GR-Impossibilities About Worlds: The Proper Response to Vander Laan Let us begin with a sample objection by David Vander Laan, which involves a

theoretical impossibility about the nature of GR-worlds. After discussing Lewis’ well- known objection against concrete impossible worlds, Vander Laan proudly claims to “add an objection of [his] own” (Vander Laan 1997: 606) against such worlds to the mix. He argues:

“If there are impossible worlds, then some world does not represent itself as concrete. Let us say that none of the propositions which suggest that W is

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concrete (W is concrete, W has mass, W is not an abstract object…) are true in W, and that their negations are. Could such a world be a concrete object? … If Lewis’ usual method applies here and a proposition is true at W just in case it is true when we quantify only over things in W, then W represents itself as concrete if and only if W is concrete (quantifiers restricted to things in W.) Here quantifier restrictions do very little work. If W is concrete (quantifiers restricted to things in

W), then W is concrete, and vice versa. By hypothesis, W does not represent itself as concrete, so W is not concrete. If representation works this way, then any theory according to which all worlds are concrete is inconsistent.” (Vander Laan 1997: 606-607)

What Vander Laan’s somewhat convoluted talk of ‘self-representation’ here points to is simply the alethic nature of GR-representation, at least for traditional GR, namely that for a proposition to be true at a GR-world, it must truly hold of it, i.e. truly describe or characterise that world. (Vander Laan’s de re talk of ‘self-representation’ here is

inessential: whether we are concerned with de re or de dicto representation, according to GR x represents y as  if and only if xis , whether x and y are identical or not, and whether they stand for individuals and  for a property or they stand for worlds, and  for a proposition.) In any case, Vander Laan proceeds to construct his reductio: Suppose GR plus impossible worlds, and suppose that it is impossible that there is a world that is not concrete. Then there is some world such that when we quantify over all things in it, it is true that some world is not concrete. But the only world there is when quantifying over some world is that world itself. So, for it to be true at a world that ‘some world is not concrete’ is for that very world to truly not be concrete. Yet according to GR all worlds are concrete. So a GR-extension into concrete impossible worlds is bound to be

inconsistent.

6.3.1 Reply to Vander Laan

Insofar as Vander Laan’s objection is simply another reductio against concrete

impossible worlds on the basis that inconsistent worlds give rise to outright contradictions, it is truly puzzling why he thought this to constitute a further objection over and above that offered by Lewis (1986a). Of course, the theoretical impossibility he considers has some interest in itself, but it is the inconsistency it generates, rather than the metaphysical

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impossibility itself, that drives the objection forward. The main thrust of Vander Laan’s objection seems to be simply that if it is true at some world w that w is concrete and that w

is not concrete, then impossibilist GR will have to embrace contradictions, for instance the following: there is a world w such that w is concrete and it is not the case that w is

concrete. But so what? We already encountered this in Lewis, and contradictions involving worlds which are both concrete and not concrete are no exception. Indeed, whatever replies we gave to Lewis in Ch IV apply here. If we simply opt for an

inconsistent theory (as per 4.3) we can still maintain that, even if some world is concrete and not concrete, still no contradiction holds about the actual world. If on the other hand we amend the truth-at-w-conditions for negation for inconsistent worlds preserving the classical home-language (as per 4.4), then the reductio cannot get going; for it might well be that a contradiction is true-at-w, but that will not translate to an outright contradiction in the theory. Hence, both our replies to Lewis apply mutatis mutandis to Vander Laan. So Vander Laan’s objection presents no new challenges to IGR. His apparently interesting question of how IGR can represent the metaphysical impossibility of the falsehood of one of its tenets collapses to the uninteresting charge that IGR cannot consistently represent contradictions.

6.3.2 Inconsistency and Representational Power

Vander Laan might now change direction, employing his objection toward different ends. He could argue, for instance, that the extended theory cannot really represent the relevant metaphysical impossibility of a non-concrete world that he puts forth here. He may retort that the proposition he put forth for representation is the perfectly consistent metaphysically impossible proposition that some world is non-concrete, whereas what we have represented instead is a logical impossibility, a contradiction, namely the proposition that some world both is and is not concrete. So, he may argue, impossibilist GR cannot represent the metaphysical impossibility of some world being only not-concrete, since that impossibility is always conflated with the logical impossibility that a world both is and isn’t concrete. Indeed, he might generalise saying that there seems to be a whole class of

metaphysical impossibilities – those contradicting GR-tenets about worlds, for instance – which, it appears, will always be conflated with certain other, logical impossibilities. The new challenge is this: how can IGR really represent such metaphysical impossibilities without conflating them with outright contradictions?

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definition, from IGR’s perspective Vander Laan’s impossibility and others like it are contradictions in terms. For if GR defines the term ‘world’ as ‘concrete mereological sum of spatiotemporally related individuals’, then a GR-object thus defined, which is not concrete, simply is a contradictory object. It is not unintuitive to think that the proposition that some GR-world is not-concrete is indeed identical with the proposition that some GR- world both is and is not concrete, if worlds are defined as concrete objects. So, yes, impossibilist GR does seem to conflate certain apparently metaphysical impossibilities (regarding worlds) with certain contradictions. But this is only because what appear to be metaphysical impossibilities are, for IGR, logical impossibilities in disguise. We can generally say that whenever we have an objection of the form ‘some world is F’ that explicitly contradicts the definition of ‘world’ provided by GR, like ‘some world is not a mereological sum of individuals’, or ‘some world contains spatiotemporally isolated parts’, we can represent such claims by means of contradictory worlds. What makes these objects worlds in the GR-sense is that, whatever else is true about them, it is also true that they are concrete mereological sums of spatiotemporally interrelated individuals.207

Now, our hypothetical objector may wish to talk about worlds, outwith GR’s definition of such objects. Surely, he may ask, there can be a sense of the word ‘world’ that allows for the metaphysical impossibility of a world that does not obey the GR- definition of the term? Sure; but if our objector wants to employ the term ‘world’ with a different sense, then IGR could make a good case that his objector was merely asking about cases – contrary to GR-theory – where the term ‘world’ is employed differently. Impossibilist GR can reply that a world where ‘world’ means something different can easily be accommodated within the representational elements of even possibilist GR. Indeed, this response would not be incompatible with what one assumes often lies behind objections such as Vander Laan’s, namely the supposition that GR is false and ersatzism true, i.e. that worlds are not as GR defines them to be but as ersatz or other abstractionist theories define them. It is well-known that ersatz theorists explicitly and openly admit their decision to use the term ‘world’ in an added new theoretical sense, besides the one we use to refer to the mass of stuff we call this world. I think, given this ersatz terminological stance, IGR seems warranted in representing the impossibility of an abstract world, in the ersatz-sense of the term, via a world, (which sees no other and) according to which some set-theoretic objects are worlds.

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While it may be hard to imagine how a concrete world could instantiate any of those things, what did we expect? They are impossible worlds after all and imagination arguably has to stop somewhere.

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Lastly, our hypothetical objector may insist that his representational needs for the metaphysical impossibility of abstract worlds are still not satisfied. For what he had in mind was the real metaphysical impossibility of a GR world really having different essential properties than the ones it has. What he had in mind was the thought that if GR- worlds have the property of being concrete essentially then it is impossible for such worlds to be abstract objects. But, here IGR can point out that the relevant impossibility is in fact

de re rather than de dicto.It concerns the question whether IGR has the means to represent the impossibility of some world lacking some of its essential properties. IGR can reply that the representation of such de re impossibilities is rather easy. The impossibility of a GR-world lacking some essential property can be represented by means of the existence of some other object that lacks the relevant property (and which presumably is not taken as a counterpart of that world). Indeed, any odd abstract thing can represent the de re

impossibility of a world impossibly being abstract, without that thing itself having to be a world, just like any cat can represent the (essentialist) impossibility that I am a cat without having to be human.

I submit that Vander Laan’s objection fails to present any new challenges to IGR over and beyond Lewis’ original challenge. Moreover, that IGR has rich resources by which to represent GR-theoretical impossibilities contrary to its definition of ‘world’ and terms like it.