Routledge Philosophy GuideBook to Leibniz and the Monadology

Anthony Savile

• Editorial: Routledge
• Año: 2012
• ISBN:
  9781134696116
• Edición: 1
• Categoría: Philosophie
• Categoría: Histoire et théorie de la philosophie

Leibniz is a major figure in western philosophy and, with Descartes and Spinoza, one of the most influential philosophers of the Rationalist School. The Monadology is his most famous work and one of the most important works of modern philosophy.
Leibniz and the Monadology introduces and assesses:
*Leibniz's life and the background to the Monadology
*the ideas and text of the Monadology *Leibniz's continuing importance to philosophy
Leibniz and the Monadology is ideal for anyone coming to Leibniz for the first time. It also includes the text of the Monadology, specially translated for this GuideBook by Anthony Savile.

Chapter 1

Two Great Principles (§§31–7)

The foundations are everywhere the same; this is a fundamental maxim for me, which governs my whole philosophy.

(NE, 490)¹

Leibniz composed the Monadology in 1714, two years before his death, as a compact statement of his mature philosophical views. Within its narrow compass he sets out an elaborate account of the world presented though the lens of pure reason. It is an account that appears quite out of touch with the world as we know it. We are to understand God’s creation as a collection of simple mental substances, a world of monads, and to see ourselves as one particular kind of such thing, namely as minds having the power to reflect on ourselves and to understand the structure that the world necessarily has and to appreciate our privileged place in God’s plan for the universe. We are to see ourselves and monads of other sorts as developing according to pre-ordained patterns, harmoniously attuned to one another and striving to achieve the good in emulation of God’s own nature. The physical world is understood as consisting of compounds of these simple things and their perceptions, apart from which nothing else exists. For all its apparent defects we are brought to appreciate that of all the worlds that God might have created the actual world is the best, the one that mirrors his power, his knowledge and his goodness as perfectly as may be.

A common reaction to this metaphysic is to dismiss it as an extravagant fairytale, one that is not seriously concerned with the reality around us at all. The highly compact and apparently dogmatic nature of Leibniz’s writing in the Monadology serves only to reinforce that impression. Nonetheless such a view is quite mistaken. As soon as we look beneath the surface we see that all the major claims that Leibniz advances are backed by reasoning that owes little or nothing to fancy, and it quickly becomes evident that the intricate story he tells is comprehensive, highly systematic and can lay claim to great explanatory power. It exemplifies to the fullest degree the rationalist conviction that the human intellect has the capacity to achieve adequate understanding of itself and of the world it inhabits, and it displays the philosophical virtue of subjecting the putative facts of experience to rigorous and taxing theoretical scrutiny.

With the Monadology Leibniz has bequeathed us a highly compressed file. The task of the commentator and guide must be to decompress it, and that is what I seek to do in this book. There exist fine books treating of Leibniz’s philosophy as a whole and others on specialized aspects of it. Here I pursue neither course but, instead, restrict my attention to the Monadology alone and limit myself to asking how Leibniz may have expected his reader to understand that work on the assumption that he or she does not have access to the full body of his philosophical writings. It was, after all, written to gain a wider audience for his views than his more specialized writings reached, and it is reasonable enough to suppose that it contains within itself many of the keys to its own understanding. However, I sometimes draw on Leibniz’s other writings to support suggestions I make about the Monadology’s darker elements or to provide evidence about views germane to matters that this work discusses but which it passes over in silence.

For the most part I follow the text through in the order in which Leibniz presented it. The major exception to this strategy concerns the fundamental logical and methodological suppositions that underlie his general procedure. These make no explicit appearance before §§31–2, and they concern what Leibniz calls the two ‘Great Principles’ on which all his reasonings are founded.² It is with these principles, and with the existence of God to which they directly lead (§§38–45), that my first two chapters are concerned. Only after treating these topics will it make sense to turn attention to the existence of the simple substances that make up the world, and whose introduction occupies the Monadology’s own opening sections.

The Principle of Contradiction

The first of Leibniz’s two avowed principles is the Principle of Contradiction, whereby ‘we judge to be false what contains a contradiction and to be true what is opposed to or contradicts the false’ (§31). In fact Leibniz is quite clear that there are two distinct ideas at work here, both of which operate throughout the Monadology. The first is the Principle of Contradiction proper, which he here phrases as a rule for recognizing a judgement to be false. When we find someone asserting both that something is the case and that it is not the case then we judge their composite assertion to be false. While it does indeed happen that people sometimes explicitly contradict themselves, what more often occurs is that something someone says implies a contradiction that he does not notice, as might be the case were I seriously to say that the vixen lodged in my garden had just fathered cubs. In that case, too, Leibniz tells that we judge what is said to be false because I have implicitly committed myself to the fox in question both being female and not being female.

Putting it in terms of what ‘we judge’, Leibniz makes it sound as if he is recording our behavioural response to contradictions. That would be to misunderstand him. As far as actual behaviour goes, as long as we do not notice a contradiction in what someone says then we are quite likely to accept it and judge it true on the assumption that our informant is trustworthy. This behavioural fact does not count against what Leibniz has in mind, though, for his ‘Great Principle’ is a normative matter, not a descriptive one. His thought is that we are rationally bound to judge contradictions to be false (assuming we notice them): we ought to reject them. The reason for this is that it is simply not possible for contradictions to be true, and we are rationally bound to judge false what cannot possibly be the case.

Someone whom Leibniz (mistakenly) thought would have disagreed about this was Descartes. At §46 he reports Descartes as holding that eternal truths are arbitrary and dependent on God’s will. On such a view, it is only because God does not want the vixen to father cubs that my illustrative statement is false: there is no absolute impossibility about it. The suggestion behind this supposedly ‘Cartesian’ idea must be that there would be blasphemy in supposing God’s power might be limited in any such way. If this were right, whether or not Descartes himself held the view, then Leibniz’s principle would have to be rejected as long as it is seen as more than a rough-and-ready empirical generalization about our actual behaviour.

Leibniz is certainly not open to the charge of blasphemy. Also, he is well placed to say just what it is that makes contradictions impossible. As for the first, to say that God is omnipotent can only mean that God is able to do whatever can be done. To hold this is not to hold that there are limits to God’s power. In particular, that something is impossible imposes no limitation on God’s capacities, for what is impossible cannot be the case and so cannot constitute a limitation on the power of anyone, let alone God. What is it, then, that permits us to say that it is not possible both that p and that not-p – that a state of affairs and its opposite cannot both obtain? Leibniz himself does not tell us, certainly not in the Monadology, but that need not stop us answering the question on his behalf.

The ‘Cartesian’ supposition is that God could permit a determinate state of affairs and its opposite to coexist.³ Now for a state to be a determinate one it has to be clear what condition must be satisfied if it is to obtain. For that to be clear it must also be clear what conditions are ruled out by its obtaining. So, for example, for it to be clear what it is for snow to be determinately white it must be ruled out that snow be black or green or any colour other than white. Were we to suppose that snow should be at once white and also some other colour, that would involve not just our supposing snow to be both, but in effect our not really supposing it to be white at all. So if it is determinately white it must be impossible that it should also be other than white. That impossibility is written into the supposition that white is the colour that it is. Likewise the impossibility of my vixen fathering cubs is written into the content of the thought that identifies the animal in question as a vixen. Her being male is something ruled out in the very supposition that that is what she is. However, since a condition of the animal’s fathering cubs is precisely that it be male, the situation I have supposed myself to be envisaging could not obtain.

I have said that the first of Leibniz’s two principles involves two ideas. This is essential for him to its having any positive utility. If we had only the Principle of Contradiction proper, as I called it, it would enable us to identify certain falsehoods, but not to assert any truths. The second limb of §31 enables us to do that by telling us that the opposite of a falsehood is a truth. Using this additional thought, we shall be able to assert as true whatever it is that is excluded by the falsehoods we have already identified, and Leibniz presumes that these will necessarily be the negations of the contradictions that have been identified as false, or of whatever propositions there may be that imply a contradiction.

In fact the ancillary principle that Leibniz is appealing to at this point must be the Law of Excluded Middle, the principle that for any proposition one might envisage either it is true or its negation is true. We could only use the second limb of §31 to identify ‘not-p’ as true if we are assured that that really is the opposite of the one that Contradiction proper has identified as false. Without reliance on Excluded Middle we should not be able to say what proposition was true when p itself was false. Just to be told, as Leibniz tells us, that we can assert as true what is the opposite of the false, whatever proposition it is that must hold if p itself does not, does not itself give us any clue what that proposition might be. For that we need to know that if ‘p’ itself is not true then ‘not-p’ is true.

That Leibniz was aware of this is clear from the statement of the Principle of Contradiction he had earlier given in the New Essays, saying:

Stated generally the principle of contradiction is: a proposition is either true or false. This contains two assertions: first that truth and falsity are incompatible in a single proposition, i.e. that a proposition cannot be true and false at once; and second, that the contradictories or negations of the true and the false are not compatible, i.e. that there is nothing intermediate between the true and the false, or better that it cannot happen that a proposition is neither true nor false.

(NE, 362)

My own remark about the second limb of Monadology §31 does no more than bring out explicitly what Leibniz chose there to leave unstated. Although he always assumed Excluded Middle holds, he nowhere offers any defence of it. It is what he would call a primary truth which is known by ‘intuition’. We can, as it were, see straight off that it expresses what he would loosely call an ‘identity’, and he thinks that it must be true because it scarcely does anything ‘but repeat the same thing without telling us anything’ (cf. NE, 361).

With the backing of Excluded Middle, then, the Principle of Contradiction proper can be put to work in the metaphysics. Contradictions are false because it is impossible that they should be true. Their falsity is necessary falsity. One way of reading the second limb of Leibniz’s principle is to take the falsity whose opposite he says is a truth to be precisely the falsity of some contradiction or other – any contradiction you like – already identified as false by the principle’s first limb. Then it will be the case that its opposite is true. What is more, since the falsehood in question is a necessary falsehood, we can conclude that its opposite is not barely true, but necessarily so. So, on occasion we shall see Leibniz arriving at metaphysical conclusions to the effect that this or that must be the case by showing that a proposition which is the negation of the thought expressing that state of affairs is itself a contradiction or that it entails a proposition which is a contradiction. In this way his first ‘Great Principle’ is not merely a trifling proposition that ‘repeats the same thing without telling us anything’, but is intellectually productive.⁴ How productive it is we shall come to appreciate.

At §33 Leibniz introduces a division of truths into truths of reasoning and truths of fact. The former are necessary truths, truths whose ‘opposites are impossible’, the latter contingent truths, those whose ‘opposites are possible’. While the Principle of Contradiction functions in its narrow form to identify certain necessary falsehoods and in its broader form productively to identify certain truths as necessary, that is not the sole way he thinks about the use to which it can be put. For Leibniz, occupied as he was with the need for philosophy to provide understanding, it also supplies answers to ‘why’-questions as they are asked of truths belonging to the former of the two broad classes. So someone might wonder why p has no terminating decimal expansion and be shown by rigorous demonstration that it must be so, and that the alternative is impossible. It is so because it must be so, and that it must be so is either something that can be demonstrated, or else is so primitive that it is discernible by intuition and ‘cannot be proved and [stands] in no need of it either’ (§35). To show that something is necessarily the case in this fashion is to explain it, to display why it is the case, and to do so by rigorous proof that is completely adequate to the demands of understanding. To the extent that we can do this, the rationalist aspiration to complete explanation and full understanding is satisfied without residue.

The Principle of Sufficient Reason

The second of Leibniz’s ‘Great Principles’ is the Principle of Sufficient Reason, articulated at §32 as that principle ‘whereby we consider that no fact can hold or be real, and no proposition can true but there be a sufficient reason why it is so and not otherwise, even though for the most part these reasons cannot be known by us’. The content of this claim is obscure and emerges gradually from the amplifications that §§36 and 37 add to it. However it is to be taken, Leibniz makes plain (§36) that it serves to assure us of the answerability of contingent truths of fact to ‘why’-questions no less fully than its companion does for necessary truths of reasoning. That is, the Principle of Sufficient Reason assures us that all contingent truths must have their explanations, even though for the most part those explanations ‘cannot be known by us’.

A first attempt to understand this second principle can be put in terms of facts or states of affairs. It appears to say that a condition of a fact or state of affairs obtaining is that there should be something or other – no matter what – that determines that that fact should obtain rather than any alternative. No fact or state of affairs can hold which is not completely accounted for and made fully explicable by reference to something else. No fact or state of affairs is accounted for by reference to anything which would equally well explain the occurrence of a different fact or state of affairs. Ruled out, then, are situations of which one might want to say: ‘This happened, but there is in principle no explanation why it happened’; equally ruled out are situations of which one might say: ‘This happened because of that, but that could equally well have brought about some other state of affairs than this.’ So, for example, it would be ruled out that there should be random events, or that at the end of the day all there is to say about some event of radio-active decay should be expressed in terms of the decaying element’s half-life. Likewise it is ruled out that a doctor should truly sa...