If I’ve accomplished nothing else in this series (previous post here), I hope to have somewhat dispersed the intimidating air that surrounds both Putnam’s model-theoretic argument and the current discussion of Newman’s objection. This air has two sources, I think.

First, both arguments make heavy use of formal model theory. Formal logic, model theory, and especially metatheory are imposing bodies of technical knowledge. They are mathematical. Most philosophers are only minimally acquainted with them. Most graduate programs in philosophy today no longer require students to take metatheory, and even in the old days, the requirement was generally limited to a single course. I would imagine that over ninety-five percent of professional philosophers today could not tell you off the top of their heads what the Löwenheim–Skolem theorems even say. The point is that when people like Hilary Putnam and Michael Friedman start talking about Shoenfield absoluteness and ω-models, nearly all their listeners know they can’t talk to them as equals on that subject.

Mathematical demonstrations are rightly impressive because of their formal rigor. Used with care, they can be quite helpful. Mathematical concepts and methods have an unfuzzy crispness that renders their proofs decisive. However, as everybody knows—or should—all that means is that the non-mathematical import of those proofs depends on the non-mathematical assumptions and premises that underlie their application to the non-mathematical world, the world outside the formalism in which they were demonstrated. As we have seen particularly in the case of Putnam—although the same considerations apply to the recent discussion of Newman’s objection—the applicability of formal model theory to the semantics of our thoughts and percepts is highly questionable. Nearly all the real work of Putnam’s “model-theoretic” argument is done, not by the formal proof, but by Putnam’s ancillary arguments intended to show that conventional model-theoretic semantics is the one true normative standard for doing semantics for general symbol systems, including natural language—and our percepts should be considered to be symbols.

Bays strongly emphasizes this point, and his summary statement is worth quoting in full:

Much of the initial attraction of [the model-theoretic] argument—much, that is, of what one might call its “philosophical sex-appeal”—stems from its claim that basic theorems of model theory show that semantic realism is untenable. But when the argument is filled out in the way I have been discussing, then all of the serious model theory—the permutation theorems, the Löwenheim–Skolem theorems, the Shoenfield absoluteness theorem, etc.—becomes superfluous. The argument now rests on the more or less trivial observation that if you are permitted to reinterpret anything you want in any way you want, then you can make any sentences you want true under any circumstances you want. We did not need fancy model theory to tell us that. (2008, 204)

Second, there is something imposingly meta about putting an argument in terms of the status of realism and the nature of truth. After all, we’re no longer talking about what is true, but about what truth is! But although imposing, it’s not clear that this “semantic ascent” brings about any greater clarity. It is well to keep in mind that statements about the relation between our percepts/thoughts and external things are statements about what is the case, no different in this respect from any other statement, such as “it’s raining.” In both cases (statements about meaning and object statements), an external state of affairs is being asserted which we have no independent means of verifying. Both are empirical claims. Our ability to know them depends on whatever means we have, such as perception, for knowing external things. On the usual way of thinking about a statement like “it’s raining,” it asserts the existence of an external, mind-independent state of affairs, and it is true if that state exists. Skeptical challenges can be raised against our ability to know such things, for example by challenging the validity of the senses. And the plain (bitter?) fact is that there is always room for doubt about any empirical knowledge claim, because we lack independent access to external things.

All this is true in exactly the same way about semantic statements, such as “’cat’ refers to cats.” This asserts the existence of an external, mind-independent state of affairs—namely, about the relation between a word and something in the external world—and it is true if that state exists. Skeptical challenges can be raised about our ability to know such relations (for example, “are there really any such things as cats?”, “does ‘cat’ really refer determinately to those things?”), just as about our ability to know that it is raining. And it is a plain fact, evidently bitter to Putnam and many others, that there is always room for doubt about our knowledge of the referents of our words, thoughts, and percepts. The point is that doubts about semantics have no special basis that makes them any stronger or more credible than skeptical doubts about any other empirical knowledge. They are all rooted in the same fundamental fact: the mind-independence of external reality.

In short, idealism (such as Putnam’s “internalism”), coherentism, pragmatism, and the like are just skepticism applied to meaning and truth. They represent attempts to address this skepticism by erecting mind-dependent criteria of meaning and truth. I suggest that it’s best to think of them that way. It is demystifying to recognize that in the end, questions about how we can know about how words or percepts connect to objects are the same sort of questions as how we can know it is raining.

Reference

• Bays, Timothy. 2008. “Two Arguments against Realism.” Philosophical Quarterly, 58: 193–213.