Abstract
In “Ramseyan Humility,” David Lewis argues that we cannot know what the fundamental properties in our world are. His arguments invoke the possibility of permutations and replacements of fundamental properties. Most responses focus on Lewis’s view on the relationship between properties and roles, and on the assumptions about knowledge that he makes. I argue that no matter how the debates about knowledge and about the metaphysics of properties turn out, Lewis’s arguments are unconvincing since they rely on a highly implausible assumption about the expressive power of our language.
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Notes
Alternatively, the content of the theory is given by a variant of the Ramsey sentence that replaces existential quantifiers with uniqueness quantifiers (\({\exists}!\)). I will disregard subtleties that arise if a theory has more than one realization in the same world.
For example, David Armstrong’s combinatorial theory of possibility (Armstrong 1989) would license an argument from permutation, but not from replacement.
For critical examination of that thesis, see Schaffer (2007).
It is faithful, but not maximally fine-grained. There are sub-arguments for some of the premises that I skip over here. This will become relevant in 3.3 below.
An item of terminological book-keeping: in my usage, a false proposition A is not knowable, even if there is a possible world where it is not just true, but known by subjects in that world.
Unfortunately, the term “quidditism” has different uses; and in “Ramseyan Humility,” Lewis himself uses it in a non-standard way. The claim he calls “quidditism” is already a trivial consequence of the claim that I call “combinatorialism.”
Here as elsewhere in the paper, I speak of properties rather than properties and relations, for the sake of simplicity. The definition of a fundamental isomorphism given here can straightforwardly be extended to relations.
If we are using the framework of centered possible worlds, then a fundamental isomorphism is also required to map the center of w to the center of w′.
I here ignore the epistemic possibility, mentioned by Lewis in note 3 (p. 218), that there is no minimal supervenience base.
For Lewis, a fundamental property is an idler at a world if it does “not play an active part in the workings of nature” (p. 215) of that world.
I am here ignoring irrelevant complications due to idlers.
“What we need to know about the Ramsey sentence is that it logically implies exactly the O-language sentences that are ... logically implied by the postulate of T” (Lewis 2009, p. 207). The postulate of T is what I am just calling ‘T’. Since it is complete, any sentence is either logically entailed or logically incompatible with it.
The same comments apply, mutatis mutandis, to Lewis’s statement of the permutation argument: “Suppose we have the actual realization of T. Maybe some members of the n-tuple that realizes T are not fundamental properties, or maybe some belong to single-membered categories. Hold those ones fixed. Permute the rest within their categories to obtain a new n-tuple. It too would realize T.” (p. 208)
‘P(x)’ here abbreviates ‘x instantiates P’. I take O to be a first-order language with singular terms for both individuals and properties, and with instantiation predicates (an n + 1-place predicate for n-adic relations) as part of its logical vocabulary.
The assumption that ‘in pain’ or a synonym is in O is entirely compatible with the anonymity constraint, discussed in 3.4. The term does not “name” F; it applies to properties other than F as well. Hence the assumption carries no commitment to the so-called “identification thesis” that Lewis rejects in the last section of Lewis (2009).
Chalmers (2006, pp. 79–80) tentatively concludes that worlds with such edenic color properties are possible.
It could be objected that on Lewis’s theory of possible worlds, it is arguably necessary that there is spacetime structure, such that there could not be a world such as w. However, Lewis is explicit that his replacement argument is not supposed to be hostage to his views about possible worlds. Indeed, the argument would be of much more limited interest if it were presupposing these views.
In fact, Lewis’s anonymity constraint, discussed in 3.4, does not look all that plausible for fundamental spatial, temporal, or spatiotemporal relations. I will not develop that objection here, though.
This would be entirely compatible with the supervenience of causation on fundamental properties and relations, a point that will be further explained in 3.4. In particular, it is also compatible with Lewis’s accounts of causation in terms of counterfactuals and indirectly in terms of laws of nature. Fundamentally isomorphic worlds may not have isomorphic laws, for the comparison of candidate systems in terms of strength may be sensitive to what the fundamental properties are. Likewise, similarity orderings among worlds, which determine which counterfactuals are true, may be sensitive to what the fundamental properties are.
To echo Zimmerman (1999, p. 213): “I am fortunate to have Lewis for challenger \(\ldots\): Lewis \(\ldots\) is willing to take the fact that something seems plainly possible as weighty evidence for its actually being possible—not just ‘epistemically possible’, i.e. true for all we know right now.”
Of course, it is a vexed question under what conditions one counts as having an attitude to a proposition. Clearly, not every relation to a proposition qualifies, but only fairly natural relations of the right kind. I will not attempt an analysis of what it is to have an attitude towards a proposition. While hard to analyse, the notion is understood reasonably well. One can replace ‘entertainable’ by ‘expressible’ if preferred. It is an interesting question whether some propositions are entertainable but not expressible, but we can abstract from it for the purpose of the argument.
Since every proposition entails itself, (1c) is weaker than the claim that every knowable proposition is entertainable.
“The language of T contains T-terms: theoretical terms implicitly defined by T. And there is all the rest of our language, call it O-language.” (p. 205)
This definition takes ‘being physical’ as a term for a second-order property that is primitive, i.e. unanalysed. Of course, Lewis does have things to say about it.
Maybe not even all of those worlds are in the inner sphere; see Lewis (1994, Sect. 1). That issue does not bear on the present discussion.
Suppose a world w has a non-physical fundamental property F. By a combinatorial principle, there is a world that differs from w in the distribution of F but not in the distribution of physical fundamental properties. Hence w is not materialistic.
Lewis himself uses a formulation of that sort in Lewis (1999, Reduction of Mind, p. 292): “[A]ll fundamental properties and relations that actually occur are physical. This is the thesis of materialism.”
Since combinatorialism needs to be appealed to here, could the argument be construed as a reductio of combinatorialism rather than Structuralism? In principle, this is a theoretical option. But it is a very unattractive one, because the reductio requires something far weaker than a general combinatorial principle for fundamental properties. What is needed is only that physical and non-physical fundamental properties can be instantiated in worlds with the same fundamental structure, which is a weak combinatorial principle indeed.
An objection: This argument only goes through if it is assumed that the second-order-property of being physical is essential to every property that has it, i.e. that no property can be physical in one world and non-physical in another. But this is a fair assumption to make, since Lewis’s definition of materialism is inadequate without it.
For suppose α is the class of actual fundamental properties, and that all members of α are physical in @. Then intuitively, materialism should be true. But suppose there is a world w where some member G of α is non-physical, and where no fundamental property not in α is instantiated. By combinatorialism, there are many worlds that differ from w only in the distribution of G, but not otherwise (in particular, not in whether the other fundamental properties are physical or not). Surely, there is at least one world w′ where G is likewise non-physical. Then w and w′ are worlds without alien properties that differ without differing physically, and hence Lewis’s definition misclassifies @ as non-materialistic.
Whether Lewis’s doctrine of Humean supervenience is susceptible is unclear. Perhaps a case can be made that properties instantiated by point-sized things, or by mereological atoms, form their own category.
The last section of “Ramseyan Humility,” entitled “Humility about Qualia,” is a partial defence of the anonymity constraint.
In my metalanguage, I use ‘C’ and ‘N’ as functional expressions applying to properties names; ‘C(F,G)’ denotes the conjunction of F and G, and ‘NF’ the negation of F. I use these symbols instead of more familiar negation and conjunction symbols to distinguish these functors from the sentential connectives which are present in O.
Or better, it is not denoted by an atomic non-logical O-term. The identity relation is trivially definable from the class of fundamental properties and relations using the identity predicate.
I am assuming here that the the non-logical terms of O, if there are any, do denote. Likewise, I am assuming in this paper that O does not contain names of individuals. Without that assumption, Lewis argument is even more vulnerable.
Lewis restricts the quantification to worlds in the “inner sphere of possibility,” where there are no alien fundamental properties. But even without this restriction, Humean supervenience does not imply structuralism.
It goes without saying that Structuralism is not implied by any combinatorial principles about fundamental properties. That O has predicates such as P 1 to P 4 is entirely compatible with F, G, and H satisfying combinatorial principles.
However, most of the answers he surveys are not answers to the expressive skeptic’s Replacement Argument, since they rely on the entertainability of the propositions whose knowability is in question.
In Lewis (1986a, pp. 154–155), Lewis suggests that we should be be agnostic with respect to these two options, and argued that it is a problem for the linguistic ersatzer that she cannot afford such agnosticim.
“Primary intension” is David Chalmers’ term, whose Chalmers (1996, pp. 52–71) is a good introduction to two-dimensionalism.
This follows immediately from the semantic clause: ‘Actually S’ is true at \(\langle v,w \rangle\) iff S is true at \(\langle v,v \rangle.\)
On Chalmers’ account (Chalmers 2004, p. 191), there are semantically neutral terms, whose primary and secondary intensions coincide (ignoring the fact that primary intensions contain centered rather than uncentered worlds). They are used in the canonical description of scenarios (roughly, ersatz possible worlds).
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Acknowledgements
Many thanks to Paul Audi, Karen Bennett, Jeremy Butterfield, David Chalmers, Adam Elga, John Hawthorne, Marco Lopez, Paul Mainwood, Jim Pryor, Denis Robinson, Gideon Rosen, Daniel Rothschild, Jonathan Schaffer, Wolfgang Schwarz, and Brett Sherman; to audiences in Princeton, Oxford, and at the Australian National University; and to several anonymous referees. The research for this paper has been partially funded by the Swiss National Science Foundation project ‘Properties and Relations’ (100011-113688).
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Leuenberger, S. Humility and constraints on O-language. Philos Stud 149, 327–354 (2010). https://doi.org/10.1007/s11098-009-9352-3
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DOI: https://doi.org/10.1007/s11098-009-9352-3