Constructive empiricists such as Bas van Fraassen hold that we should take our best scientific theories not to be true but merely empirically adequate, where a theory is empirically adequate when what it claims about observable phenomena is true. We should believe what our best theories tell us about the observable world, but remain agnostic about any unobservable phenomena they postulate. For the constructive empiricist, something is observable just in case it can in principle be detected by the unaided senses. So we should be agnostic about electrons, mitochondria, the strong nuclear force, the tricarboxylic acid cycle, etc.
Obviously, the cogency of constructive empiricism depends on whether the observable/unobservable distinction can be made to work. Van Fraassen treats observability as a property of entities. Some types of entities are such that they produce certain changes in our perceptual systems, provided we have the right kind of relation to them; these entities are observable. For example, Jupiter's moons are observable. From Earth, of course, we require telescopes to detect them, but they are in principle detectable with the unaided senses because we could travel to them, and then they would impinge on our senses in certain ways. So van Fraassen isn't agnostic about Jupiter's moons; he believes they exist.
The question is, how should the "in principle" be interpreted? What kind of relation to an entity is the "right" kind of relation? Van Fraassen, as far as I know, is fairly dismissive of this kind of problem. He thinks that "observable" is a vague predicate so there is no precise distinction between the observable and the unobservable, but this is no threat to constructive empiricism because even with a vague boundary we can still specify entities that are unambiguously unobservable. It seems to me, however, that without an answer to those questions, it isn't at all clear that there are any unambiguously unobservable entities - or at least, that the class of them becomes so small that constructive empiricism fades into realism.
Van Fraassen is happy to count distant astronomical objects such as quasars as observable, because we would detect them unaided if we travelled billions of light-years in their direction. Similarly, past entities such as dinosaurs are observable, because we would detect them unaided them if we went back into the past. The observable is not just what is detectable unaided given current technology, as Jupiter's moons are. We can also imagine technology that violates the laws of physics, that can take us millions of years into the past or billions of light-years distant.
There are various problems with this treatment of observability, but the constructive empiricist in particular surely can't accept it. Once we're allowed to imagine totally speculative technology, we might say that in principle I could see a bacterium with my unaided senses, because I could enter a miniaturization machine and be shrunk down to the bacterium's size. Indeed, it's worth noting that miniaturization appears to be more plausible than travelling to the most distant quasars, since miniaturization doesn't violate any laws of physics as far as I'm aware. So on this view, a whole host of phenomena become observable and the distinction between constructive empiricism and realism fades. One fix is to say:
(A) The observable is what is detectable with the unaided senses given current technology, here in 2017.
But now consider the situation for astronomers working, say, 300 years ago. Given the technology at the time, both Jupiter's moons and bacteria were equally inaccessible. It later turned out that space travel was feasible whereas miniaturization was not, but surely there was no justification available in the 1700s for expecting technology to develop that way. If we accept (A), then the constructive empiricist has the curious conclusion that, in the 1700s, it was reasonable to believe in Jupiter's moons even though there was good reason to think that Jupiter's moons were unobservable in the same way that microbes were unobservable.
A similar problem arises when we consider future technological developments. Maybe we will in fact develop miniaturization machines and people will directly interact with microbes. If observability is determined by current technology, then microbes will still count as unobservable and therefore our miniature descendents should remain agnostic about microbes. With these points in mind, it seems we have to drop (A) in favour of:
(B) The observable at time t is what is detectable with the unaided senses given the technology at t.
However, technology can regress. If a nuclear holocaust occurs and we lose our ability to construct telescopes, then Jupiter's moons will become unobservable again. The constructive empiricist would have to conclude that we must once again be agnostic about the existence of Jupiter's moon. To avoid this conclusion we can modify (B):
(B*) The observable at time t is what is detectable with the unaided senses given the technology at t and any time before t.
This doesn't seem to face any obvious problems. However, an interesting consequence of (B*) is that it can be used to strengthen the case against the constructive empiricist by supporting an "optimistic induction" argument for realism about unobservables. This is because (B*) allows that unobservable entities can become observable as technology develops. Briefly, the argument is that numerous entities postulated by our best theories were initially unobservable but later became observable, thus vindicating those believed in such entities; so we can similarly expect that those who believe in currently unobservable entities will be vindicated in the future if the technology develops to make those entities potentially observable.
Jupiter's moons were once unobservable. Over the past few decades we have sent machines to Jupiter, and we could probably even send a person there, though that might be a waste of time and money. In any case, Jupiter's moons clearly do exist. The astronomers of the past who believed in these objects have been vindicated. Numerous other examples can be found from astronomy: (a) Other planets and moons and their properties. We can now see directly that the Moon's surface is disfigured by craters, that Venus undergoes phases similar to the Moon, that Mars has a tenuous carbon dioxide atmosphere, etc. (b) The true properties of the Sun, such as its size and sunspots. (c) The asteroid belt. (d) Comets. (e) Certain properties of the gravitational force. We feel a particular gravitational force on the surface of the Earth; now we can ascend to space in rockets and directly feel that the force is lesser there. (f) The shape of the Earth: predicted to be an oblate spheroid on theoretical grounds, its shape can now be directly seen.
Of course, this is an inductive argument, and van Fraassen rejects induction. However, as far as I can tell, this is not a necessary feature of constructive empiricism. In any case, anybody who accepts induction has an additional reason to be wary of constructive empiricism.
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