Livingston on Semantic Doubling

In what follows I first sketch Livinston's three part journey, where he moves Derrida from Gödel to Priest. This journey intrinsically involves looking at views that engage in what Quentin Meillassoux calls "semantic doubling." In my sketch I give examples of doubling from Averroes, Berkeley, and religious Wittgetnsteinians.

To make clearer Priest's master argument I show how something like it was instanced by early critics of Kant (from whom Priest got his initial inspiration). Then I consider three other instances of semantic doubling: (1) Carnap's pragmatism, (2) Robert Kraut's "robust deflationism," and (3) Lee Braver's interpretation of Heidegger, which is a clear instance of what Meillassoux calls "correlationism." In each case, Livinston's three steps is an important part of shedding light on the positions in question.

This is a blog post, not a paper, so my citational habits are shoddy, and the arguments trade in cartoons to some extent (but as my friend Roy Cook has argued, cartoons have an important role in philosophy).

1. LIVINGSTON ON SEMANTIC DOUBLING; WITH EXAMPLES FROM AVERROES, BERKELEY, KANT, AND RELIGIOUS WITTGENSTEINIANS AS WELL AS THE UR-CRITIQUE FROM SCHOLZE

One of the really nice things about this chapter is Livingston's discussion of how an axiomatized system’s Gödel sentence only really means “I am not provable” from a perspective outside of the system. Inside of the system it is just an incredibly long sentence of number theory.

Then, when considering Derrida to be putting forward a non-mathematical version of Goedel’s demonstration with respect to a text rather than an axiomatized system, Livingston shows how the meaning of the Derridian trope in question also doubles, meaning one thing within the system of meanings of the text or discourse (in the case of ethics) and something self-referential that allows Goedelian reasoning when viewed from outside of the text or discourse in question.

This leads Livingston to raise the question about Derrida’s reasoning with respect to langauge as a whole, noting that since differance applies to all discourses it applies to language as such. And when we consider the Goedelian reasoning (diagonalization through self reference) from the perspective of what is supposed to be something total, we get the Russell/Priest paradox. In this manner Livingston’s own discussion connects up beautifully with Priest’s discussion of Derrida in Beyond the Limits of Thought.

I think that it is well worth our time to pay a little more attention to this phenomena of what Quentin Meillassoux calls “semantic doubling” and try to follow Livingston’s (and Meillassoux’s, as I will show) lead. The procedure is this. First, we find a philosopher interpreting a set of claims in two different ways where the metaphor of internal/and external seems appropriate. Then we ask what happens when the interpretation is taken to hold over all language, including the language involved in making the philosophical claim. The kind of diagonalization that Priest talks about occurs at this last self-referential point.

This procedure won’t work for all semantic doubling. The first such case was probably Averroes interpreting sentences of the Koran in two different ways, depending upon whether the reader was learned or not. The next such case is probably Berkeley, in the Three Dialogues, where claims such as “matter exists” are interpreted in two different ways. In the Averroean learned sense, we know this to be false, because in learned debates it presupposes Lockean substance, but in the unlearned sense it is perfectly true, because what is meant is consistent with unlearned “matter” being nothing more than the permanent possibility of sensation (or perhaps actual sensations in God’s mind).

Today, Wittgensteinian philosophers of religion such as John Whittaker, following D.Z. Phillips, engage in Averroean semantic doubling as well. When the unlearned say that “It is true that God exists” they are correct, because they are using the locution to manifest an expectant hopefulness. But in the context of a philosophy classroom, to say such a thing (supposedly) runs afoul of philosophical grammar.

I think in all of these cases, there is no real problem (though I think all three analyses are false!), because even though the internal/external metaphor is apposite, there is no reason to think we need to try to extend the claims to be about anything other than the discourse in question. While it might be problematic to treat all claims about existence (and claims about the truth of those claims) as a non-cognitivist, Phillips is not committed to that in the least. He is just semantically doubling claims that his philosophical interlocutors take to be about God.

Livingston’s kind of argument has much more force when the part of language in question can be argued to be genealogically necessary, in the sense that Robert Brandom and Mark Lance bring to much of their philosophy of language. For example, in articulating what he calls the Kant-Sellars thesis, Brandom argues that anything we might want to call a language must contain the expressive resources to express deontic (obligations and permissibilities) and alethic (necessities and possibilities) modalities. If Brandom is correct, then any philosophical theory of deontic and alethic modalities that involves semantic doubling will be subject to Livingston’s explosion.

Now obviously, if the semantic doubling was supposed to eliminative, then the Livingston problem will undermine the philosopher’s story. (I won’t go into this deeply here, but Brandom’s recent Between Saying and Doing: Towards an Analytic Pragmatism, contains many deep thoughts about this very phenomena; I have a nice critical notice of this book at Phil Books; if you want a copy e-mail me at joncogburn at yahoo dot com.)

In any case, if the philosophical notions in question are genealogically necessary for any discourse, then they will have to be used for discourse about discourse, which gives rise to self referential issues.

To repeat: the procedure is to (1) look at cases of semantic doubling that mark the difference in terms of what is internal and external to a given discourse; (2) see if they need to be generalized to all discourse; and then (3) apply them self-reflexively to the philosophical explanation itself. Thus far we’ve only shown how (2) might be used to undermine eliminative accounts of deontic and alethic modalities.

(3) is where a lot of the interesting stuff happens. And in this context I should note that if Averroees and Berkeley are the philosophical fathers of semantic doubling, then the German Idealists are the fathers of self-reflexive critique. This is what ties together Graham Priest and Quentin Meillassoux, as they both arrived at a deep understanding of how this kind of critique worked in early critics of Kant and then extended those very arguments to apply to the philosophical landscape as they saw it after their Beiseresque epiphanies.

For example, consider “the affection argument” that Scholze made against Kant (which was central to the development of the German Idealist tradition, including Scholze’s student, Schopenhauer). For Kant, causality was officially a category that the mind applied to phenomena. But then what happens when we apply this claim to the causal talk that Kant himself engages in? The affection argument applies the claim to Kant’s account of the relation between noumena and phenomena. Kant then either must say that he got causation wrong, or collapse the distinction between noumena and phenomena. Since noumena caused phenomena, and causation only held between phenomena, all that exists after all is phenomena.

One can make a reverse affection argument with respect to Kant’s causal talk concerning the mind imposing order on phenomena. But here, instead of noumenal causes of perception becoming phenomenal, the transcendental subject becomes phenomenal (for all that he is my favorite philosopher, I worry that Schopenhauer disastrously missed this variety of the affection argument).

Following, Livingston, Priest, and Meillassoux, I’m interested in other cases that might be subject to all three steps that take Livingston’s Derrida from Goedel to Priest. Here I will briefly discuss three: (1) Carnap’s  “Empiricism, Semantics, and Ontology” era pragmatism; (2) Robert Kraut's "Robust Deflationist"; and (3) Meillassoux’s correlationist enemy.

1. CARNAP’S PRAGMATISM

1.1. Livingston’s First Step

In “Empiricism, Semantics, and Ontology” Carnap proposes that existence claims have two different kinds of meaning. Internal to a language, they are understood in terms of the inferential role provided by the linguistic framework. For this to work, Carnap must think of languages in a pretty magical manner. That is, he wants us to think of the inductive, deductive, and observatory uses of language in some manner as analogous with formal languages where provability rules can be rigorously defined.

With formal languages it is easy to demark what is internal to the language (syntax and proofs) and what is external (semantic ascent and questions about whether the framework itself is useful for various applications). If natural language discourses are in fact analogous enough to formal languages, then one can also demarcate matters internal and external to the discourse. Matters internal will be analogous to provability relations, whatever evidential relations lead us to assert claims in the discourse. 

For Carnap, when we construe an existence question internally, we are just considering whether the norms implicit in the language lead us to assert that the existence claim is true or false. At this level there is nothing resembling metaphysics. Numbers are on a par with atoms. Terms referring to them are part of languages that lead us to existence claims involving those terms.

The pragmatism enters when we try to ask a deeper metaphysical question, such as whether numbers are “really real” or whether strings are “really real.” To just be told that true sentences of number theory quantifies over number is not to answer the metaphysician.

Carnap attempts to placate the metaphysician by semantic doubling. “Numbers exist” also has an external sense, where we are asking of the linguistic framework itself whether it is pragmatically advisable to use that framework.

Notably for Carnap, who could not make philosophical sense of objective norms, existence claims construed externally will have no truth value. It is a normative question whether one should or should not adopt a given linguistic framework, and normative answers are not truth evaluable.

1.2. Livingston’s Second Step

 Carnap’s proposal is supposed to be about all linguistic frameworks, so one should be able to consider it applied to natural language itself.

So we think of natural language as analogous to a logical framework, with inferential roles analogous to provability relations in formal languages. Then how does semantic doubling work? The internal construal would just be very much like Quine’s collapse of the distinction between metaphysics and physics. When we ask if something exists we just look at evidence for and against the existence claim.

The external construal starts to fall apart though. To externally construe an existence question from the perspective of our entire language would be to ask for pragmatic reasons to adopt our entire language. Maybe that can be made coherent (Donald Davidson would argue not). I don’t know.

1.3. Livingston’s Third Step

Now let us turn to the third step, where we self-reflexively apply the analysis to itself. Do languages in Carnap’s sense exist? Is natural language itself a Carnapian language or not?

If natural language is a Carnapian language, then there is a demarcation between questions internal and external to it, with the external questions not being part of natural language (Closure). But obviously such questions are part of natural language (Transcendence). Contradiction.

Most of Priest’s argumentative work concerns establishing Transcendence, because so much thought is inconsistent with him here. For Priest, both standard set theory and Wittgensteinian “quietism” are misguided and failed attempts to avoid Transcendence. I just wanted to see how this kind of argument might work out for Carnap. I don't take myself to have actually made it.

2. ROBERT KRAUT’S ROBUST DEFLATIONISM

In “The Status of Content” Paul Boghossian does something similar to the argument suggested above. Can one be anti-realist about semantic discourse? Carnap’s pragmatism would be an instance of the kind of thing Boghossian attacks. Boghossian basically argues that such a view is self-refuting because dividing discourses into those that can be realistically and anti-realistically construed presupposes a robust notion of truth for the former and non-robust for the latter. But if discourse about truth is itself construed non-robustly, then one can no longer differentiate between robustness and non-robustness.

Interestingly, Crispin Wright and Robert Kraut argue that one can bite the bullet here, construing the distinction between robust (e.g. Carnap’s internal questions) and non-robust (external questions) discourses in a non-robust manner. This I think is also the seed of a response to what Priest would say about Carnap. But I’m not sure that it works.

The way Kraut presents the view, there ends up being a violation of convention T for sentences construed non-robustly. Such sentences will be assertible, but it does not follow that it is assertible that they are true, since they non-robust discourses are carved out by Kraut precisely in terms of not being truth apt. Kraut demonstrates that the robust deflationist can countenance this, and moreover that the convention T failure is a common one for certain takes on three value logics (P if and only if P is true, failing on these accounts if P is neither true nor false).

Unfortunately though, Kraut’s view has two additional severe problems. First (and I don’t think this has been argued in the literature yet), the failure of convention T is much more widespread than Kraut or Wright note. Convention T does not just fail for non-truth apt sentences. It seems to also fail for sentences we would take to be true! Given that a sentences is truth apt if, and only if, it is either true or false, and where “D(P)” means that the proposition P is Dasein dependent, “T(P)” means that P is true, F(P) means that P is false, and N(P) means that P is neither true nor false, Robert Kraut’s robust deflationism is committed to the following:

(i) DP <--> N(P)                                                   (non-cognitivism)
(ii) ~D(P) <--> (T(P) v F(P))                             (robustness)
(iii) (T(P) v F(P)) <--> N(T(P) v F(P)).            (in response to Boghossian)

Kraut’s anti-Boghossian insight is the claim that a deflationist can affirm these while still affirming that semantics talk is Dasein dependent.
   
Unfortunately though, Kraut’s view entails an explanatory lacuna. By Kraut’s view, the statement that P is truth apt is itself not truth apt, which gives us N(T(P) v F(P)). Kraut’s insight is important here, as (contra Boghossian) this view is formally consistent. By non-cognitivism N(T(P) v F(P)) entails D(T(P) v F(P)), and by robustness our original statement of bivalence entails ~D(P). Kraut’s point is that the robust deflationist should say that P (or, equivalently, the truth of P) is not Dasein dependent, while the fact that P is truth apt is Dasein dependent.
   
But there is another serious problem in the neighborhood of Boghossian. Perhaps the signal claim of deflationism about truth is that the saying that a sentence is true does not say anything more or less than an assertion of that very sentence. But this immediately leads Kraut into a problem. Start with a sentence that we know to be either true or false, one for which bivalence thus non-problematically holds. Then it will be true that bivalence holds for that sentence. But by his own semantic deflationism, Kraut is committed to it being neither true nor false that bivalence holds. Contradiction.

So the robust deflationist either must adopt a substructural logic in an attempt to block part of the above argument, or further characterize the truth predicate such that convention T fails when applied to statements of bivalence for sentences we already know to be true (or false) (intuitionism won't help at this place). One might be able to motivate either of these, but the burden of proof is on the deflationist to argue that the resulting position is genuinely deflationist, for standardly one adopts a substructural logic such as intuitionism precisely because one has a robust view of what truth amounts to.

I should also note that in Truth and Objectivity Wright argued that robust deflationism is pragmatically self refuting in the sense that if it were true, then there could be no good reason to believe that it is true. The issue is complicated, because Wright’s argument depends upon accepting that non-robust discourses do have a truth predicate, and then differentiating robust from non-robust discourses in terms of whether the truth predicate satisfies his requirement of cognitive command. But even before all of that, we face the problem that Kraut is committed to true (even for the intuitionist) statements of bivalence being both true and neither true nor false.

So I think Boghossian's Priestly argument might work after all. Kraut's view is either inconsistent or non-deflationary.

3. MEILLASSOUX’S CORRELATIONIST

Quentin Meillassoux’s After Finitude contains a deep discussion of semantic doubling, in the context of his critique of correlationism. I won’t go into it here, but Lee Braver’s interpretation of the early Heidegger in A Thing of This World, involves semantic doubling as a way to make sense of the “problem” passages in Division One of Being and Time that seem to commit Heidegger both to and against idealism. So Meillassoux is not criticizing an invented strawman.

But first we need to be clear about what Meillassoux means by “correlationism.”

It’s very important thus to keep the following three theses separate (when we speak quickly we might lump them all together as correlationism).

(1) Verificationism- We cannot coherently think of reality as unthought (from the British empiricists originally, though Berkeley actually argued for it). Note that this arguably entails that if P is true, then it is possible for someone to know that P is true, but that in itself it places no restriction upon who is doing the knowing, it maybe could be "knowable by an infinite mind." Arguments concerning Finitude are typically what force the verificationism to be knowable by something human-like.

(2) Embodiment/Embeddedness-We cannot coherently think of humans without thinking of them as embedded in a reality ( Schopenhauer and then later Heidegger developing Kant's claim that concepts without intuitions are empty, Schopenhauer with respect to the body and Heidegger with respect to a reality experienced as in some sense pre-existing, modal (involving possibilities), and valuative).

(3) Finitude- We cannot coherently think of self-subsistent totalities/absolutes (from Kant’s dialectic, which is often taken to entail that we can therefore only think of finite totalities in relation to us).

At this point it is so important because it is exactly why correlationism is not Berkeleyan idealism. Berkeley’s argument (1) and Kant’s dialectic (2) move us away from naive realism, but embodiment/embeddedness is supposed to move us away from Berkeleyan idealism.

This is why most continental (and actually analogously some analytic) philosophers take themselves to be beyond the very debate between idealism and realism. But, if Meillassoux is correct, this ends up being impossible.

[Side note: What is in common to all Speculative Realists is that they use Priestian arguments to move away from the above in the process of developing speculative metaphysical systems. But the final views can be quite different. Meillassoux rejects Finitude while Graham Harman rejects Verificationism, and both accept Embodiment/Embeddedness. One should also note that by this definition, Graham Priest is a paradigm Speculative Realist.]

Consider the following ancestral statement: ‘Event Y occurred x number of years before the emergence of humans.’ The correlationist philosopher will in no way intervene in the content of this statement: he will not contest the claim that it is in fact event Y that occurred, nor will he contest the dating of this event. No - he will simply add - perhaps only to himself, but add it he will - something like a simple codicil, always the same one, which he will discretely append to the end of the phrase: event Y occurred x number of years before the emergence of humans - for humans (or even, for the human scientist). . . .Accordingly, when confronted with an ancestral statement, correlationsim postulates that there are at least two levels of meaning in such a statement: the immediate, or realist meaning; and the more originary correlationist meaning, activated by the codicil (14).

This is strikingly similar to Braver’s interpretation of early Heidegger. The “realist meaning” is the sense in which Newton’s laws have no truth value prior to Dasein, and the “correlationist meaning” is the sense in which the laws have a truth value even when they are about circumstances prior to Dasein.

3.1. Meillassoux’s Euthyphro Problematic

Meillassoux’s first problem with this view is that he sees it as coming down wrong on a Euthyphro problematic.

. . . .if ancestral statements derived their value solely from the current universality of their verification they would be completely devoid of interest for the scientists who take the trouble to validate them. One does not validate a measure just to demonstrate that this measure is valid for all scientists; one validates it in order to determine what is measured. It is because certain radioactive isotopes are capable of informing us about a past event that we try to extract from them a measure of their age: turn this age into something unthinkable and the objectyivity of the measure becomes devoid of sense and interest, indicating nothing beyond itself. Science does not experiment with a view to validating the universality of its experiments. . . (17)

We want to say with common sense that the scientists measurements come out the way they do because they measure the way things are. Meillassoux thinks that the correlationist is forced to either deny this truism or to be committed to the other Euthyphronic horn, which would make reality causally dependent upon the scientist’s measurement.

3.2. MEILLLASSOUX’S AFFECTION ARGUMENT

The correlationist is unlikely to be moved by the Euthyphronic claims, I think mostly because one can easily repeat the gesture of semantic doubling on the statement of the dilemma itself. All the correlationist has to say is that there is one (internal, empirical, Dasein dependant) sense in which the measurements depend upon the measured reality and another (external, transcendental, Dasein independent) sense in which such an assertion is either false or not truth evaluable.

However, this feeds into Meillassoux’s second line of argument, which is arrived at by self reflexively applying correlationism to itself. Meillassoux notes that post-Kantian correlationism comes from stressing the finitude of the transcendental subject. Then he asks,

But how do notions such as finitude, receptivity, horizon, regulative Ida of knowledge arise? They arise because, as we said above, the transcendental subject is posited as a point of view on the world, and hence as taking place at the heart of the world. The subject is transcendental only insofar as it is positioned in the world, of which it can only ever discover a finite aspect, and which it can never recollect in its totality (24-5).

But once the subject is positioned as essentially in the world, it no longer makes sense to say that the world is dependent upon the subject. Thus Meillassoux thinks that correlationism is pragmatically self defeating in an even stronger sense than Wright took robust deflationism to be. The very reasons one has to subscribe to it (finitude, embedded/embodiment) end up being inconsistent with the position itself.

4. CONCLUDING THOUGHTS

I realize that all of the above is sketchy and that semantic doublers have many responses. The Carnap stuff absolutely rests on the validity of Priest’s attempted refutation of Wittgensteinian quietism. The point is that quietism is analogous to transcendental idealism, with the questions we cannot ask being a linguistic analogue to the thing in itself. Given the analogy, Priest is able to apply his interpretation of the affection argument against Wittgenstein. This is particularly important because Robert Brandom and John McDowell both consider themselves to be Hegelians after a fashion. Yet if Priest (and Beiser for that matter) are right, by affirming quietism they blind themselves to one of the major motors that led from Kant to Hegel.

This being said, Schopenhauer accepted and used the affection argument while also defending views that could be seen to be the precursor to Wittgensteinian quietism (it is no accident that Schopenhauer was the only philosopher Wittgenstein ever studied closely). So, assuming Priest's arguments don't work against Schopenhauer (a big if), one might in the end talk about Pittsburgh Schopenhauerians.

In any case, for our purposes I think that it is enough to show that Livingston’s three-step Priestian deconstruction of semantic doubling is something that has great resonance across large swaths of analytic and continental philosophy.

I feel lucky to have read Livingston’s chapter on Derrida, and look forward to reading the rest of the book.