How to Account for Nothing(ness)

Marco Simionato

(Università Ca’ Foscari Venezia)
marco.simionato@hotmail.com

 
 
Artaud mosaique cirque
Abstract: Graham Priest, Alex Oliver with Timothy Smiley, and Alberto Voltolini have proposed respectively three different accounts of the phrase ‘nothing’, by arguing that there are sentences where it cannot be reduced to a negative quantifier phrase. In this paper I show that a more preferable account of nothing(ness) is given by the notion of an absolutely empty possible world (i.e. a world that represents no objects at all), rather than Priest or Oliver-Smiley’s accounts, since the use of the empty world allows us to avoid some disadvantages that occur in Priest and Oliver-Smiley’s accounts. In particular, in order to consider nothing(ness) without reducing it to a quantifier phrase, Priest’s commitment to a contradictory object will appear unnecessary. The paper also show how the empty world’s account is able to satisfy two desiderata that characterize Voltolini’s conception of nothing(ness).
 
Keywords: Nothing; Empty Possible World; Empty Term; A. Oliver and T. Smiley; G. Priest.
 
 

  1. Contemporary relevant accounts of nothingness

Oliver-Smiley (2013), Priest (2000, 2002, 2014a, 2014b) and Voltolini (2012) have proposed three different accounts for the phrase ‘nothing(ness)’[1], by arguing that there are sentences where it cannot be reduced to a negative quantifier phrase. In this article I will show that a more preferable account of nothing(ness) is given by the notion of absolutely empty possible world (i.e. a world that represents no objects at all)[2], rather than Oliver-Smiley or Priest’s accounts, since the use of the empty world allows us to avoid some disadvantages that occur in Oliver-Smiley and Priest’s accounts. Finally I also propose a way to connect the absolutely empty world account of nothing(ness) to Voltolini’s account.

Oliver and Smiley propose to distinguish (the use of) ‘nothing’ as a quantifier from (the use of) ‘nothing’ as an empty term. To this end, they introduce the empty term ‘zilch’, with its symbol O, a term such that «[it] is empty as a matter of logical necessity. Any logically unsatisfiable condition will do to define it via description. […] With an eye on formalization, we opt for ‘the non self-identical thing’, tx x ≠ x» (Oliver-Smiley 2013, 602). Since everything is self-identical, ‘zilch’ does not denote anything «whether existent or subsistent, real or imaginary, concrete or abstract, possible or impossible» (Oliver-Smiley 2013, 602).

Priest (2002) argues that ‘nothing’ can be used not only as a quantifier, but also as a substantive:
 

‘Nothing’ can be used as a substantive. If this is not clear, merely ponder the sentence ‘Heidegger and Hegel both talked about nothing, but they made different claims about it’. ‘Nothing’ cannot be a quantifier here. Or consider the sentence:
(*) God brought the universe into being out of nothing.
This means that God arranged for nothingness to give way to the universe. In (*) ‘nothing’ cannot be parsed as a quantifier. If we do so, we obtain: For no x did God bring the universe into existence out of x. And whilst no doubt this is true if God brought the universe into existence out of nothing, it is equally true if the universe has existed for all time: if it was not brought into existence at a time, it was not brought into existence out of anything. And the eternal existence of the universe is, in part, what (*) is denying. (Priest 2002, 241).

So, when ‘nothing’ cannot be reduced to a quantifier phrase, what is it? Priest offers the follow reply: nothing[3] is the absence of all things (absolutely nothing, nihil absolutum). Therefore it is also linked to a quantifier, since it is no object. But ‘nothing’ cannot be considered only as a quantifier: there are sentences where it is a noun phrase that refers to an object that is the absence of all objects[4]. So – Priest concludes – nothing is a contradictory object, «it both is and is not an object; it both is and is not something» (Priest 2014a, 7).

Finally I am going to consider Voltolini (2012)’s account of nothing(ness), used for reading Heidegger’s sentence
 
(H) The nothingness nothings [das Nicht nichtet]
 
in order to compare the above-mentioned account with the empty world-account. Voltolini’s strategy is represented by the treatment of ‘nothingness’ as a definite description that should be eliminated by Russellian strategy. To this end, Voltolini introduces the property of being a thing such that there is no thing that is identical to it, i.e. λx ((¬y) (y = x)); consequently nothingness can be considered as the thing that has this property, i.e. the thing that is identical to no thing. By means of Russellian elimination of definite descriptions, a sentence like (H) becomes:
 
(H*) (∃x) ((¬∃y) (y = x) ∧ (∀z) ((¬∃y) (y = z) ⇒ (z = x)) ∧ Nx)
 
(Voltolini 2012, 102. I do not recall Voltolini’s read of the predicate ‘to nothing’, since it does not concern the main topic of my paper).

Secondly, Voltolini argues that the above mentioned definite description could have a Russellian denotation only if such a denotation was an impossible object (therefore only in an ontology that admits impossibilia). According to Voltolini, the thing that is identical to no thing is an impossible object because only an impossible object could instantiate the property λx ((¬y) (y = x)). Indeed, each object is self-identical, but this object cannot be identical to itself because it cannot be identical to anything. However, as an object, it is at least identical to itself. Therefore that object is identical to something (since it is identical to itself) and – at the same time – it is not identical to anything (since it is identical to no object at all).

Such an introduction of an impossible object induces Voltolini to review his treatment of ‘nothingness’ in order to reply to the objection according to which ‘nothingness’ could not have a denotation, since there is no object that could instantiate the property λx ((¬y) (y = x)). At this end, he uses a sort of Meinongianist strategy. Let us consider, for example, an impossible object as a square-non-square. It is a thing such that it is a square and it is a non-square, rather than a thing such that it is a square and it is not a square. Following this strategy, ‘nothingness’ as a definite description should be considered as the thing that is identical to something and it is non-(identical to something), rather than the thing according to which there is no thing that is identical to it and there is something that is identical to it. Since the property of being non-(identical to something) is the property of being not identical to every thing, i.e. λx ((∀y) (y ≠ x)), we should read (H) as follows:
 
(H**)  (∃x) ((∀y) (y ≠ x) ∧ (∀z) ((∀y) (y ≠ z) ⇒ (z = x)) ∧ Nx)
 
Since at the same time this thing is not identical to every thing, but it is identical to something (because it is identical to itself), it is an impossible object.
 
 

  1. The vindication of the absolutely empty world

Let us consider the sentence (*). According to Priest’s account, it would become:
 
(*p) God brought the universe into being out of nothing, i.e. out of the absence of all objects that is a (contradictory) object.
 

According to Oliver-Smiley’s account, the sentence (*) would become:
 
(*os) God brought the universe into being out of zilch;
 
(*p) seems more preferable than (*os) since it allows us to distinguish a sentence like (*) from a sentence like
 
(**) The universe eternally exists
 
as Priest’s above quotation shows, whereas (*os) fails since there would not be an object out of which God creates the universe. However, (*p) seems to undermine the notion of absolute nothing itself: since it is the absence of all objects, the commitment of (*p) to a (contradictory) object inevitably weakens the success of the paraphrase. Instead, (*os) can avoid such a commitment in order to preserve the notion of creation out of nothing (i.e. the absence of all objects), but – as I have pointed out – it cannot offer a sufficient account for distinguishing (*) from its negations. (I recall that – as Priest notes – a sentence like (**) is a sort of negation of (*) because it de facto would state that the universe would not be created, if (*) was read as <the universe was not brought into existence out of anything>, by considering the occurrence of ‘nothing’ in (*) as a quantifier phrase). Therefore, let us try to evaluate another account of nothing(ness), i.e. nothing(ness) as absolutely empty possible world.

I return again to nothing(ness) as the absolute absence of all objects, as Priest suggests; but I don’t consider this absence as an object. Rather, I propose to consider that absence simply as the maximal (all-encompassing) consistent situation according to which there are no objects at all. Since a maximal consistent situation according to which things could be is – broadly speaking – represented by a (possible) world, the maximal consistent situation according to which there are no objects at all is what is represented by what is called empty world, i.e. a world that represents the absence of all objects (namely the global absence)[5]. So nothing(ness) is an entity – i.e. a possible world – that represents the absence of all objects. One should note that the absence of all objects cannot be – say – separated from the empty world, because the absence of all objects is exactly represented by the possible world according to which there are no objects at all. But this thesis does not mean that the global absence is not different from the empty world itself: as in each world, one can distinguish the world as such from its “content”, i.e. from what it represents[6]. Therefore, when ‘nothing(ness)’ is not used as a negative quantifier phrase, I mean that we can use ‘nothing(ness)’ for referring to the absence of everything (the maximal consistent situation of the global absence), but only if we are aware that at the same time we are referring to the entity according to which there are no objects at all, i.e. we are referring at the same time to the empty possible world. This is neither a misunderstanding, nor a contradiction. The absence of everything cannot be separated from the empty world that represents it; and the empty world cannot be separated from the absence of everything, i.e. from what it represents. But – as I said – one can distinguish the world as such from its “content”, as in any world[7].

By means of the empty world account, the sentence (*) would become:
 
(*m) God brought the universe into being out of the absence of all objects that is represented by the empty world, i.e. an entity that exactly represents the maximal consistent situation according to which there are no objects at all.
 
This account does not undermine the notion of the absence of all objects, since the empty world allows us to represent it without considering this absolute absence as a (contradictory) object. Indeed, the absence of all objects is not an object, but it is represented by an entity that is a possible world which we can quantify over. Besides, by means of (*m), one can avoid to appeal to a contradictory object[8]. Finally, this account is able to distinguish the sentence (*) from its negation, since (*m) does not state that God created the universe out of no thing, but it affirms that God created the universe out of the global absence that is represented by something, namely the empty world. So we can quantify over the empty world itself in order to represent the global absence from which God created the universe.

Anyway the paraphrase (*m) seems to be incoherent since one could intend it as <God created the universe out of the empty world>; that seems very odd. (As an alternative, one could hold that (*m) does not entail a quantification on something, since the global absence is not an object. But in that case my paraphrase would have no advantage respect to a paraphrase that simply read ‘nothing’ as a quantifier phrase. Therefore we need to quantify over something, namely the empty world as world). I would reply as follows. Let us employ the difference between what is for a world to be actual existing and what is for a world to be actualized. In a – broadly speaking – actualist realism conception of possible worlds (see Divers 2002, 169 ff.) each possible world actually exist, but «among the many possible worlds that actually exist, one possible world is distinguished from the others by being (absolutely) actualized» (Divers  2002, 169). Therefore, if the absolutely empty world was actualized, then there would be neither concrete objects, nor abstract objects, included the world itself. So, when God created the universe, there was just the empty world, but it was actualized, so one cannot affirm that there was an entity (the empty world) before God’s creation.

Certainly, one could object that also (*m) undermines the notion of the absence of all objects, since it appeals to the existence of an entity, i.e. the empty world. But I would reply by highlighting that the notion of empty world does not merely coincide with the notion of the absence of everything, since the latter is not the former; rather it is what is represented by the former, whereas in Priest’s account the notion of the absence of everything coincides with an object (i.e. the contradictory object nothing). Instead, the absence of all things is different from the empty world itself, even if it cannot be separated from the empty world[9].

At this end, one could object that Oliver and Smiley’s account could be preferable as well as (*m): where (*m) uses an empty world for representing the absence of all objects, they propose an empty term for denoting the non-self-identical thing, i.e. no objects at all. However I think that their account should be reduced to my account for the following reason. Let us consider the sentence
 
(Z1) ‘Zilch’ does not denote anything (i.e. ‘zilch’ denotes the non self-identical thing)
 
as Oliver and Smiley state. Since the non self-identical thing is no objects at all, (Z1) affirms that ‘zilch’ denotes no entity at all. Therefore (Z1) could be read as follows:
 
(Z1*) ‘Zilch’ denotes the absence of all objects;
 
that is
 
(Z1**) ‘Zilch’ denotes the all-encompassing situation according to which there are no objects at all;
 
that is
 
(Z1***) ‘Zilch’ denotes what is represented by the absolutely empty (possible) world.
 

Let us recall the following point: (*m) allows us to distinguish (*) from its negations, since a sentence as <God brought the universe into being out of no thing> (i.e. a sentence that contradicts the genuine meaning of (*)) is different from <God brought the universe into being out of the global absence that is represented by the absolutely empty world>. In order to avoid the notion of God as creator[10] that could mislead the reader from the real aim of this paper, we can also use the following sentence by Priest (2000)
 
(B) The cosmos came into existence out of nothing.
 
Priest uses (B) as a further example for showing that ‘nothing’ cannot be always reduced to a negative quantifier phrase:
 

Consider the cosmos […]. Either it stretches back infinitely into time past, or at some partλ≠icular time it came into existence. In the first case, it had no beginning, but was always there; in the second, it began at some particular time. […] just consider the second possibility. In this case, the cosmos came into existence out of nothing – or nothing physical, anyway, the cosmos being the totality of everything physical. Now consider that sentence, ‘The cosmos came into existence out of nothing’. Let c be the cosmos, and let us write ‘x came into existence out of y’ as xEy. Then given our understanding of quantifiers, this sentence should mean ¬∃x cEx. But it does not mean this; for this is equally true in the first alternative cosmology. (Priest 2000, p. 23).

Similarly to the paraphrase of (*), according to Priest, also in the case of (B) we should appeal to the object nothing (that in Priest 2000 is called simply ‘nothingness’ for distinguishing it from the use of ‘nothing’ as quantifier phrase), in order to distinguish (B) – and so the second cosmological theory – from the first cosmological theory (i.e. the eternal existence of the cosmos). Therefore, by arguing as before, Priest’s paraphrase of (B) would be:
 
(Bp) The cosmos came into existence out of nothing, i.e. out of the absence of all objects that is a (contradictory) object;
 
Oliver-Smiley’s paraphrase of (B) would be:
 
(Bos) The cosmos came into existence out of zilch;
 
my paraphrase by means of empty world account would be:
 
(Bm) The cosmos came into existence out of the absence of all objects that is represented by the empty world, i.e. an entity that exactly represents the maximal consistent situation according to which there are no objects at all.
 
I am not going to repeat again the arguments about these paraphrases, since they are the same arguments about the paraphrases of (*). I just point out that in this case we do not need to use the notion of God’s creation. Besides – as in God’s creation case – we should affirm that before the cosmos being into existence, the empty world was actualized, so there would be neither concrete objects, nor abstract objects, included the world itself[11].

Let us consider again the account of nothing(ness) as empty world together with Voltolini’s account. I think it can hold together the intuitive idea of nothing(ness) as non-(identical to something)[12] and nothing(ness) as identical to itself. Indeed, the empty world as world is self-identical, since it is an existing (probably abstract) object, but what it represents is non-(identical to something) since there are no objects at all in such an empty world. Therefore, given that all objects are self-identical, the “content” of the empty world – i.e. what is represented by the empty world – vacuously satisfies the property of being non-(identical to something), whereas – of course – the empty world is identical to itself. In this way, if one uses ‘nothing(ness)’ for referring to the empty world, then one can state that nothing(ness) is self-identical and at the same time, but in different respect (so avoiding the contradiction), one can state that it is non-(identical to something) because by means of the empty world one is representing the absence of all objects, and therefore the content of the world is non-(identical to something).

The existence of a possible empty world is the topic of a debate about a thesis called metaphysical nihilism, i.e. the thesis according to which there is a possible empty world. In this paper I will not deal with the question whether such a world can be (or should be) counted among possible worlds. Indeed my aim is just to propose a good account of nothing(ness) and in particular an account that is able to distinguish a sentence like (*) from its negation (or a cosmological theory like (B) from its alternative) and such that the genuine notion of absence of all objects is not undermined. Then, my aim is to propose an account that does not need a commitment to impossible or contradictory objects.

Anyway, I am going to consider at least an interesting objection by Heil (2013) against the notion of empty world itself. According to Heil, «the empty world is not a world with nothing in it. It is nothing at all. The empty world is not a world that would cease to be empty where something added to it […]. The empty world is not a it» (Heil 2013, 173). I think that such an objection can be overcome by means of the strategy that I showed before, i.e. by primarily noting that a notion as ‘nothing at all’ simply means ‘absence of all objects’ (as Priest suggests); but this absence is the maximal situation according to which there are no objects at all that is exactly represented by an absolutely empty world. Therefore Heil in actu signato negates that the empty world is an entity, but he in actu exercito is appealing to it (since he is representing the absence of everything).

A similar strategy can be used for avoiding Priest (2014)’s “potential objection” against the empty world[13], where he claims that «philosophers often wonder why there is something rather than nothing. However, even if there were nothing – even if everything would be entirely absent – there would be something, namely nothing» (Priest 2014a, 7). Even in this case, the absence of all objects is separated by Priest from the entity (namely the empty world) that represents the situation according to which there are no objects at all. If one did not treat the absence of all things as a (contradictory) object, as instead Priest seems to do, the notion of empty world would be perfectly sensible since the entity would be the empty world as such and it would not be its “content”. I think that even Priest’s use of mereology for giving an account of nothing should be reduced to the account of the empty world. According to Priest, «[nothingness] is the fusion of the empty set  […]. Nothing is what you get when you fuse no things. There is nothing in the empty set, so nothing is absolute absence: the absence of all objects, as one would expect» (Priest 2014a, 7). I think it would be less problematic to conceive the absence of all objects as the “content” of (i.e. what is represented by) an absolutely empty world, rather than an ontological commitment to a self-contradictory object as nothing.

Finally, let us consider another fundamental topic about the existence of an (absolutely) empty world. One should evaluate whether an empty world counts among the possible worlds or among the impossible worlds…or even one should establish whether an empty world is really a world at all. I will not deal with this topic in this paper (for an overview see Coggins 2010). I just propose two brief considerations for counting the empty world among the possible worlds.

First, if one simply assumes that «an impossible world is a world that realizes explicit logical contradictions» (Berto 2013), then it seems more reasonable to count the empty world among the possible worlds because it could not realize explicit contradictions, since it does not represent anything at all.

Secondly, even if there are mainly two kinds of arguments against the existence of a possible empty world[14], I think that they are not very uncontroversial, given the contemporary debate on the so-called metaphysical nihilism (the thesis according to which there might be nothing). The two strategies against metaphysical nihilism are the following: one should argue that there is a necessary (concrete) object (for example through an ontological argument), so that all worlds are non-empty, since in each of them there is at least that necessary object; or one should argue that necessarily there is at least one concrete object in every world (but not necessarily the same object)[15]. The first strategy is based on the truth of (some version of) the ontological argument; therefore it is not uncontroversial, as I suggested before. The second strategy is usually represented by Lowes’s argument[16] that grounds on two relevant premises: i) at least some abstract objects exist in all possible worlds; ii) abstract objects existentially depend on concrete objects. Therefore – the argument concludes – there are concrete objects in all possible worlds. Since i) and ii) are not uncontroversial, also this strategy cannot be considered as a decisive rejection of the empty world.

Given the advantages that the notion of empty world offers for treating the phrase ‘nothing(ness)’, as I have argued in the previous sections, and since the ontological argument is not uncontroversial and since neither the necessary existence of some abstract objects, nor the existential dependence of abstracta on concreta  are not uncontroversial too, I think that the use of empty world as possible world for giving an account of nothing(ness) could be very reasonable.

In conclusion, in this paper I have argued that the notion of absolutely empty world gives an account of nothing (when ‘nothing’ is not used as a quantifier) that is better than Priest (say P), Oliver-Smiley (say OS) and Voltolini (say V) ’s accounts. The empty world account (say EW) allows us to distinguish ‘nothing’ as negative quantifier from its other occurrences, as P, OS and V. Unlike OS, EW is able to distinguish a sentence like (*) from its negation (or the cosmological theory expressed by (B) from its alternative), as well as P. But unlike P, EW does not undermine the notion of absence of every thing, since EW does not identify it with an object. Besides, unlike P, EW does not commit itself to a contradictory object[17].

Finally, EW is able to express two ideas about nothingness that V points out: its self-identity and at the same time its property of being non-(identical to every thing)[18]. But unlike V, EW can do that without appealing to an impossible object.

That is – say – the vindication of the absolutely empty world account. However, does such a vindication simply provide an account for the linguistic and metaphysical plausibility of the notion of nothingness, or this account entails some metaphysical insights on the debate concerning the existence/non-existence of a reference for the phrase ‘nothingness’[19]? I think the reply to this fundamental question can be found within the “duplicity” of the EW-account. Nothingness exists and it does not exist at the same time, but according to different respects (then avoiding any contradictory result). Nothingness exists as (possible) empty world, i.e. a representational device that “depicts” the maximal consistent situation according to which there are no objects at all; at the same time nothingness does not exist as the absence of all things, although we can quantify over it (we can refer to it, we can think about it, etc.) through the empty world as (possible) world, that in fact represents the situation according to which there are no objects at all[20].
 
 
References
 
Baldwin, T. (1996), There might be nothing, «Analysis», 56: 231-238.
Berto, F. (2013), Impossible Worlds, in Zalta, E.N. (ed.), The Stanford Encyclopedia of Philosophy (Winter 2013 Edition), available at URL = <http://plato.stanford.edu/archives/win2013/entries/impossible-worlds/>.
Coggins, G. (2010), Could There Have Been Nothing? Against Metaphysical Nihilism, London: Palgrave Macmillan.
Heil, J. (2013), Contingency, in Goldschmidt, T. (ed.), The puzzle of existence. Why is there something rather than nothing?, London and New York: Routledge.
Lowe, E. J. (2013), Metaphysical nihilism revisited, in Goldschmidt, T. (ed.), The puzzle of existence. Why is there something rather than nothing?. London and New York: Routledge.
Menzel, C. (2014), Possible Worlds, in Zalta E.N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), available at URL = <http://plato.stanford.edu/archives/spr2014/entries/possible-worlds/>.
Oliver, A., Smiley, T. (2013), Zilch, «Analysis», 73: 601-613.
Priest, G. (2000), Logic. A very short introduction, Oxford: Oxford University Press.
Priest, G. (2002), Beyond the limits of thought, Oxford: Oxford University Press.
Priest, G. (2014a), Much ado about nothing [forthcoming in Australasian journal of logic]
Priest, G. (2014b), One, Oxford: Oxford University Press.
Simionato, M. (2015a), The metaphysics of the empty world, Ph.D. Dissertation, University ca’ Foscari of Venice.
Simionato, M. (2015b), Is God Creator out of nothing and necessary being?, in “Verifiche” – Rivista di Scienze Umane, vol. XLVI: 121-133.
Van Inwagen, P. (1996), Why Is There Anything at All?, «Proceedings of the Aristotelian Society», 70: 95–110.
Voltolini, A. (2012), Il nulla nulleggia ancora, «Rivista di Estetica», 52: 99-113.
 
 
Note al testo
 
[1] When I use ‘nothing(ness)’ (with brackets), I refer to a notion of nothing that either needs to be disentangled, or that is a non-quantificational phrase. That does not exclude other devices (for example Priest’s use of boldface type or simply ‘nothing’) whose meanings will appear depending on the context of the discussion.
[2] Several metaphysicians, at least after Van Inwagen (1996), consider nothing(ness) as an empty world. It means a world with no concrete objects in it, or a world with neither abstract nor concrete objects in it. In this paper I almost always mean an absolutely empty world, i.e. a world with no objects at all, either using the expression ‘absolutely empty (possible) world’, or simply the expression ‘empty (possible) world’.
[3] Priest (2014a) distinguishes ‘nothing’ as noun phrase from ‘nothing’ as quantifier phrase by means of bold type (nothing) when he uses ‘nothing’ as noun phrase.
[4] In Priest (2014a) such an object is a non-existent object (assuming that to exist is to have the potential to enter into causal interactions) (see Priest 2014a, 2); and Priest admits that «the domain of objects comprises […] both existent and non-existent objects» (Priest 2014a, 1).
[5] In this paper I will not deal with the question about which accounts of possible worlds could be compatible with an absolutely empty world. For an overview on this topic, see Coggins (2010) (however she deals mainly with an empty world as world without concrete objects, rather than an absolutely empty world). Anyway, I recall that a good account should be – say – “abstractionist”, rather than “concretist” (I use these phrases as they appear in Menzel 2013). Besides, since I use the notion of representation, I suppose that a good account could be for instance an account within those that Divers (2002) calls “book realism”: «the possible worlds are all and only the maximal consistent sets of sentences. A set of sentences, S, is maximal iff for every atomic sentence, p, S has a member either p or its negation; a set of sentences, S, entails a sentence p iff the conjunction of the members of S ∪{¬p}is inconsistent (not consistent). For any possible worlds, w,v: w, is actualized (simpliciter) iff all and only the true sentences are entailed by w; at w, any possible world v is actualized iff w is equivalent to v (i.e. w entails v and v entails w): at w, there exists an individual a iff w entails that ∃y [y=????]» (p. 179). Finally, we will see that the difference between actual existing worlds and actualized existing world is important for the sake of my argument. I will return to that topic later.
[6] Again, I ask the reader to assume a “representative” account of possible worlds.
[7] It could be useful recall Hegelian use of ‘moment’ (‘das Moment’). A moment is not an instant of time, but it is an aspect of a structure that cannot be separated from the structure itself or from the other aspects of it; yet such an aspect can be distinguished from the structure or from the other aspects of it. The empty world as possible world and the “content” of the empty world, i.e. the absence of everything, are two moments of the same structure, i.e. two moments of the empty world. One can use ‘nothing(ness)’ in order to refer to the empty world as world (therefore as an entity) or to the absence of everything that the empty world represents. But one should not forget that referring to a moment implies referring to the other moment. So one cannot refer to the absence of everything without implicitly referring to the empty world and viceversa.
[8] Certainly from Priest’s point of view the commitment to a contradictory object is not a problem and such a result is not an unintended consequence of his account. However, the empty world allows us to account for nothing(ness) with more parsimony and by means of a strategy that can be also accepted by a non-dialetheist.
[9] One could object that the philosophers – like Heidegger – that use ‘nothing(ness)’ as a noun phrase do not mean to refer to a possible world. I would reply that the naïve (or pre-theoretical) conception of nothing(ness) as absence of all objects is exactly what the above-mentioned philosophers try to think and such a conception is exactly what is accounted by means of empty possible world, as I have shown. Therefore, the empty world does not change the naïve (or pre-theoretical)  meaning of ‘nothing(ness)’.
[10] I consider the relation between God as creator and nothingness in Simionato (2015b).
[11] One could object that possible worlds are atemporal; therefore we should not use them for representing a temporal sequence of situations, namely the maximal consistent situation at t0 according to which there are no objects at all and the maximal consistent situation(s) at t1, t2, …, tn according to which there are some objects. However, the objection can be avoided by assuming that the empty world and the actual world overlap before God’s creation or before the coming into existence of the cosmos. Then, after God’s creation or after the coming into existence of the cosmos, the actual world does not overlap with the actual world, as well as we can conceive that our actual world and a possible world w overlap in respect to what is true of that world in a range of time r, being identical only for the “content” within that range, whereas they are different for the “content” outside that range (for example, suppose that our actual world is identical to a possible world w for the range of time from the beginning until 1789, and it is different from w for the range of time after 1789, since at the first world there was the French Revolution, whereas at w there was not).
[12] λx ((∀y) (y ≠ x)).
[13] I say “potential objection” because Priest does not explicitly present his argument as an argument against the absolutely empty possible world, but I think that his argument could be used (by a “potential objector”) for undermining the notion of such a world, since an absolutely empty world does not represent any object, whether possible or impossible, concrete or abstract, non-contradictory or contradictory.
[14] There are also arguments for the truth of metaphysical nihilism: the so called “subtraction argument” by Baldwin (1996) and other versions of it by other philosophers (see Coggins 2010 for an overview). Anyway, the subtraction argument is able to show just the existence of a possible world with no concrete objects in it, but where there could be abstract objects.
[15] See Coggins (2010).
[16] For the more recent version of this argument, see Lowe (2013).
[17] P argues that ‘nothing(ness)’ as ‘the absence of everything’ is a noun phrase that refers to an object, whereas I have argued that is more preferable to say that ‘nothing(ness)’ is a noun phrase that refers to an empty possible world and that the absence of everything is represented by such an empty world.
[18] i.e. non-(identical to something): λx ((∀y) (y ≠ x)).
[19] Thanks to the anonymous referee for this question.
[20] See Simionato (2015a).

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