Locke held that the mind deals with abstractions by forming abstract ideas, by which he meant – or seems to have meant, or was interpreted to mean – mental images with less than fully determinate content. For example, on Locke’s view the abstract concept of a triangle is a generic mental image – an image whose content is a triangle, but not specifically an acute or obtuse or equilateral, not specifically a right or isosceles or ….
To many of Locke’s empiricist successors – notably Berkeley and Hume – Locke’s solution was unacceptable, because, so they argued, all mental images are determinate. We can’t form an image of a triangle, they maintained, without its being the image of some specific kind of triangle. So the possession of an abstract concept, they concluded, must consist not in the contemplation of an indeterminate image but rather in what we do with our determinate images.
Now on the whole I’m on the side of Locke’s critics here (even if their conception of what sort of “doing” the possession of a concept consists in was rather impoverished). But I think they picked the wrong criticism to make of Locke’s position.
Here’s why. Locke’s critics were quite wrong in thinking we can’t form indeterminate mental images. On the contrary, our mental images generally are somewhat indeterminate; so, for that matter, are our very perceptions. When we see a tiger and observe that it has stripes, there is, I claim, no particular number of stripes we perceive it as having. If Locke’s critics thought otherwise, it was probably in part because they failed to see the difference between the indeterminate idea of a tiger and the idea of an indeterminate tiger, and partly because in typical representationalist fashion they thought of the field of vision (and the field of imagination too) as something like an internal viewing screen covered with pixels. Since there’s always more determinacy available to see if we look more closely, they implicitly figured such determinacy was already there on the internal screen (whereas for us direct realists it’s the external world we’re looking at to find the inexhaustible additional determinacy, so it needn’t be inside our minds already).
But while Locke is thus correct in holding we can form indeterminate mental images (if, again, that’s indeed what he means by abstract ideas), he’s surely wrong in thinking that these images can do the work of abstract concepts. For even if our mental images are not perfectly determinate, Locke’s critics were right to insist that they are more determinate than their associated concepts. When I think about tigers, the mental image that I form may not represent a determinate number of stripes, but it does represent the tiger as orange. My concept of a tiger, however, is not so determinate as to be restricted to orange tigers; it applies to white tigers too. So although I may form a mental image when I think about tigers, my concept is not identical with that mental image. Perhaps thinking about tigers involves, Aristotelean-wise, selective attention to certain generic features of my image, but it is not and cannot be simply a matter of having the image. Conceiving is an activity, not a static condition.
This raises the question: suppose there were an intelligent species capable (as we seem not to be) of forming mental images to any desired degree of indeterminacy, so that just as we can imagine a tiger without imagining any specific number of stripes, they could imagine a tiger without imagining anything more specific than tigerhood. (This might have to be a species with a special perpetual system just for detecting tigers.) Could their mental images serve as abstract concepts?
Again, no, methinks. For just as my mental image of an orange tiger could serve as the occasion either for thinking about orange tigers or for thinking about tigers generally, so our hypothetical Martian’s image of a tiger simpliciter might serve as the occasion either for thinking about tigers or for thinking about some still broader category, e.g., mammals. For Martians as for us, what a mental image means depends on what we do with it. (Wittgenstein made just this point when he noted that thinking of a visit from Mr. B and thinking of a visit from Mr. B’s identical twin brother, or thinking of Oxford on fire and thinking of a university that looks just like Oxford on fire, are distinct mental activities, yet the associated mental images are identical.)