Dear David,

I am sorry that the argument didn't get anything like a full discussion, or even a full hearing yesterday.  I believe that I should have controlled the discussion better, and channeled it into more fruitful directions.  I think that understanding The Second Reductio depends on understanding where it came from more than I realized.  It derives from an initial claim I made, accepted by Peacocke (and I think clearly correct), that a Method I language (with obliqueness and systematic contextual ambiguity) cannot give a truth theory for itself or for English because substitution is so restricted.  The same point would apply to a Carnapian language.  The claim of the Reductio argument is that for any Method II meta-language into which embedded sentences (whether of Method I, English, or Method II) of an object language are given a reasonably close translation, the reductio will apply to the Method II language. 

I am aware that it is open to one to doubt that "reasonably close" translation is needed in order to give a semantical theory of an object language.  (The semantical theory is not ultimately what is important, and the relation between translation and such a theory is itself complicated, of course.) Let's table all that.  Understanding the argument first might help put these other issues in better perspective.

I think that too much attention was diverted to issues that aren't under control and not enough time was spent on the things that are under control.  The argument applies to a Method II language that is the closest translation from either English or a Method I language that is possible. 

I believe that a Method I language is subject to direct application of an analogous argument (without going through a Method II language).  But I will have to write it out to be sure.  So I bracket that issue too.

I believe that neither a Method I language nor a Carnapian language should have been under discussion until the argument that I in fact gave as applied to a Method II language was more fully discussed.  This was partly my fault.  But I think that if my paper had been read, some of the issues that came up would have been in a better perspective.  So here goes on an attempt to explain it better.  I hope you'll take the time to read this.

I assumed, and Peacocke assumed, that a Carnapian language is inadequate as an account of English because of its treatment of that-clauses as not singular terms.  I also think its treatment of representational contents (or modes of presentation or perspectives) for belief as intensions is inadequate--intensions aren't fine-grained enough. I think that these problems are decisive.  And prima facie the first of the problems is very relevant to the issues at hand.  If one rectifies these problems, I think that the language will have to choose between the hierarchy and giving up principles that have considerable attractiveness especially for a theory of the specification of thoughts.  But I can leave that as a challenge.  As things stand, I think that a revision of a Carnapian language that avoids the crippling problems the actual Carnapian view has is too indefinite an idea for it to be clear how to evaluate it, until it is developed much more fully.  And besides, the issue for me is what principles emerge as distinct and possibly fundamental from the argument I actually give.  (I continue to believe that it is more perspicuous to fix on the three principles I use than the two Tony cited Linsky as using; but that is perhaps a matter of taste and explanatory focus.  I believe that my three principles are clearly present in computational psychology, and I do not think it evident that one of Linsky's principles is.)  

It seems to me that in view of the fact that denotation (Bedeutung) is for Frege a technical notion that really is best understood as something like: semantical value that is relevant to determining truth value (after the simplest cases, it is relatively free of the idea of naming), it is not clear that Carnap's idea of evaluating sentences for truth value sometimes in terms of intension, sometimes in terms of extension, is really fundamentally different from a Fregean Method I language (except that the latter avoids the mistake of relying on intensions rather than more fine-grained senses).  I respect your instinct or view that something interesting and different can emerge from reviving Carnap without the obvious failures.  But we should be allowed to see the theory, before rejecting (in the hopes of a better theory along those lines), what seems to me prima facie a very attractive approach, especially given that none of the usual grounds for rejecting a hierarchical account of embedded contexts seem to count against it (unlearnability, ontological extravagance, problems with eternal context-free Fregean senses, the existential generalization issue you raised earlier, etc.).  The view that higher senses are perspectives on perspectives (or ways of thinking about ways of thinking) grounded in an understanding of the lowest level of customary sense accords with the intuitive understanding of what is being attributed in embedded contexts.  This is something I discussed in the paper, but skipped in the hand-out.

Now let me go through the argument of the hand-out (The Second Reductio), revised only to show that certain issues that were discussed are not basic.

The initial step of the argument 

a)  <<Opus 132>> = <Opus 132>  

is motivated by in effect asking one's opponent to choose the expression in the truth-theoretic Method II language that translates or most closely translates the obliquely occurring expressions in the Method I language, or most closely translates English obliquely occurring expressions.  

One of the possible "ways out" that I explicitly allow for--but disapprove of--is the claim that English doesn't translate into a Method II language, so no truth theoretic semantics that relies on translation can be given for English.  One could hold that one can give a semantics for English or Method I, but no translational semantics (i.e. no truth theory that respects Tarski's schema where the right side translates the object-language sentence mentioned on the left side).  That's an issue that I discuss both in the 1979 paper and in the Postscript, but which I skipped in the workshop.  So let's table it here.  I don't think denial of translation is plausible.  But the the reductio proof doesn't purport to defeat the denial directly.

There is no question that "<Opus 132>" is the term in Peacocke's truth-theoretic, Method II, meta-language that is supposed to translate the obliquely occurring expression in English.  He's quite explicit about that.  He is purportedly answering the challenge of my 1979 paper which was put in these terms.  And I don't know of a better choice.  It is a canonical name that "gives" the sense, not simply describes it.  One must understand the sense denoted if one is to understand this name of the customary sense.  In these respects, the canonical name "<Opus 132>" matches the English obliquely occurring expression.  

Given that that name is the closest translator in the Method II language, and prima facie a good translator, we can ask what the sense of "<Opus 132>"  is.  Peacocke doesn't ask this question.  Peacocke is explicit, however, that the sense of the obliquely occurring expression in English is identical with its oblique reference, and that no need for a further sense is necessary.  To stay as close to the way that the term that it translates is supposed to work, we can say that the sense of "<Opus 132>" should be nothing other than its customary sense.  I don't see how to stay closer to Peacocke's intentions.

I think that there may have been some confusion in the workshop at this point.  It doesn't matter at all to the argument I go on to give how this "indirect" sense is denoted in the argument.  We can use a definite description, or any name, to denote it.  The double pointed bracket name is legitimate, but any other way of denoting the customary sense is ok, as long as it is clear that this is the sense of the name "<Opus 132>", which has been agreed to be the closest translation (in fact, for Peacocke, explicitly the correct translation of obliquely occurring English expressions into the meta-language).  Let us use a definite description for denoting the sense of "<Opus 132>", just to show that iteration of pointy brackets isn't relied upon.  Let us also use a definite description for all other ways of denoting senses, other than the way that is supposed to translate the obliquely occurring expressions into a Method II language.  

So we can equally use a') instead of a):

a') The sense of "<Opus 132>" = <Opus 132>.

This says that the sense of the term that translates singley obliquely occurring expressions is identical with the (customary) sense denoted by such expressions.  What more could be asked for matching in "<Opus 132>" the semantical behavior of the obliquely occurring expressions in the Method II truth-theoretic meta-language?

b)  The sense of "<Opus 132> = <Opus 132>"  =  the sense of "<Opus 132>" composed appropriately with the sense of "=" composed appropriately with the sense of "<Opus 132>".

b) depends only on the principle that one can decompose the sense of a whole sentence (the trivial identity sentence) into the senses of its parts.  This seems to me a deeply plausible principle for thought.  It is accepted in all cognitive computational theories of psychology that I know of.

c)  The sense of "<Opus 132>" composed appropriately with the sense of "=" composed appropriately with the sense of "<Opus 132>" =
     The sense of "<Opus 132>" composed appropriately with the sense of "=" composed appropriately with <Opus 132>.

c) follows from a') and b) by substitutivity of identity.

d) The sense of "<Opus 132>" composed appropriately with the sense of "=" composed appropriately with <Opus 132>  =
      The sense of  "<Opus 132> = Opus 132".

d) follows from c) by the compositionality of sense.  The sense (or sense-proposition or thought) composed appropriately of the senses of the semantically relevant parts of a sentence is identical with the the sense (or sense-proposition or thought) expressed by the whole sentence.  Again, although one can think of historical precedent for denying the principle, I don't know of a *reason*, relevant to understanding thought or propositional attitudes, for denying it.

e) The sense of "<Opus 132> = <Opus 132>" = the sense of "<Opus 132> = Opus 132"

e) follows from b)-d) by transitivity of identity.

f) <Opus 132> = Opus 132.

f) follows from e) by the truth of self-identities, propositional calculus, and the principle that sentences with the same sense have the same truth value.  Note that contextual reference isn't really at issue.

The principles of functional compositionality of sense and decomposability of sense, though deniable, seem to me deeply embedded in actual computational psychological theories of thought.  The principle that sentences with the same sense have the same truth value seems equally fundamental, especially if ways of thinking (senses) are theoretical entities developed in the context of an assumption that attitudes and the thoughts (propositional perspectives that type-identify them) are true or false.  The principles are deniable.  But they are present and basic in all theories of cognitive computational psychology I know of.  A scientific language fit to specify such thoughts for explanatory purposes in psychology should plausibly respect them.  Such a Method II language can account well for embedded attributions.  This is, in my view, an interesting result.

One can of course simply deny that the fact that a translational truth theory for embedded contexts is of any interest.  A lot of semantics isn't translational.  One needs to argue for the denial.  I claim that a Method II language can represent embedded contexts and accords with principles that, especially as principles of thought, are more plausible than the principles (for giving explanatory theories of thought) that the alternative languages would operate under.  Whether or not this is true, it seems to me that the argument given is interesting and deserves reflection, not just parrying in favor of principles or languages that aren't really developed or argued for.

The point of the argument is not to "force" one against one's will to accept the hierarchy in an account of embedded contexts.  It is to show that theoretically powerful principles (not just Fregean principles, though there are texts that show that he accepted all three principles) argue for treating sentences specifying embedded propositional attitudes as engendering a hierarchy in its semantics.  Is English such a language?  So far, I don't see why not.  If it isn't, I think it is still plausible that a language for scientific psychology is.

I hope that you will give these matters at least some reflection before you and the workshop move on to other matters.  Thanks for your hard thinking on the spot in the workshop.  I wish I'd channeled the discussion better, or at least differently.

Best,

Tyler 

PS. (I'm asking Terry to put this letter on the web for the workshop.  I'll put a hard copy in your box, which might be easier to read.)