Russell uses sets in order to establish a theory of logical propositions. So, in order to understand a statement such as 'Julius Caesar was bald', he first reconfigures it as 'there is some x such that x is Julius Caesar and x is bald'; which is to say, 'there is one, and only one, x that belongs both to the set of 'bald people' and the set 'individuals who were Julius Caesar'. This is all fine; I understand (or I think I do) why Russell wanted to do this. But it strikes me that it entails redefining a predicate in terms of two things: one that actually exists in the world (or actually existed: 'Julius Caesar') and one that doesn't -- the 'set'. I'm not saying sets aren't real; but I am saying that they don't exist outside human minds; that in other words, human minds are the things that recognise 'similarities' between things, and that sets are simply the extrapolation of massed lists of similarities.
Russell himself, of course, wouldn't have accepted the force of this distinction. To quote the Stanford Encyclopedia of Philosophy's entry on him at some length:
One final major contribution to philosophy was Russell's defence of neutral monism, the view that the world consists of just one type of substance that is neither exclusively mental nor exclusively physical. Like idealism (the view that there exists nothing but the mental) and physicalism (the view that there exists nothing but the physical), neutral monism rejects dualism (the view that there exist distinct mental and physical substances). However, unlike both idealism and physicalism, neutral monism holds that this single existing substance may be viewed in some contexts as being mental and in others as being physical. As Russell puts it,I don't find this very persuasive, myself: but that's not what exercises me here (it seems to me it would be more accurate to say 'there is only one kind of stuff out of which the world is made, and this stuff is called mental in one arrangement, physical in the other' is a description of the world as it occurs in our minds, and as such (a) it lacks the force Russell wishes to grant it, and (b) being a purely mental construct, it possesses a necessarily elasticity that undermines Russell's point -- for just as Russell can have Caesar call up Charlemagne in his mind, so I may divide the world into two distinct and different things, matter and mentition.
“Neutral monism”—as opposed to idealistic monism and materialistic monism—is the theory that the things commonly regarded as mental and the things commonly regarded as physical do not differ in respect of any intrinsic property possessed by the one set and not by the other, but differ only in respect of arrangement and context. (CP, Vol. 7, 15)
To help understand this general suggestion, Russell introduces the analogy of a postal directory:
The theory may be illustrated by comparison with a postal directory, in which the same names comes twice over, once in alphabetical and once in geographical order; we may compare the alphabetical order to the mental, and the geographical order to the physical. The affinities of a given thing are quite different in the two orders, and its causes and effects obey different laws. Two objects may be connected in the mental world by the association of ideas, and in the physical world by the law of gravitation. … Just as every man in the directory has two kinds of neighbours, namely alphabetical neighbours and geographical neighbours, so every object will lie at the intersection of two causal series with different laws, namely the mental series and the physical series. ‘Thoughts’ are not different in substance from ‘things’; the stream of my thoughts is a stream of things, namely of the things which I should commonly be said to be thinking of; what leads to its being called a stream of thoughts is merely that the laws of succession are different from the physical laws. (CP, Vol. 7, 15)
In other words, when viewed as being mental, a thought or idea may have associated with it other thoughts or ideas that seem related even though, when viewed as being physical, they have very little in common. As Russell explains, “In my mind, Caesar may call up Charlemagne, whereas in the physical world the two were widely sundered” (CP, Vol. 7, 15). Even so, it is a mistake, on this view, to postulate two distinct types of thing (the idea of Caesar, and the man Caesar) that are composed to two distinct substances (the mental and the physical). Instead, “The whole duality of mind and matter, according to this theory, is a mistake; there is only one kind of stuff out of which the world is made, and this stuff is called mental in one arrangement, physical in the other” (CP, Vol. 7, 15).
Russell appears to have developed this theory around 1913, while he was working on his Theory of Knowledge manuscript, and on his 1914 Monist article, “On the Nature of Acquaintance.” Decades later, in 1964, he remarked that “I am not conscious of any serious change in my philosophy since I adopted neutral monism” (Eames 1967, 511).
But at the moment I'm more exercised by the idea that Russell takes a simple thing (me saying 'the cheese in the fridge is off') and deliberately reconcocting it as a laminate of the material and the mental. That's not the purpose, or intention, of his theory of mentition, I know; but isn't it a necessary and debilitating aspect of it?