Pearson’s view that science is the only way to attain knowledge, as laid out in The Grammar of Science (1900), is ingenious—and he was a very clever man. However, his view is easily refuted:
Pearson states that although the scientific method is the only way to know anything about reality, it relies on imagination to work, at least in some modest respects;
He concedes that imagination is outside the scientific realm, you cannot have knowledge about it—the more imaginative you become, the less scientific you are;
Hence his “only real knowledge” relies on a thing that, by his own definition, is not real knowledge;
And so it is impossible to say that reality is reducible to that which is investigated by science—because science requires that which is non-scientific to function.
It is the case that science might be said to require “minimum imagination”—just enough to “prime the pump”, perhaps to formulate a hypothesis.
However, very little is still some—and so science, by Pearson’s own admission, stands on ground that it cannot itself investigate. That which, in Pearson’s own terms, “it is impossible to have knowledge about”.
It could be said that Pearson asserts “our only real knowledge is based on that which, by our own definition of knowledge, it is impossible to have knowledge about.”
This suggests that the purported “only real knowledge” is not the only real knowledge, since it relies, if only to a modest extent, on that which it claims to exclude as “not real knowledge” to produce any knowledge at all.
The “unknowable realm” includes religion, metaphysics, philosophy itself, and, finally, art.
And it should be noted that just because it is imaginative does not mean that it cannot be investigated by reason—philosophy and metaphysics are rational and logical investigations into the imagination (and realms beyond the imagination).
It can also be approached through faith and gnosis, as well as through symbolic representation—art.
Hence while material science is a way to attain knowledge, it cannot be said to be the only way—for it can only be the “single way” if it denies what it stands on.