“Aporia” is Aristotle’s Greek technical term used by many philosophers in English for what Sachs in his glossary to the Metaphysics calls an “impasse” or “logical stalemate that seems to make a question unanswerable. In fact, it is the impasses that reveal what the genuine questions are” (p. lv).
Book III of the Metaphysics develops many such impasses. I take this as evidence of Aristotle’s extraordinary intellectual honesty and depth of insight.
Aristotle writes, “[T]hose who inquire without first coming to an impasse are like people who are ignorant of which way they need to walk, and on top of these things, …one never knows whether one has found the thing sought for or not. For the end is not apparent to this one, but to the one who has first been at an impasse it is clear. And further, one must be better off for judging if one has heard all the disputing arguments as if they were opponents in a lawsuit” (p. 35).
“About all these things it is not only difficult to find a way to the truth, but it is not even an easy thing to articulate the difficulties well” (p. 37).
For anyone who has been following recent posts a little, we have seen abundant examples of such challenging but fruitful impasses in the development of Hegel’s Logic. Those were not just some weird things that Hegel cooked up, but yet more evidence of Hegel’s profoundly Aristotelian approach.
Aristotle mentions a long series of such impasses related to the subject matter of the Metaphysics, including those about the nature and number of causes; whether causes are universal or particular; whether there are things beyond perceptible things; the status of mathematical objects; and whether there are causes that are independent of what he calls matter (or “material”, as Sachs calls it to help disambiguate Aristotle’s more “logical” distinction from modern physicalistic concepts).
“Furthermore, the most difficult question of all, that has in it the greatest impasse, is whether one and being, as the Pythagoreans and Plato said, are not anything different, but are the thinghood of things — or whether this is not so, but the underlying thing is something different” (p. 36).
“And there is a question whether the sources of things are universal or like particular things, and whether they have being potentially or at work, and in turn whether they are at work in some other way or by way of motion” (p. 37).
“But now if there are a number of kinds of knowledge of the causes, and a different one for a different source, which of these ought one to say is the one… being sought?” (ibid).
“And in general, is there one or more than one kind of knowledge about all beings? And if there is not one, with what sort of beings ought one to place this kind of knowledge? But that there is one about them all is not reasonable; for then there would also be one kind of demonstrative knowledge about all attributes” (p. 39).
“But it is not possible for either oneness or being to be a single genus of things…. [I]f oneness or being is a genus, no differentia would either be or be one…. And on top of these things, the differentia are sources still more than are the genera” (p. 43).
“So from these things, it seems that the predicates applied directly to the individual things are sources more than are the general classes; but then in turn, in what way one ought to understand these to be sources is not easy to say…. For if there is nothing apart from particular things, while the particulars are infinite, how is it possible to get a hold of a knowledge of infinitely many things? For insofar as something is one and the same, and insofar as it is present as a universal, in this way we know everything. But if this is necessary, and there has to be something apart from particulars, the general classes of things would have to have being apart from the particulars…. But we just went through an argument that this is impossible” (p. 44).
“Now if there is nothing apart from the particulars, there could be nothing intelligible, but everything would be perceptible and of nothing could there be knowledge, unless someone claims that perception is knowledge. What’s more, neither could there be anything everlasting or motionless (since all perceptible things pass away and are in motion). But surely if there is nothing everlasting, neither could there be coming-into-being. For there must be something that comes into being and something out of which it comes into being” (pp. 44-45).
“And an impasse no lesser than any has been neglected by both present and earlier thinkers, as to whether the sources of destructible and indestructible things are the same or different. For if they are the same, in what way and through what cause are some things destructible and others indestructible?…. But about mythological subtleties it is not worthwhile to inquire seriously; but on the part of those who speak by means of demonstrations, one must learn by persistent questioning why in the world, when things come from the same sources, some of the things have an everlasting nature but others pass away. But since they neither state any cause, nor is it reasonable that it be so, it is clear that there could not be the same sources or causes of them” (p. 46).
“[B]ut if there are different sources, one impasse is whether they themselves would be destructible or indestructible…. Furthermore, no one has even tried to speak about different sources, but all say that the same sources belong to all things. But they gulp down the thing first stated as an impasse as though taking it to be something small.”
“But the most difficult thing of all to examine, as well as the most necessary for knowing the truth, is whether being and oneness are the thinghood of things…. But surely if there should be some being-itself and one-itself, there is a considerable impasse about how there would be anything besides these — I mean how things will be more than one” (pp. 47-48).
“So it is necessary to raise both these impasses about the sources, and one as to whether they are universal or what we call particular. For if they are universals, they will not be independent things. (For none of the common predicates signifies a this but rather an of-this-sort, while an independent thing is a this….) So if the sources are universal, these things follow; but if they are not universal but are in the same way as particulars, there will be no knowledge, since of all things the knowledge is universal” (pp. 51-52).