Crispin Wright, Martin Davies (in some places but not others), and most explicitly Martin Smith seem sympathetic with the following diagnosis of Moore’s Proof (I have a hand therefore there is at least one material object): “Moore’s Proof (MP) seems to be a bad argument, but intuitive closure principles seem too plausible to reject. This tension can be resolved when MP is treated as an instance of transmission rather than closure failure. MP seems to be a bad argument and is a bad argument because it fails to transmit justification to its conclusion; it is not, however, a counterexample to intuitive closure principles.”
The alleged virtue of this diagnosis is that it preserves intuitive closure principles while explaining why the inference is genuinely bad. The explanation of badness is that the inference fails to transmit. This diagnosis is no good because Wright, etc. don’t salvage the closure principles that epistemologists find too plausible to reject.
An inference fails to transmit justification to belief in its conclusion when it doesn’t make belief in its conclusion justified. A closure principle says if Pa and Rab, then Pb. A transmission principle says if Pa and Rab, then Pb in virtue of Pa and Rab. Let us say that a deduction is competent just in case the premises are well-justified; the premises provide deductive (so maximal) support for their conclusions; there are no relevant defeaters; and it is not premise circular (i.e. the premise of MP isn’t based on a chain of reasoning that uses the conclusion of MP as a premise).
The closure principle that people find attractive is something like this:
Strong Closure (SC): If S justifiably believes P and S competently deduces Q from P, then S justifiably believes Q.
There are various concerns with Strong Closure in the literature, but I get the impression that epistemologists often think something like Strong Closure will turn out to be true. (Most discussions of closure focus on the closure of knowledge rather than doxastic justification, but I’m less optimistic about knowledge closure principles.)
The closure principle that Wright et al are able to endorse is:
Weak Closure (WC): If S justifiably believes P and S competently deduces Q from P, then S has some epistemic status for Q, no matter how weak.
Suppose S competently deduces Q from her justified belief that P. SC holds that S must justifiably believe Q. WC, on the other hand, says only that S must have some positive epistemic status for Q, no matter how weak. Wright et al say that MP fails to make its conclusion justifiably believed, so it fails to transmit (doxastic) justification. Yet Wright et al endorse a view of perceptual justification according to which one has, by default, some very weak epistemic status, entitlement, for the conclusion (that there is a material object) and this entitlement is an essential part of what justifies the person in believing the premise (that one has a hand). So anytime one is justified in believing the premise, one has entitlement for the conclusion. Thus, Weak Closure is true. But Strong Closure is false because the conclusion is not justifiably believed (and on their view, the conclusion cannot be justifiably believed via MP).
I say it is no advantage to accommodate only WC, because epistemologists find something like SC too plausible to reject. Hence, those who say that MP is an instance of transmission failure must say that it also is a counterexample to the closure principles epistemologists find too plausible to reject.
For further clarification of the above argument, see 4.C of my forthcoming IEP entry on transmission failure. I defend a transmission principle that entails SC in my “When Transmission Fails,” esp. sec. 4 (forthcoming Phil Review). Both papers are available on my website.