In On the Plurality of Worlds David Lewis resists an objection to his view by appealing to functionalism. The problem is roughly that for any number of worlds you suppose are in the pluriverse, you’ll be committed to the absurd thesis that there are more worlds than there really are.
Here is the argument.
(I don’t have the book with me, but this is pretty much verbatim from Lewis. I’ll come back and put in the page numbers when I get a chance)
More Worlds Than There Are Argument
- Suppose the cardinality of the set of possible worlds is K.
- Each subset of this set is a proposition, namely the proposition which would be expressed by a sentence which was true with respect to precisely the worlds in that subset.
- There are 2K such propositions (and 2K is strictly greater than K)
- Consider some man and time. For each proposition, it is possible that he should have been thinking a thought at that time whose content would be specifiable by a sentence expressing that proposition; and that this should have been his only thought at that time.
- So there is a distinct possible situation corresponding to each such proposition.
- So there are at least 2K possible worlds – contradicting our assumptions.
(2K is supposed to be 2 to the K – superscripting isn’t showing up. Probably something with my stylesheet.)
Lewis responds by appealing to functionalism. He maintains that thoughts are individuated by functional roles. He then claims that there are not 2K functional roles. So (4) is the premise Lewis rejects.
I have a few worries about this move, and this may span a few posts. In this post I want to pick on something he says regarding the number of functional roles. Lewis says he can’t even think of a prima facie reason to think there could possibly be as many functional roles as there are propositions. I want to address that claim first.
Suppose you had good reason to think that propositions played the role of thought contents. After all, that is supposed to be one of the theoretical benefits of positing the existence of propositions.
Now suppose you are told about the existence of proposition N (you’re not told what N is). You are asked: Is it possible for some being to think that N? Given that you’re convinced that propositions play the role of being thought contents – don’t you have some prima facie reason to think that N could be thought? It seems that you do. Again, remember prima facie reasons are pretty easy to come by, and they can be defeated by other considerations.
Now suppose that you came to have very good reasons to believe that functionalism was true. Without any additional information, don’t you now have some prima facie reason to think that there is some functional role that corresponds to N (that would make it possible for N to the be the content of a thought).
But that was about some generic proposition N. Can’t we run the same sort of reasoning if we learn there are 2K propositions, and thereby have prima facie reason to think there are 2K functional roles.
So someone in Lewis’ position who had good reason to think that functionalism was true and had good reason to think that propositions play the role of thought contents would have prima facie reason to think that there are 2K functional roles.
Indeed, it is your CSS. You have a whole host of elements getting a bunch of identical styles – specifically, font-size of 100% and vertical-align:baseline are causing the superscripts to not show properly.
Adding the style “font-size: .83em; vertical-align: super;” in a more specific place should do the trick – either in your tags or with a #id.
Thanks Thom
“But that was about some generic proposition N. Can’t we run the same sort of reasoning if we learn there are 2K propositions, and thereby have prima facie reason to think there are 2K propositions.”
I don’t think so. A prima facie reason for each is not a prima facie reason for all. Compare: I tell you 80% of Fs are G. So, for any arbitrary F, you have prima facie reason to expect it to be G. But you do not expect all Fs to be G: you know that only 80% of them are.
(btw, I assume you meant to write “…thereby have prima facie reason to think there are 2K functional roles.” The typo appears in the final paragraph too.)
Thanks Richard,
I did mean “functional roles” – that’s been fixed.
Hi Richard,
This is a good case, but it does seem to be an odd sort of limiting case. In the case you describe the thing that gives you prima facie reason that the F will be a G also constitutes evidence that not all Fs are Gs.
So I seemed to be assuming some generic principle like
(1) If C is prima facie reason to think that any given arbitrary A is B, then you have prima facie reason to think that all As are B.
Your case is a counter example to (1)
Suppose we modify (1)
(1*) If C is prima facie reason to think that any given arbitrary A is B and C is not also prima facie reason to think that not all As are B, then C is prima facie reason to think that all As are B.
Hello,
I like this post. I have a potential response on behalf of Lewis which I am not sure Lewis would accept. I am uncertain about whether Lewis would accept this response partly because I am not sure I completely understand what functionalism about thoughts amounts to. But, let me give my response anyway and see what you think.
Your objection seems to rely on some kind of identification of thoughts with propositions. But, it seems to me that Lewis could easily reject this. He might believe that thoughts are intrinsic mental states that express propositions. If he does reject the identification of thoughts with mental states, then he might be able to reject the inference to (5) by associating a single possible (world bound) individual’s intrinsic mental state at a time with several different possibilities some of which involve the individual thinking different propositions than others.
To illustrate, consider a single possible (world bound) individual, Frank, who has a particular intrinsic mental state S at a particular time in his world. Now consider two propositions P1 and P2. Let’s suppose for simplicity that P1 is the proposition that water is wet and P2 is the proposition that twater is wet. Now consider two actual individuals, Andrew and his twin earth double Tandrew. Neither of these guys is thinking about water or twater at all. But, it might be that Frank is a counterpart of Andrew and that fact makes it true that Andrew could be thinking that water is wet and he is also a counterpart of Tandrew and that fact makes it true that Tandrew could be thinking that water is wet. Now what we have here is a single possible individual, Frank, and a single intrinsic mental state, but two possible thinkings of two different propositions: thinking that P1 and thinking that P2. If this is all correct, then perhaps there are 2^k propositions but less than 2^k possible worlds. I’m not sure if this response would ultimately work out, but I think it might be worth thinking about.
One interesting thing about this response is that it requires some kind of counterpart theory (or perhaps a kind of contingent identity). This would be a striking commitment of the modal realist especially since some modal realists seem to be inclined to reject counterpart theory (and contingent identity).
Joshua
Hey Joshua,
This is interesting. So the idea I take it is we have an example where Frank is the individual that makes it true that Andy could think water is wet, but also make it true that Twandy could think that Twater is Wet. But presumably since Frank is an individual thinking a single thought, there must be one functional role that is sufficient to ground the possibility for each of two different propositions being thought. (So, we can get by with less functional roles than there are propositions)
Yes, that is what I was thinking. I wonder if it was what Lewis was thinking as well.
I want to take back the last bit of my comment. I do not think this kind of response requires counterpart theory or any kind of contingent identity.