Ultimate Explanations of the Universe (20 page)

Summarising Isaac Newton’s philosophical views is a relatively simple matter. Although they are scattered throughout his greater and lesser works, letters and treatises, they were crystallised fairly quickly and were always consistent later. Newton was precise and well-ordered not only in his works on physics and mathematics, and his philosophical commentaries were associated with his physics in a fairly natural manner: as soon as one manages to comprehend his interpretative principles it is not difficult to reconstruct the ideas espoused by the pioneer of classical physics. With Leibniz the situation is completely different. Certainly he had no want of genius, but he was occupied with too many matters, not only ones connected with science and philosophy, to concentrate resolutely and systematically on any one subject. He devised calculus as if incidentally; he had so many excellent ideas in physics but never formulated them systematically; he created his metaphysical system while busy with numerous other activities and engaged in several debates. His only major work,
Theodicée
, is more of a collection of essays than a systematic treatise. Leibniz’s philosophy is original, profound, and it staked out the paths for future developments, but it is not easy to interpret. The first difficulty is that his texts may be selected and arranged in diverse ways. Their chronology is not always the best guide to them. The history of the continuators of the ideas initiated by the Great Librarian of Hanover shows that those ideas may be read in a variety of ways. This certainly does not mean that Leibniz is a “dark” philosopher and may be understood in any arbitrary way. His ideas have clearly defined boundaries (beyond which there is only territory alien to him), easily distinguishable from the views of other philosophers, but it is precisely because of the abundance of his ideas that they may be pursued and taken in different directions, and in point of fact one never knows which of these directions was the one Leibniz himself chose – or would have chosen.

All of this induces me to refrain in this chapter from giving a faithful account of Leibniz’s views. After all, I’m not writing a textbook on the history of philosophy; my aim is to follow the development of the concept of the ultimate comprehension of the universe and its Christian version, that is the concept of creation. The ideas held by other people are only a guide to my own deliberations. In this chapter, more than in the preceding ones, I shall allow myself to present my own interpretation. Of course I shall try to “keep to Leibniz,” but following only those things in his works which I have discovered for myself.

If I had to choose one statement out of all the writings of Leibniz which gives the fullest expression of his idea of the creation of the world, my choice would be the following sentence which Leibniz wrote in the margin of a text entitled
Dialogus
¹
: “When God calculates and thinks things through, the world is made.”
²
But, as is usually the case with formulations that say it in a nutshell, you have to put a lot of effort and profound attention into unravelling the full sense of this sentence. The rest of this chapter will essentially be a commentary on this sentence by Leibniz.

Every one of us has had some experience of calculation. Whenever the numbers are not too big calculation is mechanical, done almost without thinking, and once you master the basic techniques of calculation you can also say the same thing of operations carried out on big numbers. Real mathematical thinking only starts when you have to solve a more complicated problem, or formulate and prove a theorem – in other words, whenever you have to find a mathematical structure, understand the way it works (for mathematical structures are not static, even if they do not change with time!), construct a new structure starting from a given one, and see its relationship with other structures… Manipulation of this kind with structures is usually associated with calculation, or lead to calculation, since mathematical structures tend to dress up in numbers and the language of calculation is their natural language.

This is the sort of image we should attach to Leibniz’s expression that when God “calculates and thinks things through” the world comes into being. The Latin verb phrase
cogitationem exercet
, translated as “thinks things through,” literally means “exerts his thinking” or “applies his mind.” To understand what Leibniz meant, we may imagine the work he must have done to devise calculus – differentiation and integration. First of all he had to identify the problem, assemble the components which eventually went into his solution but were scattered throughout the work of his predecessors, make a few crucial approximations, prove a number of theorems which express the relationships between the components of the new structure, perform the calculations for many examples, formulate new computational procedures, and finally show that the structure which emerges as a result of all these steps works perfectly when applied to the theories of physics.

Now Leibniz’s metaphor of God creating the world by calculation and the exertion of His mind is more comprehensible. All we have to do now is to liberate it from all the human limitations and imperfections, and supply it with an important corollary: that for God to obtain a result means that the result has come into being. This intuition, too, will be more readily comprehensible if we imagine a mathematician at work on a new scientific theory. Whenever a mathematical structure is devised for application in physics, its definitions are selected in such a way as to correspond to the experimental results, the structure’s most readily comprehensible components are given an appropriate interpretation, sometimes with a certain amount of modification to make them work better. And when thanks to all these steps the structure has reached the required level of maturity – hey presto! The mathematical structure turns into a theory of physics. Not only does it explain something we have already observed in the world, but it also predicts new, sometimes very subtle phenomena.

But when God calculates and exerts His mind, there is no trial and error, no fitting together of this or that. The universe simply comes into existence.

The word “link” deserves to be emphasised. What Leibniz had in mind were not “truths” in themselves, but also the connections between them by chains of deduction. At any rate, according to him, such is “strict and true reason.” Elsewhere Leibniz stresses that “Right reason is a linking together of truths, corrupt reason is mixed with prejudices and passions.”
⁵

God simply encompasses all the possibilities (Leibniz speaks of “possible worlds”) and all the logical relations between them. These relations have the nature of mathematical deduction. This is what Leibniz’s “When God calculates…” means.

Thus, by analysing the way we reason we may attempt to understand the way in which God “calculates and thinks things through,” the way He creates the world.

There are two kinds of truth corresponding to these two principles: truths of reasoning, true on the grounds of the principle of contradiction: they are “necessary, and their opposite is impossible;” and truths of fact, which are true on the grounds of the principle of sufficient reason. If something cannot be determined on the principle of contradiction, we must search for a sufficient cause why it is so and no otherwise. Since the world is the result of God’s calculation and planning it is as rational as possible and contains nothing for which there is no rational cause.

There may be situations in which there are an infinite number of deductive steps from the premises to the conclusion. But that is no obstacle for God to recognise such a conclusion as a necessary rational truth. Of course human reason is not able to cover the infinite distance separating the premise from the conclusion; for human reason such a conclusion may be only a truth of fact. In such a situation human reason can search for a sufficient reason why things should be so and no otherwise. As Leibniz writes, “God has given us a concession,” allowing us to give a sufficient reason to justify what we are unable to deduce on the principles of logic.
¹⁰
When confronted with a contingent truth our procedure could consist in decomposing reasons into their component elements, but in this way we shall never obtain a full proof. In such cases only God, “Who alone in a single spiritual glance comprehends the infinite chain of causes,” understands the “reason of the truth.”
¹¹

Does this mean that in His recognition of necessary truths on the grounds of deduction God Himself is subject to necessity? Yes, but He Himself is that necessity: “…necessary truths depend solely on God’s understanding, of which they are the internal object.”
¹²

Of the infinite number of all possible worlds God has chosen one, the one which exists in reality. What determined His choice? Since He is the Best and Most Rational Being, He chose the best of all possible worlds.

Every perturbation, even a small one, in every possible world, causes a consequence even in the remote parts of the whole. The evaluation of the optimum must take into account all the possible perturbations of this kind.

If in His calculations God has selected the best possible world, then it is the world which contains the least amount of nothingness and the maximum of existence.

Leibniz would probably have said that those who make fun of his arguments exist because nonetheless they must be contributing in some way or other to the maximisation of the good of the entirety.