C.E.M.Joad, for one, and J.B.S.Haldane
Firstly the opinions of 2 people hardly justifies your claim that 'It is widely agreed that that is self-defeating'.
Secondly - Joad was a philosopher, Haldane was an evolutionary geneticist - we are discussing neuroscience and cognitive science - neither were experts in this field so their opinion in an area outside (Haldane) and massively outside (Joad) their area of expertise is rather irrelevant.
Thirdly both have been dead for more than 50 years - neuroscience has moved on massively just in the past 10 years and is unrecognisible from the middle of the 20th century. Therefore they cannot be acquainted with current knowledge and understanding of neurophysiology and its relationship to behaviour, cognition and psychology for the simple reason that they have been dead for during the period of the neuroscience revolution.
Finally, your quote from Haldane (famous you claim - I've never heard it before) is merely an opinion (and from 1927!), an assertion without any evidential base to support it. And actually the evidence does not support it as we know without a shadow of doubt that our thought etc can be faulty. So Haldane opines that:
'For if my mental processes are determined wholly by the motions of atoms in my brain I have no reason to suppose that my beliefs are true.'
And of course there is no reason to suppose that beliefs are true and often they can be demonstrated not to be true.
'And hence I have no reason for supposing my brain to be composed of atoms.'
In which case what exactly is the brain composed of? If anything is 'widely accepted' I think it would be that our brains are composed of atoms.