that from one before, and that from one before that, and so on: even if the line extended back for ever, we should have been given no reason why there should be such things as geometry textbooks at all.
myra
I am not happy with an illustration taken from something which is quite certainly impossible.
leslie
Leibniz’s point surely was just that, that it was impossible. But let me put it another way. There might be more than one possible universe—I mean, there is more than one way in which a universe might be put together. Indeed, there surely are many. A Newtonian universe, with no relativity or quantum physics, would be quite possible. And in it every event would doubtless follow on from others. The difference between it and the actual universe we live in is that one exists and the other does not. What I am insisting on is that an explanation for the existence of the actual universe may legitimately be asked for—and the natural explanation is the creative will of God.
geoffrey
It may seem natural to you, but it doesn’t to me. I do not see that explanation in terms of God is really any advance. You said that any explanation must include an element of brute fact. Now you have your brute fact—indeed, you really have two of them, the existence of God and his decision to create—which have no explanations at all. But so have I. Granted for the sake of argument that basic facts are inevitable, that we have to have some unexplained element, then the obvious one is the existence of the universe as a whole. After all, we do actually know that the universe exists. We do not know for certain that a God exists; that is what this whole dialogue is about.
The Question of “Simplicity”
leslie
I should say that the difference is that my explanation is simpler.
geoffrey
How do you work that out? Your explanation actually adds to the complexity of things. Remember the old slogan called Ockham’s Razor: “do not multiply entities unless you have to.”
leslie
I don’t see why we shouldn’t have a Hair-Restorer as well as a Razor. If there is no God, we have as our ultimate inexplicability: (1) whatever minimum of scientific laws is needed to describe the way the universe behaves; (2) a description of the universe over a stretch of space and time sufficient to entail a description of it at all other times; and (3) any undetermined, partially uncaused events occurring in the universe. If there is a God, however, we have as inexplicables (I) the existence of a God and (II) His free decision to create an ordered universe of the sort described by (1) (2) and (3). This does require one more entity than the first, I admit; on the other hand, it has replaced (1) (2) and (3) by a set of rational decisions whose possibility flows from (I). In other words, by adding one entity we have simplified the explanation.
To take the universe as “brute fact” is preposterous. This is where “contingency” really does come in. The universe is contingent through and through—it could have been different in an unimaginable number of ways. If it is to be the way it is, it had to have strong initial conditions or restrictions on its nature. More than that: it is the most complex thing of which we know; all other complexities are contained within it. But God is One. Some have even held that He is totally simple, with no elements within Him that can be separated even in thought. I should not wish to defend such a position myself; it seems hard to square with the idea of the Trinity. But certainly God could not be otherwise than the way He is, His free will alone excepted.
Alter your description of the universe, and you have just a universe that is different, perhaps only slightly different: alter your description of God and you do not have God at all. A being like God in all respects except that he, she or it was powerless, or imperfectly good, or the like, would not be a different kind of God but something else altogether, and probably an impossibility at that. God has often, as was mentioned, been thought to be a “necessary being,” one who could not not-exist, and could not be otherwise than He is; but the universe quite certainly might not have existed, and might have been quite different. So that an unexplained and inexplicable God is far, far easier to swallow than an unexplained and inexplicable universe in all its vastness and variety through space and time.
geoffrey
You forget that if God did create the universe, he presumably had in mind a plan for it. Every complexity there is in the universe has an answering complexity in the divine brain. God is not simpler than the universe, but much more complicated; for presumably he has other ideas besides that of the universe, and these add to his complexity.
leslie
I’m not sure of that. That in fact is one reason I mentioned God’s free will! An architect’s drawings for a house are in a sense as complex as the house itself (disregarding such things as the composition of the bricks). But the architect’s thoughts, which produced the drawings, did not just leap into existence of themselves. They began with the idea of a two-bedroomed bungalow or whatever, and evolved from that simple beginning. Again, the postulates and axioms of a formal mathematical system are not infinitely complex—they may be very simple indeed—however complex the system itself is which derives from them. And similarly, while the ultimate state of an infinite mind may be infinitely complex, its original essence need not be. God may be simple in Himself, and yet have thoughts which develop and become more complex. That is not so with the universe.
geoffrey
Why not? A basically simple universe might contain great potential for development—like your mathematical postulates and axioms. Have you come across the Mandelbrot Set? It is in effect a kind of graph, based on the extremely simple formula “z squared plus c,” where you start with z=0 and c=anything you like, and each succeeding result of the equation is fed back into it, so to speak, to become the next z. This formula becomes the basis for a graph or pattern of incredible—in fact, literally infinite—complexity. A universe that was very simple at root might come to look very complicated indeed as it developed.
leslie
Along any particular lines?
geoffrey
Along lines dictated by the scientific laws that govern it.
leslie
But these require explanation, don’t they? They can’t be included in the basic “brute fact.”
geoffrey
Possibly: we can discuss that later. But to bring in that argument would be in effect to abandon the last and (you told us) the strongest of your first group of arguments.
leslie
But I haven’t finished yet! “A simple universe might contain great potential for development,” you say. But in so doing you have abandoned your earlier position, that the whole spread of the universe through space and time could be treated as self-sufficient, as a unit. If it can, it is enormously complex, and, what is more, there is nothing in it that is in any way “special” or “privileged” as logically prior to the rest, in the way that God’s decision to create is logically prior to His decision to create this or that detail of the world. If it can’t be treated as a unit, then we are back to the first sub-group: this “simple” universe had a beginning and I want to know what caused this.
A Universe That Happened by Chance?
geoffrey
Some cosmologists have made
