Monday, September 22, 2008

Soames and King are friends

After reading the Soames article I noticed a few parallels between it and what was going on in King chapter 4. I'll reconstruct a simple version of Soames' argument, note some considerations from King, and then see if a moral can be drawn.
So, here's the digression from Soames as to what an unstructured proposition would be like. First, we have to build a language. Suppose we have a domain D which is a set populated with individuals {d1,d2,...}. Next, we have a stock of predicates of varying addicity. We would have a stock of constants which would function like proper names, directly referring to a single member of the domain. We would have a stock of variables, which would also refer to a single member of the domain. Logical connectives and quantifiers would work as expected.
An interpretation would assign members of the domain to the constants, and there would be another assignment function assigning members of the domain to the variables.
At first glance, the unstructured propositions advocate "UPA" would equate the proposition expressed by a sentence in the language with the set of complete and consistent interpretations which make that sentence true. This won't work because all necessary propositions would be equated, and all necessarily false propositions would be equated. So the next move is to drop the completeness requirement. There may be some n-place predicate P and some set of n individuals {n1,n2,...} such that the interpretation doesn't make Pn1n2... true, but it doesn't make Pn1n1... false either. This still has the consequence of making all necessarily false propositions be the same. The next step is to drop the consistency requirement. So, an interpretation may assign Pn1n2... true, AND it may assign Pn1n2... false. So why isn't this a fine-grained enough notion to act as propositional content? Here's where the argument comes in. Consider Soames's (7)(p.205-206)
(^ signs will act as corner quotes here)
(7a) The semantic content of a conjunction (relative to a context) is the intersection of the semantic content of the conjuncts (relative to a context)
(7b) The semantic content of a disjunction (relative to a context) is the union of the semantic contents of the disjuncts (relative to a context).
(7c) The semantic content of an existential generalization ^for some x: Fx^ is the set of circumstances E such that for some object o in E, o “is f” in, or relative to, E.
I won't need (7d) and (7e) here. It's worth noting that the UPA needs some clause like (7) to account for the semantic content of complex sentences. Here's a simplified version of Soames' argument:
(1)A proposition is a set of fine-grained interpretations that abide by (7a-c) (assume for reductio)
(2)Proper names directly refer
(3)belief is a relation between an individual and a proposition expressible as 'Rap' which is itself a sentence of the language
(4)Lois believes that Clark can't fly and that Superman can fly.
(5)Lois believes the set of interpretations that makes 'Clark can't fly and Superman can fly' true (1,3,4)
(6)Clark is necessarily identical to Superman
(7)The situations that make 'Clark can't fly and Superman can fly' true are just those situations in which Kelal (who is Superman/Clark) is in the extension of the predicate can fly and in the extension of the predicate can't fly (2,6,7a)
(8)Lois believes the situations in which Kelal is in the extension of the predicate can fly and in the extension of the predicate can't fly (3,5,7)
(9)Lois believes the set of interpretations in which Clark can't fly, Superman can fly, and there is something such that it can't fly and it can fly (3,8,7c,7a)
(10)Lois believes that Clark can't fly, Superman can fly, and there is something such that it cant' fly and it can fly (1,9)
Soames doesn't spend much time defending (2) and (3). Luckily, Soames has another version of the argument that doesn't include (2), and King spends a great deal of time defending (3). I already wrote a post about King's defense of (3), so I'll cheat here and leave that aside. (2) is a fairly trivial consequence of Millianism.(4) and (6) are stipulated.
(5) follows from (1), (3) and (4) because on the view we're considering, the proposition which Lois believes just is the interpretation described in (5). (3) comes in to complete the picture by saying Lois's belief is correctly described as a relation between her and a proposition. Let Lois be l, and the believes relation be B. If Blp and p=p' then Blp'. So we can legitimately move from the fact that Lois believes that Clark can's fly and Superman can fly to her bearing the believing relation to the thing that is the proposition that Superman can fly and Clark can't fly (I.e. the situations that make it true). It's worth noting that if the relational account of propositional attitude verbs wasn't correct (for instance, if it were a 3 place relation involving modes of presentation) this move wouldn't work.
The inference to (7) is justified from (2),(6) and (7a). (2) states that if a proper name is used, the semantic content is just its referent. The referent of Clark and Superman is Kelal. (6) could've been rephrased as 'Clark and Superman both refer to Kelal', or something like that. (7a) states that when you have a conjunction, the semantic content is just those interpretations that make both conjuncts true. The state that makes 'Clark can't fly' is the state involving Kelal (premise (2)) being in the extension of can't fly. Likewise, 'Superman can fly' is the state involving Kelal being in the extension of can fly. The situation that makes both of those true is the one in which Kelal is in the extension of can fly and in the extension of can't fly. It's also worth nothing that without (2) this move wouldn't work. For instance, it could be held that the semantic content of names are descriptions that only derivatively refer to their referents. If this were so, then under different interpretations each name could change its referent. This would allow for an interpretation in which 'Clark' and 'Superman' don't co-refer.
(8) follows from (3), (5) and (7). (5) states that Lois believes a particular interpretation. (7) describes that same interpretation in different terms. (3) licenses the inference that therefore Lois believes the newly described interpretation (which is really the same as the old one). (9) is justified in a similar way as (8), invoking 7a and 7c to construct a different description of the interpretation that Lois believes. Note that 'there exists something which can fly and which can't fly' is a consequence of 'Kelal can fly and Kelal can't fly'. That means the latter claim is a subset of the existential claim. Since & denotes the intersection of the two propositions, adding '& there exists something which can fly and can't fly' won't change the set of situations reffered to. (10) finaly states the conclusion that Lois believes the interpretation under this new implausible description.
It should be noted that Soames reproduces the argument with no proper names (using demonstratives instead). This means a Fregian is not immune from this argument by denying (2). A Fregian might deny that demonstratives directly refer, but it's hard to see how one would do that. The major heavy-lifting premise in here is (3).
Aside from his rather extensive treatment of (3), King has an argument similar to this one against FC. Cresswell says that FC combined with a few other principles leads to the conclusion that propositions are unstructured. Let's look at FC again:
FC: The semantic value of a whole sentence is obtained by functions which are the semantic values of parts of that sentence operating on the semantic values of other parts. (p.113)
Take a look at Soames's 7a-7e, and then take a look at FC. Eureka! 7a-7e is just a more precise version of FC. 7a-7e gives rules for determining the semantic value of a sentence, based on functions which are themselves semantic values of parts of that sentence.
King argues against FC, again using (3). He makes reference to a particular sentence:
(17)That first order logic is complete is necessarily true and believed by Cresswell.
He sets thing up:(117)
“A verb of attitude is more than the intension of the sentence if embeds”
and strikes:
“it would seem that being necessary and being true must also be predicated of a structured entity in (17). But then it would appear that natural language sentences containing that-clauses in which truth or modality is ascribed, as well as sentences containing verbs of propositional attitude, must have parts whose semantic values are structured meanings or structured propositions”
King takes the argument I think one step further than Soames, offering an explanation for its conclusion. When we speak of propositions, predicating truth or necessity to them, we're simply not talking about interpretations, or truth-supporting circumstances. The proof is that if we assume we are (by assuming either 7a-7e or FC) then the truth conditions are just wrong.
The only way I can see to escape this argument is to deny the relational analysis of propositional attitude verbs.

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