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Take the language ML_P@cand make two copies of it,M C−ML_P@candT N−ML@_Pc. The two copies are just like ML@_Pcexcept that each expression ofT−ML@_Pcis superscripted withT. For instance,

M C

∀ is the universal quantifier ofM C−ML@_PcandT N∀ is the universal quantifier ofT N−ML@_Pc. LetTϕsignal thatϕis a formula ofT−ML@_Pc.

Let theT N∗-mapping be a mapping just like theT N-mapping, except that it goes from language

M C−ML@_Pcto languageT N−ML@_Pc. Similarly, let theM C∗-mapping be a mapping just like the

M C-mapping, except that it goes from languageT N−ML@_Pcto languageM C−ML@_Pc For eachT N-modelM, interpretT N−ML@c

P as the language ML@Pcwould be interpreted inM.

Let me call each domain of typetof worldwthedomain ofT N∀vtat worldw. Define the domain of M C

∀ veat a worldwas the subset of the domain of T N

∀ veat worldwwhose members are the elements

ofT N∀vethat are either concrete or necessarily nonconcrete atw. Let the value ofM C= at a worldw

consist in the set of pairs of elements in the domain of entities of typeeofM that are either concrete or necessarily nonconcrete atw. Finally, define the domain ofM C∀ vtat a worldw, for allt6=e, as in

general models (on the basis of the domain ofM C∀ ve).

We have thatM, w(

T N(ϕ)

T N∗ _{if and only ifM, w(} T N

M C

ϕ . The upshot is that eachT N-model may thus be seen also as aM C-model. In particular,M satisfies the commitments of bothT N (as expected) andM C. I will call anyT N-modelMexpanded in this way anT N+M C-model.

For eachM C-modelM, interpretM C −ML@_Pcas the language ML@_Pcwould be interpreted in

M. Let me call each domain of typetof worldwthedomain ofM C∀ vtat worldw. Define the domain

ofT N∀veat worldwas the subset of the domain of M C

∀ vheiat worldwwhose members are possibly haecceities of something. Let the value ofT N= at a worldwconsist in the set of all pairsho, oiof elementsoin the domain ofT N∀ veofM. Define the domain of

T N

∀vtat a worldw, for allt6=e, as in

general models (on the basis of the domain ofT N∀ ve). Finally, define the value of T N

c at a worldwas the set of haecceities in the domain ofM C∀ vheithat are had by some entity of typeethat is concrete at worldw. We have that,M, w ( M C(ϕ) M C∗_{if and only ifM, w (} M C T N

ϕ. The upshot is that eachM C-model may thus be seen also as aT N-model. In particular,M satisfies the commitments of bothM C(as expected) andT N. I will call anyM C-modelMexpanded in this way anM C+T N-model.

Roughly, eachT N +M C-model depicts both one way that modal reality might be according to Williamsonians and how that reality may be redescribed according to how Plantingans interpret ML@c

P .

Similarly, eachM C +T N-model depicts both one way that modal reality might be according to Plantingans and how that reality may be redescribed according to how Williamsonians interpret ML@_Pc. Since Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are equivalent, the two classes of models should be the same, right?

Well, they aren’t. One quick way to see this is by appealing to the following facts:

Mismatch.

1. The domain ofT N∀veat worldwof anyM C+T N-model consists of functions from worlds

to sets of things in the domain ofM C∀ veat worldw(roughly, representing haecceities);

2. The domain ofT N∀ veat worldwofT N+M C-models doesnotconsist of functions from

worlds to sets of things in the domain ofM C∀ veat worldw.

One may be tempted to see Mismatch as showing that Plantingan Moderate Contingentism and Williamsonian Thorough Necessitism are not equivalent. Plantingans must think of the individuals that Williamsonians talk about aspropertiesof individuals. But Williamsonians are not talking about properties of individuals. Hence, the two theories are not equivalent. TheM C-mapping thus

misrepresentsWilliamsonians as speaking about properties of individuals instead of individuals. Mismatch shows no such thing. TheT N- andM C-mappings are deeply correct only if the quantifiers of the two theories have different meanings. That is, theT N- andM C-mappings preserve meaning only if there is quantifier variance, in the sense that the quantifiers of the two theories may have different meanings, even if they are intended to be unrestricted.

The models of each theory reflect how that theory understands ‘individual’ and the relationship between what they call ‘individuals’ and ‘higher-order entities’. Since Plantingans and Williamsonians take the universal and existential quantifiers to have different meanings, they also take ‘individual’ and ‘higher-order entity’ to have different meanings. So, to say that theM C-mapping misrepresents Williamsonians as speaking about properties of individuals instead of individuals is toequivocateon ‘individual’.

What Williamsonians express in terms oftheirunderstanding of the first order quantifiers is expressed by Plantingans in terms of howPlantingansunderstand the second-order quantifiers (over haecceities). So, Mismatch does not show that the theories are not equivalent. It shows what was already clear. Plantingans and Williamsonians appeal to expressions with different meanings to describe the same reality. Moreover, Mismatch reminds us that the language of the metatheory is itself not neutral.

Now, a different objection to the claim thatT N- andM C- are deeply correct translation schemes is simply that their deep correctness requires quantifier variance. This is thought to be an objec- tion because, according to the objector, quantifier variance is false, the reason being that quantifier expressions pick the joint-carving candidate meanings.

This objection is successful only if there is only one candidate meaning for each quantifier expression. But there does not seem to be convincing justification for the claim that there is only one candidate meaning for each of the quantifier expressions. Hence, the objection is not successful.