Externalism and the Expressibility Gap: What Putnam's BIV Argument Really Shows

Externalism¹ and the Expressibility Gap²: What Putnam's BIV Argument Really Shows

What, exactly, does Putnam’s brain-in-a-vat (herein “BIV”) argument show? He claims that “[under externalism],³ the supposition that we are actually brains in a vat … cannot possibly be true, because it is, in a certain way, self-refuting.”⁴ I aim to demonstrate that, for the externalist, his argument has no metaphysical implications—that is, it does not establish that we are not brains in vats. Instead, Putnam’s reasoning demonstrates that self-refuting statements yield an interesting semantic constraint on what we can and cannot say about the world. First, I will explain the foundational assumptions granted by externalism. Next, I will summarize Putnam’s two‑part argument, exposing a faulty supplied premise that involves what I call the expressibility gap in the process. Finally, I will show that, while Putnam proved the BIV utterance is self-refuting from the inside, he did not establish the metaphysical conclusion that we aren’t brains in vats; he only identified a limitation on who can say what truly—an expressibility gap.

The BIV argument is based on a set of externalist assumptions about how words acquire meaning: through causal histories that anchor terms to worldly items and events. That is, the use of our words must be anchored to the world through some chain of past events. For the sake of the argument, I am granting these assumptions because the externalist position is highly contested, and discussing it would be out of scope for this paper.⁵

Now, suppose that since birth, a subject really has been just a brain, floating in a vat of nutrients, hooked up to a supercomputer capable of simulating their entire existence. Because they have no reference to the outside world, the causal histories from which their words derive meaning cannot escape the simulation. In other words, they cannot conceive of a world outside of the simulation. The meanings of the words “brain” and “vat” can only extend as far as simulated images. In this scenario, it would be false for the subject to claim they are a brain in a vat, because their words “brain” and “vat” do not refer to brains and vats; instead, they refer to simulated brains and simulated vats. Either they are a brain in a vat, or they aren’t. In the positive case, the supposition implies its own falsity. In the negative case, it’s already false.⁶ Therefore, the statement “I am a brain in a vat” is self-refuting.⁷

So far, the argument seems sound, but issues arise when Putnam makes further claims. Due to their nature, self-refuting statements must be false, so to claim “I am a brain in a vat” would be false. But claiming to be a brain in a vat is not the same as just being a brain in a vat. It is not the action that is self-refuting, but the statement of it. Putnam’s conclusion requires a further bridge principle: if no subject can truly assert P (given externalist constraints on reference), then ~P. This bridge is not a consequence of externalism; it is an extra metaphysical inference from a semantic limitation. This mistaken leap marks what I call the expressibility gap: the difference between what can be truly said by a speaker (given their causal history) and what might nevertheless be the case in the world. Putnam’s bridge principle attempts to close that gap illegitimately.

Consider the standard BIV setup. From the third‑person perspective, “the subject is a brain in a vat” is true. In this hypothetical, the subject never even entertains the thought “I am a brain in a vat”; they never try to form or utter that specific proposition. It never crosses their mind. As a result, nothing breaks: the subject simply lacks the resources to conceive of objects beyond their causal history. So when we confront ~P in the inside case, we should not read it as (1) the world is inconsistent with the words in the sentence. The better reading is (2) I am unable to conceive of or otherwise coherently refer to a world that is consistent with the words in the sentence. An outside observer—whose “brain” and “vat” terms are fixed by actual brains and vats—can truly say of the subject, “the subject is a brain in a vat.” The inside subject cannot truly say, “I am a brain in a vat.” That difference doesn’t show anything about the world; it only marks whose words manage to latch onto the right things. The failure attaches to the inside assertion, not to the world. One might object that, as a condition of externalism, there is, in principle, a single true and complete description of “the way the world is,” and that it should apply to all perspectives (i.e., everyone must interpret things the same way). This seems to threaten my view. However, I think that would be a misinterpretation of externalism in the way that Putnam intends. In my understanding, mind-independent truth does not imply that every perspective can state it. For example, one person’s limited understanding of a topic does not define the bounds of that topic, because others may have a deeper understanding. A toddler cannot truly assert “Water is H2O” because their term H20 does not latch onto the chemical kind, but the proposition is still true. The premise is that externalism guarantees a mind-independent world, not that it guarantees uniform assertibility across speakers with different reference histories.

Putnam’s BIV thought experiment, read through an externalist lens,⁸ is not a metaphysical refutation but a semantic restriction. The utterance of “I am a brain in a vat” by a subject inside the simulation defeats itself because the subject’s terms latch onto simulated counterparts; the sentence does not come out true in that speaker’s mouth. The further conclusion he wants—that we aren’t BIVs—requires a bridge from inexpressibility to impossibility that neither he nor externalism provides. An outside observer can truly say what the inside subject cannot. This is the expressibility gap: the mismatch between how the world is and what a given speaker, given their causal history, can truthfully say. It is the semantic boundary that Putnam uncovered but misinterpreted as a metaphysical one. His argument identifies a limit on what can be said, not on what can be.

Footnotes

1. By externalism (more precisely, metaphysical realism, in Putnam's framing) I am referring to a philosophical perspective which holds that the world exists independently of our minds, and that the meaning of our words is fixed by that world—that there is, in principle, a single true and complete description of "the way the world is". Putnam later contrasts this with what he calls "internalism" and develops further—better—arguments against the BIV hypothesis. ↩

2. By expressibility gap I mean a systematic mismatch between what is the case and what an agent—given their externalist reference conditions—can truthfully state about it. ↩

3. I decided to emphasize the externalist supposition here because I wanted to make explicit what Putnam failed to until later in chapter 3. ↩

4. Hilary Putnam, Reason, Truth and History (Cambridge: Cambridge University Press, 1981), 7. ↩

5. See Putnam, Reason, Truth, and History, ch. 3. Putnam goes on to refute the BIV scenario using internalism as well. However, that point is not a good objection to my argument, because he reiterates his position that externalists—while they may have a harder time compared to internalists like himself—are still able to refute the BIV scenario using the argument he presented in ch. 1. ↩

6. I figured this goes without saying, but to be explicit: if you are not a brain in a vat, then it would be false to claim that you are. ↩

7. Whole argument reconstruction roughly summarized from Putnam, Reason, Truth, and History, ch. 1, ch. 3. ↩

8. I still can't decide if this was his intended reading or not. I was doing some research online, and it sounds like he may have flipped half way through his career from metaphysical realism (his externalism) to his internalism? That must have been at the time he wrote this book or just before. ↩