that hypothesis. The SI contents

are contents about the familiar humanly representable categories of things. So the other relatum

in this ineffable propositional structure must also be subject to existential generalization (direct

or indirect) for the same kinds of reasons that we initially gave for the claim that the original

alien formula must be subject to that effable inference. Hence, again for the same reasons

articulated above, the other relatum must also be in either Fx or xRy form.

So, what we have here is a propositional structure that binds together two or more

contents in either subject-predicate or relational form (we are excluding other effable forms

like universally generalized ones since these are not strictly speaking, subsentential, and we

are not concerned with such propositional structures in the paper). In effect, the allegedly SI

formula represents some relation between states of affairs or propositions, which are in turn in

familiar to us propositional structure. And propositional contents are just the sorts of things of

which one can also predicate properties and judge them to stand in relations. Now, at this point

we can see that the formula must, contrary to initial assumptions, just represent a basic

relational form that takes as relata propositional contents or sentences representing states of

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which the represented states of affairs in familiar propositional structures stand is an ineffable

for us relation but that kind of ineffability is content ineffability, i.e. it does not represent a

structural source of ineffability in our sense.

One may object that representing the alien formula as a basic relational one that takes

as arguments propositional contents conflates propositional with non-propositional relations.

The relation between the two or more propositional contents in the alien formula is not just

another relation like the spatial relation between objects. It is an irreducible propositional

relation, which is different in kind. Consider, for instance, an example of a propositional

structure in English which does not seem to be reducible to aRb, the basic relational form,

namely a structure like p because q. Just as we do not seem able to capture sentences of this form in English in the basic aRb form, we cannot capture the alien formula with that form and

so show, contrary to initial assumptions, that it does, after all, have an effable for us structure.

But this line of argument is unconvincing. It might well be true that we cannot represent

a sentence like p because q in the familiar relational form xRy construed in the usual way. But that will be because the variables here range over objects in the domain rather than states of

affairs or propositions. So, one might accept that we cannot represent such sentences in our

best formal system for English, i.e. first-order logic. But that is not to say that such sentences

do not have a basic relational form. It is just a relational form different from the familiar one

that binds together variables ranging over and singular terms standing for individuals. In some

formal system yet to be developed, such sentences will after all be represented in terms of a

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over and names standing for, say, states of affairs or propositional contents.20 Most

importantly, such a conceivable formal system will display fully effable forms. It may well be

the case that the alien formulas embedding subject-predicate and relational structures within

larger ones represent some ineffable for us relation between states of affairs or propositions.

But that is not to say that these formulas are therefore structurally ineffable. They are just in

some basic relational form which we certainly can grasp. Accordingly, we can also make

effable for us inferences from such a formula, i.e. existentially generalize and this is to be

expected since states of affairs and propositions can, of course, be logical subjects. 21

If, on the other hand, we suppose that the larger structure of the alien formula involves

something not propositionally complex, then it must the same sort of thing as our singular and

general terms, by hypothesis. So, we will have, on the one hand, something like Fe***a, where

“a” is a name for some object, say. But that just represents another relation between an individual and a content in subject-predicate form. This kind of structure is certainly effable

for us. It is also in relational form. It is just that one of the relata is a propositionally complex

thing and the other one is an individual.

20 _{One may argue that on the best analysis of our quantification over propositions, propositions must also be}

taken as objects in our domain of quantification along with other objects. But I take this to be controversial and, in any case, the sentences with a form like p because q can be seen as representing some relation between states of affairs rather than propositions, and states of affairs can hardly be understood as individuals in our domain of quantification.

21 _{A complex issues that arises on the basis of the foregoing discussion is to what extent the argument of this}

section might be proving too much. After all, the very same grounds on which I try to argue that the new alien

formula must be in an effable for us form also seem to show that “because” does not represent any irreducible

propositional structure in a proposition like “p because q.” If the latter is also in a basic relational form, even

though it relates propositions (or states of affairs), then the explanatory relation here belongs to content. But some would want to dispute this result. This could be a fair critique. To complete the argument of the section, I will have to give principled grounds for excluding such candidates for additional, irreducible propositional structures like p because q. In a forthcoming work, I deal with the more general issue of how to provide criteria for distinguishing between form vs. content in controversial cases. The results in that work will clearly bear on the discussion in this section.

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Finally, we can see why it cannot help the opponent to adopt (ii.b) above. Suppose that

the allegedly ineffable structure in the alien formula is embedded within a relational form. We

are dealing with a case in which one of the relata is just the individual e. So we have eR******.

The other relatum is supposed to be some propositional content. But, by hypothesis, whatever

structure that content has will have to involve the same kinds of terms our sentences involve,

e.g. names for individuals. But the same argument we gave for the claim that the original alien

formula must be in subject-predicate or relational form, can be given now. The other relatum

in eR**** must also be in an effable for us form. One could of course make the same move

here and grant some effable structure within that relatum while insisting at the same time that

there is additional ineffable structure. But this just sets a vicious regress since we can rehearse

the same arguments given above and show that none of the options about how that additional

structure can be related to the effable one can help sustain the assumption that we have a SI

content here.