(1) Based on your reading of Lewis’ On the
Plurality of Worlds do you think that his arguments against ersatzism are
convincing. If they are, would you give up on modality, accept concrete worlds,
or do you have some other response?
Lewis’
arguments against ersatzism about modality in On the Plurality of Worlds are extremely strong philosophical
arguments. Paralleling the Quinean indispensability argument for mathematical
Platonism (appealing to the indispensability of mathematics in our best
scientific theories), Lewis appeals to the implausibility of all attempts to
account for the massive philosophical utility of modal language and possible
worlds semantics without postulating concrete entities to which this can be
‘reduced’. I argue that he successfully argues that the ‘ersatzers’ either
lapse into mystery, incoherence or problematically fall back on primitive
modality when trying to explicate the logical constructions or articulate the non-mathematical
abstractions that supposedly provide the ‘truthmakers’ for our modal language
and logic. Despite this, I contend that it would be irrational to be confident about Lewis’ conclusion – and
not just because of the “incredulous stare”. The one major reason I have time
to discuss is that contemporary physics seems to reduce the ‘urgency’ of Lewis’
motivations and, as Alastair Wilson shows, makes plausible a set of views that
are neither ersatzist nor fall under Lewisian modal realism. A contemporary sceptic
of metaphysically motivated modal extravagance is seemingly in a much better
position to ‘account for’ possible worlds semantics if just one of the contemporary
physics couplet of (eternal) inflation theory and the Everettian interpretation
of quantum mechanics is true.
In his 1986 book On the
Plurality of Worlds, David Lewis argues that there concretely exists a
world for all possible “ways a world could be” [2], where these worlds are
understood as fully spatio-temporally isolated ‘block-universe’ wholes, and
where actuality is indexical. He argues that this is a plausible view because,
however terrifying and insane it may appear, there seems little question that
it makes sense (it is “serviceable”), and it gives us a non-spooky, allegedly
non-circular way of ‘grounding’ the phenomenal philosophical success of modal
language and logic in “philosophy of logic, of mind, of language, and of
science” (with a particular importance for Lewis’ counterfactual analysis of
causation) [3]. Lewis claims that his argument is fundamentally abductive: following the principles of
his mentor Quine, he maintains that the appeal to modal realism represents inference to the best explanation,
since, despite its lack of ontological parsimony, the other explanations for
the indispensability seem mysterious, circular or incoherent.
As the question requests, I’ll skip Lewis’ specific positive
defences of modal realism and move onto his critiques of all forms of
‘ersatzism’: i.e. the attempts to avoid modal realism while defending the
existence of truthmakers for modal language and logic by trying either give a
formal account of a possible world as some kind of mathematical object (which
he calls the ‘linguistic version of ersatzism’) or by insisting that not
essentially abstract things (people, objects) can exist abstractly (which he
calls the ‘pictorial version of ersatzism’[1]).
In chapter 3 of the book, “Paradise on the Cheap?”, Lewis
attempts to rebut all the various strategies for reducing modal language and
logic without sliding down the rabbit hole of modal realism. While he (of
course) admits that ersatzism is “attractive” and doesn’t for a minute claim
that he has proof of the impossibility of all ersatzist strategies, his thesis
is that “each version, in its own way, is in serious trouble” [140].
The first general ‘version’ of ersatzism Lewis attempts to
rebut is what he calls “linguistic ersatzism”. Before mounting any direct
attack, Lewis spends many pages exploring the best possible ways of
implementing this strategy. As Lewis immediately notes, possible worlds can’t
be identified with just colossal natural-language ‘books’ because the
worldmaking language must be “disambiguated and precise” [142]. One proposed
solution then is to make the ersatz worlds “set-theoretic constructions out of
parts of the concrete world” [143]. This general form of solution, Lewis notes,
would have the advantage that mathematical Platonists are already committed to
the ‘existence’ of sets. Carnap was an early pioneer of such an approach, but
Lewis observes that his original version – identifying ersatz worlds with
“maximal consistent sets of sentences of a worldmaking language which is a
fragment of the given system” [142] – didn’t specify a solution to the ‘naming’
problem: that “everything must have a name” (because all states of affairs must
be described) and “nothing may have two names” (to avoid contradiction in
predication) [143]. Fortunately, however, Carnap later developed a solution to
this, according to what Lewis calls the “Lagadonian method”: create some kind
of set, a “state description”, where every element of a domain ‘names itself’.
In “A Basic System of Inductive Logic”, for example, Carnap formalised “ersatz
worlds as models, in the standard model-theoretic sense”, where each model
corresponded “one-to-one with state descriptions in the Lagadonian language”
[145]. A similar system with universals added was, Lewis notes, later developed
by Brian Skyrm in his 1981 paper “Tractarian Nominalism” [145].
After continuing his discussion beyond Carnap for several
more pages, Lewis begins his attack. His first family of objections concern the
problem of primitive modality (which modal realism allegedly doesn’t face). The
first two objections of this kind he raises are as follows: the set-theoretic
approach is taking modality as a primitive, first via the requirements of
consistency and maximality (fundamentally modal concepts), and second via
“implicit representation” (since a set of sentences has to imply so-and-so “iff
those sentences could not all be true
together unless it were also true that so-and-so” – clearly modal [151]). Lewis
also raises an awkward ‘trade-off’ dilemma for linguistic ersatzism: whilst the
‘sparseness’ of Carnap’s state-description ‘language’ obviates any worries
about inconsistency, it does this at the cost of colliding with the implicit
representation problem in a big way (richer languages could do more explicit
representation). Then comes the second, more specific couplet of primitive
modality issues. The first specific primitive modality problem is how to avoid,
as it were, ‘physical inconsistencies’ in a set-theoretic construction which is
only designed to avoid logical inconsistencies: for example, how to avoid
predicating of a “point particle” both “positive and negative charge” [155].
Lewis proposes that this requires an
axiom – in this case, “the axiom of unique charge” [155]. And, as Lewis
notes, even if one is not sure that such an axiom wouldn’t misrepresent the
facts of modality (maybe some worlds can have particles with positive and
negative charge), one would still have to resort to primitive modality to
account for the possibility that it does: “if
it is possible for one particle to be both positively and negatively
charged, then let there be an axiom
of unique charge” [155]. The second specific problem “has to do with the
relation of local to global descriptions” [155]. As he puts it, “We have a
problem about consistency if the worldmaking language speaks both of local and
global matters […] Or we have a problem about implicit representation if the
worldmaking language speaks only of local matters” [155]. But no-one could
possibly provide the possibly infinitary “connecting axioms” required to do the
repair.[2]
Lewis’ second cluster of objections to linguistic ersatzism
concern “the descriptive power of the worldmaking language” [157]. First, there
is a problem about indiscernibles. It may be fine that linguistic ersatzism
cannot generate two identical worlds, but Lewis claims there is something very
troubling about the notion that, if there are indiscernible individuals in
different possible worlds, then linguistic ersatzism only has one description
for all of them. I think Lewis probably overstates this objection, since a) it
may be that only strictly indiscernible worlds allow strictly indiscernible macroscopic individuals, and b) even if that
is false, I just don’t see why the consequence is all that “troubling”. The second “problem of descriptive power” is,
however, much deeper. It is a more profound ‘naming’ issue than the one solved
by the ‘Lagadonian’ method: it is the problem that “if we only have words for
natural properties that are instantiated within our actual world, then we are
not in a position to describe completely in which there are extra natural
properties, alien to actuality” [159]. Lewis recognises that “an ersatzer will
not agree that there are any properties instantiated off in other worlds, since
he does not believe there are any other worlds” [160]. But he points out that
if the ersatzer wants to be able to say “there might have been other natural
properties” (which he surely does, lest he slide towards robust scepticism
about modal language), then he is immediately ensnared [160].
Lewis considers pictorial ersatzism much weaker than linguistic
ersatzism, even despite all his objections to linguistic ersatzism. As I
suggested in the first footnote, whilst philosophers like Timothy Williamson
and Derek Parfit don’t conceive of their extravagant-abstractionist ontological
views as in any sense ‘pictorial’, I think that Lewis’ objections to pictorial
ersatzism apply to them.
Lewis sees the one big advantage of pictorial ersatzism over
linguistic ersatzism as its ability to ‘deal with’ “possibilities that involve
alien natural properties”, which it can do because abstract pictures could in
theory represent “diverse alien natural properties beyond the reach of our
thought and language”, neither omitting nor conflating these possibilities
[167]. However, he has three general objections to the approach. The first two are primitive-modality issues
once again. Lewis thinks the pictorialist faces no consistency problem (Escher
drawings are not “truly pictorial” [168]), but there is an implicit
representation problem. Since you can’t have an isomorphism to an unactualised
world, what makes an abstract pictorial talking donkey in a pictorial world
isomorphic to a talking donkey “is just that it could have been isomorphic to a talking donkey that was part of the
concrete world, and it would have
been if the world had been different, and it couldn’t have
been isomorphic to any part of the concrete world that wasn’t a talking donkey”
[168]. As Lewis notes, this is “no advance toward an analysis of the modal
statement that we began with” [168].
Lewis’ third, “and
most serious”, objection is that pictorial ersatzism represents an ontology
that is, at least to some sensibilities, even weirder than modal realism and
very possibly incoherent. Lewis is raising the same fundamental intelligibility
problem that I mentioned in relation to Parfit and Williamson. Although Lewis
initially uses the word “abstract” to describe the worldmaking pictures, he
points out that they couldn’t really be worldmaking of concrete worlds if they
were perfectly abstract. They have to fall into some mysterious middle-ground
category – and this thought seems to draw one to the more cynical thought that pictorialism
is just modal realism for people who
don’t want to admit it. His specific objection along these lines is
significantly more detailed than that, but I don’t have the words to review it
properly. I will also ignore Lewis’ objections to the final ersatzist
‘strategy’, which he calls “magical ersatzism” (Lewis thinks that in fact most
philosophers are secretly “modal magicians”, in the sense that they don’t give
a proper truthmaker ‘story’).[3]
Overall, I think
Lewis’ arguments against ersatzism are extremely powerful. Nevertheless, I don’t think it would be
rational to be confident about modal realism.[4] I don’t just mean that I don’t think Lewis’
arguments are decisive, because (of course) most metaphysical stances aren’t provable
theorems – and it would never be rational (so it seems to me) to be highly confident about any properly metaphysical
(non-testable) theory with unambiguously coherent competitors).
I say this instead because I think physics has opened up a form of strongly
naturalistic modal reductionism which is more
plausible.
In particular, I
think that one should have a higher credence that at least that one of the following possibilities is
true:
1.)
As Alastair Wilson argues, the ‘Many Worlds
Interpretation’ of quantum mechanics (EQM) is correct and “modal necessitarianism”
is true (there is an infinity of quantum-branch worlds, all of which obey the
same fundamental laws). (Incidentally, modal necessitarianism implies the
negation of “eternal inflation theory”.)
2.)
“Eternal inflation theory” is true, EQM is
false, and there therefore exist an infinity of worlds described perhaps by
some formulation of String Theory. The main pioneer of inflation theory in
cosmology, the esteemed MIT physicist Alan Guth, claims that “Most models of
inflation do lead to a multiverse” [https://www.space.com/25100-multiverse-cosmic-inflation-gravitational-waves.html].
This clearly strongly counts in favour of the possibility that eternal
inflation is true, considering that cosmologists are highly confident about
inflation, on account of its ability to account for key features of the observable
universe that the original Big Bang Theory could not (the “flatness problem”,
the “horizon problem” and the “Magnetic-monopole problem”).
3.)
Both EQM and eternal inflation theory are true.
Alistair Wilson has argued [e.g. in
“Schaffer on Laws of Nature, 2013] that his “modal necessitarian” view,
assuming “quantum indeterminism”, could basically effect the same reduction of
standard cause-isolating counterfactuals as Lewis’ determinism-assuming “small
miracles” reductions, and without having to invoke “miracles” per se. The other
two possibilities seem possibly to preserve reductions of even more of our
modal language. All of them would sever the gap between “conceivability” and
metaphysical possibility to some degree, but I think Wilson is correct that
this is no knock-down.
In summary, I believe that Lewis
successfully seriously impugns all forms of modal ‘ersatzism’. At the same
time, I believe it would be irrational to be confident about the truth of modal
realism (or at least I think I’m not
being irrational in having credence
< 0.5). [5]
Reference List
Lewis, David (1986). On the Plurality of Worlds, Blackwell.
Parfit, Derek (2011). On What Matters, Oxford University Press.
Williamson, Timothy (2012). Modal Logic as Metaphysics, Oxford
University Press.
Wilson, Alastair (2013). "Schaffer on
Laws of Nature", Philosophical
Studies 164(3):653-657,
[1] He
never describes the ‘pictorial’ version in the terms I just used, but the
‘pictorial’ version of ersatzism doesn’t really exist anyway: he clearly
smuggles under this label really any kind of non-mathematical modal
abstractionism – recent examples are Parfit’s “possibilism” [2011] or Timothy
Williamson’s “Necessitarianism” [2012], views which are committed to the
possibly incoherent proposition that non-essentially abstract things
can exist in the ‘wide sense’ abstractly (i.e. “subsist”). Such views simultaneously
fall under what he calls ‘magical ersatzism’.
[2] It
should be pointed out that both this and the previous objection are assuming something
about the facts of modality and metaphysics which someone like Alistair Wilson
would dispute (as we’ll see), but that doesn’t lessen their force against
ersatzers (who want, like Lewis, conceivability to be a strong guide to
metaphysical possibility).
[3] I
myself have written as if pictorial ersatzers is another word for magical
ersatzers.
[4] I
think it may have been rational to be confident about modal realism when Lewis
was writing.
[5] I
also believe the epistemic possibility (in the Bayesian sense) that there is
one universe and extreme modal fictionalism is true should slightly lower one’s
confidence in modal realism, ersatzism and the more Wilsonian view.
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