What Bennett and Hacker call “the mereological fallacy” is the view that psychological predicates attributable to whole organisms may also be attributed to proper parts of organisms. It’s consistent with such a view that my cat may remember where the litter-box is in virtue of his brain’s remembering where the litter-box is. Bennett and Hacker’s hostility toward this view goes beyond merely thinking it false: they reject it as incoherent and nonsensical.
In contrast, I regard it as at worst mostly harmless, probably true, and thus far from incoherent. A lot of the difference between us likely hinges on differing views regarding the mutability of concepts and the scientific worth of conceptual analysis.
Let’s, however, indulge in a little analysis, especially of the concept of a fallacy. I regard fallacies as invalid arguments, and if there is an invalid argument form deserving of the title “mereological fallacy” it goes something like this.
1. a is F
2. b is a proper part of a
3. Therefore, b is F
You can’t plug just any old predicate in for “F” and expect 1, 2, and 3 to come out true. However, it’s fully consistent with this that there are some substitution instances whereby 1, 2, and 3 do come out true. Let a = Mandik, b = Mandik’s left foot, and F = in the Earth’s gravitational field.
There are lots of occasions in which 1, 2, & 3 come out true. Why not, then, regard occasions in which F is a psychological predicate as such occasions?
Consider some relevant analogies. If my computer crashes and investigation reveals that all of its parts are in working order except for the hard-drive, then no confusion ensues in saying that the hard-drive crashed. If my cat digests a meal and investigation of all his parts reveals that his stomach did most of the work, then no confusion ensues in saying that his stomach digests the meal. Medieval philosophers, concerned with the doctrine of bodily resurrection, used to engage in a priori speculations about how digestion worked. It seems silly to engage in such practices now.
It should, at a minimum, be regarded as an open question, not something ruled out a priori, that further investigation will uncover facts we may summarize as that the brain remembers, is conscious, has beliefs, etc.
Bennett, M.R. and P.M.S. Hacker (2003). Philosophical Foundations of Neuroscience. Berlin, Blackwell Publishing.
Bennett, M.R., D. Dennett, P.M.S. Hacker, J. Searle. (2007). Neuroscience and Philosophy. Brain, Mind and Language. N.Y., Columbia University Press.

I am Associate Professor and Chair of Philosophy and Coordinator of the Cognitive Science Laboratory at William Paterson University in New Jersey. This blog largely concerns my interests in the Philosophy of Mind and Philosophy of Neuroscience, but also contains evidence of my messing around with art, photography, fiction, and robotics. Find out way more about me and my work