We can’t know what it’s like to be a bat. This is an instance of a more general truth: no one can grasp the nature of experiences that are radically different from their own. We can grasp the nature of experiences similar to our own, but we can’t grasp experiences that are qualitatively different from ours. We are ignorant of phenomenological facts that diverge from our own. Bats can know what it’s like to be a bat, and so presumably can dolphins, which employ a similar echolocation sense; but beings that have no such sense are in the dark about the experiences involved. It is the same story for the congenitally blind: they can’t know what it’s like to see—as the deaf can’t know what it’s like to hear, or the pain-free to understand what pain is, or the nasally challenged to appreciate smells, or the emotionless to know what anger is. In the realm of the phenomenological there are sharp constraints on what is knowable and by whom. You can’t even know what it’s like to experience red if you have only experienced blue. This is an epistemic limitation—a limitation on what can be known, understood, or grasped. It is not an absolute limitation—a reflection of the intrinsic nature of the fact in question—since it can be overcome by creatures that happen to participate in that fact; it is a relative limitation—X can’t be known by Y (though it can be known by Z). It isn’t universal ignorance but creature-relative ignorance.
The question I am concerned with is why such ignorance exists: what is its explanation? We have a kind of extrapolation problem: how do I move from knowledge of my own phenomenology to knowledge of the phenomenology of others? It appears that I can do this when there is similarity, but not when there is (radical) difference. My ability to extrapolate is blocked by dissimilarity. The question is why such extrapolation limitations exist. To see the problem let us review some cases in which there are no such extrapolation restrictions. Consider geometry: are we limited only to knowledge of shapes we have encountered? Are alien geometries incomprehensible to us? We have certainly not experienced all possible polygons, so what about those that lie beyond our geometrical experience? Here the answer is obvious: we are not so limited. To simplify, suppose a person never to have experienced rectilinear figures but only curvilinear ones, so that he has never seen a triangle (say). Does that mean he can’t understand what a triangle is? No, it can be explained to him perfectly well and he will thereby understand the word “triangle”. So while we can’t grasp a type of experience we have never encountered in ourselves, we can grasp a type of geometrical figure we have never encountered in the perceptible world. We can extrapolate in the latter case but not in the former. We don’t have acquaintance-restricted knowledge in geometry, but we do in phenomenology. There are gaps in our understanding where experience is concerned, but not where shapes are concerned. It is the same for animal species: you don’t need to have seen an elephant to know what an elephant is (or a bat). Elephants can be described to you, pictured, and imagined; and they don’t need to be similar to animals you have seen with your own eyes. You know what an animal is and you understand what kind of animal an elephant is by description. But you don’t know what kind of experience a bat has even though it has been described to you (based on echoes, having such and such brain correlates, etc.). Also: suppose you had never heard of odd numbers, having been brought up only to deal with even numbers. That would not prevent you grasping the concept of an odd number once someone explained it to you. There are no irremediable gaps in our grasp of numbers analogous to the gaps in our grasp of phenomenology. Likewise, our knowledge of astronomy is not limited by the extent of our acquaintance: we grasp the concept of remote and alien galaxies without ever experiencing them. But our general concept of experience doesn’t enable us to fill in the gaps in our acquaintance with experience: we can’t say, “Oh, bat experience is simply this” and feel that we know what we are talking about. Our knowledge of phenomenology is thus gappy in a way our knowledge of other things is not. We can’t use a form of induction to extrapolate to types of experience that we have not ourselves directly (introspectively) encountered. The question is why. And the question should seem pressing, because the epistemic limitation is so anomalous and local—in general, there are no such limitations on knowledge.  It is surprising that we don’t know what it’s like to be a bat.
We must canvas some putative explanations. One possible explanation is that experiences concern the mind, while the other cases I mentioned concern the non-mental world. But this explanation is inadequate because (a) some facts about the mind are not so limited and (b) there are facts about physical objects that are subject to the same limitation. I can understand what beliefs you have even though they are quite alien to me—their odd content isn’t an obstacle to my knowledge; and I can’t grasp a color that I have not seen if it is different from any I have seen. Color blindness will result in color ignorance, even though colors are perceptible properties of physical objects; but my unfamiliarity with crazy conspiracy theories isn’t an impediment to my knowing what weird belief is in question. So the epistemic limitation we are interested in isn’t just a reflection of a general truth about knowledge of the mind versus knowledge of non-mental things. But even if it were such an instance that would not answer our question, because that question would now shift to the more general question: how come we can extrapolate about things outside the mind but not things inside the mind? What is the source of that difference?
A more promising suggestion is that the realm of experience is simply less homogeneous than the realm of the physical (to speak loosely), so that it would involve greater cognitive leaps to extrapolate across this realm. Geometry is about essentially similar things while phenomenology includes very diverse things. But by what criterion is bat experience so different from (say) visual experience while circles and squares are deemed essentially similar? The concept of similarity will not bear this kind of weight. Some people have urged that bat experience is not really all that different from ours: it is a type of auditory experience for one thing, and for another it has many of the properties of visual experience (a distance sense used to navigate and locate objects in space). These points may be conceded while still insisting on the alien character of such experience: but then how are triangles and circles to be supposed more similar? One loses one’s grip on what notion of similarity is at issue here. There is really no objective basis for distinguishing the cases; the difference arises rather from our mode of knowledge in the two cases. The phenomenological realm is not objectively more diverse than the geometrical realm (or the mathematical realm or the zoological realm); it is rather that our method of knowing somehow differs—we find it easier to extrapolate in the one case than the other. But why is that?
Along the same lines it might be said that we are actually just as limited in geometry as we are in phenomenology, because geometry also includes extreme knowledge-blocking diversity. Thus non-Euclidian geometry might be said to differ dramatically from Euclidian geometry—as radically as bat experience differs from human experience—so that it is impossible to extrapolate from one to the other. Accordingly, we don’t really grasp non-Euclidian geometry, just as we don’t grasp non-human phenomenology. Since there is then no epistemological asymmetry between the cases, there is nothing to explain—no epistemological anomaly to account for. Alien geometry is as incomprehensible as alien phenomenology (and the same might be said for such things as irrational numbers or alien types of animal). The weakness of this position is that it is by no means clear that there is any epistemic limitation attending the allegedly alien types of fact. We do grasp non-Euclidian geometry (and irrational numbers and the platypus). So the epistemic asymmetry still exists in undiluted form. The puzzle thus persists as to what the basis of the asymmetry might be: why is it harder to know one thing than the other? What makes alien phenomenology peculiarly recalcitrant to understanding?
Here is a completely different approach: alien phenomenology is like alien language. Humans are born with a specifically structured language capacity that prepares them for the particular languages they will encounter, but it is not suitable for the acquisition of languages with a different kind of structure. The human language faculty will not work to produce knowledge of alien grammars—as it might be, non-discrete elements that combine according to quite different grammatical principles from those of natural human languages (no recursion, for example); or don’t combine at all. It is dedicated and differentially structured, not an all-purpose learning device. If you place a human infant in a linguistic environment that is radically alien, she will not end up with knowledge of the language in question. Suppose bats were to speak such a language: the human child would not come to know its grammar and speak it like a native upon exposure to that language. Linguistic knowledge is thus subject to epistemic limitation as part of its innate character. At best a person might laboriously decipher the grammar of a radically alien language and speak it awkwardly and unnaturally—rather as someone might develop an abstract and unintuitive conception of bat experience. So the suggestion is that the reason we don’t grasp bat phenomenology is that our innate phenomenology module isn’t designed to extend to types of phenomenology that are alien to our own. That is, our innate knowledge of phenomenology is restricted to types of mind whose phenomenological “grammar” matches our own. It is not that alien grammars are objectively more difficult or complex than human grammar; it is just that there is a bias built into the human language module that favors one type of grammar over others. From an evolutionary point of view, it is important for us to have a solid grasp of our own minds (“theory of mind”), so we are genetically equipped with such knowledge; but there is no biological reason to have a solid grasp of bat minds, so lacunae there are acceptable. It is not as if there has been natural selection operating on humans to improve their grasp of bat psychology! Human phenomenological knowledge is domain-specific and geared to our environmental niche, so it is simply not designed to cover bats and their ilk.
This theory of phenomenological ignorance has the look of what we are seeking, but it might be wondered whether it is strong enough to deliver the epistemic limitation that apparently exists. In the language case, as noted, it is possible in principle for us to overcome our innate bias and acquire knowledge of the grammar of an alien language, albeit laboriously; but is it possible in principle to come to know what it’s like to be a bat? Isn’t that limitation a lot harder to overcome? I don’t know the answer to this: I don’t know whether intensive training, especially during the sensitive periods of child learning, could yield intuitive knowledge of bat phenomenology. Certainly, given that the experiential modality is auditory, the building blocks are there, and maybe training in echo-navigation in the first few years of life could produce a sense of the structure and operations of bat experience (hearing aids would help). So the obstacle may not be insurmountable. Also, we can surely imagine beings that can’t overcome their linguistic bias and so can’t learn an alien language even in principle. So the cases might not be as all-or-nothing as they seem at first sight. The idea of an innate phenomenology module certainly seems intelligible enough, and it delivers an explanation of the puzzling asymmetry I have noted. Just as we have an innate module for our belief-desire theory of mind, so we have an innate module for our phenomenological theory of mind. We could have been born knowing what bat experience is like, as we are born knowing what human experience is like; but actually we aren’t and that produces the epistemic gaps in question. Our knowledge of geometry, arithmetic, and zoology is different, not being based on a selective module like the language faculty (or not as selective); but our knowledge of phenomenology is sharply constrained and not easily overcome (if at all). We are not, as they say, plastic when it comes to phenomenology.
Notice that according to this theory it is not really correct to suppose that our knowledge of phenomenology is based on our acquaintance with our own experience. That is an empiricist theory of such knowledge analogous to empiricist theories of knowledge of the external world (we possess concepts by abstraction of properties from perceived particulars). But the nativist theory of phenomenological knowledge holds instead that we have such knowledge independently of acquaintance with our experiences. We know what experiential types are without any such operation of acquaintance and associated abstraction, but innately. So the problem isn’t that what we abstract from own experience doesn’t fit the experience of bats, but rather that we are not innately equipped with a faculty of knowledge that includes the knowledge in question. In short, we don’t know bat psychology innately. No doubt acquaintance plays a triggering role in the production of phenomenological knowledge, but it doesn’t play an originative role (as with other innate knowledge systems). Maybe even producing actual bat experience in us wouldn’t itself be sufficient to acquire knowledge of the nature of bat experience, because that requires the cooperation of an innate faculty of phenomenological knowledge geared to bat experiences, which is absent in humans. In any case, an empiricist theory of phenomenological knowledge is by no means to be assumed (if it’s false generally, why should it be true here?). 
I want to emphasize not so much the proposed solution as the problem it is designed to solve. We know there are phenomenological facts in the world with a nature we can’t grasp, though other beings can; this poses a problem of explanation. The case looks very different from other types of knowledge. It is a non-trivial question why this is so, raising some deep issues. It challenges conceptions of knowledge that have been long entrenched, notably how we know the nature of our own experiences. How exactly do I know what pain is, or experiences of red, or anger?
 It is an interesting fact that an empiricist theory of phenomenological knowledge is attractive even to people who are skeptical of an empiricist theory of knowledge of physical objects. I’m not sure why this is—is it because it is easy to conflate experience with knowledge of experience? In fact, actual bats may not know what it’s like to be a bat simply because they lack this kind of introspective knowledge, despite possessing the corresponding experiences.