Neo-Carnapianism and The Question of Ontology in Contemporary Analytic Philosophy

A new reading for Quine's argument against Carnap, with some original developments.

Those of you who have read some of my writings here and there might be somewhat surprised that I actually completed my first degree in philosophy in a very analytical department. In fact, I don't know of any philosophy department in Israel that is as analytically oriented as the Hebrew University. In some ways, this was a great stroke of luck. I arrived at the university after "devouring" (without much discernment and in a very unsystematic way) many philosophy books. I only touched the analytical tradition superficially: I knew the big names, the major articles, and that was it. In a sense, this still didn't save me. My undergraduate degree encountered many "logistical" difficulties, let's say, and my interest in the analytical tradition never really took off.

However, I had some rather concrete reasons for why the analytical tradition didn't particularly interest me. Among them was that on one hand, the methods of analytical philosophy are largely borrowed from the British tradition, for which I had an interest, but it was not extensive. One of the surprising things that developed in this tradition, so closely tied to the methods of mathematical logic, is how little orientation certain analytical academics have to the relevant parts of it regarding their research. A tradition that includes, as mentioned, British philosophy, new mathematical logic, and in some ways the Vienna Circle. For example, moral philosophers throw around terms like "second-order" and build enormous towers on them, without fully understanding the methodological foundation - do we even have a sweeping motivation to talk about two orders in moral questions where the separation between them is hermetic...? We can ask questions about morality and we can make moral judgments about questions about moral questions. It's really not trivial that it's not correct to make such moves, and they are certainly not prevented because of something trivial like the meaning of the questions. There's a kind of uncritical reliance on the foundation of the logical-mathematical tradition here, but we'll get to that.

In some ways, one could say that today's tradition has matured from this stage. The reliance on mathematical logic is no longer as naive as it once was. Beyond that, there's a noticeable tendency to create historical identity through methods well-anchored in tradition. The uncontested popularity of David Lewis, for example, owes much to the fact that the method he proposes has application to a variety of philosophical problems, and it deepened the understanding of the power of such a position. On the other hand, one can also see a flourishing of more successful readers of the European philosophical tradition than those the British tradition had for generations, as can be seen for example in the Pittsburgh school. In any case, in one of the courses I'm taking now, I happened to encounter a nice demonstration of this phenomenon of insufficient familiarity with mathematical logic among academics working in this tradition - while they still adopting its methods in an uncritical way.

Carnap, as is known, opposed the historical metaphysical tradition almost entirely. However, since metaphysics has come back into fashion in analytic philosophy (again, part of the maturation trend), various young researchers have begun to try to understand Carnap differently. Carnap, from their perspective, didn't oppose metaphysics as clearly and unequivocally as history has marked him. At the purely historical level, I've already heard the comment, which I can only agree with, that Carnap's exaggerated publicistic opposition to metaphysics stemmed from understandable political reasons. This might be an exaggeration of the point, but not by much. The young researchers are right. However, it seems they may lack, perhaps, the basic tools to understand the foundation of his debate with Quine, a debate on which many of them rely to extract Carnap's ontology, whatever it may be.

To demonstrate this, I won't need to rely much on the current literature on this topic. On the contrary. What I'll do is simply focus on Quine's critique of Carnap. I'll try to show that Quine likely understood Carnap correctly, and also largely showed the limitations of his method. In a sense, I'll try to develop the missing part in Quine's critique. One of Carnap's characteristics that intrigues contemporary academics is that according to his position, there are only three types of questions: (1) Questions that are nonsense, which are broadly characterized as questions presented by traditional philosophy. (2) Pragmatic questions concerning which frame of reference we should adopt, external questions. (3) Questions internal to a given frame of reference.

This intriguing component has led certain researchers to talk about the "pluralism" implied in Carnap's position. Things that exist are the things that a certain frame of reference tells us exist. According to Quine's reading, which I accept, the primary way to understand what Carnap did - at least at the historical level - is to understand that the background to his work is the Principia Mathematica and Russell's theory of types. Now within the framework of type theory, these are indeed very different questions to ask: whether there is an irrational number between 1 and 2, versus whether there are numbers at all. Within the framework of type theory, these two questions can actually be addressed at two different "levels" of language. The question of the second type cannot be asked at the level of the question of the first type in order to avoid the famous paradoxes of set theory.

Therefore, Quine notes the name of what Carnap arranges under questions of the first type under the heading "category questions" and questions of the second type under the heading "subclass questions". Questions of the first type try to refer to an entire "domain" - and therefore, under type theory, need to be "external" or "higher" in the logical hierarchy - and questions of the second type are more focused and therefore ask about specific entities within the framework of a given domain. Quine rightly argues that this distinction underlies Carnap's distinction between the question types (2) and (3) referred to earlier. Now, according to Quine, there's unnecessary duplication here, and to show this, he essentially shatters the basis of the logical foundation that underlies Carnap's distinction. Quine's move is significant because in order to maintain such a distinction between the second and third levels as Carnap distinguishes between them, we need to assume something that is at least equivalent to type theory. In other words: The common talk in today's research about "multiple languages" in relation to Carnap's position is completely incidental. From one perspective, that of type theory, one can indeed talk about "different languages" insofar as they are equivalent to something that maintains at minimum the explanatory power of type theory. From another perspective, say that of the Zermelo-Fraenkel system, the multiplicity here is unnecessary. Then Quine makes a move regarding Carnap's theory, as it is, which I think has slipped under the radar of the literature I'm familiar with on this topic.

Quine proposes two innocent moves to "simplify" Carnap's theory, given the distinction between category questions and subclass questions. In general, Quine thinks that Carnap thinks of a "frame of reference" as one where a proposition of the style of questions that specify, say, the entire range of numbers (x) between two given numbers,

and questions about numbers in general (categories) will need to be subject to another universal quantifier that can in no way be identical with x. For example, regarding the statement that all numbers are abstract, we would say something like:

The idea is that at no point are we allowed to mix the variables w and x as part of the same proposition without explicit reference to the subordination of propositions of the subclass type to propositions of the category type. However, as Quine points out, Russell himself recognized that this requirement, when expressed at the syntax level of the language, makes the use of language unnecessarily cumbersome. Therefore, Russell allowed himself to use a syntactic tool that says roughly this: as long as a certain syntactic statement can be translated back into the normal syntax of type language, then the statement is correct at the syntactic level. This simplification that seems innocent, and that there seems no reason why someone like Carnap or someone with at least an equivalent language conception to Carnap's, would not accept.

In this sense, what Quine doesn't tell Carnap, or the reader, is that this statement is more or less equivalent to the (limited) separation axiom of ZFC. According to the separation axiom, we can build a subset from any given set under restrictions that prevent problems of the kind that type theory was built to prevent. It does this in a slightly different way: it simply characterizes parent sets so that their subsets are under it, and there's no option for the parent set to "pop up" again in the subsets, so we avoid the circularity that led naive set theory to certain paradoxes.

Then Quine takes another step. Suppose our Carnapian accepted the argument that at least at the syntactic level, he is not required to abstain from syntactic structures that don't look like those of type theory, as long as he can still translate his statements back into the syntax of type theory. Now Quine says: Wait a minute. If we're already accepting this, why not completely abandon the universe that type theory "hints at" of entities of different types? After all, in the end we have a free license here to use certain syntactic structures as long as they don't take the form of some specific sequences that we know are problematic. Syntactically, we no longer need types.

In this sense, we've received through the back door something like the extensionality axiom of ZFC. The "entities" in our logical system are no longer distinguished by types, but only by the things our sets contain. In this sense, we are no longer required at all for the hermetic separation we saw at the beginning between the ranges of different variables, given that we introduce only a few syntactic rules that don't need anything like types at any stage, and implicitly, to distinguish between questions asked within a given framework and questions asked about a given framework.

Now, perhaps a more robust neo-Carnapian position can be developed that really asks interesting questions about the relationship between different logical systems. But these were certainly not the questions that occupied Carnap, whose familiarity with formal systems from the "family" of ZFC at the time he wrote his article was not particularly deep. To ask such questions, in my opinion, we will first need to give examples of concrete problems of the kind that Quine's nonchalant strategy will not be able to handle. This is not a trivial challenge, but it seems to me the minimal challenge facing anyone who seeks to establish a neo-Carnapian position to deal with the situation we find ourselves in today.

Either way, I'm tempted to think that we can take another step here that I think Quine didn't take. We can offer Carnap the following: Actually, it may be that you think that despite the reformulation, the distinction between questions about which frame of reference it would be efficient for us to accept has not only the role of depositing different "types", but it may be that sometimes there is a real practical question. Suppose, given that we don't know in some situation whether the set of entities we need for our theory to work, say, a, b, and c all stand in the rules of designation. Suppose we know how to say that a is "Moby Dick" and b is "Plato's writings", but for some reason, maybe we lost the cover, we don't know what the name of book c is. Our logical system is very lean, and all it needs to do is sort books into prose books (d) and philosophy books (e). To do this, it uses the function Sxy. In such a situation, our Carnapian might say, we face a certain limitation that cannot be dealt with only in terms "internal to the system or frame of reference" and there is sense to the separation between external questions and internal questions.

Now it's very likely that we can offer him the following solution: We still want the system to work, because what's important to us is to say something along the lines of "every book has a category" and for it to be true. It's possible and desirable to think here of analogies to physical theories that often require ambivalent entities of this kind so that we can say about the given physical system that it is in some sense true. In this case, we'll suggest that we simply "choose" that every object in the domain of our system has an interpretation. If our Carnapian accepts our solution for the same reasons that Carnap accepts such questions, namely, for pragmatic reasons, we may have removed another stone from the motivation for the distinction between internal questions and external questions - this time we simply introduced our Carnapian to the axiom of choice. This proposal also has the interesting advantage that it captures the axiom of choice not necessarily as an expansion of our axiomatic system, but as an addition of a rule of inference. This is a hypothesis that still needs to be developed, of course.

But if the hypothesis is correct, it also indirectly preserves Carnap's requirement that external questions, or pragmatic statements in the context of system choice, will not have a truth value. Even if I'm completely wrong in my suggestions, it seems to me that there are weighty questions here that at least should have been considered more seriously before shaping a neo-Carnapian position. In this sense, a contemporary philosopher named Vera Flocke should be commended. In fact, her article (and I've only read two others on the topic, one with a clear position and the other that does an excellent review of existing positions on the subject in research) on Carnap as a non-cognitivist expresses and considers Quine's critique seriously enough, also at the level of logical infrastructure. In any case, it seems unique to me in the landscape in this sense.