Putnam's Paradox
I was thinking about Putnam's paradox the other day. I thought of a parallel between Putnam's paradox and a problem in the vagueness literature that seems interesting. I'd like to talk about this parallell in this post, but let me warn everyone that there are two things that I don't know much about that play an important role in this post: First, I don't know much about Putnam's paradox and second, I don't know much about vagueness. So, I might be completely confused and not really understand the issues.
First, let me present Putnam's paradox and a kind of naive response. then, I'll present an objection to that response. finally, I'll introduce a vagueness problem and a naive response along with an objection to that response. I hope to give a kind of response to both objections that might seem unsatisfactory.
So, here is my attempt to remember Putnam's paradox. I might be misremembering the problem and I am very sorry if I am. Let's take a theory to be a set of sentences in a first order language. Now, these three things seem true, but cannot all be true: (1) The meaning of the terms in a theory is determined by our use of those terms. But, (2) for any consistent theory, there is an interpretation of that theory which is both consistent with our use of the terms in the theory and that makes the theory true of the actual world. And, of course, (3) not every theory is true of the actual world.
I believe that the standard reply is to reject (1) and say that something besides our use determines reference (perhaps some entities are reference magnets). However, here is a different, naive response that appeals to a hiarchy of theories. Let's take theory T and take a second theory T* that is a theory about the referents of the words in T. Perhaps T* says something about causal connections betweem various objects and terms or perhaps it says something about spatiotemporal eligability. Who knows. It doesn't really matter. What does matter is that there is a theory that says that some interpretation of T that is the intended interpretation and explains why that is the intended interpretation. This is the niave response. Hee is what I like about it. It does not metaphysically privilage any particular properties in the world. Unfortunately, I am not exactly sure which of (1)-(3) this view rejects.
Putnam has an objection to this kind of response. He points out that T* is just more theory. For any theory about T, there will be an interpretation of that theory which is both consistent with our use of the terms in the theory and that makes the theory true of the actual world. the paradox just arises again at another level. Of course, we can go up another level, but the paradox will rear its ugly head up there as well. There is no way to escape the problem.
So, that is the paradox, the naive response and the objection to that response. Now, I'd like to consider a problem concerning vagueness.
Some people like linguistic theories of vagueness. They say that vagueness is rooted in our failure to determine by our word use one particular meaning over some other meanings. What a niave linguistic theorist would like to say is that there are a bunch of vague terms T1, T2, ..., Tn and that T1 is vague because out use of it indicates that it might mean P or Q or R and T2 is vague because out use of it indicates that it might mean . . . and so on.
Unfortunatley, one can object to the niave view by pointing out that the niave linguistic theorists theory is expressed in a vague language as well. Moreover, although we might be able to give an account of the vagueness in that second langauge, we will only do so by introducing more vagueness. Just as with Putnam's paradox, there is no escape.
What I'd like to say in response to the objection to the niave linguistic view of vagueness is that there is just vagueness all the way up. sure we have a theory T that is vague and a theory about T that is also vague and a thoery about that that is also vague. But, that is just the nature of vagueness. T is vague, our theory about T is vague, our theory about our theory about T is vague and so on.
I'd like to say something similar about Putnam's paradox. Lets say a theory that is subject to radical interpretation is Putnamable. Now, a theory T is putnamable. And there is a theory about T that indicates why one interpretation is favored over another. But that theory is Putnamable as well. Moreover, there is a theory about the theory about T and this third theory is Putnamable and so on.
First, let me present Putnam's paradox and a kind of naive response. then, I'll present an objection to that response. finally, I'll introduce a vagueness problem and a naive response along with an objection to that response. I hope to give a kind of response to both objections that might seem unsatisfactory.
So, here is my attempt to remember Putnam's paradox. I might be misremembering the problem and I am very sorry if I am. Let's take a theory to be a set of sentences in a first order language. Now, these three things seem true, but cannot all be true: (1) The meaning of the terms in a theory is determined by our use of those terms. But, (2) for any consistent theory, there is an interpretation of that theory which is both consistent with our use of the terms in the theory and that makes the theory true of the actual world. And, of course, (3) not every theory is true of the actual world.
I believe that the standard reply is to reject (1) and say that something besides our use determines reference (perhaps some entities are reference magnets). However, here is a different, naive response that appeals to a hiarchy of theories. Let's take theory T and take a second theory T* that is a theory about the referents of the words in T. Perhaps T* says something about causal connections betweem various objects and terms or perhaps it says something about spatiotemporal eligability. Who knows. It doesn't really matter. What does matter is that there is a theory that says that some interpretation of T that is the intended interpretation and explains why that is the intended interpretation. This is the niave response. Hee is what I like about it. It does not metaphysically privilage any particular properties in the world. Unfortunately, I am not exactly sure which of (1)-(3) this view rejects.
Putnam has an objection to this kind of response. He points out that T* is just more theory. For any theory about T, there will be an interpretation of that theory which is both consistent with our use of the terms in the theory and that makes the theory true of the actual world. the paradox just arises again at another level. Of course, we can go up another level, but the paradox will rear its ugly head up there as well. There is no way to escape the problem.
So, that is the paradox, the naive response and the objection to that response. Now, I'd like to consider a problem concerning vagueness.
Some people like linguistic theories of vagueness. They say that vagueness is rooted in our failure to determine by our word use one particular meaning over some other meanings. What a niave linguistic theorist would like to say is that there are a bunch of vague terms T1, T2, ..., Tn and that T1 is vague because out use of it indicates that it might mean P or Q or R and T2 is vague because out use of it indicates that it might mean . . . and so on.
Unfortunatley, one can object to the niave view by pointing out that the niave linguistic theorists theory is expressed in a vague language as well. Moreover, although we might be able to give an account of the vagueness in that second langauge, we will only do so by introducing more vagueness. Just as with Putnam's paradox, there is no escape.
What I'd like to say in response to the objection to the niave linguistic view of vagueness is that there is just vagueness all the way up. sure we have a theory T that is vague and a theory about T that is also vague and a thoery about that that is also vague. But, that is just the nature of vagueness. T is vague, our theory about T is vague, our theory about our theory about T is vague and so on.
I'd like to say something similar about Putnam's paradox. Lets say a theory that is subject to radical interpretation is Putnamable. Now, a theory T is putnamable. And there is a theory about T that indicates why one interpretation is favored over another. But that theory is Putnamable as well. Moreover, there is a theory about the theory about T and this third theory is Putnamable and so on.
posted by Joshua at 7:28 AM
3 Comments:
Joshua,
I'm a bit confused. Suppose one denies (1) and appeals to naturalness, or magnetism, or whatever, as features that, in addition to use, determine meaning. The same goes for theories about theories, and so on.
You say Putnam claims this is "just more theory" but I'm having a hard time seeing what this objection is supposed to be. Could you say more on his behalf.
I'm sorry, what I said is a bit confusing. I am not considering the standard reply when I talk about a hierarchy of theories. I do not know that Putnam's objection involvign more theories works as a response to the standard view. But, it definitely spells trouble for the naive response that I want to consider. After all, the naive response simply is that we can have a meta-theory about the referents of words in an object theory. But, insofar as Putnam's paradox applies to the object theory, it will also apply to the meta-theory.
I see. If we restrict T*, the theory about how the expressions in T achieve their referents, I agree. What I meant to suggest is that we need not restrict T* in such a way. We could let T* be a theory about the ways in which expressions in T and T* (or any language) achieve their referents. But this is more sophisticated than the Naive Theory. Perhaps though it is a move a defender of the Naive theory should make in response to Putnam's "that's just more theory" charge.
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