This whole chapter gives me the headache. For one thing, I had more trouble here than usual in separating Dühring, Hegel, and Engels. I wish he’d used more direct quotes, or been more precise about when he was summarizing. But even aside from that, contemplating infinity hurts, and, before I attempt it, I want some reason to believe it will be useful. I mean, I accept that Herr Dühring said some idiotic things about it, but that isn’t the point of reading this book. Do Engels’ considerations about infinity of time and space actually produce any positive knowledge? Let’s see.
Okay, we’re mostly dealing with absurd definitions of infinity, and attempts to treat it as if it were finite, with predictable results.
And then he quotes Kant, about whom the most that can be said is that he is more easily comprehended than Hegel. But then, so is Cervantes in the original Spanish, and I don’t speak Spanish.
Alright, that next part I sort of get. There is a distinction between an infinite series–which starts at 1 and continues forever; and infinity in space, which has no starting point in any direction. Gotcha. Now onto time:
“But if we think of time as a series counted from one forward, or as a line starting from a definite point, we imply in advance that time has a beginning: we put forward as a premise precisely what we are to prove.”
“For that matter, Herr Dühring will never succeed in conceiving real infinity without contradiction. Infinity is a contradiction, and is full of contradictions. From the outset it is a contradiction that an infinity is composed of nothing but finites, and yet this is the case.”
“It is just because infinity is a contradiction that it is an infinite process, unrolling endlessly in time and in space. The removal of the contradiction would be the end of infinity.”
Okay, yeah. Infinity is itself a contradiction–that is, simultaneously one thing and its opposite (I know there are those who do not believe contradictions are possible in nature; we will deal with them in due course).
“For the basic forms of all being are space and time, and being out of time is just as gross an absurdity as being out of space.”
In essence, Herr Dühring is suggesting a state previous to time, and thus previous to motion. With the entire world in such a state, whence would come the initial motion? Answer: from outside the world, or, in other words, God. Therefore, if we are not to become hopelessly tangled in absurd contradictions–or bring in God by the back door–we cannot assign a beginning to time apart from matter. Time exists as the motion of matter; matter moves through in time. Engels does not actually say that time is a fourth dimension, but he sniffs around it a bit, which is fairly impressive in the 1870s.
Really, I didn’t find a lot in this chapter that did more than crush Herr Dühring. This by itself may give us a clue as to the importance of infinity to Engels’ worldview.