In recent literature there has been increasing attention to the thought that mereological nihilists and near‐nihilists like Peter van Inwagen and Trenton Merricks face a challenge that they cannot adequately meet (see Bennett 2009, Elder 2011; Tallant 2014; Unger 2014).

The challenge, as it is put most explicitly by Tallant, is that they need to answer a question logically analogous to the question with which they confront their opponents, the Special Composition Question (SCQ), but that they cannot do so satisfactorily. The Special Composition Question, roughly expressed for the moment, concerns the conditions under which parts compose a whole (some whole or other). The logically analogous question, again roughly expressed for the moment, is supposed to be: ‘Under what conditions are some things arranged F‐wise, for some or other reading of “F”?’, which Tallant calls ‘the Special Arrangement Question’ (SAQ).1

A discussion complementary to mine is Brenner 2015. But Brenner does not question the meaningfulness of what he follows Tallant in calling ‘the Special Arrangement Question’. That this question is meaningless is the main contention of the first half of this paper.

So I argue that the SAQ is no challenge to the nihilists since they need not accept that it is meaningful. There are meaningful questions with which this supposed question might be being confused, they can allow. However, they can say, these are questions the nihilist can answer satisfactorily. Indeed, answers are implicit and very nearly explicit in the work of, in particular, van Inwagen, who of course introduced the talk of things being arranged F‐wise.

In what follows I therefore focus on Tallant's discussion and his criticisms of van Inwagen.

First we need an exact statement of the Special Composition Question.

Van Inwagen defines the relation of composition between the xs and an individual y as follows: the xs compose y if and only if everything which is one of the xs is a part of y, everything which is a part of y overlaps one of the xs and no xs overlap.2 Thus the bricks on the building site compose 57 Elm Street just in case every brick is a part of 57 Elm Street, everything which is a part of 57 Elm Street overlaps some brick and no bricks overlap. This can be expressed in the vocabulary of first–order predicate logic: for every x, if x is a brick on the site x is a part of 57 Elm Street and for every y, if y is a part of 57 Elm Street then for some z, for some u, z is a brick on the site and u is a part of y and u is a part of z and for every u, for every w, if u is a brick on the site and w is a brick on the site then it is not the case that there is a v such that v is a part of u and v is a part of w.3 This definition of composition fixes the meaning of the two–place open sentence ‘the xs compose y’ and hence the one–place open sentence ‘for some y, the xs compose y’. So we can now formulate the SCQ: ‘When is it the case that for some y, the xs compose y?’ That is, under what conditions is the one–place open sentence ‘for some y, the xs compose y’ satisfied? The SCQ is so‐called, of course, by contrast with the General Composition Question (GCQ): under what conditions is the two–place open sentence ‘the xs compose y’ satisfied?

Van Inwagen's examination considers answers to the SCQ of the form: the xs compose something, just in case…the xs…, in which the condition given on the xs is formulated without mention of identity or parthood or using a quantifier the domain of which is more inclusive than the xs. So, for example, he considers Contact, that the xs compose something just in case they are in contact. His challenge to common–sense ontology is to answer the question so understood.

The SAQ, as defined by Tallant, is supposed to be analogous to the SCQ. Whilst remaining neutral about the existence of houses we can speak of the bricks as being arranged house‐wise, van Inwagen thinks. So Tallant thinks that as he defines it the SAQ is a question the nihilists must answer. The difficulty, however, is that he fails to give the SAQ a meaningful formulation.

He puts forward three proposals as to what this question is.

The first is that it is the question: when is it true that the xs (the mereological simples) are arranged F‐wise? (2014:1511).

However, this is analogous not to the SCQ, but to the GCQ (‘when is it true that the xs compose y?’). Moreover, it is meaningful only if ‘F’ is a bindable variable (as ‘y’ is in the GCQ), so that the open sentence ‘the xs are arranged F‐wise’ denotes a relation. Whether this is so is also the chief question about Tallant's second proposed identification of the SAQ.

This is that the SAQ is to be identified with the question: ‘When is it true that for some xx, the xs are arranged F‐wise?’.

Obviously, this is confused; this question is not structurally analogous to the SCQ (When is it true that for some y, the xs compose y?). The structurally analogous question Tallant intends has to be: ‘When is it true that for some F, the xs are arranged thing‐y‐such‐ that‐Fy‐wise?’4 Tallant's actual formulation uses a plural quantifier which should not be present, and omits a second–order quantifier which is required. It is structurally analogous, not to the SCQ, but to the meaningless question: when is it true that some things compose it? Now just as it is only because ‘the xs compose y’ is an open sentence containing the free but bindable plural variable ‘the xs’ and the free but bindable individual variable ‘y’ and so denotes a relation, that the SCQ makes sense, so it is only if ‘the xs are arranged thing‐y‐such‐that‐Fy‐wise’ is an open sentence which contains the free, but bindable, plural variable ‘the xs’ and the free, but bindable, predicate variable ‘F’ and denotes a relation that the SAQ, as presently understood, makes sense. In that case we can speak of the xs as being arranged simpliciter by binding the predicate variable with an existential quantifier. But we cannot do so if ‘the xs are arranged thing‐y‐such‐that‐Fy‐wise’ does not denote a relation. So the SAQ, on this understanding only makes sense if it does.

But there is no reason to suppose that ‘the xs are arranged thing‐y‐such‐that‐Fy‐wise’ does denote a relation. I shall come back to this crucial point after looking at Tallant's third proposed identification of the SAQ.

… the nihilist equally needs to say something about what the world has to be like to contain simples arranged table‐wise. If the believer should tell us when some simples compose a thing of kind F, the nihilist should tell us when and how some simples are arranged F‐wise’ (Bennett 2009: 66). This is simply that the SAQ is a question already identified by Bennett. Tallant quotes Bennett as follows.

But Bennett is not here identifying a single question, structurally analogous to the SCQ. She is simply pointing out that the nihilist (and near‐nihilist) must provide answers to a whole set of questions. How must the world be to contain simples arranged table‐wise though there are no tables? How must the world be to contain simples arranged artefact‐wise though there are no artefacts? How must the world be to contain simples arranged complex‐object‐wise though there are no complex objects? These are obviously good questions, but they are not ones nihilists have been unaware of and, as we shall see, there are answers to them in van Inwagen's work which are left unimpaired by Tallant's discussion.

So if the supposed SAQ is to have the significance Tallant thinks it has the crucial question is the one posed three paragraphs back. Does ‘the xs are arranged thing‐y‐such‐that‐Fy‐wise’ denote a relation?

Van Inwagen takes great care to explain exactly what relation ‘the xs compose y’ denotes. He makes no attempt to explain what relation ‘the xs are arranged F‐wise’ denotes.5 So, given that talk of things being arranged F‐wise is his coinage, there is no reason to think that it denotes any relation, or therefore to think that the SAQ makes sense.

Nor does the way in which he introduces the talk of things being arranged F‐wise give any reason to think that it makes sense. As we shall see in more detail in a moment he does so by reference to the man in the street's beliefs. Roughly speaking, he suggests that the xs are arranged F‐wise just in case they occupy a region which is believed to contain an F by someone who believes that there are Fs, or would be so believed by such a person if he was aware of the arrangement of the xs there. This statement ascribes a property to the xs, but it is not at all obvious and never suggested by van Inwagen that it asserts a relation to hold between the xs and the property of being an F. If I say of the Ortcutts that Ralph believes them to be a spy ring, I ascribe a property to the Ortcutts, but it is highly controversial that I thereby assert a relation to hold between the Ortcutts and something else, indicated by the predicate ‘are a spy ring’. Of course, there are analyses on which this is the case. According to an analysis inspired by Frege, for example (Kaplan 1968) I assert that the Ortcutts stand in a relation to the sense of the predicate ‘are a spy ring’ which is a constituent of a thought Ralph believes to be true. According to an analysis inspired by Quine (Quine 1977) I assert that the Ortcutts are related to an open sentence ‘the xs are a spy ring’, which is a constituent of a sentence Ralph believes‐true. So if we understand being arranged F‐wise in these terms we can perhaps make sense of the idea that ‘the xs are arranged F‐wise’ denotes a relation, not between the xs and a property, that is, the (direct) reference of a predicate, but between the xs and the Fregean sense of the predicate ‘is an F’ or the predicate itself. But it is clear that all this is far from Van Inwagen's interests. There is no reason to think that he uses locutions of the form ‘the xs are arranged F‐wise’ to denote a relation at all. Nor does he need this to be so for his purposes.

Consider also that as well as such locutions van Inwagen will also allow locutions of the form ‘the xs are arranged a‐wise’ in which ‘a’ takes the places of a singular term. So as well as the SAQ, ‘when is it true for some F, the xs are arranged F‐wise?’, there is apparently also to be considered the question, ‘When is it true that for some y, the xs are arranged y‐wise?’ (we might call this the ‘Special Arrangement as Individuals Question’, or SAIQ). But, of course, just because van Inwagen is happy to say that ‘these particles are arranged Everest‐wise’ would be true as uttered by a suitably located speaker making a suitable ostension, he is not committed to saying that it would be also true to say in the same context that for some y, these particles are arranged y‐wise, that is, that some individual is such that these particles are arranged that‐individual‐wise. He can think that ‘these particles are arranged Everest‐wise’ would express a truth uttered in the appropriate context without having to accept that in this locution ‘Everest’ occupies the place of a bindable singular individual variable. So he is not obliged to regard the SAIQ as meaningful. The same is true, mutatis mutandis of the SAQ. Of course, someone inspired by Frege might say that ‘these particles are arranged Everest‐wise’, understood along the lines van Inwagen suggests, does assert a relation between the particles and the Fregean sense of ‘Everest’ (and mutatis mutandis for someone inspired by Quine). But this is a commitment van Inwagen need not take on.

Van Inwagen is not required to regard the SAQ and the SAIQ as significant because, for his purposes, he does not need to regard the forms ‘the xs are arranged F/a‐wise’ as denoting relations at all.6

The reason van Inwagen introduces these locutions is to explain why, despite not believing in tables, chairs, mountains in general, Mount Everest, in particular, or even the Moon (1990: 105), he is not a madman. The reason, he thinks, is that he has something in common with the defender of common sense which the madman who does not believe that there are tables etc., (because he believes that his experience of the world is a product of a deceiving demon, or that he is a brain in a vat, or inhabits the Matrix) does not, namely the belief that there are particles arranged table‐wise. According to van Inwagen the reason why what he says in his study when he assertorically utters the words ‘there are no tables’ or ‘there is no Moon’ is consistent with what is said by the common–sense man speaking outside the ontology room who assertorically utters the sentence ‘there are six antique tables in the next room’ or ‘there is a Moon’ is that the common–sense man is speaking in a loose and popular manner, whereas he is speaking strictly and philosophically. The negative existential proposition he expresses is not rendered false by the fact that there are particles arranged table‐wise, whereas the proposition the ordinary man expresses by the sentence ‘there are six antique tables in the next room’ is true just in case there are in that region appropriately related particles arranged table‐wise. Thus the ordinary man's belief, as he would express it, that there are tables, is true just in case there are particles arranged table‐wise. But van Inwagen means more than that when he utters the sentence ‘there are tables’ and the extra thing this sentence expresses in his mouth, he thinks, is false.

But none of this requires van Inwagen to regard the open sentence ‘the xs are arranged F‐wise’ as denoting a relation.

So the Special Arrangement Question and the Special Arrangement as Individuals Question are not questions van Inwagen is required to answer, since he is not required for his purposes so much as to regard them as intelligible,

Van Inwagen's response to the accusation of madness can be adopted by nihilists to defend their even sparser ontology. And like van Inwagen to do so they need not acknowledge that the so‐called SAQ and SAIQ make sense. Tallant's supposed SAQ is thus a red (or dead) herring.

However, though there is no obligation on the nihilist or near‐nihilist to provide an answer to the SAQ, since they need not acknowledge such a question, the obligations they do have, which Bennett notes, might confusedly be identified with this illusory one. And, in fact, the later part of Tallant's discussion can be understood as arguing, unconvincingly as we shall see, that they cannot meet these genuine obligations and cannot even explain what is meant by ‘the xs are arranged table‐wise’.

Van Inwagen thinks that there are no tables, but thinks that he has something in common with the man in the street who thinks that there are (i.e., who would assent to the sentence ‘there are tables’ understood in what van Inwagen would call the loose and popular sense) which the madman cannot claim to have in common with him, namely, the belief that there are particles arranged table‐wise. So he needs to explain what this means if it does not mean that there are particles which compose a table. He also thinks that there are no artefacts composed of particles at all, but he does not think that even this puts him at odds with the man in the street. Consequently, he needs to explain what ‘there are things arranged artefact‐wise’ means consistently with his belief that its truth is not incompatible with his belief that there are no artefacts. And he has similarly to explain the meaning of ‘there are things arranged inanimate‐complex‐object‐wise’ in the sense he thinks this is true. Van Inwagen is very well aware of all this. Of course, the nihilist incurs all these obligations too, on pain of being grouped with the madman, and in addition is obliged to explain what he means by ‘there are things arranged animal/plant/living‐thing/complex‐object‐wise’ in the sense he thinks these sentences true, given that he thinks that there are no complex things at all. This is just Bennett's thought again.

The latter part of Tallant's discussion, then, is best viewed as arguing that the attempts nihilists and near‐nihilists have made to meet these obligations are inadequate.

He considers the proposals about the meaning of the form of words ‘there are things arranged F‐wise’ from Dorr and Rosen, Merricks and van Inwagen and argues that none of them are satisfactory. Of these I shall consider only his criticism of van Inwagen and show that it is unsuccessful.

The starting point of Tallant's argument is Kripke's thought that since there are no unicorns there could not have been, or at least there is no saying under what circumstances there would have been. This is generalised by Williams (2006), who suggested that a range of terms, including natural kind terms, have no intension unless they have a non–empty extension. So, just as there could not have been unicorns since there are none, if van Inwagen is right there could not have been water molecules since there are none, and if the nihilist is right there could not have been dogs or other complex living things since there are none.

1990 ‘The xs are arranged chair‐wise’ is true iff they fill a chair‐receptacle and satisfy certain other conditions. Tallant uses these ideas to criticise van Inwagen's proposed explanation of the form ‘there are things arranged F‐wise’ (which Tallant calls REGIONS). 7 van Inwagen (: 109):

Consider those regions of space that, according to those who believe in the existence of chairs, are occupied by chairs. Call them chair‐receptacles. And (1990: 104‐105):

Thus, according to van Inwagen, there are simples arranged table‐wise if there is a table‐receptacle, a region believed to contain a table by someone who thinks there are tables, which is filled by simples (also satisfying certain other conditions). There are simples arranged water–molecule‐wise if there is a water‐molecule‐receptacle, a region believed to contain a water molecule by someone who thinks that there are water molecules, which is filled by simples (also satisfying certain other conditions). And so on. The nihilist can adopt this proposal and explain what ‘there are things arranged living‐thing/complex‐thing‐wise’ means in terms of the notion of a living thing/complex thing‐receptacle. (This explanation is analogous to Hume's second definition of cause, ‘an object followed by another, and whose appearance always conveys the thought to that other’. There remains the question what it is about the way particles are arranged in a region which prompts, or would prompt, a believer in tables to say that there is a table in that region. This question would have to be answered by something logically analogous to Hume's first definition of cause. But of course, van Inwagen knows this.)

The structure of this move is, I think as follows. Begin with the concept of a chair. Imagine that there is a thing that corresponds to the concept. It occupies some space. Whatever space it occupies is a chair‐receptacle. I think that we should reject REGIONS. Suppose, for instance, that we wished to say that there is a collection of simples arranged ‘cat‐wise’. The truth‐conditions for this sentence will, according to REGIONS, make reference to the existence of a cat‐receptacle. We must understand ‘cat‐receptacle’ in terms of the terms ‘cat’ and ‘receptacle’. But the term ‘cat’ has no intension (if there are no cats). Since REGIONS is stated in terms of the existence of such receptacles, so it turns out that the nihilist cannot generalise the strategy described in REGIONS (2014: 1517). Tallant's objection is the following:

The objection simply ignores van Inwagen's appeal to the notion of belief. Granted Kripke's point about the concept of a unicorn, it does not follow that one cannot have a belief about unicorns (perhaps Tallant's idea is that this follows if ‘unicorn’ has no intension8 ). In fact, Kripke does; he believes that there are no unicorns and could not be.9 If one can have beliefs about unicorns the notion of a unicorn‐receptacle, understood in van Inwagen's terms, makes perfect sense, and hence so does the statement ‘there are simples arranged unicorn‐wise’ understood in terms of van Inwagen's account and mutatis mutandis for ‘there are simples arranged water‐molecule‐wise’, ‘there are simples arranged cat‐wise’ and so on. So Tallant has not shown that van Inwagen and the nihilist cannot use the former's definition of the form ‘there are simples arranged F‐wise’ to meet the obligations they incur.10

In the following section, Tallant changes tack. He argues that even if the nihilist and near‐nihilist can give a satisfactory account of the locutions of the form ‘the xs are arranged F‐wise’ to which they must ascribe sense (some account other than the ones he has refuted), they cannot give such an account without ‘undermining’ the motivation they have for their restricted ontologies.

Specifically, he considers what he refers to as an ‘argument from elimination’ (which purports to eliminate every answer to the SCQ except nihilism [and near‐nihilism]) which can, he says, be easily constructed from van Inwagen's writings and claims that this reasoning applies to it. This argument from elimination is not van Inwagen's explicit argument for his near‐nihilism, he says. It is rather the same in structure as an argument of Markosian's (2014: foonote 8). But it is not Markosian's argument either since it has a different conclusion. So the crucial question to be asked about Tallant's criticism of his constructed argument from elimination – since it is not identified with any argument actually given by any actual nihilist or near‐nihilist – is whether it undermines the actual motivation any actual nihilist or near‐nihilist has for his position. And, in particular, most saliently, whether it undermines the motivation van Inwagen's explicit argument for his near‐nihilism gives him. If not, the criticism of the constructed argument is pointless.

… if we require that for every case of composition, there is a paraphrase that can be given in terms of the xs being arranged F‐wise, then contra the argument from elimination, we do have a paraphrase that will suffice to describe all the cases in which composition occurs. After all, for every putatively true sentence about the xs composing an F, there is a paraphrase to be given in terms of the xs being arranged F‐wise. There is, thus, a 1:1 match between cases in which we think of as composition occurring and cases that our paraphrase describes as ones in which the x's are arranged F‐wise. Given the presence of such a match, why not treat the latter as an answer to the SCQ? Certainly this would give us a putative answer to the SCQ that is neither too liberal nor too conservative. It will be just right. … If the answer to the SAQ delivers these results – a true sentence in all and only cases where we intuit it to be true that there are composite objects – then we have a resource that would seem to give us truth‐conditions for all of our putatively true sentences of English about composite objects. This it seems is just a way of answering the SCQ. (2014: 1521) According to Tallant the argument from elimination for nihilism which he constructs from van Inwagen's writings can be undermined as follows:

Now van Inwagen does indeed say, as we have seen, that whenever we (the folk) intuit it to be true that there are complex objects of some kind, that is, assent to the claim that there are such complex objects, there is a sentence which is true by his own lights of the form ‘there are things arranged F‐wise’ which expresses what he and the folk both believe. That is emphatically part of his position and it is what Tallant appears to be arguing to be the case. But how this allows us to reject the argument van Inwagen actually gives earlier in his text against the existence of complex (non–living) things is difficult to discern.11 Tallant does not go into the details of van Inwagen's argument, nor how the considerations he emphasises undermine it. But if we fill in some of its details this looks implausible.

Van Inwagen argues that there are no tables because there cannot be. There cannot be because tables exist only if they have been made. And to be made they must be made out of smaller things. But nothing we can do, by bringing together and arranging smaller things, can suffice to make a table. For otherwise by combining other things in the same way we could bring into existence complex objects which clearly could not be brought into existence in this way. So, for example, if one way to make a table were simply to bring various smaller things into contact one could bring a new object into existence just by getting two people to shake hands, which one clearly cannot do. Similarly, if one could bring a table into existence by tying together smaller things in an appropriate way one could also create a complex object by tying two people together, but, again, clearly one cannot. Van Inwagen runs through various possibilities and concludes that there is nothing one could do that would bring a table into existence. For however one arranged and bonded together smaller things in the attempt to make a table one could so arrange and bond together people or other living things. But doing so could not bring a complex object into existence, ‘it is pretty clear that one cannot bring a composite object into existence by bonding … human beings – or other living things of any sort – to each other… Try to imagine bringing something into existence by gluing hamsters or snakes together’ (1990: 62 and endnote 21). So he concludes that there is nothing one could do that would create a table. So tables do not exist because they could not exist. And if so nor do any other complex non–living things. (Van Inwagen has a subsidiary argument for the existence of complex living things.)

Now the argument briefly sketched here is van Inwagen's explicit argument for his near‐nihilism.12 And it is utterly unclear how it is supposed to be undermined by his introducing talk of things being arranged F‐wise when distinguishing himself from the madman. Clearly it does not occur to van Inwagen that it might be so undermined. To undermine van Inwagen's argument one would have to find fault with one of the premises or one of the steps. But Tallant does not go into details to explain how this might be done.13 Of course not, since he is not discussing van Inwagen's explicit argument. But then, as noted, his discussion of his constructed argument provides no reason to object to van Inwagen's argument, nor for that matter, to reject any actual argument actual nihilists have put forward for their position.

This is not to say that van Inwagen's argument cannot be challenged. One might query his conviction that nothing one could do to living things could bring into existence a complex non–living object composed of them, for example. But Tallant does not raise this query and does not engage at all with the details of van Inwagen's argument. So whatever is true of the ‘argument from elimination’ he constructs from van Inwagen's writings, van Inwagen's actual argument appears unscathed.

Another challenge to van Inwagen that someone could raise is for him to identify the proposition he expresses when he says that there are no tables. Clearly, it is not the proposition that there are no simples which are tables because that is too obvious to need saying. Nor, for the same reason, is it the proposition that there are no living things which are tables. But then it is difficult to identify the proposition, of the many consistent with what is said by the man in the street when he says such things as that there are several antique tables in the next room, that van Inwagen expresses when he says that there are no tables. But however one might reply to this apparent difficulty,14 it is clear that it is not involved in Tallant's criticism of his constructed argument from elimination. The present difficulty, if there is one, relates to the content of van Inwagen's belief that there are no tables, not to what meaning he can give to the statement that there are simples arranged table‐wise, given that he believes that there are no tables.

I conclude that nihilists and near‐nihilists have no obligation to answer the SAQ since there is no such question to recognise and that the questions that they are obliged to answer they can answer and can do so without undermining the motivations they have for their positions. Or at least, we have not yet been given reason to think otherwise, certainly not by Tallant, nor as far as I am aware by anyone else.