Uppsala University, Sweden, summer 2019
In this essay, I argue that Putnam’s model-theoretic argument against metaphysical realism (from now on also “M-realism”) is unlikely to impress the metaphysical realist (henceforth “M-realist”).
Here is a quick sketch of my argument. A key premise of Putnam’s attack is that M-realism entails methodological fallibilism, on which even a theory that “we were most justified in accepting” might “not really be true” (Putnam 1995, p. 352). I argue that the notion of a maximally justified theory (MJT) relies on an instance of universal quantification regarding the object of our cognition (everything). This may not be a problem for Putnam’s case if we accept an additional model-theoretic argument that purports to show that our universal quantifiers can only range over limited domains. However, I agree with Einheuser (2010) that an actual user of universal quantifiers is unlikely to be moved by this argument. This is because understanding the argument in the first place requires speakers to distinguish between intended and unintended interpretations. This in turn allows them to reject any unintended interpretation. In other words, the M-realist can always maintain that the intended domain of the universal quantifier contained in the MJT is really everything. But if that is the case, the MJT will necessarily account for everything, including the exact nature of the relation between our cognitive tools and the world. This defence of metaphysical realism is compatible with a form of methodological fallibilism based on a distinction between a theory being true and a theory being complete.
Here is an outline of the essay. In section 2, I recount Putnam’s argument against M-realism and make explicit the universal quantifier implied by the notion of an MJT. I then explain how this universal quantifier, hidden in plain sight, can be used as a defence against Putnam. In section 3, I help Putnam’s case by using a model-theoretic argument to suggest that the universal quantifier implied by the MJT may not be truly universal. In section 4, I switch camps again. Following Einheuser, I argue that the M-realist’s very ability to use language to distinguish between truly universal quantification and limited universal quantification makes her unreceptive to the model-theoretic objection. Finally, in section 5 I consider the question whether my naïve defence is compatible with metaphysical realism as it is generally understood.
2. The universal quantifier in Putnam’s model-theoretic argument
My presentation of the model-theoretic argument against metaphysical realism is, to varying degrees, based on Putnam (1995), Putnam (2014), Douven (1999), and Hale & Wright (2017), with added emphasis on the notion of a maximally justified theory (MJT).
Let us follow Putnam in assuming that the M-realist holds the following beliefs:
(1) The world has a certain fixed structure that is independent of our language or thought.
(2) There is just one true description of the world.
(3) Truth is a correspondence relation between elements of our sign systems and the world.
(4) Whatever fixes the correct reference relations between the world and our signs can have a naturalistic explanation (semantic naturalism).
(5) Even a theory that appears maximally justified to us might not be really true if it lacks the right kind of correspondence to the world (methodological fallibilism).
On Putnam’s view, (5) is what definitively outs the M-realist as a metaphysical realist; methodological fallibilism is the clearest symptom of the M-realist’s conviction that truth is “radically non-epistemic” (Putnam 1995, p. 352). It might be worth noting that methodological fallibilism follows from (1) and (2) only in conjunction with another assumption: that our capacity to understand the world might be permanently limited. This seems like a reasonable assumption, though it is arguably tricky to accept in epistemic practice. For now, it is enough to note that Putnam’s argument does not require our epistemic imperfection to be actual. It only assumes that the M-realist thinks it possible.
Suppose now that we have developed a maximally justified theory. Following Putnam (1995, p. 353; 2014, p. 272), there are several things we can say about such a theory. First, it answers all empirical questions that can be answered by human scientists. In other words, it satisfies all of our observational constraints. Second, it satisfies all of our theoretical constraints. It is internally consistent, and it meets other requirements we tend to impose on theories, such as simplicity, elegance and subjective plausibility.
Next, suppose that this ideal theory is stated in a language that lends itself to model-theoretic formalization. In other words, we can think of the MJT as a formal structure whose terms have specified reference relations to things in the world. The M-realist, says Putnam, believes that even the MJT may not be quite true. Let us grant that this is indeed the case: while the MJT is a useful approximation of what the world is like, it is still false in some important respects.
Now comes the model-theoretic part of the argument. We can assume that the M-realist is largely happy with the MJT; otherwise, she would not regard it as maximally justified. As part of her all-things-considered satisfaction with the MJT, the M-realist believes to have specified the maximally justified reference relations between things in the world on the one hand and the constants and predicates of the MJT on the other. In other words, she has found an interpretation of the MJT terms that satisfies all of her observational and theoretical constraints.
However, because the MJT has a large number of elements (after all, it purports to describe the world), model theory tells us that the MJT also has a large number of different interpretations. Crucially, the MJT has a large number of different interpretations that fully satisfy the observational constraints. This, Putnam argues, puts the M-realist in an odd position. As long as she allows that the MJT is not entirely true, she must also accept that on some other possible interpretation the MJT will come out “more true” than on her own interpretation. In other words, the M-realist’s maximally justified, intended reference assignments for the MJT terms are “incorrect”, while the ultimately “correct” reference assignments that would give us a genuinely true version of the MJT are both unintended and unjustified. But this, Putnam concludes, makes no sense unless the M-realist has an account of reference relations between language and language-independent reality that does not rely on observational or theoretical constraints.
Putnam’s follow-up arguments, variously developed in various publications, aim to show that the M-realist can’t provide such an account. Hale and Wright (2017) make a convincing case that Putnam’s most promising line of further attack is against semantic naturalism. This is because the prospects for a causal account of reference free of any intentional vocabulary currently look bleak. This seems to push the M-realist towards what Putnam calls a “magical theory of reference” – or what Hale and Wright poetically describe as “a conviction in the reality of relations constituted, [the M-realist] knows not how, between his thought and a world wholly alien to it” (2017, p. 720).
Invoking the ineffable to explain a phenomenon as mundane as reference seems like a high price to pay to maintain one’s credentials as a metaphysical realist. Is there a way for the M-realist to resist the dilemma?
I believe that there is. The move I propose, while pointedly naïve, is in the spirit of Putnam’s own view of reference, which is perfectly compatible with intentional vocabulary. It is worth stressing here that even though Putnam was keen to force the M-realist to abandon semantic naturalism, he managed to remain a semantic naturalist himself (Putnam 2014, pp. 280-284). He achieved this by ditching the requirement that a naturalist account of reference should involve reduction to non-intentional vocabulary, e.g. that of mathematical physics. Instead, Putnam suggests, we should accept that some intentional predicates, notably “refers to”, might have to stay irreducibly intentional – even as natural sciences such as evolutionary biology successfully explain their origin and mechanism in functional terms. For instance, one naturalistic way to understand the correspondence relation necessary for truth is to see it as a complex interaction between sign-using organisms and their environment. Such a view might explain both how our use of signs is anchored in reality and how it has been shaped by evolution and culture.
That said, the exact details of non-reductionist naturalist semantics do not really matter for the purpose of my proposal. What matters is the license that Putnam’s view grants the M-realist to talk about reference in intentional terms. To be sure, this license is useless at the last stage of the model-theoretic argument. This is because a non-reductionist naturalist account of reference is certainly not a “magical theory”; it is still subject to observational and theoretical constraints. However, the M-realist can use an irreducibly intentional notion of reference to throw a spanner in the works of the argument much earlier – as soon as she is asked to imagine a maximally justified theory.
Recall that the two core features of the MJT are that it satisfies all of our observational and theoretical constraints. Suppose that the M-realist wants to make sure she correctly understands the implications of those features and asks us to restate the question in plain English.
“The MJT”, we say, “explains everything in a satisfactory way.”
“It is just as I thought”, the M-realist replies. “Let F mean ‘is a feature of reality’ and E mean ‘is explained by the MJT’. Then ∀x (F(x) → E(x)). I intend the universal quantifier to range over everything. This is why the MJT explains everything. The reference relations between our language and thought on the one side and reality on the other are features of reality. Therefore, the MJT explains them as well – just as it explains any other feature of reality. Of course, the human species might never develop an MJT, but that is another matter. It can’t be settled by armchair reflection; it can only be decided by further scientific investigation.”
What can the anti-M-realist say to this naïve defence against the model-theoretic argument (from now on “the Naïve Defence”)? One immediate objection is that by embracing the Naïve Defence the M-realist seems to abandon methodological fallibilism. The claim that the MJT necessarily explains everything is suspiciously similar to a claim that the MJT is necessarily true. But if the M-realist believes that our maximally justified theory of reality can’t fail to be true, in what sense is she a metaphysical realist?
I return to this objection in section 5. In the next section, I consider a different riposte that presents itself to the anti-M-realist. In a nutshell, the objection is this: the M-realist is wrong to think that she can quantify over everything, and we can use a version of the model-theoretic argument to show that.
3. Why we cannot quantify over everything
Recall that the linguistic basis of the Naïve Defence is a plain English description of the MJT: “The MJT explains everything in a satisfactory way”. To remind ourselves that universal quantification is a language-mediated but not language-specific phenomenon, let us restate the predicate in some other Indo-European dialects of Human (the counterparts of everything are in italics):
German Human: erklärt alles auf eine befriedigende Weise
Russian Human: удовлетворительным образом всё объясняет
Italian Human: spiega tutto in modo soddisfacente
And so on. We can assume that any form of Human ever used to discuss ontological issues has an expression that is, at least in some speech acts, intended to quantify over absolutely everything that exists. Do these expressions succeed in quantifying over everything? The anti-M-realist can use a model-theoretic argument to show that the answer is no.
The argument goes as follows (my presentation is based on Einheuser 2010; the choice of Human rather than English is mine). Suppose Human is a first-order language with a countable number of terms. Since Human is an actually used language, it has an intended interpretation. Let this interpretation be model ℰ and range over domain E, i.e.everything, and let thecardinality of domain E be greater than the set of all natural numbers, i.e. uncountable.Then it follows by the Downward Löwenheim-Skolem theorem that domain E has a countable submodel. Let us call this submodel sub-ℰ. Consequently, whatever sentences of Human are true of ℰ are also true of sub-ℰ. In other words, whatever we say is true of everything and its model is also true of a small subset of everything and the model of that subset.
Now comes the crucial part: sub-E, i.e. the domain of sub-ℰ, can include any countable set of things we can name. Since “we can only name countably many things” (Einheuser 2010, p. 237), this must mean that we can never know whether our intended interpretation of Human uniquely picks out the entire domain of everything or a subdomain of everything. To be sure, speakers of Human may intend their quantifiers to range over absolutely everything there is, but from the point of view of “an outside interpreter” (Einheuser 2010, p. 238) every single instance of human quantifier use has a multitude of possible unintended interpretations that still make all sentences of Human come out true.
Thus, the anti-M-realist concludes, the Naïve Defence never gets off the ground because the M-realist’s universal quantification does not uniquely pick out the domain of everything there is. In other words, the M-realist can’t say that the MJT explains everything. She can only say that the MJT explains whatever is picked out by Human expressions such as everything, alles or всё on a reference relation that satisfies some meta-MJT worked out by speakers of Human.
As Einheuser notes (2010, p. 238), it is possible to question some of the premises of this model-theoretic argument. However, the definitive weakness of the argument lies elsewhere. Even if the M-realist does happily accept the premises, it is hard to see how the argument can convince her. She can always point to the very distinction between intended and unintended interpretations, crucial to the argument, as evidence that she can dismiss any unintended interpretations of her quantifiers. This objection, which I borrow from Einheuser (2010), is the subject of the next section.
4. Why we can quantify over everything
Before I go on, let me emphasize that Einheuser’s objection is not an attempt to undermine the model-theoretic argument as such. That human languages, once suitably formalized, can have unintended interpretations is the outcome of a mathematical proof. As long as we grant the premises of the argument, we have no reason to doubt its conclusion. The question is, rather, whether a human user of quantifying expressions needs to worry about this conclusion.
The answer to that question will probably depend on the user’s philosophical temperament. The model-theoretic argument may well impress those inclined to see something profound in the obvious limitations of our cognitive tools compared to the epistemic superpowers of hypothetical non-human agents, such as God or an advanced alien civilization. However, an M-realist who is not so inclined may remain unperturbed. Here is why.
Consider again how exactly the argument’s conclusion is supposed to send the M-realist soul-searching. When the M-realist says “explains everything in a satisfactory way”, she intends for her interpretation of Human to cover everything that exists. The argument, however, tells the M-realist that besides her intended interpretation there is a multitude of unintended interpretations of Human. Each of these interpretations only covers some fragment of everything. The M-realist has no way of knowing that her intended interpretation is the one that uniquely picks out everything – and not any of the legion of interpretations that do not.
“But that can’t be right”, says the M-realist. “The only interpretation I have in mind is the one that picks out everything. If you show me an interpretation that picks out a part of everything, that’s not the one I have in mind. It doesn’t matter how many unintended interpretations of Human there are as long as I can point at them and say that they are unintended”.
In order to understand the model-theoretic argument, the M-realist has to understand the distinction between her intended quantification domain and all the other, smaller domains. But if she understands that distinction, she can also say that she is not talking about any of those smaller domains. That is the essence of Einheuser’s objection to the usefulness of the model-theoretic argument against quantifying over everything.
5. Can metaphysical realism stay metaphysical?
Let me summarize the main strand of my discussion up to this point. Putnam takes the M-realist to believe – per definitionem – that even a maximally justified theory of the world could be false. The model-theoretic argument is meant to push the M-realist either to abandon this belief or to embrace an ineffable theory of reference, on which the correct interpretation of our signs is not dictated by our observational or theoretical considerations. The M-realist can resist this push by adopting what I call the Naïve Defence: she can point out that the MJT explains everything, including correct reference assignments. In response to this, the Putnamian skeptic can wheel out a version of the model-theoretic argument that purports to show that everything, being an expression of human language, does not uniquely pick out absolutely everything. However, the M-realist remains unconvinced by this argument because in order to understand it in the first place she needs to distinguish the kind of everything she has in mind from any other kind.
Assume now that the skeptic backtracks to the point where the M-realist first employs the Naïve Defence. Saying that the MJT necessarily explains everything, the skeptic argues, is tantamount to saying that the MJT is necessarily true. If the M-realist believes that the MJT has to be true, she seems to give up on methodological fallibilism. But if she abandons methodological fallibilism, she thereby abandons her non-epistemic view of truth. With that accomplished, in what sense is she still a metaphysical realist?
The best response I can suggest is this. When Putnam defines methodological realism, he makes demands on the M-realist that seem to lie outside its core tenets. Consider some definitions of metaphysical realism put forward by other authors:
“[The belief that t]he objects the world contains, together with their properties and the relations they enter into, fix the world’s nature and these objects exist independently of our ability to discover they do” (Khlentzos 2016).
“[T]he view that most of the objects that populate the world exist independently of our thought and have their natures independently of how, if at all, we conceive of them” (Lowe 2008).
“[T]he claim that the world has intrinsic structure – structure that would exist even if our cognitive activities didn’t” (Nolt 2004).
These definitions accord well with my own intuitive understanding of metaphysical realism. To be an M-realist is to believe that the world has structure that exists even when no one is describing it. Putnam holds that this commits the M-realist to two further beliefs: that there is just one true description of the world and that even a maximally justified theory can be false. Indeed, the model-theoretic argument is predicated on the M-realist’s sharing these beliefs. Even in his later period, when Putnam had long since abandoned internal realism and instead advocated a position he variously called “common sense realism” or “scientific realism”, he rejected metaphysical realism on the grounds that the same fact can be truthfully described in different ways (Putnam 2012, p. 9).
However, it is far from clear why the M-realist has to commit herself to these further views. Let us begin with the stipulated belief in the One True Description. Why would anyone want to hold such a belief? The fact that the same truth can be expressed differently is trivial to the point where I will stick my neck out and say that it is not philosophically interesting. Anyone familiar with more than one language will know that different linguistic systems can state the same fact not only by means of wildly different material signifiers but also by drawing on different semantic content. For instance, the Russian dialect of Human often makes a topological distinction between a hole that goes all the way through (dyrá, dýrka) and a hole that doesn’t, such as a hole in the ground (yáma, yámka). The English dialect of Human normally ignores this distinction. Yet, if it is true that I dug a hole in my garden in 2018, I can surely convey that truth to the same degree of accuracy in both languages; we have as much empirical evidence for the possibility of translation as we can ever hope to have.
A Putnamian might reply that the formalized language of the MJT is a different matter. If the MJT is to describe metaphysical truth, its language has to be a unique formal system with unique reference assignments. But this demand has the distinct feel of gratuitously loading the dice against the M-realist. It seems especially odd if we bear in mind that Putnam himself eventually came to see nothing wrong in using different vocabulary – including irreducibly intentional vocabulary – to describe different features of reality (Putnam 2014). It seems odder still if we consider that this requirement seems to make the MJT essentially untranslatable and thus ascribes to the M-realist what I can only call a Holy Quran theory of the goal of science.
At this point, the Putnamian might counter that I still fail to appreciate the difference between describing the whole of reality by means of the MJT and describing bits of reality by means of natural languages. Translation between natural languages, he might point out, seems so easy because all dialects of Human are anthropocentric and coarse-grained, and they deal with accordingly coarse-grained features of reality salient for their speakers. They never give a complete description of what is going on. The MJT, on the other hand, is meant to be a complete description of the world. Its model is supposed to have the same cardinality as the set of all things in the world, or at least the set of all metaphysically salient kinds of things. This model can certainly be mapped onto an equally fine-grained structure – hence the model-theoretic argument – but it can’t be translated in the everyday sense of the term “translate”.
Note, however, that this is exactly the point the M-realist makes in her Naïve Defence: the MJT explains everything. Not only is it true; it is also complete. The distinction between being true and being complete is important. It allows the M-realist to hold a form of methodological fallibilism compatible with the Naïve Defence. Just like sentences of natural languages, our scientific theories can be true without being a complete representation of reality. A textbook case in point is Newtonian physics. We know now that Newtonian physics is not complete, but there is an important sense in which it is true: it captures the world structure within a certain domain of application up to a certain level of precision. Likewise, while we have reason to believe that our current physics is incomplete, we also have compelling reasons to believe that quantum mechanics and general relativity are true. To be sure, human theories may never become complete. But – as I had the M-realist say back in section 3 – that only means that we may never develop the MJT. It does not mean that the MJT does not explain everything in a satisfactory way.
To conclude, the M-realist can resort to the Naïve Defence against the model-theoretic argument without fear of losing her credentials as a metaphysical realist. As long as she believes that the world has structure that exists even when no one is describing it, she can proudly call herself a metaphysical realist. At the end of the day, the qualms that Putnam still had about metaphysical realism in his later period, when he was happy to call himself a realist of other sorts, might have more to do with the peculiar intension he assigned to the term. On the interpretation I have adopted above, Putnam himself may well end up in the extension of the predicate “is a metaphysical realist”.
In case anyone cares to cite this essay:
Zarubin, K. (2019). A naïve defence of metaphysical realism against Putnam. Unpublished manuscript. Retrieved from https://kostia.me/metaphysical-realism/
Douven, I. (1999). Putnam’s Model-Theoretic Argument Reconstructed. The Journal of Philosophy, 96(9), 479–490.
Einheuser, I. (2010). The model-theoretic argument against quantifying over everything. Dialectica, 64(2), 237–246.
Hale, B., & Wright, C. (2017). Putnam’s model-theoretic argument against metaphysical realism. In B. Hale, C. Wright, & A. Miller (Eds.), A companion to the philosophy of language (pp. 703–733). John Wiley & Sons Ltd.
Khlentzos, D. (2016). Challenges to Metaphysical Realism. In E. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Winter 2016 Edition). Retrieved from https://plato.stanford.edu/archives/win2016/entries/realism-sem-challenge/
Lowe, E. J. (2008). Essentialism, Metaphysical Realism, and the Errors of Conceptualism. Philosophia Scientiæ, 12(1). Retrieved from http://journals.openedition.org/philosophiascientiae/222
Nolt, J. (2004). An argument for metaphysical realism. Journal for General Philosophy of Science, 35, 71–90.
Putnam, H. (1995). Model Theory and the ‘Factuality’ of Semantics. In J. Conant (Ed.), Words and life (pp. 351–370). Harvard University Press.
Putnam, H. (2012). Realismo e senso comune. In M. De Caro & M. Ferraris (Eds.), Bentornata realtà: Il nuovo realismo in discussione (pp. 5–20). Turin: Einaudi. Putnam, H. (2014). Mit der Realität korrespondieren. In M. Gabriel (Ed.), Der Neue Realismus (pp. 268–291). Berlin: Suhrkamp.