In the third chapter, "The Nature of Matter", Russell wants to describe what "persists independently of my perception of it" (page 43).
Consider the full paragraph from which the quote is taken:
It is not only colours and sounds and so on that are absent from the scientific world of matter, but also space as we get it through sight or touch. It is essential to science that its matter should be in a space, but the space in which it is cannot be exactly the space we see or feel. To begin with, space as we see it is not the same as space as we get it by the sense of touch; it is only by experience in infancy that we learn how to touch things we see, or how to get a sight of things which we feel touching us. But the space of science is neutral as between touch and sight; thus it cannot be either the space of touch or the space of sight.
I put in bold the quote. Here is the question:
I do not understand this. Does anyone mind rewording, rephrasing it or explaining it?
I understand (I think) the overall point he is making: our experience of space, is not space itself, it is not like matter is in our experience of space, if matter is to be shown as independent of our experiences then it must be somewhere and this somewhere must be public ‘space’.
The space of science is independent (or neutral) with respect to our perceptions, that is, with respect to our senses of touch or sight.
Each of these senses creates a space that Russell calls the "space of touch" or the "space of sight". These are not the space that science considers. We get these spaces through our perceptions, but science wants to consider matter independently of these perceptions.
So these spaces must be abstracted away to reach a neutral space, independent of perceptions, in which science can describe matter.
Bertrand Russell, The Problems of Philosophy Chapter 3 The Nature of Matter, Wikisource: https://en.wikisource.org/wiki/The_Problems_of_Philosophy/Chapter_3