G. E. Moore takes up, in "Proof of an External World" (1939) Kant's challenge to prove the existence of "the external world". A necessary preliminary step is to clarity just what "the external world" is taken to mean. Moore intends a characterization as general as possible of "the external world", without getting into any avoidable metaphysical commitments.
The "external world" is roughly the physical world, but without any reference to actual physical concepts. That is because the philosophical proof is largely independent of physics, in the sense that the proof should hold even if the actual physics were very different than what it actually is.
To prove the existence of "the external world" would be to prove the existence of objects in space. It is for these that Moore chooses the formulation "objects that are met with in space". By that he means, on the one hand, objects that are not necessarily "physical bodies" (bodies are, roughly, objects that can be manipulated directly by interaction), but also merely optical "objects" such as shadows and rainbows.
But the phrase "things that are to be met with in space" can be naturally understood as applying also in cases where the names "physical object," "material thing," or "body" can hardly be applied. For instance, shadows naturally understood as synonymous with whatever can be met with in space, and this is an expression which can quite properly be understood to include shadows.
On the other hand, Moore did not intend to include in "objects that are met with in space" phenomena such as after-images, even though an after-image is perceived as-if it were out there in space. An after-image is also not a mere illusion or day-dream, in the sense that it is systematically related to the perception of actual bodies.
But it is easy to find examples of "things," of which it can hardly be denied that they are "presented in space," but of which it could, quite naturally, be emphatically denied that they are "to be met with in space." Consider, for instance, the following description of one set of circumstances under which what
some psychologists have called a "negative after-image" and others a "negative after-sensation" can be obtained. "If, after looking steadfastly at a white patch on a black ground, the eye be turned to a white ground, a grey patch is seen for some little time."
Why is an after-image less than a shadow? Moore is suggesting that two persons who perceive a shadow, perceive the same shadow. But two persons that perceive an after-image, perceive two different after-images, even if the two after-images are qualitatively the same and are perceived at the same place and under the same conditions. And this is the reason not to include after-images among "objects that are met with in space".
When I say that the white four-pointed paper star, at which I looked steadfastly, was a "physical object" and was "to be met with in space," I am implying that anyone, who had been in the room at the time, and who had normal eyesight and a normal sense of touch, might have seen and felt it. But, in the case of those grey after-images which I saw, it is not conceivable that any one besides myself should have seen any one of them . . . It is natural so to understand the phrase "to be met with in space," that to say of anything which a man perceived that it was to be met with in space is to say that it might have been perceived by others as well as by the man in question.