Louis Doulas (McGill University), “Moore’s Fourth Condition”
Journal of the History of Philosophy (2026)
By Louis Doulas
Here’s an argument you’ve likely read about, taught, or encountered in graduate school:
I can prove now, for instance, that human hands exist. How? By holding up my two hands, and saying, as I make a certain gesture with the right hand, “Here is one hand,” and adding, as I make a certain gesture with the left, “and here is another.” And if, by doing this, I have proved ipso facto the existence of external things, you will all see that I can also do it now in numbers of other ways: there is no need to multiply examples. (1939, 165–66)
That’s G. E. Moore’s “Proof of an External World” (1939). Reactions vary, but Penelope Maddy captures it best: “Even years of familiarity hardly dim the blunt audacity of this passage. What does Moore think he’s doing?” (2022, 138). In “Moore’s Fourth Condition” (Journal of the History of Philosophy, 2026), I try to answer that question by drawing on new archival evidence.
What does Moore think he’s doing? He isn’t offering an argument against radical skepticism, as many readers assume.[1] He takes himself to be offering a “perfectly rigorous proof” against a kind of idealism.[2] The question is whether he is successful. Consider a standard reconstruction of Moore’s argument:
M1. Here are two hands.
M2. If here are two hands, then there is an external world.
M3. There is an external world.
Moore defends the success of this argument by showing that it satisfies three conditions:
1) The premises must be different from the conclusion.
2) The premises must be known to be true.
3) The conclusion must follow from the premises.
Any perfectly rigorous proof, Moore says, must satisfy these conditions. His own argument appears to check all of the boxes. It’s valid. Its premises are different from the conclusion. And even an idealist can grant that Moore knows (and doesn’t merely have a justified belief) that he has two hands. His three conditions for a rigorous proof have been met.
But even so, readers can be forgiven for feeling that something is amiss. For example, it’s hard to imagine being rationally compelled to believe Moore’s conclusion on the basis of his premises alone if (say) you already had doubts about it. It’s for precisely this reason that many believe the proof is question-begging or epistemically circular: the support Moore has for his belief that he has two hands seems to depend on whatever support he already has for his belief that there is an external world. That’s circular. And circular arguments are bad. Escaping this fate might require an additional condition on proof—a fourth condition:
4) Knowledge of the premises must be independent of the conclusion.
Call this the epistemic independence condition. Arguably, if Moore’s proof satisfied this condition, the proof would rationally persuade someone who doubted its conclusion; it would give them a new, non-question-begging reason to believe an external world exists—rather than simply displaying commitments they might have previously held.
Hands down, one of the most puzzling things about Moore’s essay is his failure to anticipate the circularity worry. Even an additional anti-circularity condition seems to elude him: “Are there any other conditions necessary for a rigorous proof, such that perhaps it did not satisfy one of them? Perhaps there may be; I do not know” (1939, 167). Yet Moore was not generally unfamiliar with the fallacy of circular or question-begging reasoning.[3] And when the proof appeared, his contemporaries raised similar concerns, so the worry isn’t anachronistic.[4] So, what gives?
In the archives at the Cambridge University Library, I made a discovery that changes things.[5] While Moore is completely silent on these issues in his 1939 essay, it turns out that he was wrestling with them behind the scenes. Not only was he remarkably attentive to worries surrounding circular proof (worries which naturally extend to his own 1939 proof), but he seems to anticipate the very discussions that commentators would raise in the massive literature surrounding his proof six decades later, such as the issue of “transmission failure.”[6]
Moore’s proof was delivered on November 22, 1939, and published shortly thereafter. Not long before that, in some lecture material from the academic year of 1938–39, he was putting his thoughts about circular proof together. There he explicitly distinguishes two senses of “begging the question” (ML, MS Add. 8875 13/38/2). The first is what he calls the “unimportant” sense. Paraphrasing Moore:
An argument begs the question in the unimportant sense when the premise is merely identical to the conclusion.
The “unimportant” sense appears in Moore’s 1939 essay in everything but name (“The premises must be different from the conclusion”). What does not appear in 1939 is what Moore calls the “important” sense:
An argument begs the question in the important sense when one’s knowledge of the premise fails to be independent of one’s knowledge of the conclusion.
In these lectures, Moore maintains that a genuine proof should avoid both kinds of circularity. That’s striking, since avoiding the “important” kind would amount to satisfying the fourth condition above. It naturally raises the question of whether Moore’s standard for proof changed in the months leading up to his 1939 proof and, if so, how this might illuminate what we think Moore is doing.
In these same lectures, we find an answer. “I’m not going to say any more about begging the question,” Moore concludes, “because I can’t find anything clear to say. I can’t see what the answer is to the following question” (ML, MS Add. 8875 13/38/2).
The question he’s grappling with corresponds to a passage that is too long to quote here and takes some effort to unpack (see my essay). But here’s the gist. Moore comes to think that the fourth, epistemic independence condition is both too strong (ruling out paradigmatic cases of legitimate, everyday proofs) and too weak (failing to capture what makes question-begging arguments defective). Because the condition cannot helpfully distinguish good proofs from bad ones, Moore ends up stuck. If the condition can’t reliably sort good proofs from bad ones, what exactly makes an argument circular? As he puts it: “one puzzle is what relation must hold between two propositions p and q, in order that we may rightfully say that: p proves r and r proves q is circular” (ML, MS Add. 8875 13/38/2).
I argue that we cannot properly appreciate Moore’s proof without taking stock of these unpublished lecture discussions. They illuminate what is otherwise a puzzling omission: why Moore never squarely addresses the worry about circularity. What we learn from my article isn’t that he was unaware of the problem, or that he took it to be insignificant—quite the opposite. He saw it clearly and was torn by it, wrestling with it intensely without ever fully resolving it: “This question is what I can’t answer” (ML, MS Add. 8875 13/38/2).
But this material also sheds light on Moore’s proof in another way: it helps explain why the proof so often strikes readers as simultaneously compelling and defective. The answer may be surprising: it isn’t simply because the proof is epistemically defective (Wright) or dialectically ineffective (Pryor). It’s that Moore was caught between two incompatible ideals of rigor and was unable to reconcile them in the months leading up to his famous 1939 performance. Moore’s proof, as I propose we read it, embodies the unresolved tension. On the one hand, he insists that his proof is “perfectly rigorous” because it meets his three stated conditions. On the other hand, he also claims that it can “settle questions as to which we were previously in doubt” (1939, 167)—a much stronger demand that seems to require the fourth condition over which he was conflicted.[7]
Moore appears to want his proof to do both things at once, but it can’t. The air of paradox that hangs over the proof reflects these philosophical struggles—ones that remained unsettled even as he stood before the British Academy, hands raised, insisting he had proved the existence of an external world.
I’m grateful to Thomas Baldwin, literary executor of G. E. Moore’s manuscripts and unpublished papers, for permission to reproduce and quote the archival materials included here.
References
Baldwin, Thomas. G. E. Moore. Routledge, 1990.
Coliva, Annalisa. “What Do Philosophers Do? Maddy, Moore (and Wittgenstein) II.” In The Philosophy of Penelope Maddy, edited by Sophia Arbeiter and Juliette Kennedy, 299–310. Springer, 2024.
Maddy, Penelope. A Plea for Natural Philosophy and Other Essays. Oxford University Press, 2022.
———. “Reply to Coliva.” In The Philosophy of Penelope Maddy, edited by Sophia Arbeiter and Juliette Kennedy, 311–317. Springer, 2024.
Moore, G. E. “Hume’s Philosophy.” 1909. In Moore, Philosophical Studies, 147–67.
———. Philosophical Studies. Routledge & Kegan Paul, 1922.
———. “Metaphysics Lectures 1938–1939.” Cambridge University Library, GBR/0012/MS Add. 8875. 13/38/2. [ML]
———. “Proof of an External World.” 1939. In G. E. Moore: Selected Writings, edited by Thomas Baldwin, 147–70. Routledge, 1993.
———. “A Reply to My Critics.” In The Philosophy of G. E. Moore, edited by Paul Arthur Schilpp, 535–677. Northwestern University Press, 1942.
Morris, Kevin and Consuelo Preti. “How to Read Moore’s ‘Proof of an External World.’” Journal for the History of Analytic Philosophy 4 (2015) : 1–16.
Pryor, James. “The Skeptic and the Dogmatist.” Noûs 34 (2000) : 517–49.
Wright, Crispin. “(Anti-)Sceptics Simple and Subtle: Moore and McDowell.” Philosophy and Phenomenological Research 65 (2002) : 330–48.
[1] So-called “epistemological” readings of the proof are legion, yet they seem to contradict Moore (1942, 674, 668). That said, there’s lively discussion about this. See especially Baldwin (1990), Morris and Preti (2015), and the exchange between Coliva (2024) and Maddy (2024).
[2] What kind of idealism is hard to say, though I have some thoughts. For now, it’s worth noting that Moore clarifies that his target is those philosophers who think that “There are no human hands” follows from “There are no material things” (1942, 670).
[3] See Moore ([1909] 1922, 159–60).
[4] I’ve also uncovered a letter from the Welsh philosopher, Richard Ithamar Aaron, who raises the issue even earlier in a letter to Moore six months after the proof’s publication. See my article.
[5] I also draw on some important passages from Moore’s posthumously published Lectures on Philosophy.
[6] See especially Wright (2002) and Pryor (2000). Of course, it would be anachronistic to think that Moore’s discussion maps perfectly onto contemporary discussions. But there is striking overlap that my discussion makes salient, which I hope to explore more fully in future work.
[7] This captures a distinction philosophers sometimes draw between display proofs and persuasive proofs. See my paper for discussion.