Principles of Engineering Mechanics Book

Let me start by saying that I admire Russell more than almost any other philosopher. He was a deep, penetrating, witty (and humorous) thinker. I have learned a lot by reading him.

On the other hand, I think it is fair to say, that he was not totally reliable (but then, who is?) when he was explaining other people’s philosophy (as can be seen by his introduction to the Tractatus or his very popular Western Philosophy.)

At the same time he always seems to be very confident that his views are correct (until he rejected them. Something he is rightfully famous for as well.) What I mean is that he very occasionally throws in an "in my opion", "as far as I understand". And in this book, I found that very irritating. Because one of the philosophers I admire even more than Russell is Leibniz. Russell was quite young when he wrote the book and maybe he thought he could build a reputation by attacking a famous philosopher. But I think a more humble approach would have been a wise decision. As it is he assures us constantly of ideas he found in Leibniz that are "confused", "inconsistent", "viscious circles" or even "scandalous".

It is not that I think that Leibniz is consistent to 100%. He did write an awful lot and he also changed his mind. And it is true that very often, especially when writing letters he tried to convince his addressee by whichever argument he thought was going to work. And he also tried to fit in views that do seem to be foreign to his philosophy, for example when he tries to explain why miracles occur. That seems bizarre when the world could run like a clockwork (and does most of the time – the whole point of preestablished harmony). Why then allow miracles? Russell’s example of vinculum substantiale is a case in point. (Leibniz tried to reconcile with the dogma of transubstantiation.)

And yet some of Russell’s accusations seem outrageous to me. To give just one example. Russell thinks it is a great error of Leibniz to think that extension and duration are prior to space and time. Extension, he says it is sufficiently evident, logically presupposes space. And Leibniz "overlooked this fact" (p. 101). I admit that I have no idea how extension is possible without space but I would not dare to suggest that Leibniz was too stupid to see it. I am much happier with the view that Leibniz will have had a good reason thinking that extension is real but space is not. Even though I can not grasp it. I come back to this in a minute.

If you know anything at all about Leibniz you know that he believed we live in the best of all possible worlds. Maybe you know that monads have no windows, or you have heard of the mill metaphor. None of this you will find in this book. (It seems Russell did not bother to read the Theodicy.)

Instead, Russell begins his exposition by telling us that Leibniz had five premisses for his philosophy. This seems odd since Leibniz never tires of repeating that he had two principles. The principle of contradiction and the principle of sufficient reason (e.g. on page 210 in the Appendix). Maybe a principle is something different than a premise. Or maybe Russell saw more clearly the foundation of Leibniz’s philosophy than the man himself. Which seems unlikely to me, but possible.

The premises according to Russell:

1. Every proposition has subject and predicate
2. Subject may have predicates which are qualities existing at various times (called a substance.)
3. True propositions not asserting existence are necessary and analytic. Propositions asserting existence are contingent and synthetic.
4. The Ego is a substance
5. Perception yields knowledge of the external world.


The first two premises seem valid. One of Russell’s objections to Leibniz, although as a mathematician he should have known better, is that he denies the importance of relations. Leibniz holds the view that substances have properties that mirrors the grammatical subject-predicate structure. (As quoted in the Appendix: "I hold that paternity in David is one thing, and filiation in Solomon another, but the relation common to both is a merely mental thing." p. 206)

I happen to think it is the other way round. But it is easy to see why Leibniz thinks that paternity in David is more real than the relation. The paternity is something that is included in David for all times. The predicate that he is the father of Solomon is independent of the temporary existence of the relation itself. Every predicate is eternal.

The third premise is problematic. Probably Russell was proud of this observation because it sounds a bit paradoxical. But it does, I think, capture an important point in Leibniz’s philosophy. But why did he have to introduce the analytic-synthetic distinction? He is aware that it is anachronistic. Why does he use it (except to please his Kant-educated readers)? I think it is not a good idea to employ modern terminology because the danger is that one misrepresents the intentions of the philosopher in question. (And ever since Quine there are at least serious doubts as to the usefulness of the analytic-synthetic distinction.)

This is strange because Leibniz’s terminology is crystal clear. I do believe that his distinction between eternal truths and truths of fact is of the highest importance. To understand why a truth of fact, although contingent, is morally necessary is the main thing we can learn from Leibniz. Knowledge, Leibniz says is either obscure or clear. Clear knowledge is confused or distinct. Distinct knowledge is either adequate or inadequate and also symbolical or intuitive. Perfect knowledge is adequate and intuitive. Russell mentions this in passing at the end of the book. Which is okay, because he wanted to criticize Leibniz not to explain – or learn from him. But he did himself and his readers no favour in concentrating on the dynamics of Leibniz that is to say on Leibniz's theory of how the world is actually built. How the monads (immaterial "points" with "perception") actually "interact" with "bodies". They do not, of course, hence the pre-established harmony. But there is extension. And continuity (the most mysterious concept to me).

I found this part of the book (chapters IV to X) most interesting. I still do not understand it but I also think it is of (almost) only historical interest. But to come back to the question of the reality of space and time. Leibniz thought (for purely philosophical reasons and in contrast to Newton) that space could not be absolute. God would have no reason to put something here and not there which is impossible because of the principle of sufficient reason. That space is only defined by the relative positions of objects certainly does make sense. Russell published his book five years before the Special Theory of Relativity. I am not saying that this proves Leibniz was right (maybe on the contrary). But when Russell suggests that Leibniz should have known "the modern dynamics of the ether" (p. 90) then this surely sounds funny today.

I will now come briefly to Russell’s critique of Leibniz’s ontological proof of God’s existence. Since the concept of God includes perfection and something existing is more perfect than the same thing non-existing, God must exist. This has appealed to some people whereas others e.g. Kant rejected it. Now, Leibniz adds an important caveat (and to me, it is the most amazing of Leibniz’s accomplishments) he said the argument is valid but it still must be proved that the concept of God is possible.

Russell is content in just repeating the Kantian (the imagined 100 thalers are exactly the same as the existing) "argument". I never understood that. If I have a melody in my head how can that be exactly the same as the melody I hum - or write down? "Leibniz ought not," Russell says, "to have held existence to be a predicate at all, since two subjects, one of which has a given predicate, while the other does not have it, cannot possibly be alike.” (p. 174f.) Why not? Leibniz does discuss the possibility that Aristoteles could have had other predicates than he actually had. (He might have been a shepherd.) So he admits the possibility of "identity across possible worlds". So it is not quite true that "existing" is contingent and e.g. "being father" (in the case of David) is not. But the predicate "existing" does not really belong to David at all but to the possible world that David belongs to. A world is the smallest ontological unit. So things are a bit more complicated.

But anyway, is God possible? Leibniz thinks that he is and thinks he can prove it. But he might be mistaken in this. Consider the case of the vacuum. Leibniz thought he could prove that a vacuum is impossible. Because he says "God could have put matter in it without derogating in any respect from all other things..." (p. 236) Really? Imagine God wants to create (an instance) of a game of chess. Could he just put 64 chessmen on the board because he dislikes empty fields – without derogating in any respect? He could not. It would not be chess.

My favorite example of an error by Leibniz when he was sure he has proved some "eternal truth" is when he argues that there cannot be a finite speed. Imagine a point on a rotating wheel, he suggests. Increase the radius and the speed increases. That seemed to be to him a conclusive proof. But we now think that the meaning of the words (and the concepts) of space and speed are different. An infinite speed is not possible. And so it might just be the case that the concept of God is not possible. (On the other hand, if we live in a simulation as some people now seriously think then it would be bizarre to not call the creator of the simulation God.)

And finally, in the last chapter on Ethics (where we do get a glimpse of Russell’s humour when he says that "Leibniz’s Ethics suffers from non-existence" - p. 197) he argues that in "Leibniz philosophy everything, from the Law of Sufficient reason onwards, depends, through the introduction of final causes, upon Ethics". This is just plain wrong. That God chose to create this (best of all possible) worlds has only very indirectly to do with his goodness. He chose this world because he could not help it. Again, if he chooses a game as in peg-solitaire (one of Leibniz’s examples) he must choose the one where at the end one piece is in the center because that is the object of the game. If our world would not "stick out" he would (could) not have created it.


[And really finally: I read the edition in the forgotten books series. I am thankful to the publisher. But there is such a thing as Tippex. They should have hired a student to get rid of the underlinings. And a good part of the index is missing.]