Intellect and Imagination are two of the primary powers of the human mind. They are very distinct in their operations, yet human beings have a tendency to confuse the two. Most human beings, Plato observed, have great difficulty in rising above the level of sensuous thought, that it, thought which makes use of imagery—for Plato, a philosopher who was also a great poet—it was a matter of course to enlist the imagination in the service of the intellect, giving us so wondrous images as the famous Cave described by Socrates in the Republic.
The Greeks had a conception of two distinct powers of mind that we call “imagination” in English: the εἰκασία and the φαντασία, the “image-ination” proper and the “fantasy.” English poets briefly attempted to distinguish the imagination from “the fancy,” but it never caught on. Generally speaking, the εἰκασία deals with veridical images, images that are related to an original through which the original in some way shows itself; it is the higher of the two functions. For Plato, it is necessary for wisdom to proceed ever-higher in the scale of being, for which the εἰκασία is necessary: in a sense, the Platonic conception of being is one of layers in which each level is a kind of image of the level above it. So in the Cave Image (itself an image) Plato presents “shadows of artificial things,” “artificial copies of real things,” “natural copies of real things (e.g. reflections in water)”, and finally “real things.” The things which are ὄντως ὄν (“beingly being”, which doesn’t work in English, or “really real” which does) are the εἰδή, the Platonic “ideas” or forms, with visible beings being in a sense copies or images of these originals. It is by grasping an image as an image that one is enabled to see through the image and allow one’s gaze to pass on to the original of which the image is an image. This is the function of the εἰκασία.
The φαντασία on the other hand is a lower power. It is not limited to producing images of originals (copies) but can pull apart and recombine all manner of things that one has experienced before. Thus one can combine a horse and wings to make Pegasus, or the torso of a man and the lower body of a horse to make a centaur. And so on. The φαντασία is probably what most modern people mean when they speak of the imagination.
Here’s the problem I wish to point out. Quite simply, human beings in general, and modern Westerners in particular (for reasons in the history of philosophy I won’t get into), tend to conflate the imagination and the intellect. That is to say, they take “unimaginable” and “inconceivable” to be synonyms, and also “imaginable” and “conceivable” to be the same.
They are not, however, and I am going to prove it, with two very simple arguments.
The first is straight from Descartes. He asks that one consider an equilateral triangle. One can both easily conceive of (understand) an equilateral triangle: “a three-sided plane figure in which all sides are of equal length.” One can also easily imagine or picture such a triangle, thus
A “four-sided plane figure in which all sides are of equal length” is a square. Again, this is both easy to understand and to picture, that is, to cognize with the intellect and image with the imagination.
But how high can we go? How many sides can one distinctly imagine? Descartes suggests we try out a chiliagon (chilo- is a variant of kilo-); this is also easy to understand by means of the intellect. It is a “thousand-sided plane figure in which all sides are of equal length.” Conceptually, this presents no more difficulty than the equilateral triangle or the square. But can one imagine a chiliagon? Clearly and distinctly in one’s mind’s eye? Obviously not. One would arrive, at best, at a vaguely circular picture that even if one had it drawn out, one could not distinguish from a 999-sided figure nor a 1001-sided figure. How many sides does this have?
Wikipedia informs me it is a chiliagon. I’ll take their word for it (if not much else). You may count if you like.
Descartes’ conclusion? The intellect and the imagination are very different. Some things may be easily grasped by the intellect, such as, “1000-sided equilateral figure,” which are impossible to imagine.
And it also seems the case that we can imagine things that are impossible to conceive. We can be fooled by pictures into thinking something real that is, strictly, impossible. Consider this famous picture by M. C. Escher
Here we have an endless stair that is “all down” in one direction and “all up” in another, looping back on itself. The image makes visual “sense” in a way because we don’t take it all in at once. Each segment of stairs looks like it descends or ascends to the next, but clearly this can’t actually happen. And then there’s the famous trident:
Does it have three prongs or two? Needless to say, there is no precise mathematical description of this “figure” since it is impossible. Which is to say, it cannot be conceived of, other than has an illusion, an combining together by the φαντασία of things which cannot be so combined.
And this is problem with the φαντασία: by giving us an illusion of conceivability, it can distort our thinking.
The most famous case in the history of philosophy I can think of is Hume’s “proof” that it is possible to conceive of something coming to be without a cause. He does this simply by asking us to imagine an object appearing suddenly, “appearing from nowhere” as our English expression goes, and then, a smirk on his pudgy face, says “See?”
But as Elizabeth Anscombe (and others, including Hume’s contemporary enemy Thomas Reid—who should be read more) point out, Hume has not shown the conceivability of a thing “popping” into being from nothing or of an event occurring for no reason: he has simply imagined a thing appearing abruptly, for reasons and with causes unknown.
Philosophers, and of course regular people also, can get into a great deal of conceptual trouble when they mistake the imaginable for the conceivable or the unimaginable for the inconceivable.
Be careful not to make this mistake. It could end badly for you.