For me the question has brought out the different senses of left and right, which may or may not be interrelated.
The distinction is between a question like:
How does a right-handed object relate its left-handed counterpart?
and one like:
How does a human subject know his right hand from left hand?
One way to bring out the distinction is to consider the statement in JDH’s answer:
There may be little reason at first to believe that the actual physical universe is orientable, although we do experience this as a local phenomenon. But it is conceivable that a right-handed space traveler, having followed a certain path, would return as left-handed, while still insisting that he or she is right-handed. In such a universe, there would seem to be no fact of the matter about left and right.
Suppose we accept that there would be no fact of the matter about left and right in such a universe. This alone would, however, not make the traveler’s insistence nonsensical. To him, his right hand remains the right one in spite of any orientation swapping. (Of course we don’t have to call it the ‘right’ hand.)
I believe the question of how a human subject knows the right hand from the left is assimilable to how he knows the right hand from the right foot, or the nose. Again, we can strip the questions of ‘right’ and ‘left’ and also of ‘hand’ and ‘foot.’ We can also strip them of epistemology by asking what it is for a sensation in the right hand to be in the right hand. Or if we are allowed the terminology ‘tactile location’ we are asking what individuates tactile locations.
We may ask the same question of ‘visual location.’ When I open my eye I am confronted with what looks like a surface. I can divide it into left, center and right regions, or upper, center and lower ones. I believe I could do this even if I were floating in space without any gravitational pull and didn’t have the benefit of my right hand often appearing in the right region or my hair often falling in from the upper. Of course I may not have the ‘right and left’ and ‘upper and lower’ vocabulary. Again we are speaking of individuation of visual locations.
I don’t think there is any necessity about the correlation between visual and tactile locations. In each of these, I think something fundamental is going on. That is to say, I don’t think one ‘learns’ that a pain is in one’s right foot and not elsewhere. ‘At first I only knew there was some pain, but didn’t know where. But by and by, I came to learn to locate them. I had to hire a teacher and practice it on my free time.’ This is not our experience; I don’t even know it makes sense to speak of ‘knowing’ or ‘not knowing’ there. In the same way, I don’t think we ‘learn’ that a thing is in the center of our visual field, or to the left, or to the right.
Of course, our visual and tactile locations happen to correlate. My right hand often appears to the right of my visual field. Or the sight of a dog biting the hand ‘over here’ in my visual field often (all right, always) correlates to my having pain ‘over here’ in my tactile field.
Suppose then I hold an apple in my left hand and see it in the corner of my left eye. The apple is ‘to my left in space’ as it were. This location in space would bear a certain relation to the ‘left’ region in my visual field as well as the ‘left’ region of my tactile field. We may say any number of things about this relation (not all of them right). E.g. the left region in space, existing independently, is sensed, tracked etc. by sensory events in me; is a ‘construct’ of my sensory locations; is mere shorthand for saying what happened in my sensory fields; etc.
According to this view, the concept of spatial left and right to a human subject would in some way or other derive from the locations in his sensory fields. The individuation of locations in a particular sensory field would be fundamental, meaning not the sort of thing one learns.
I believe that the visual experience may lead the way (as it were) in the assignment of location. That is to say, while my nose, neck, left and right arms and hands, the groins, the two legs and feet, the twenty digits, while all these are distinct without my having to learn the distinction, I don’t know that they stack neatly one way or other. For example, could I have known that my thumb is farthest away from the pinky without seeing the five fingers?
I don’t intend to tell a physiological or developmental story. I believe there would be a way to strip the thing above of all that stuff so that we are left with a thin analytical statement about the reducibility of spatial location to individuation of location in sensory fields, which is not a thing to be learned.
Such location would survive any orientation swapping as is imagined in the other answer because we are talking about two different things. I want to add that I am not sure about this, but only propose it as a possibility. I certainly have not argued for it. Thanks.