The more people I ask, the more people seem okay with the idea that most of what we see, most of the time (roughly, everything not in the region of optical focus), is double. Whoa! I get the heebie-jeebies. Either common sense is badly wrong -- if common sense is what I take it to be! -- or a substantial number of introspectors (including such eminent ones as Helmholtz and Titchener) are badly wrong. Grist for my skeptical mill. But not happy grist. Now I'm walking around thinking maybe I'm crazy for not seeing the persistent doubling that so many say is always there!
I take comfort, though, that Stephen Palmer, whose 1999 textbook Vision Science is generally considered standard in the field, analyzes the phenomenon much as I would:
One question that naturally arises from all this talk about disparity between the two retinal images is why don't we normally experience double images?... The answer has at least two parts. One is that points on or near the horopter [roughly, points at the same distance as the point on which you are focusing and on which your eyes are converging] are fused perceptually into a single experienced image. The region around the horopter within which such disparate images are perceptually fused is called Panum's fusional area. The second part of the answer is that for points that lie outside Panum's area, the disparity is normally experienced as depth. You can experience double images if you attend to disparity as "doubleness," however, or if the amount of disparity is great enough, as whenyou cross your eyes by focusing on your nose (p. 209).
Palmer seems to be saying that normally we don't see double, unless we attend to disparity as doubleness. He might then say -- as I would say -- that the reason so many people seem willing to attribute doubleness to their daily experience, when prompted to attend to double images created on the spot, is that they illegitimately infer that their normal visual experience is like their experience during such doubling exercises. But if so, that suggests an interesting instability and suggestibility among people in their judgments about ordinary visual experience!
Conversely, someone might argue against me, and against Palmer, that our experience when we think about doubling is our typical experience: We just ordinarily miss it in ordinary experience because we don't really think about or register the actual double-experiences we have of things off the horopter (or outside Panum's area) in the everyday run of life.