I just finished Chapter 1 of Robert Brandom's Between Saying and Doing and I have a lot of unanswered questions.
Overview of Brandom's Project
The task of task of the book is to see one much of the classical project of analysis can be justified in light of critiques of meaning coming from Wittgenstein, Quine, and Mark Wilson (he should have cited Stephen Stich in this regard too). The upshot of all of these thinkers is that the way use constrains meaning entails that meaning itself is underdetermined. This form of underdetermination is not normal vagueness. For a word like "red" the meaning unambiguously determines that some objects will be vaguely red. And part of the grasp of "red" is being sensitive to contexts where this vagueness arises. This is quite different from cases where the world surprises you and it is not even clear if the word determines that the object in question is vague with respect to it. Legal cases involving precedent, scientific cases where new and surprising empirical phenomena, and new interactions between different cultures and species always bring to fore this kind of meaning underdetermination.
Unfortunately for the classical project of philosophical analysis, weird thought experiments about what should be the case in far away possible worlds tend to involve possible objects that illustrate the undeterermination of word meaning. At some point when reading the latest Gettier style counterexample to some fantastically complicated definition of knowledge your intuitions just drop out and you start to wonder if the meaning of "knowledge" is just underdetermined in this regard.
Brandom, rightfully so, does not want to conclude from this that anything a philosopher does that might be considered "analysis" is automatically ruled out. It would be incredibly lazy to disagree with Nietzsche's Genealogy of Morals, or Sellars brilliant account of "seems" talk, just because the meaning of moral terms are underdetermined.
So Brandom wants to keep the pragmatist's insight into the connection between use and meaning, and keep what is right about how this limits a priori approaches to philosophy, but retain some facets of the linguistic turn.
Brandom's Meaning-Use diagrams
This is where things start to get difficult. Brandom explicates a lot of what he is doing in terms of these "meaning-use" diagrams, and in explaining the key notion of "pragmatic expressive bootstrapping" he gives an example from the Chomsky hierarchy in recursion theory. I have real questions about what the diagrams mean, and whether the Chomsky hierarchy does what it is supposed to for him. Here's the diagram from page 23.
O.K. This is supposed to be a paradigm case of strict pragamtic semantic bootstrapping. Let me first use Nietzsche to explain this. One interpretation of Nietzsche on ethics is that he was explaining what people must be doing to successfully engage in discourse involving good and evil, but that Nietzsche's own explanation did not involve commitment to the truth of this discourse. One could also use Marx on ideology and Freud on religion here. Brandom uses Huw Price's naturalistic theory of normativity (which from the spiel is similar in the respect I've isolated to the view of Nietzsche presented). Brandom spiels this kind of thing in terms of expressive power of vocabularies:
At least one sort of result that could be of considerable potential significance, I think, is if it turned out that, in some cases, pragmatic metavocabularies exist that differ significantly in their expressive power form the vocabularies for the deployment of which they speify sufficient practices-or-abilities. I will call that phenomenon "pragmatic expressive bootstrapping." If one vocabulary is strictly weaker in expressive power than the other, I will call that strict expressive bootstrapping. We are familiar with this sort of phenomenon in ordinary semantics, where sometimes a semantic metalanguage differs substantially in expressive power from its object language--for instance, where we can produce an extensional metalanguage for intensional languages, as in the case of posible worlds semantics for modality. One example of a claim of this shape in the case of pragmatically mediated semantic relations--though of course it is not expressed in terms of the machinery I have been introducing--is Huw Price's pragmatic normative natrualism. {/footnote "Naturalism without Representationism" in Mario de Caro and David Macarthur (eds.), Naturalism in Question (Harvard Unviersity Press, 2004), 71-90.} He argues in effect that although normative vocabulary is not reducible to naturalistic vocabulary it might still be possible to say what one must do to be using normative vocabulary (Brandom 2010, 12)
Now look at the diagram above. Brandom takes this strict pragmatic bootstrapping to hold when one vocabulary is strictly less expressive than another but when nontheless correct use of the first vocabulary is sufficient to express what one must do in order to correctly use the second vocabulary. The diagram itself expresses this sufficiency in terms of the "Res1: VV 1,2" claim and the diagonal arrow it is over. This claim is defined as the composition the two claims over the other two arrows. The definition is a mouthful, so please look at the diagram.
. . .the relation that holds between vocabulary V' and vocabulary V when V' is VP-sufficient to specify practices-or-abilities P that are PV sufficient to deploy vocabuary V. This VV-relation is the composition of the two basic MURs. When it obtains I will say that V' is a pragmatic metavocabulary for V (Brandom 2010, 10).
To make sense of this we only need to make sense of the weird Rortian way Brandom is talking about "vocabularies" as well as the way these are related to practices. Unfortunately Chapter 1 is not at all clear on just this point.
PV-sufficiency is defined in the following way:
We must look at what it is to use locutions as expressing meanings--that is, at what one must do in order to count as saying what the vocabulary lets practitioners express. i am going to call this kind of relation "practice-vocabulary" sufficiency"--or, usually "PV-sufficiency" for short. It obtains when engaging in a specified set of practices or exercising a pseccified set of abilities is sufficient for someone to count as deploying a specified vocabulary (Brandom 2010, 9)
First problem- If by vocabulary we just mean the words in a language, then from context it is clear that Brandom means this to only count if the person is correctly deploying the vocabulary. I'm not sure this is what Brandom means by vocabulary though. If you look at the ovals above, he treats the vocabulary for recursive enumerability differently from the vocabulary for context freeness. But by the normal use of the word "vocabulary" the difference in these two notions is not one of vocabulary. The same set of words yield different possible languages depending upon whether the grammar is context free or recursively enumerable, with the first set of languages being a proper subset of the second. I don't know how big a deal this is going to be as I go forward in the book. I hope by going over his examples it will be clear to me just what a vocabulary is for Brandom.
VP-sufficiency is defined in the following manner:
. . ."vocabulary-practice sufficiency,' or just "VP-sufficiency," is the relation that holds between a vocabulary and a set of practices-or-abilities when the vocabulary is sufficient to specify those practices-or-abilities. VP-sufficient vocabularies that specify PV-sufficient practices let one say what it is one must do to count as engaging in those practices or exercising those abilities, and as to deploy a vocabulary to say something (Brandom 2010, 10).
Again, I have no idea what he means by "vocabulary" here. If he just means "set of words" this doesn't make much sense, as we could just use natural number numerals for all of our morphemes (since there are only a finite number of morphemes). From this perspective the only thing that is relevant expressively is the number of distinct words you can make (with zero and a genuine successor function you can make an infinite number of distinct words).
I mean, vocabularies on their own, separated from the practices of using them, are completely inert. They don't specify anything. So why doesn't Brandom say that a PV pair is sufficient to specify another practice and read his diagrams in that manner. I don't get it, and conjecture that he must mean something different by "vocabulary" than is meant in normal discourse. Unfortunately by the end of Chapter 1 I still don't know what this is.
Brandom's use of the Chomsky Hierarchy
Given that I don't know what a vocabulary is, it's very difficult for me to make sense of the diagram above. Normally, when doing these things one thinks in terms of four things, (1) a program specification, (2) a machine to run the program, (3) a set of possible inputs, and (4) the outputs of the machine running the program, given the inputs.
Brandom's rectangles elide the difference between (1) and (2)! On page 19 he has two different boxes for two different ways to specify the same program, the first a state-table (for the "laughing santa" autamaton) and the second a flow chart (which he just calls "the laughing Santa automaton"). These are just two different ways to represent programs run by a context free machine. But on page 23 you see the diagram represented above, where each box contains different machines (the pushdown automaton and the Turing machine). Turing machines can be represented in flow charts, graphs, etc. Why just one box for all of them now? This is not a trivial matter, as differentiating not just different individual programs, but different ways to specify the programs gives you a deeper level of intensionality than just identifying machines the most abstractly in terms of input output relations, or in terms of a way of executing the program (e.g. the actual "Turing machine" the same kind of which can be though of as executing a flow chart, or a graph, or a linear representation, etc.)
Unfortunately, he never says what the vocabulary ovals represent either. Sets of input-output pairs corresponding to each infinite run-through of a specified program by a machine? I think that's the only thing that would work.
Then, to get this as a paradigm case of strict pragmatic bootstrapping. Brandom notes,
The surprising fact is that the abilities codified in Turing machines--the abilities to recognize and produce arbitrary recursively enumerable vocabularies--can quite generally be specified in context free vocabularies. It is demonstrable that context-free vocabularies are strictly weaker in syntactic expressive resources than recursively enumerable vocabularies. the PDAs that read and write only context-free vocabularies cannot read and write recursively enumerable vocabularies in general. But it is possible to say in a context-free vocabulary what one needs to be able to do in order to deploy recursively enumerable vocabularies in general (Brandom 2010, 22).
Unfortunately, from a logical perspective, it is not at all clear what theorem he is gesturing at. I take it (and I haven't looked at the Chomsky hierarchy in a long time) that he is saying that a push down automaton can enumerate the set of Turing machine programs. Or he could be saying that a push down automaton can enumerate both the set of Turing machine programs and the set of strings that do not count as Turing machine programs. This latter claim is much stronger, as it would imply that push down automatons could yield a decision procedure to tell of any arbitrary string whether it is a Turing machine program.
The thing is, I'm not sure that this property is decidable (I'm going to go back and dig through the relevant logic this week). My intuition is that it being decidable probably entails the decidability of first order logic (which is not decidable), or vice versa, and so it's not decidable. If that's true, then what we have is something very weak, better expressed in this manner: The practices contained in the push-down automaton box are sufficient to produce what can be interpreted as enumeration of Turing machine programs, which will be one of the enumerations in the box for the "vocabulary" of context free grammars.
Then, given a method of intepreting the enumeration of programs, one can then specify the practices necessary for running a Turing Machine. Now the method of interpreting will be straightforward and pretheoretically algorithmic/computable as long as the interpreter already knows what a Turing machine does. But if one already needs to know how a Turing machine runs to get from the enumeration to the practices, in what sense is it true to say that "that the abilities codified in Turing machines--the abilities to
recognize and produce arbitrary recursively enumerable
vocabularies--can quite generally be specified in context free vocabularies."
This is independent of the concern about whether a push-down automaton can merely enumerate the set of programs or also enumerate the set of non-programs and hence yield a decision procedure. Even if it could do this, we would still need to understand how a Turing machine worked to be able to use the enumerations as a Turing machine. But if push down automatons could only enumerate the set of programs, there is another disanalogy.
The Nietzschean, Freudian, and Marxist "hermeneutics of suspicion" involve explaining a given discourse without commitment to the truth of important claims in that discourse. But for them to succeed they presumably have to not just give a list of all the times people in the discourse succeed in using the relevant vocabulary. They also need to explain when people get it wrong according to their own standards. So Nietzsche is not just explaining when people successfully use the word "good." It is part of his explanation when people take themselves to get it wrong and use the word "good" incorrectly (his whole point about the evolution of this word from an aesthetic good/bad polarity to a moralistic good/evil polarity could not be expressed if he weren't explaining people's failures in their respective communities as well). But this would be analogous to the push-down automaton also enumerating the set of strings that do not yield Turing machine programs.
Brandom is just too unclear on all of this. He doesn't differentiate effective enumeration from decidability, and his unclarity about distinguishing program specification from machines and how that goes into his V and P boxes makes him unclear about the process of decoding whatever is supposed to be in the V box (it's quite possible that there is more in the V box than sets of enumerations or (perhaps also) printouts of run throughs; as far as I can tell one has no idea from anything he says). Again, consider:
The proof of this claim is tedious but not difficult, and the claim itself is not at all controversial--though computational linguists make nothing of it, having theoretical concerns very different from those that lead me to underly the fact. (My introductory textbook leaves the proof as an exercise to the reader.{/footnote Thomas A. Sudkamp, Languages and Machines, 2nd ed. (Addison Wesley Longman, 1998).} General-purpose computer langauges such as Pascal and C++ can specify the algorithsm a Turing machine, or any other universal computer, uses to comptue an recursively enumerable function, hence to recognize or produce any recursively enumberable vocabulary. And they are invariably context-free languages{/footnote. . .}--in no small part just because the simplicity of this type of grammar makes it easy to write parsers for them. yet they suffice to specivy the state-table, contents of the tape (or of the dual stacks), and primitive operations of any and every Turing machine (Brandom 2010, 23)
Again, "specify" does not differentiate between "enumerate" and "decide." I suspect it is just "enumerate," which is not analogous to the kind of explanation he attributes to Huw Price, and that Nietzsche, Freud, and Marx engaged in. It's interesting in this quote how he includes the fact that the context free language can print instructions for how to interpret the primitive operations. But as I said above, these are still just bits of inert language if one does not know how to interpret them. And the real question (analogous to the issue Price is concerned with) should then be whether the practices modeled by a push down automaton are sufficient for being able to so interpret them. I suspect that the interesting kind of "expressive" limitations in this context are when they are not.
I'll find this out this week (as Brandom writes, these aren't difficult theorems), as well as forge ahead and hopefully figure out exactly what a practice and vocabulary are from other examples Brandom gives in Chapter 2.
[Addendum: After reading Chapter 2 I'm wondering if Humean "skeptical solutions" and if Dennett's "heterophenomenology" count as attempted strict pragmatic bootstrapping for Brandom. I think there might be a priori limits on how far this can go for Brandom that give rise to a critique of both Hume/Kripke and Dennett in just this way, but I need to read his chapter on normativity first. This will be worth keeping up with.]