Realisms and Anti-Realisms
We reflexively speak of realism and anti-realism, as if we had a dichotomy of positions: you are either a realist or an anti-realist about a given subject matter. But this is too simple: there is a range of positions going from one extreme to another, depending upon the ostensible relation between the subject matter in question and human knowledge and experience. Consider material objects: the further the nature of such objects is removed from human knowledge and experience the more of a realist one becomes, and the closer the more of an anti-realist. Suppose you hold that material objects have only unknowable properties, so that their nature is totally distinct from anything revealed to the human mind. Then you hold an extreme realist view of material objects—they are maximally unrelated to human knowledge. The objects are objectively a certain way, but that way transcends the capacities of the human mind. But you might hold to a weaker thesis, namely that the properties of objects are knowable and yet independent of the mind: objects would be that way even if no minds existed, though all properties are in principle knowable. This also would be a realist thesis. You might even hold that all properties of objects are actually known and still be a realist about them.
But you might want to go a step further towards the mind: every property of an object must be the categorical basis of a disposition for the object to appear in a certain way. This position combines a non-identity thesis with respect to properties and their disposition to appear with a limit to properties that form the basis of such dispositions; if a putative property fails to correlate with any such disposition, it is deemed not to exist. Next you might choose to dispense with the categorical bases and simply identify properties with dispositions to appear: to be square, say, is just to have a disposition to appear square. Now you are moving into phenomenalist territory–objects as possibilities of sensations. That sounds decidedly anti-realist, but you are not quite there yet: for it might be supposed that the features of sensations that define material objects are not known to the subject of experience. This possible position is not typically recognized in the area of philosophy dedicated to these questions, but it exists in logical space. Thus it might be supposed that sensations are identical to brain processes, so that being square is identified with a disposition to cause certain brain processes in subjects (those correlated with its seeming that there is something square there). But these brain processes are not known to the subject, so objects are both dependent on sentient beings and yet removed form such beings’ knowledge. This strikes us as a weak form of anti-realism about material objects; and we can envisage variations on this theme that detect hidden aspects to conscious experience. A stronger form of anti-realism maintains, familiarly, that properties of objects are identical to dispositions to produce experiences that appear a certain way (“sense-data”). And then we have the most extreme anti-realist thesis of all, namely that so-called material objects have no existence save that of actually producing experiences with a certain appearance—to be square is just to actually appear square to someone at some time. We thus move from the thesis that material objects have a completely unknown nature to the thesis that they are nothing but fully known experiences—but this movement goes through a number of intermediate steps, not an abrupt switch from realism to anti-realism. That dichotomy does not do justice to the range of philosophical positions available to the theorist of material objects.
We can run a similar gamut for realism and anti-realism about the mind. A strong realist might hold that mental states exist but are never revealed in behavior, being cut off completely from third-person knowledge: the properties of mental states are completely unknowable to the outside observer, so that their existence and nature is independent of any behavioral evidence that might be adduced. Or they might be thought to be knowable via behavior but not identical to behavior (or dispositions to behavior). Or they might be thought to be the categorical basis of dispositions to behavior. Or they might be taken to be the dispositions themselves. Now we are squarely in anti-realist behaviorist territory, but again there is a neglected position here: what if the aspects of behavior that constitute mental states are hidden to observers? It might be supposed that they are the muscular and neural events that underlie observable behavior, so that they are not the evidence we normally use to ascribe mental states to others. This position combines an ontological claim about the nature of mental states—they are identical to episodes of behavior—but it removes them from ordinary third-person observation. The standard behaviorist position is that mental states are identical to observable behavior (under some notion of observation). This position is clearly anti-realist because it ties the mental facts to our evidence for asserting these facts, but the weaker behaviorist position doesn’t claim this connection to evidence—it is quasi anti-realist. Once again, the usual dichotomy of realist and anti-realist fails to capture the full range of options. We have gone from maximally realist to maximally anti-realist, as gauged by proximity to evidence, via a number of intermediate positions. The usual dichotomy is too crude.
The moral case follows a similar pattern. You could hold that some moral truths are completely unknowable, or even that all are (though that is certainly hard to credit). Or you could hold that, though knowable, moral truths are not mental in nature. Or you could hold that moral values are dispositions to elicit approval, or just approval itself. The neglected position would be that moral facts reduce to mental facts but that mental facts have a hidden aspect that constitutes moral facts (substitute for “facts” here anything you like). That is, moral facts might be mind-dependent and yet inaccessible to the subject, because the relevant mental states have a hidden aspect—as it might be, brain states or some other inaccessible property. What if you thought that moral approval is really an unconscious matter inaccessible to the conscious mind? Again, we have a range of conceivable positions, differing in strength, not a simple dichotomy. If someone says he is a moral realist, we need to ask what specific kind of realism he has in mind; and similarly for the moral anti-realist. There are clearly degrees of inaccessibility relating facts and our knowledge of them, and these define different kinds of metaphysical position. The same situation obtains for the mathematical and modal cases, though I won’t spell out how this goes, as it should be obvious by now.
The case of time is instructive. An extreme realist view would be that we can’t know anything of the past and the future, even though these stretches of time exist as determinately as the present. A less extreme view is that some facts about the past and future can be known but these facts have nothing intrinsically to do with what obtains in the present—they are in no way constituted by present facts. The anti-realist will insist, by contrast, that past and future facts are constituted by present facts or else do not exist at all; but again there is room for two strengths of position here—do these present facts provide our evidence for assertions about the past and future, or are they merely present whether evidential or not? That is, might they be currently inaccessible present facts? Maybe the past consists in current microphysical facts of which we have no knowledge, or the future consists of current facts of divine dispensation about which we are ignorant. This is recognizably anti-realist, though there is no claim of reduction to evidence. The stronger kind of anti-realism claims that past and future reduce to current evidence, presumably observable evidence of the kind we typically rely on to make statements about other times. This in turn can be regarded as mental in nature, as when it is held that the past reduces to present facts about sense data and not to external physical traces. There is thus no such thing as the anti-realist about the past, since a number of different positions can qualify for that description; and similarly for the realist about the past. What we really have is the comparative locution “A is more realist than B”, and likewise for “anti-realist”.
This also shows that it is not a helpful formulation to describe the realism versus anti-realism dispute as a contest between truth-condition semantics and assertion-condition semantics. That distinction is indeed dichotomous, but the distinction of metaphysical realism and anti-realism is not; so we had better not try to formulate the latter in terms of the former. We should not, here as elsewhere, let the metaphysical debate take a linguistic turn.
 I will mention that nominalism admits of varying strengths of anti-realism depending on how symbols are conceived. If symbols are observable marks on paper, then we get a close proximity between numbers and sensory evidence; but if instead they are viewed as internal mental entities in an unconscious language of thought, then we get distance between numbers and perceptual evidence, since such symbols are not perceived at all.