A Précis of Hilary Putnam's Model Theoretic Argument for Internal Realism

Metaphysical Realism (MR) is not one claim but, Putnam argues, a package of interrelated claims about the mind-world relationship. The key components of MR are 1) the independence thesis; 2) the correspondence thesis; 3) the uniqueness thesis. The independence thesis states that there is a fixed totality of mind independent objects (the world). The correspondence thesis states that there are determinate reference relations between bits of language or mental representations and the bits of the world to which they refer. The uniqueness theory states that there is a theory whose sentences correctly describe the states of all these objects. This implies a singular correspondence between the terms belonging to this theory and the objects and properties that they refer to (Putnam 1981, 49). As a package it is cohesive. One needs mind-independent properties and objects as objects/properties to correspond to. There must be some unique total fact about these objects if there is to be one correct way in which a theory can represent this total fact.

We can imagine this theory being expressed in a language consisting of names like “Fido” and “Shlomo”, property and relation terms like “…is a dog”, “…is a cat” or “…is father of…”, as well as all the quantificational apparatus that we need to make multiple generalizations: e.g. “There is at least one thing that is a cat” or “All dogs hate at least one cat”. Of course, since this is the one true theory we might expect it to contain enough mathematics (e.g. set theory) to express the true laws of physics, the true laws of chemistry, etc. However, for this to be one true theory each true sentence that we can derive from it – e.g. “Shlomo is a cat” – must hook up with the world in the right way. For example, “Shlomo” must determinately refer to a unique object and this object must have the property referred to by “…is a cat” (this property might be the set of all cats or it might be universal property of catness – again, depending on the metaphysical facts). [i]

An assignment of referents to terms along these lines is called an interpretation function. The set of objects, properties, relations, etc. that are matched up to terms by a particular interpretation function is called a model. Putnam’s account of metaphysical realism then, in effect says that metaphysical realism is the claim that there is a unique description of the world hooked up to that world by a single true interpretation function (matching names to objects, property terms to properties, etc.).

The uniqueness of the corresponding interpretation function is crucial here because if there were more than one good way of interpreting the terms of the one true theory, there would be alternative theories, each one corresponding to a different interpretation function for the constituent terms of its language.[ii] In that case, there would not be one correct description of the world. But if realism comes down to a commitment to there being a God’s eye view of the world – a uniquely true theory which picks out the way the world is – then realism would have to be rejected.

What is the virtue that makes the one true theory unique? Well, to count as the one true theory, it would, at minimum, need to satisfy all the “operational constraints” that ideally rational inquirers would impose on such a theory. For example, if one imagines science progressing to an ideal limit at which no improvements can be made in its explanatory power, coherence, elegance or simplicity, then the one true theory would have to be as acceptable to ideally rational enquirers as that theory (Putnam 1981, 30).

Putnam’s argument against realism is that given a theory that satisfies this ideal of operational virtue there would always be a second equally good theory that can be constructed by giving the sentences of the first different interpretations. Further, he argues, that there is nothing beyond operational virtue that might distinguish the first theory from the second because there are no mind-independent semantic facts that specify the right interpretation. If this is right, then there cannot be a one true theory that completely describes the world.

The argument begins with a theorem of model theory.[iii] The model-theoretic notion of a theory is that it is a language L under a given interpretation function I which maps the terms of L onto a universe of objects and properties (properties are treated as sets of objects. For example, the relation of fatherhood would be the set of all ordered pairs, the second member of which is the son of the first member.). The theorem states that for every theory T1 (consisting of a language L under interpretation I) it is possible to gerrymander a function J that interprets each term L “in violently different ways, each of them compatible with the requirement that the truth value of each sentence in each possible world be the one specified” (Putnam 1981, 33, 217-218). The basic idea is that under these “permutated” interpretation functions, the sentences that come out true in T1 in a given possible world would come out true in T2 in that world.[iv]  The two theories T1 and T2 would not differ in assignments of truth values to sentences in any possible world and – being expressed in the same words – would have exactly the same structure, so each would be as simple and as elegant as the other.

However, metaphysical realism is committed to the view that even an ideally confirmed and simple theory could be comprehensively false because truth is “radically non-epistemic” – that is truth is a matter of whether a sentence corresponds with the world, not of how well confirmed that sentence is. This is, of course, the position that Descartes is committed to in his Evil Demon thought experiment. The semantic facts that give my beliefs reference to a possible world are unaffected by the existence or nature of the mind-external world. Putnam’s version of this realist conceit is the science fictional notion that we might be brains in vats being fed simulated experiences by a mad neurophysiologist. Thus, according to metaphysical realism, even a theory T1 that is operationally ideal and irrefutable for vat brains could be still be false (Putnam 1978, 125). However, unlike Descartes, Putnam argues that this conceit is incoherent. If T1 is consistent it is possible to find an interpretation function that maps the language of T1 onto a model containing elements of whatever world happens to exist – even if that is vat-world. So under this interpretation T1 comes out true, not false (Putnam 1978, 126).

It can be objected that this would not be the interpretation “intended” by the vat brains (or the ensorcelled Descartes, if one prefers). But T1 would be operationally as good as it gets for the envatted. It would inform their practices of inference and prediction in just the same way that it would were it true. There seems to be nothing beyond these practices of judgment and inference that could fix the meaning of terms like “cat” or “dog” – though these are clearly not sufficient to give uniquely determinate meaning.

Some philosophers have argued that uniquely intended interpretations can be imposed by our contents of our beliefs or ideas. For example, maybe my idea of a cat and actual cats shares a mysterious essence of catness which “exists both in the thing and (minus the latter) in our minds” which, in turn, fixes the reference of property terms like “cat” (Putnam 1983, 206; 1981, 59-61). Putnam argues that this response makes recourse to a magic language of self-interpreting mental-signs: it states, in effect, that there are mental representations that just mean what they mean irrespective of how the world is or of their role in inference. Here Putnam is in agreement with the French deconstructionist, Jacques Derrida. For Derrida, as for Putnam, a sign is a mark that acquires it meaning by being used differently from other signs, whether the mark is spoken, written or occurs in the brain or in some purely mental medium (if such a thing exits). A particular inscription or brain state or sound only counts as a sign insofar as it functions or is used differently from other signs. The obvious candidate for “use” and “function” here are the roles of signs in inferences and in interpretative practices. But these, as has been seen, are unable to fix a unique model for T1.

So it does not matter whether we are talking about mental signs or signs in language: they derive meaning from their differential functioning. For Derrida this has the complicating consequence that any mark must be “iterable”: i.e. can be lifted from its standard contexts and grafted into new ones, thereby acquiring different functions (Derrida 1988, 9-10). However, for our purposes, the important consequence is that appealing to “inner” or mental signs to fix the intended meanings of T1 seems to presents us with exactly the same problem of indeterminacy as we had with T1 itself (Putnam 1978, 127; 1983, 207).

If this is right, then the realist claim that an ideally confirmed theory could be false just comes down to the claim that there are self-standing minds or self-standing languages whose meanings are fixed regardless of how things lie in the world. But if Putnam is right, there are no self-standing meanings in this sense. Descartes thought experiment in either its 17th Century Demonic version or its modern Neuro or Simulationist versions is incoherent.

But, Putnam argues, this means that the idea that truth is non-epistemic is incoherent. To suppose that our beliefs could all be false, no matter how well they conform to experience and canons of enquiry makes no sense (Putnam 1978, 128-130).  And (assuming the soundness of Putnam’s model theoretic argument) this also means that the idea of a privileged, God’s eye view of the world – MR -is incoherent. There is no single theory that uniquely corresponds to the nature of a mind-independent world because there are always other interpretation functions with which to generate new theories with the same degree of epistemic virtue. Thus the assumption that the world has an intrinsic nature independently of how it is construed from the standpoint of a particular theory or form of life is as much an ungrounded superstition as the notion of substantial forms.

Rather than aspiring to the idealized God’s eye view of metaphysical realism, Putnam argues that we should recognize that truth, reference and objectivity are properties that our claims and experiences have in virtue of “our” practices of inference, confirmation and observation. To say that the sentence “’Cow’ refers to cows” is true is not to make a claim about some determinate relationship – reference – between word and world but to say something about the situations in which a competent speaker of English should use the term ‘cow’ (Putnam 1978, 128, 136).  From within the shared practices of English speaker, this fact just shows up as an a priori truth. But this (as Kant also claimed) does not reflect some impossible insight into the mind-independent nature of things, but simply reflects our acculturated understanding of what is appropriate to say, when (137). Even the metaphysical structure of the world is – according to this view – a perspective that reflects the background understanding and interests of creatures who share the relevant concerns and practices.  Reference is, as Putnam puts it elsewhere, a “matter of interpretation” which presupposes “a sophisticated understanding of the way words are used by the community whose words one is interpreting” (Putnam 1995, 119). So, by the same token, there can be no ready-made totality of objects of reference since (again) this presupposes the discredited God’s eye view:

[From] my “internal realist” perspective at least, there is no such totality as All the Objects There are, inside or outside science. “Object” itself has many uses, and as we creatively invent new uses of words, we find that we can speak of “objects that were not “values of any variable” in any language we previous spoke (The invention of “set theory” by Cantor is a good example of this.) (Putnam 1995, 120)


Derrida, Jacques (1988). Limited Inc. Samuel Weber and Jeffrey Mehlman (trans.),Evanston Ill.:

Northwestern University Press.

Putnam, Hilary (1978). Meaning and the Moral Sciences. Routledge & K. Paul.

Putnam, Hilary (1981). Reason, Truth, and History. Cambridge University Press.

Putnam, Hilary (1983). Realism and Reason: Philosophical Papers Volume 3. Cambridge University Press.


[i] We can summarise this state of affairs as follows:


“Fido”  —> the object Fido

“Shlomo” —> the object Shlomo

“…is a cat…” —> property of cattiness

“…is a dog…” —> property of dogginess

“…is the father of…” —> relation of fatherhood


[ii] For example, we can imagine a deviant interpretation function that maps up terms in the “wrong” way:


“Fido” —> the object Fido’s shadow

“Shlomo” —> the object Shlomo’s shadow

“…is a cat…” —> property of being the shadow of a cat

“…is a dog…” —> property of being the shadow of a dog

“…is the father of…” —> relation of fatherhood


[iii] The branch of mathematical logic that examines the formal relationships between languages and the models assigned to them under interpretation functions.

[iv] Suppose T1 has an interpretation function I that includes the first set of assignments given above (“Fido” refers to Fido, “Shlomo” refers to Shlomo, etc.) whereas T2’s interpretation function has the second. Thus the sentence “Shlomo is a cat” says that the object Shlomo is a cat in T1 whereas the same sentence say that a particular shadow is the shadow of a cat, which also happens to be true.


3 thoughts on “A Précis of Hilary Putnam's Model Theoretic Argument for Internal Realism

  1. Great linkage between Putnam and Derrida. I wish I had your gift for clarity!

    For me the most interesting question about these dismantlings of univocal truth is *why they have to be made at all.* Why does univocal truth tend to be the assumptive default? Why is *ignorance* required to fix certainty? when one would think precisely the opposite would be the case.

    • Thanks Scott – a pretty cheeseparing gift, but it’s something, I suppose. I think the Putnam-Derrida connection is more complex than I had space to describe here. For one thing, I think Derrida would question the assumption of internality, arguing that the iterability of marks militates against the synchronic conception of language games that Putnam seems to buy into.

  2. Pingback: Internal Realism and Correlationism

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