Maximum Effect, Minimum Outlay: The Coherence of Leibniz's Fruitfulness Criterion

1

Maximum effect, minimum outlay: the coherence of Leibniz’

fruitfulness criterion

Leibniz’ belief that the actual world is the best possible

world is one of the most well-known aspects of his

philosophy.1 It is also well known that Leibniz offers a

number of apparently very different definitions of “best

possible world”.2 In this paper I want to consider just one

of these definitions, upon which much of the recent

literature has focused, which we may call the “fruitfulness

criterion”.3 On this criterion, put simply, the best

possible world has the simplest laws but the most complex

phenomena. The laws can be called “fruitful” because they

produce much more complexity than they possess themselves.

Recent literature has questioned whether the fruitfulness

criterion means that, in Leibniz’ view, God was forced to

trade some complexity of phenomena for the sake of having

simpler laws, or whether Leibniz thinks that the actual

world has more complex phenomena than any other and

2

unusually simple laws.4 And there is disagreement over

whether the fruitfulness criterion is supposed to be

definitive of the best possible world or simply a feature

that it happens to instantiate. Was God’s motive in choosing

to instantiate this possible world the fact that it has

simple laws and complex phenomena, or did he follow other

criteria? Are there other features which both laws and

phenomena may have which are also desirable, but not linked

to their simplicity and complexity?5

In this paper, however, I want to consider something

slightly different, namely whether the fruitfulness

criterion – as Leibniz defines it – is coherent at all; and

whether, supposing that it is coherent, it is consistent

with other elements of his philosophy.

I

What exactly is the fruitfulness criterion for ranking

possible worlds? The main text in which Leibniz sets it out

3

is the Discourse on metaphysics, sections 5 and 6. There, he

writes:

God has chosen that world which is the most perfect, that is to say,

which is at the same time the simplest in its hypotheses and the richest

in phenomena, as might be a geometric line whose construction would be

easy but whose properties and effects would be very remarkable and of a

wide reach.6

What does Leibniz mean by “hypotheses”? He explains in the

preceding passage:

...if someone draws an uninterrupted curve which is now straight, now

circular, and now of some other nature, it is possible to find a

concept, a rule, or an equation common to all the points of the line, in

accordance with which these very changes must take place. There is no

face, for example, whose contour does not form part of a geometric curve

and cannot be drawn in one stroke by a certain regular movement. But

when the rule for this movement is very complex, the line which conforms

to it passes for irregular.7

4

We can see here an ambiguity in Leibniz’ understanding of

“hypotheses”. On the one hand, a “hypothesis” is a description

of a phenomenon or group of phenomena. Leibniz imagines a

curve being drawn, and an observer deducing a rule or

equation which describes each part of it accurately. In

theory, we could find such an equation to describe any

geometrical figure that we come across. But on the other

hand, a “hypothesis” is a rule for creating a phenomenon or

group of phenomena. Leibniz imagines a pen drawing a curve

by following a rule which has already been specified.

For the moment, we can set that ambiguity aside. In the case

of a mathematical figure which is described by an equation,

that equation functions as both a description and a rule; it

can describe a pre-existing figure or be used as an

instruction for creating a new one. So if there is ambiguity

in Leibniz’ understanding of the relation between

“hypothesis” and “phenomenon”, it may not be a problematic

ambiguity, at least as far as defining fruitfulness goes.

5

What of the dual criteria of “simplicity” and “richness”,

applied to hypotheses and phenomena respectively? Donald

Rutherford has argued that “simplicity” of hypotheses means

universality:

…Leibniz equates the simplicity of laws with their degree of

universality, or freedom from exceptions. On this reading, the simplest

natural laws would be those, like Newton’s law of gravitation, applying

to the greatest variety of cases under the widest range of

circumstances. Such laws could be understood as more “productive” of

phenomena insofar as a richer variety of types of phenomena are subsumed

under them.8

But it is hard to find textual basis for this

interpretation. In fact, the geometrical illustration that

Leibniz gives surely rules it out. In the passage quoted

above, he envisages a collection of dots connected by a

single line. In any such geometrical pattern, all of the

dots lie on the line: he tells us that “there is no face…

whose contour does not form part of a geometric curve”. So

in the context of geometrical figures of this kind, all of

6

the “phenomena” are necessarily captured by the

“hypothesis”. There are no dots that are not on the line;

there are no features of the face that are not part of the

geometric curve. In a geometrical context, then, simplicity

cannot mean universality, because all hypotheses have

universal application by definition. Simplicity here must

mean something else. The obvious candidate is parsimony of

mathematical terms. A line that is described by the formula

x=y has a simpler formula than one that is described by

x=y*y, and we could say that a simpler formula is one that

contains fewer terms. Rutherford suggests that there is

“little reason” to think that Leibniz conceives of the

simplicity of natural laws in this same sense.9 But the fact

that Leibniz offers the example of geometrical lines and

curves as an illustration of what he means by “hypotheses”

in the natural world is surely a very good reason to think

that this is precisely what he means by simplicity of

hypotheses.10

7

Richness, in the context of geometrical figures, seems a

little harder to define. Leibniz’ examples imply that he is

thinking of figures that are simply more interesting, “whose

properties and effects [are] very remarkable and of a wide

reach”.11 This seems rather vague. Some kind of complexity

seems to be implied, but it must be a regular complexity;

elsewhere, Leibniz likens evils to unexpected irregularities

in a geometrical figure.12 Had fractal geometry existed in

Leibniz’ day, perhaps he would have used that as an

illustration: figures that are, in theory, infinitely

complex, but in a regular way, following the recursion of

relatively simple rules.

We can, then, define the fruitfulness criterion simply like

this. On this criterion, the more a possible world has the

following characteristics, the better it is:

Definition 1: As many interesting and complex phenomena as

possible, described by rules that contain the fewest terms

possible.

8

But there is a problem with this. Rules themselves are

phenomena. There is a fundamental disanalogy between

geometry and possible world description: in geometry, the

figure being drawn and the formula that describes it are

1 It is the first thing he argues in the Discourse on metaphysics G IV 427; L

303. I use the following abbreviations for editions of Leibniz’

writings: Couturat, L., ed. (1966) Opuscules et fragments inédits de Leibniz

Hildesheim: Olms (C); Gerhardt, K., ed. (1965) Die philosophischen Schriften

Hildesheim: Olms (G); Mason, H., ed. (1967) The Leibniz-Arnauld correspondence

Manchester: Manchester University Press (M); Remnant, P. and Bennett,

J., eds. (2003) New Essays on human understanding Cambridge: Cambridge

University Press (R&B); Loemker, L., ed. (1956) Philosophical papers and letters

Chicago, IL: University of Chicago Press (L); Farrer, A. and Huggard,

E., eds. (1951) Theodicy London: Routledge & Kegan Paul (H).

2 The passage that enumerates the most of these definitions in one place

is perhaps Principles of nature and grace G VI 603; L 639. For an account of

the differing opinions on how to relate these different definitions to

each other, see Jolley, N. Leibniz London: Routledge 2005 pp. 162-66.

3 The literature on the “fruitfulness criterion” includes Gale, G. “On

what God chose: perfection and God’s freedom” in Studia Leibnitiana vol. 8

no. 1 1976; Wilson, C. “Leibnizian optimism” in The journal of philosophy vol.

80 no. 11 1983; Blumenfield, D. “Perfection and happiness in the best

9

clearly different things. The formula is not part of the

figure.13 But Leibniz is very clear that the rules according

to which a possible world operates are part of that world.

This is a key element in his attempt to overthrow

Malebranche’s belief that the existing world is not the best

possible world” in Jolley, N., ed. The Cambridge companion to Leibniz

Cambridge: Cambridge University Press 1995; Rescher, N. “On some

purported obstacles to Leibniz’s optimalism” in Studia Leibnitiana vol. 37

no. 2 2005; and Strickland, L. Leibniz reinterpreted London: Continuum 2006,

ch. 4 and especially ch. 5.

4 Nicholas Rescher has argued for the first of these interpretations

(Leibniz’s metaphysics of nature Dordrecht: Reidel 1981 p. 11), as has Nicholas

Jolley (2005) pp. 165-66; while David Blumenfield (1995) has argued for

the second (pp. 386-87). Indeed, Blumenfield argues that Leibniz holds

that the actual world has more complex phenomena than any other and also

simpler laws than any other, making it not only the best possible but

completely perfect, at least on the fruitfulness criterion. Lloyd

Strickland (2006) pp. 70-73 agrees with Blumenfield.

5 On these latter points, see Rutherford, D. Leibniz and the rational order of

nature Cambridge: Cambridge University Press 1995 (hereafter 1995a) pp.

22-31. Rutherford argues that, for Leibniz, “simplicity” of laws is

really a matter of “order” rather than simplicity per se, and that order

tends to produce optimal phenomena, so God faces no dilemma in trying to

10

possible. Like Leibniz, Malebranche had insisted that God

wants to have the simplest laws he can, and that this is a

determining factor in God’s choice of possible world to

actualise. However, Malebranche conceived of the laws as

distinct from the worlds; on his view, God is constrained to

maximise both. Moreover, both laws and phenomena have other optimality-

producing features, such as “quantity of essence” in the case of

phenomena (p. 23) and force-preservation in the case of laws (p. 28). On

the latter point, Rutherford is surely right, which leads to the

question of how the fruitfulness criterion is to be related to other

criteria of ranking possible worlds. That is a question that lies

outside the scope of this paper. On the former point, however, I

disagree with Rutherford’s analysis of what Leibniz means by

“simplicity”. As I argue (below), Leibniz does appeal to “order” in the

context of defending the fruitfulness criterion, but he does not suggest

that “order” and “simplicity” are the same thing.

6 Discourse on metaphysics G IV 43; L 306. Rutherford (1995a) p. 27 expresses

a doubt that Leibniz’ reference to “the most perfect” world is meant “in

its strict technical sense”. The main reason for thinking this is that

the fruitfulness criterion described here seems to conflict with other

definitions of the best possible world that Leibniz gives elsewhere. As

I have indicated, I do not aim here to address the question of the

relation between the fruitfulness criterion and other possible

11

choose a particular possible world over the others because

he can actualise that possible world by using simpler laws.

God therefore makes the best choice that he can, but the

world he actualises is not the best. Leibniz, by contrast,

conceives of the laws as part of the possible world in

definitions of optimality.

7 Discourse on metaphysics G IV 43; L 306

8 Rutherford (1995a) p. 27

9 Rutherford (1995a) p. 27

10 Strickland (2006) p. 69 rejects Rutherford’s interpretation for a

similar reason.

11 A similar idea is suggested in the Theodicy, where Leibniz argues that

it is undesirable to have everything always the same, even if they are

the best – we would not want to have only copies of Virgil in the

library, or to drink only out of golden cups, or to eat only partridges.

See Theodicy 124; H 198. The implication is that richness is a matter not

simply of having many individuals in the world, but of these individuals

being of many different kinds. See Strickland (2006) p. 49. Moreover,

although Leibniz does not explicitly say so, he may also consider

richness to involve gradation within the many different kinds; so there

is variety not simply in the fact that different individuals instantiate

different properties, but that even among those that instantiate the

same properties, they do so to different degrees. See Tlumak, J. Classical

12

question. For Leibniz, if God makes the best choice that he

can, then he has created the best possible world.14

So for Leibniz, the laws that determine what the world is

like are part of the world. They are among the things that

God actualises, not simply one of the constraints upon what

he decides to actualise. And if that is so, then the simple

distinction between formula and figure, which makes sense in

geometry, breaks down when one tries to transfer it to

modern philosophy Abingdon; New York: Routledge 2007 p. 162-63.

12 Theodicy 242; H 277

13 Analytic geometry holds that formulae and geometric figures are in

some sense the same thing: they are merely different ways of expressing

or describing the same mathematical object. Even on such an

understanding, however, the formula and the figure themselves are

distinct expressions of that object, just as “The cat is black” and “Le

chat est noir” are different sentences that express the same

proposition. Similarly, in the passage we are considering, Leibniz

distinguishes between the line that is drawn on paper and the rule that

describes (or prescribes) the drawing of that line. Although they may

express the same thing, the rule and the line are not identical.

14 See Wilson (1983) pp. 770-72, 774-77; Jolley (2005) pp. 160-61.

13

phenomena and rules. We can see that this is so when we bear

in mind that the rules – such as natural laws – are among

the elements of the world that we can consider. That is, a

natural philosopher may deduce the inverse square law of

gravitational attraction from his study of the behaviour of

the planets; both the planets and the law that governs their

movements are therefore the objects of his study. For the

natural philosopher, the law is among the phenomena of the

universe.

But this means that the definition of fruitfulness that we

have suggested is inadequate. It cannot be the case that the

fruitfulness criterion requires simple laws and complex

phenomena simpliciter, because laws are a subset of

phenomena. There is therefore an inconsistency at the heart

of our first definition; so we must revise it to this:

Definition 2: The phenomena apart from the rules must be as

complex and interesting as possible, described by rules that

contain the fewest terms possible.

14

This immediately raises the question why laws are the one

kind of phenomenon that, in the best possible world, are

simple, when all the other kinds of phenomena are complex.

What is it about laws that makes their value vary in a way

that is the opposite to everything else? This is a question

to which we will return later.

II

There is another problem: the same set of phenomena can be

described by different rules. This is true in three different

ways. The first is this. In the passages we have seen

already, Leibniz speaks in terms of a single “rule” that

describes the phenomena in question; he envisages, for

example, a single equation that describes a geometrical

figure, no matter how complex and irregular-seeming that

figure may be. And he tells us that, ideally, this equation

should be as simple as possible. But in other passages he

seems to envisage a number of rules underlying a given set

15

of phenomena, and he tells us that rather than having a

simpler rule, we should desire fewer of them:

...where wisdom is concerned, decrees or hypotheses are comparable to

expenditures, in the degree to which they are independent of each other,

for reason demands that we avoid multiplying hypotheses or principles,

somewhat as the simplest system is always preferred in astronomy.15

Here, the concern is over the number of laws or decrees, not

their internal structure. Simplicity, then, is a dual

criterion – it means, first, having as few rules as

possible, and second, having rules that are themselves as

simple as possible. We can thus amend our definition of

fruitfulness like this:

Definition 3: The phenomena apart from the rules must be as

complex and interesting as possible, described by as few

rules as possible, and those rules must contain the fewest

terms possible.

15 Discourse on metaphysics G IV 43; L 306

16

The other two ways in which a single set of phenomena may be

described by different rules are more problematic, however.

The first is based upon Leibniz’ argument that any haphazard

collection of objects can be described by some set of

general laws:

...not only does nothing happen in the world which is absolutely

irregular but one cannot even imagine such an event. For let us assume

that someone puts down a number of points on paper entirely at random,

as do those who practice the ludicrous art of geomancy; I maintain that

it is possible to find a geometric line whose law is constant and

uniform and follows a certain rule which will pass through all these

points and in the same order in which they were drawn.16

Although Leibniz speaks of “a” line, there is of course, for

any pattern of points, an infinite number of lines that

could be drawn to pass through them; moreover, on Leibniz’

principles, every one of these lines (and not simply a small

subset of them) would be constant, uniform, and describable

by a rule. This means that the “fewer laws” element of

simplicity becomes meaningless, since it is logically 16 Discourse on metaphysics G IV 43; L 306. See also Theodicy 242; H 277

17

impossible to have anything other than an infinite number of

laws no matter what the phenomena are. It also means that

the “simpler laws” element of simplicity becomes

meaningless, because these laws must vary in complexity. For

any pattern of dots, there are an infinite number of rules

available describing lines that pass through them all, and

these rules vary enormously in complexity; among them there

will always be incredibly complex rules.

If the analogy between points and lines on paper, on the one

hand, and phenomena and laws in possible worlds, on the

other, is to stand up, then for any possible world, the

phenomena it contains (other than the laws themselves) might

have been generated by a different set of laws. Indeed,

there are presumably an infinite number of possible sets of

laws for any given set of phenomena which might have

generated those phenomena; and these sets of laws will vary

enormously in complexity. But if this is so, then we cannot

talk about “the” rule or set of rules that underlies any

given possible set of phenomena. And we cannot rank possible

18

sets of phenomena by the simplicity or complexity of their

rules, because not only can each set of phenomena be

described by an infinite number of rules, but in all cases,

many of those rules will be extremely complex.

We must therefore refine our definition of fruitfulness to

take account of this. Although there are an infinite number

of rules for any possible set of phenomena, there is

presumably one rule which is the simplest. Or if there is no

single simplest rule, there will be several equally simple

ones which are not surpassed in simplicity by any other. It

is the complexity of this simplest rule or set of simplest

rules that is important, because we can rank different sets

of phenomena by the complexity of their simplest rules. In

other words, despite the infinite number of rules (and

massive complexity of many of those rules) available for

every possible set of phenomena, we can still rank sets of

phenomena by simplicity. So we can refine the definition of

fruitfulness like this:

19

Definition 4: The phenomena apart from the rules must be as

complex and interesting as possible, and among the sets of

rules that describe them, there should be a set which

contains as few rules as possible, and these rules should

contain the fewest terms possible.

III

I stated above that there are three different ways in which

the same phenomena can be described by different sets of

rules. The third way is this. In Leibniz’ view, there are

what we might call different levels of rules. He tells us:

...from the first essential laws of the series – true without exception,

and containing the entre purpose of God in choosing the universe, and so

including even miracles – there can be derived subordinate laws of

nature, which have only physical necessity and which are not repealed

except by a miracle, through consideration of some more powerful final

cause. Finally, from these there are inferred others whose universality

is still less; and God can reveal even to creatures the demonstrations

of universal propositions of this kind, which are intermediate to one

20

another, and of which a part constitutes physical science. But never, by

any analysis, can one arrive at the absolutely universal laws nor at the

perfect reasons for individual things; for that knowledge necessarily

belongs to God alone.17

There are, then, three kinds of law at work in the universe,

but Leibniz’ analysis is rather confusing. The first problem

concerns the “first essential” laws, which are absolutely

universal and have no exceptions at all.18 Leibniz states

that these are the laws that God follows in choosing which

possible world to create. He also tells us that no-one can

know these laws. But here there is a contradiction, for

Leibniz himself frequently tells us that one of the laws God

follows in deciding which possible world to create is the

principle of the best: he creates the best of all the

possible worlds, and this is because God always does what is

best. That seems to be an essential law governing God’s

behaviour, to which there are no exceptions at all, which

17 Necessary and contingent truths C 19-20; P 99-100

18 He also calls them “primary free” (libres primitifs) laws – see Letter to

Arnauld, 14 July 1686 G II 51; L 333.

21

can be known – at least, Leibniz thinks he knows it. On the

assumption that Leibniz would not be guilty of such a

glaring inconsistency, it makes sense to understand these

“first essential” laws not as laws that govern the way God

makes his choices but as laws that govern the possible world

itself. In surveying the various possible worlds, God also

surveys the laws that govern them. One of the factors

influencing his choice of which world to create is the kind

of laws that govern it; he wants laws of a particular kind

that will produce phenomena of a particular kind. It is in

this sense that these “first essential” or primary laws

influence God’s decision; they are part of the universe

itself which is the object of the divine will, not external

constraints upon that will.19 The fact that God always

follows the principle of the best should therefore not be

considered a primary law of the kind that Leibniz is

speaking of here, so there is no contradiction in his saying

that it can be known while primary laws are unknowable.

22

What of the second and third kinds of law? With the second

category, Leibniz seems to be thinking of general physical

laws. He goes on to give the example of the tendency of

things to fall towards each other. Gravitational attraction,

then, is a law of the second kind. But in the passage quoted

above, Leibniz specifies that laws of the third kind are also

found in physical science. What sort of laws could these be?

Perhaps Leibniz is thinking of the laws of biology, such as

the law that all living things respire, or something along

those lines. These laws are universal in a sense, but they

do not apply to all objects in the universe. A key

difference between these laws and those of the second group

is that we can understand why the former hold, but not the 19 By “external constraints” here I mean external to God. The laws

governing the different possible worlds are constraints upon God’s will,

and they are external to that will in the sense that possible worlds are

within God’s understanding rather than his will, but by the same token

they are constraints that are internal to God’s understanding. For

Leibniz, it is God’s understanding that both constrains and determines

his will; as elements of the possible worlds that are contained in his

understanding, natural laws play this role too. See, for example,

Theodicy 225; H 267-68.

23

latter. Thus, if we know the physical laws of the universe –

or at least some of them – we can understand why a cow would

die if dropped from a great height; we know that it would

fall, and we know the effects that this would have upon its

body. But although we know that it would fall in the first

place (we know of a law or group of laws which entail this),

we do not really understand why (we do not know how or why

those laws operate).

We have, then, three kinds of law, which correspond to three

degrees of knowledge that we can have about them:

1. Primary laws, which are completely universal, and which

we cannot know or understand at all.

2. Secondary laws, which are universal except when

suspended by a miracle, and which we can know, but not

understand.20

3. Tertiary laws, which are universal only within certain

contexts, and which we can both know and understand.

24

Moreover, the later levels of laws are parasitic upon the

earlier ones. That is, these are not simply different sets

of laws with different properties; secondary laws arise from

the operation of primary laws, and tertiary laws arise from

the operation of secondary ones. Leibniz expresses this when

he tells us that secondary laws are “derived” from primary

ones, and that tertiary ones can be “inferred” from

secondary ones. Precisely what relation this is meant to

denote is unclear. It cannot mean that we, human beings,

deduce tertiary laws from our knowledge of secondary laws,

20 As the passage from Necessary and contingent truths makes clear, Leibniz

regards miracles not as violations of natural laws but as events where

the operation of primary laws requires the suspension of the operation

of secondary laws. Since we may know secondary laws but not primary

laws, they appear to us to be exceptions or violations to natural laws.

The fact that non-miraculous events are in principle understandable as

arising from the operation of natural laws, while miraculous ones are

not understandable in this way, is an important distinction – see

Rutherford (1995) p. 241 – but it does not obscure the fact that

miracles nevertheless do arise from the operation of natural laws. They

are merely primary laws rather than secondary ones, and thus hidden from

our understanding. See Jolley (2005) pp. 44, 150

25

and secondary laws from our knowledge of primary laws,

because we do not know primary laws at all. The idea seems,

rather, to be that the operation of primary laws gives rise

to that of secondary laws, and the operation of secondary

laws gives rise to that of tertiary laws. Thus, it is

because the laws of nature are as they are that dropping

cows tends to kill them; it is not that God has decided to

create certain secondary laws and then decided to create

certain tertiary ones. Creating the secondary laws

automatically means creating the tertiary ones. That is why

we can understand tertiary laws, because we can know the

secondary laws upon which they are based. And that, too, is

why although we can know secondary laws, we cannot

understand them, because they are based upon the primary

laws that we do not know at all. We may say, then, that

secondary laws supervene upon primary laws, understanding

this in a strong sense to mean that the (near-universal)

operation of the secondary laws is simply part of the

(universal) operation of the primary laws. Similarly, the

operation of the tertiary laws is simply part of the

26

operation of the secondary laws. For example, the operation

of the laws that govern the biological functions of

organisms is really just part of the operation of the laws

that govern physical bodies in general; within the physical

world, governed by physical laws, some bodies are

constituted in such a way that the operation of the physical

laws upon them produces behaviour which may also be

understood as following biological laws, which govern those

bodies alone. It is in this sense that tertiary laws are

“derived” from secondary laws, and secondary laws are

“derived” from primary ones.

Which entities do the laws govern? We have spoken of

“objects” and “phenomena”; does this mean “substances”?21 As

is well known, Leibniz’ views on which entities qualify as

substances developed over the course of his career. Broadly

speaking, early in his career he believed that individual

bodies – the kind that Aristotle treats as primary

substances in the Categories – were substances, but later in

his career he shifted to the position that monads, which are

27

immaterial, are the only true substances, and that bodies

are merely well founded phenomena.22 The texts we are

considering date from before the time when Leibniz had fully

developed the later view; we may, then, legitimately suppose

that the objects which he considers to be governed by the

laws he mentions are either substances or phenomenal objects

(such as bodies), since there is not a clear distinction

between them. But how should we interpret Leibniz’ texts on

the laws within the context of his later monad theory? Since

the laws of gravity are given as an example of secondary

laws, it seems that secondary laws must govern phenomenal

objects, not monads – whatever laws monads may follow, they

are not subject to gravity. Does that mean that secondary

laws operate at the level of phenomenal objects in virtue of

the fact that primary laws govern the monads? This does not

seem to me a viable interpretation. Leibniz does not suggest

that the distinction between primary and secondary laws is

to be understood as a distinction between laws that govern

entities of different ontological status (substances on the

one hand and phenomenal objects on the other). Rather,

28

monads operate as they do because of their appetition and

perception, and the behaviour of phenomenal objects results

from the operations of monads.23 It seems reasonable, then,

to suppose that Leibniz envisages both primary and secondary

laws, at least, as governing the created universe in general

– not as governing substances and bodies respectively.

Given this, what are we to make of the definition of

fruitfulness? In an optimally fruitful universe, are all of

these laws to be as simple as possible, or only some of

them? In fact it seems impossible for Leibniz to want all

three levels of laws to be as simple as possible, because

having different levels of laws itself breeds complexity.

This is clear if we consider the relation between secondary

and tertiary laws. However many secondary laws there may be,

there are evidently far more tertiary laws. It is a tertiary

law that dropping cows from a great height kills them – that

is a law that is universal in scope (so it is a law) but it

has a limited universality (it applies to all cows but not

to all seagulls). But there is a similar law applying to all

29

donkeys, a rather different law applying to all mice, and a

very different one applying to all spiders. Yet all of these

different tertiary laws are “derived” from the same

secondary ones, in the sense of “derived” from explained

above. It seems, then, that all kinds of laws in the best

possible world cannot be equally simple or few in number.

When Leibniz speaks of the desirability of having simple

laws, he must be excluding tertiary laws. What of secondary

laws? Here the situation is harder: because we do not know

any primary laws at all, we cannot tell if having just a few

primary laws tends to result in the existence of lots of

secondary laws in the same way that we can tell that having

a just a few secondary laws tends to result in the existence

of lots of tertiary ones. Perhaps it is possible to have a

universe with a very few, very simple primary laws that also

has very few, very simple secondary laws, and perhaps

Leibniz’ criterion of fruitfulness is meant to encompass

both kinds.

30

However, as we have seen, there is a sense in which the

rules that are to be simple are those that produce the other

phenomena that characterise a possible world. Remember that

the best possible world is the one that features “the

greatest effect produced by the simplest means”.24 But the

21 Although I address this question here, I do not think it is crucial

in considering Leibniz’ use of the fruitfulness criterion. This is

partly because his understanding of that criterion, as examined in this

paper, does not depend upon any particular understanding of the nature

or identity of substances; and partly because while Leibniz remained

committed throughout his career to key claims about the nature of

substance, his understanding of which things counted as substances was

still in flux during the period when he wrote about the fruitfulness

criterion. As I indicate below, the criterion is primarily a feature of

his writings of the 1680s and early 1690s, predating the publication of

his New system. To ask whether Leibniz thinks that the laws which,

according to the fruitfulness criterion, should be kept simple apply to

monads or to bodies is thus to overlook, to some degree, the ways in

which his thinking developed.

22 On this, see Rutherford, D. “Metaphysics: the late period” in Jolley

(1995) pp. (123-32); and Jolley (2005) pp. 58-63, 74-81. The details of

how Leibniz’ thought developed are, needless to say, disputed. See

Tlumak (2007) pp. 155-58.

31

secondary laws are “derived” from the primary ones, and the

tertiary laws are in turn “derived” from the secondary ones.

The primary laws therefore determine all of the other laws;

it is the primary laws that produce all the other phenomena

in the possible world. It seems reasonable, therefore, to

suppose that the “simplest means” to which Leibniz refers in

this and similar formulations is just the primary laws.

This means that we can refine our definition of fruitfulness

one more time:

Definition 5: The phenomena apart from the rules must be as

complex and interesting as possible, and among the sets of

primary rules that describe them, there should be a set

which contains as few primary rules as possible, and these

primary rules should contain the fewest terms possible.

IV

23 See Jolley (2005) p. 80.

32

But why should we believe that possible worlds with more

fruitful laws are preferable to those with less fruitful

ones?

Leibniz offers a number of arguments to support this claim.

None, however, is the subject of any sustained treatment on

his part. I focus on the two most important.25

The first major argument is based upon the fact that it is

simply more economical to do more with less.26 This is the

main argument Leibniz offers in the most well-known passage

supporting the fruitfulness criterion:24 Principles of nature and grace G VI 603; L 639

25 Leibniz’ most interesting argument other than those treated here is

his claim that simple laws allow God to “fill” the universe most

efficiently and completely: Letter to Malebranche, 22 July/2 June 1679 G I 331; L

211. Leibniz attributes the argument to Malebranche, although in this

letter he is discussing the Meditations sur la metaphysique by the Abbé de

Lanion, which he erroneously ascribes to Malebranche. Malebranche

corrects him in his reply – see G I 339. But Leibniz never specifies why

simpler laws have this property.

26 Discourse on metaphysics G IV 447; L 317

33

As for the simplicity of the ways of God, this is shown especially in

the means which he uses, whereas the variety, opulence, and abundance

appears in regard to the ends or results. The one ought thus to be in

equilibrium with the other, just as the funds intended for a building

should be proportional to the size and beauty one requires in it.27

Can laws really be compared to expenditures? After all, they

are not the “stuff” out of which God makes things; they do

not cost him anything. Leibniz himself recognises the

inadequacy of the analogy when he immediately goes on to

add:

It is true that nothing costs God anything, even less than it costs a

philosopher to build the fabric of his imaginary world out of

hypotheses, since God has only to make his decrees in order to create a

real world. But where wisdom is concerned, decrees or hypotheses are

comparable to expenditures, in the degree to which they are independent

of each other, for reason demands that we avoid multiplying hypotheses

or principles, somewhat as the simplest system is always preferred in

astronomy.28

27 Discourse on metaphysics G IV 43; L 306

34

But is Leibniz entitled to talk in this glib fashion of

“decrees” as equivalent to “expenditures” for God? Only a

short time after writing this passage, he states in the

Arnauld correspondence that when God decides to create any

individual substance, he is (at the same time) deciding to

create every individual substance that is compossible with

it, because the complete concept of the one contains

information about all of the others. One therefore cannot

separate God’s decision to create Adam from his decision to

create any of Adam’s descendants, and vice versa; he takes

into account the pros and cons of each individual in a

possible world before deciding whether to actualise them all

en masse or not.29 There is, then, only one decree that God

actually makes: the decree to actualise this possible world

and all its inhabitants. The same would have been true had

he chosen to actualise a different one – in that case, he

would have made only one decree, namely the decree to 28 Discourse on metaphysics G IV 43; L 306. I consider the appeal to

astronomy below.

29 To Landgraf Ernst von Hessen-Rheinfels, 12 April 1686 G II 19; M 14

35

actualise that possible world and all its inhabitants. How,

then, can we talk about a number of decrees at all? There

was – and could only have been – only one.

But of course, laws themselves are part of the possible

world, as we saw earlier, and as Leibniz insists later in

that same Arnauld correspondence. They are thus distinct

from the decrees (or decree) that God makes in actualising

one possible world.30 Perhaps, then, we should interpret

30 Strickland (2006) pp. 69-70 considers this distinction – between the

decrees that God enacts in actualising the world, and the laws that

operate within that world – to be crucial. He argues (pp. 71-84) that

when Leibniz talks about simplicity in the context of his fruitfulness

criterion, he is referring to God’s decrees, not the laws that operate

in the world. On this interpretation, fruitfulness means that “God

brings this richest composite about… by using the smallest number of

decrees” (pp. 83-84). But this interpretation falls foul of the point

made above, that God cannot actualise any possible world by using more

than a single decree – not to mention the fact that for Leibniz, as we

also saw above, fruitfulness, including simplicity of laws, is a feature

of the possible world itself and not of God’s action in selecting or actualising

that world. That was his point of disagreement with Malebranche.

36

Leibniz more charitably; the “decrees” he speaks of in this

passage are not the decrees that God makes in choosing to

create one world over another, but the laws that operate

within that world that make it preferable to another. But

here again Leibniz seems to be hampered by his own

principles – above all his nominalism. Leibniz believes that

abstract terms must be avoided, where possible, because they

are misleading: they fool us into thinking that they refer

to things when in fact they do not. The only things that

really exist, for Leibniz, are individual substances and

their qualities.31 Where, then, do laws fit in? Surely a

natural law is about as abstract and insubstantial as a

thing can be. Although Leibniz does not say anything about

laws in the context of his texts on nominalism, it seems

that those texts must commit him to the view that a natural

law is simply an abstraction which the mind makes on the

basis of the qualities that individual substances possess.

31 On this, see Mates, B. The philosophy of Leibniz: metaphysics and language

Oxford: Oxford University Press 1986 pp. 171-73; and also Fichant (1998)

pp. 147-48.

37

For example, the Moon possesses the quality of revolving

around the Earth in a certain way.32 The Earth, and other

planets, possess the quality of revolving around the Sun in

a way which is similar in certain respects. We can therefore

abstract from these particular qualities, possessed by the

different celestial bodies, a general “law” that all such

bodies behave in a certain way, and call that the inverse

square law of gravitational attraction. So we can

meaningfully talk about this and other laws, but there is

nothing “out there” that answers to the name “inverse square

law of gravitational attraction”.

But if laws are simply abstractions, extrapolated from

individual substances, then Leibniz is arbitrary in his

insistence that “fruitful” laws are to be preferred. In a

situation with few, simple laws and many, complex

32 As I have already noted, physical objects such as celestial bodies

may count as “substances” in the context of Leibniz’ early philosophy

but not his later, when they are only phenomenal objects. But I have

suggested that these objects are still governed by secondary laws

whether we call them “substances” or not.

38

substances, one might speak of barren substances just as

well as of fruitful laws. And why would such a situation be

preferable to one with barren laws but fruitful substances,

that is, one with few, simple substances and many, complex

laws? But to make this objection is to overlook the fact

that, for Leibniz, laws do not simply describe phenomena;

they bring them about too. We have already seen that Leibniz

likens laws to “expenditures”, or even “costs”:

There is always a principle of determination in nature which must be

sought by maxima and minima; namely, that a maximum effect should be

achieved with a minimum outlay, so to speak.33

If the rules are “outlay” or “cost” (sumtu) – or comparable

in some significant way to it – then they are what produce

phenomena. So we are to think of the laws of the universe as

tools, as it were, that God uses to bring about the other

phenomena in the universe. We find the same conception

elsewhere:

33 On the radical origination of things G VII 303; L 487

39

The ways of God are those most simple and uniform: for he chooses rules

that least restrict one another. They are also the most productive in

proportion to the simplicity of ways and means. It is as if one said that a

certain house was the best that could have been constructed at a certain

cost... For the wisest mind so acts, as far as it is possible, that the

means are also in a sense ends, that is, they are desirable not only on

account of what they do, but on account of what they are. The more

intricate processes take up too much ground, too much space, too much

place, too much time that might have been better employed.34

On this conception, the laws are in some way ontologically

prior to the other phenomena. The way in which Leibniz

hedges around his use of terms such as “outlay” or “cost”

indicates that these are not to be taken literally, but he

does seem to intend us to understand that the laws actually

bring about the other phenomena. They explain why the other

phenomena are the way that they are.

How can this be so if “laws” are just abstracted from the

properties of the phenomena they govern? The answer is that

creaturely phenomena are not the only things from which 34 Theodicy G VI 241; H 257

40

“laws” are abstracted: they also describe God’s actions. In

his paper On nature itself, Leibniz considers the concept of

“nature” as an explanatory principle distinct from

individual substances, and rejects it. But he does accept it

as a circumlocution for qualities that individual substances

have in virtue of God’s actions upon them:

...since this command [God’s initial decree about how created things

should behave] no longer exists at present, it can accomplish nothing

unless it has left some subsistent effect behind which has lasted and

operated until now, and whoever thinks otherwise renounces any distinct

explanation of things, if I am any judge, for if that which is remote in

time and space can operate here and now without any intermediary,

anything can be said to follow from anything else with equal right. It

is not enough, therefore, to say that in creating things in the

beginning, God willed that they should observe a certain law in their

progression, if his will is imagined to have been so ineffective that

things were not affected by it and no durable result was produced in

them... If on the other hand, the law set up by God does in fact leave

some vestige of him expressed in things, if things have been so formed

by the command that they are made capable of fulfilling the will of him

who commanded them, then it must be granted that there is a certain

41

efficacy residing in things, a form or force such as we usually

designate by the name of nature, from which the series of phenomena

follows according to the prescription of the first command.35

So we are not to think of natural or divine laws as existing

independently of individual substances. It is not as if God

makes a decree at the beginning of time and it remains

floating around somewhere for ever more, directing what

happens in the universe. On the contrary, to say that a

divine decree exists is to say that God decides to create an

individual substance in a certain way. The way he sets it up

determines how it will be at each subsequent stage in its

existence. At these later stages, the law or the decree

exists only in the sense of the “vestige” in the individual

substance which determines each subsequent stage. It is

rather as if I were to wind up a clockwork toy and set it

running; the spring that I wound up continues to provide

power to the toy, and in that sense my original decision to

set it running continues to cause it to run, but only

35 On nature itself G IV 507; L 500-501; see also Specimen dynamicum G VI 234;

L 450

42

because of the agency of the spring. My decision continues

to exist in the sense that it continues to cause the toy to

run through the spring, not because I continue to do

anything myself, and certainly not because my decision has

taken on some kind of tenuous existence of its own and has

to supervise the toy itself.

So “laws”, “rules”, and “decrees” – which are all different

words for the same thing – are just abstractions. They do

not really do anything at all. What actually exists are God

and his creatures. When we say that there is a natural law,

we are really making two claims – one concerning God, and

one concerning his creatures. The first claim concerns God’s

actions in setting up the world. And the second concerns the

way that the creatures in that world behave, as a result of

God’s actions. But neither of these things can reasonably be

considered means that God uses. If we consider laws in the

former sense, they are God’s actions or decisions

themselves, not the means he uses to put them into effect.

If we consider laws in the second sense, as properties of

43

creatures, they may be useful to God in choosing which

possible world to actualise, but not as means to actualise

it. For example, suppose that Law X is a primary law that

holds in possible world A but not in possible world B. To

say that Law X holds in possible world A is really to say

that, were that world to be actual, every individual in it

would behave in a certain way. Let us also suppose that Law

X is highly fruitful; the behaviour that it describes among

the individuals in world A is complex and interesting. The

fact that Law X holds in world A but not in world B is one

of the factors that influence God’s decision to actualise

world A but not world B. All of this is consistent, but it

leaves Leibniz unable to draw any meaningful analogy between

the laws that obtain in worlds and the means that an artisan

uses to create objects or the capital that an investor puts

into a project. The laws are not means for creating worlds

at all – not even in the loosest possible sense in which God

could be said to employ “means” – but qualities of worlds

according to which they are ranked. That is central to

Leibniz’ attack upon Malebranche’s denial of optimalism.

44

V

Little wonder that in the last sentence of the passage from

the Discourse quoted above, Leibniz suggests an alternative

rationale for the fruitfulness criterion. He tells us that

we can think of the divine decrees or laws as expenditures

because “we avoid multiplying hypotheses or principles,

somewhat as the simplest system is always preferred in

astronomy”.

This second major argument for the fruitfulness criterion,

then, is that fruitfulness is a desirable characteristic in

metaphysical principles. In fact, throughout Leibniz’

writings, “fruitful” is an adjective that is most often

applied not to laws or worlds but to philosophical theories.

Leibniz believes that a good metaphysical theory or

principle is one that is “fruitful”, that is, it explains a

lot without being itself complex.36 But this is a criterion

for evaluating explanatory principles, that is, principles

45

that we formulate in an attempt to explain phenomena that we

perceive. Why should it also apply to causative principles,

that is, the principles which actually cause those

phenomena? For this to work, there must be some kind of

direct parallel between the two kinds of principles, and

Leibniz seeks to establish it by appeal to the principle of

parsimony in natural philosophy. Because simpler hypotheses

are preferable in natural philosophy, the laws which natural

philosophy seeks to uncover must themselves be relatively

simple. We have seen this argument hinted at in the

reference to astronomy in the passage from the Discourse

quoted above. We can also see it in the following passage

from the Arnauld correspondence:

... I say that the connexion between Adam and human occurrences is not

independent of all the free decrees of God; but also it does not depend

upon them completely, in such a way as if every occurrence happened or

was foreseen only by virtue of a primary particular decree made

respecting it. I therefore believe that there are few free primary

decrees capable of being called laws of the universe and regulating the

sequences of things, which, when linked to the free decree to create

46

Adam, bring about the consequence, as very similarly there are few

hypotheses to explain phenomena...37

The argument is, or can be, rather complex. Benson Mates

suggests that, for Leibniz, the principle of parsimony holds

in philosophy and science because God follows it in

creation:

...in creating the actual world, God’s task was to maximize its variety

while minimizing the complexity of its laws. In view of this, when

explaining natural phenomena, the scientist should give preference to

the simplest hypotheses, for they are the ones most likely to be true.38

36 See, for example, Leibniz’ evaluation of his theory of substance in

On the correction of metaphysics and the concept of substance G IV 469; L 433. See

also On nature itself G IV 506; L 500; and Brown, S. Leibniz Brighton:

Harvester 1984 pp. 78-79. Leibniz was hardly unique in considering

“fruitfulness” a desirable quality of philosophical principles – see

Berkeley, Principles of human knowledge §133.

37 Remarks upon M Arnauld’s letter G II 40; M 43

38 Mates (1986) p. 168

47

Even if this were Leibniz’ argument, it would not establish

what he needs, which is that having simple laws of nature is

better than having complex ones. It would only establish

that the actual world has simple laws of nature, not that

this is a feature (let alone the main feature!) which makes

it the best possible world. Besides, I do not know of any

text where Leibniz actually gives God’s preference for

simple laws in creating the world as the reason why one

48

should favour simple explanations in science.39 On the

contrary, Leibniz normally seems to cite the apparent

success of the principle of parsimony in science as a reason

for supposing that God prefers simple laws. There is surely

some circularity at work here, which we can see more clearly

if we distinguish between a number of claims that Leibniz

might be making:

39 Mates (p. 169) cites the paper Tentamen anagogicum, G VII 270-79; L

477-84, as an example of Leibniz trying to use the principle of the best

in problems of physics. But in this paper, Leibniz does not explicitly

appeal to the principle of simple laws – he speaks only of rays of light

and other objects of physics following the paths of “the greatest ease”

(la plus grande facilité) (G VII 274; L 479). The same thing is true of

Leibniz’ later claim that “the maxim that nature acts by the shortest

way, or at least by the most determinate way, is sufficient by itself to

explain almost the whole of optics” (New essays G V 404;R&B 423). This is

not an appeal to simplicity as we have defined it for the fruitfulness

criterion; Leibniz speaks only of “the shortest way” or “the most

determinate way”. For more on the relation between laws of nature,

simplicity, and scientific method in Leibniz, see Couturat, L. La logique

de Leibniz Paris: Alcan 1901 pp. 229-33.

49

1. Because God favours simple laws when creating the

universe, scientists should favour simple hypotheses

when explaining natural phenomena.

2. Because we know that God favours simple laws when

creating the universe, we know that scientists should

favour simple hypotheses when explaining natural

phenomena.

3. Because the adoption of simple hypotheses in science

seems to work, it is reasonable to suppose that God

favours simple laws when creating the universe.

(1) seems a reasonable claim, but it rests upon the

supposition that God does favour simple laws when creating

the universe. How, then, do we know that? As we have seen,

Leibniz appeals to the principle of parsimony in science.

But there are two directions in which the inference might

run. (2) suggests that use of the principle of parsimony is

derived from prior knowledge that God favours simple laws in

creation. (3), by contrast, runs the other way: we infer

that God favours simple laws from the success of the

50

principle of parsimony. Together, (2) and (3) are circular.

The circularity need not be wholly vicious. We can imagine a

scientist starting with the empirical fact that the adoption

of simple hypotheses in science seems to yield results, and

concluding (as in (3)) that God probably favours simple

laws; the scientist might then use that as a provisional

supposition and favour simple hypotheses even more (as in

(2)), finding that this yields even better scientific

results, and so on.

But how much of this picture can reasonably be attributed to

Leibniz? Not much of it. For one thing, the justification

that he gives for preferring simple formulations of

hypotheses in philosophy is not that the laws of nature

themselves are simple, but that simple hypotheses are easier

to understand and draw inferences from.40 More importantly,

however, the argument or method outlined above is

incompatible with what Leibniz says elsewhere about the

knowability of natural laws. As we have seen, he insists

40 Letter to Gabriel Wagner G VII 520; L 466

51

that human beings cannot know the primary laws that operate

within the universe; by necessity, only God can know these.

It follows, then, that no natural laws which science ever

has established, or ever will do, can be identified with

these primary laws. Science can establish only derivative

laws, that is, secondary and tertiary laws. But if that is

so, then all of (1), (2), and (3) are fatally undermined.

They all assume some kind of parallel between the

fundamental laws followed by God in setting up the universe

and the laws discovered by science, namely simplicity: they

all suggest that the more simple one kind of law is, the

more simple the other is likely to be.

But is that an unreasonable assumption? It may be that the

laws that science uncovers are not the fundamental laws of

the universe, but only secondary or tertiary ones. But

still, if these secondary and tertiary laws turn out to be

simple, then it might be reasonable to suppose that the

primary ones, which the secondary and tertiary laws are

“derived” from in the sense that we saw earlier, are simple

52

too. But on what basis could that supposition be made, given

that Leibniz tells us that we can never know any of these

primary laws? The fact that we do not, and cannot, know what

any of the primary laws are does not, in itself, entail that

we cannot know facts about primary laws in general; after

all, Leibniz certainly thinks we know some things about

them, such as the fact that they exist. Perhaps we could, in

theory, know some facts about the kind of relations that

hold between primary and secondary laws. But it is difficult

to see how we could come to know such facts given that we

cannot know what any of the primary laws are. Certainly

Leibniz does not give us any clues. And there is a stronger

argument for supposing that the existence of simple

secondary laws does not, in itself, give a good reason for

supposing that the primary laws are also simple, which is

that Leibniz himself at least entertains the possibility

that there could exist secondary laws which are “derived”

from more complex primary laws:

53

The laws of nature are not so arbitrary and so indifferent as many

people imagine. For example, if God were to decree that all bodies

should have a tendency to move in circles and that the radii of the

circles should be proportional to the magnitude of the bodies, one would

either have to say that there is a method of carrying this out by means

of simpler laws, or one would have to admit that God must carry it out

miraculously, or at least through angels charged expressly with this

responsibility, somewhat in the manner of those that were once assigned

to the celestial spheres.41

Remember that secondary laws are derived entirely from

primary laws; there is no such thing as a secondary law

whose operation cannot be wholly explained in terms of the

operation of primary laws (at least by God, if not by

humans, who cannot know the primary laws). In this passage,

Leibniz distinguishes between two possible explanations for

any given secondary law: first, it might be derived from

simpler primary laws; or second, it might not. The succession

of miracles that Leibniz imagines in the latter case would

thus be derived from a number of primary laws, or a single

complex primary law, or a combination of both. Since Leibniz

41 Clarification of Bayle’s difficulties G IV 520-21; L 494

54

is quick to make it clear that he believes in the existence

of miracles – they are cases where the operation of a

primary law requires the suspension of a secondary law – it

seems that he is willing to suppose that cases such as this

succession of miracles are at least possible. There are at

least some possible worlds in which secondary laws are

derived from primary laws that are more complex than those

secondary laws. Whether the actual world is one of these

possible worlds is unclear – the implication is that God

would tend to avoid situations like this, which would

suggest that any such situations in the actual world must at

least be very rare – but for our purposes it does not really

matter. The important point is that primary laws are not

necessarily simpler than the secondary laws that are derived

from them. And if that is so, then the apparent simplicity

of secondary laws, as revealed by natural philosophy, cannot

in itself be any reason for assuming the simplicity of the

primary laws from which they are derived.

VI

55

It seems, then, that while it may be possible to formulate

the fruitfulness criterion in line with Leibniz’ other

claims, he cannot offer any good reason to suppose that the

criterion is true. His nominalism about natural laws, and in

particular his insistence that natural laws form a part of

the universe rather than an external constraint upon it,

make a nonsense of his argument that it is more efficient

for God to use fewer and simpler natural laws to bring about

the phenomena of the universe. And his insistence that we

cannot know primary laws fatally undermines his argument

that the effectiveness of the principle of parsimony in

scientific reasoning points to simplicity in the primary

laws of the actual universe. But this is potentially very

damaging to Leibniz’ whole theodicy. He tells us:

I have shown on several occasions that the final analysis of the laws of

nature leads us to the most sublime principles of order and perfection,

which indicate that the universe is the effect of a universal

intelligent power.42

42 Tentamen anagogicum G VII 270; L 477

56

But the fruitfulness criterion – which for Leibniz expresses

these “sublime principles of order and perfection” – cannot

be established by “analysis of the laws of nature” or of

anything else. If that is so, then it represents at best a

very shaky plank in his enterprise and at worst a fatal flaw

in it. It may therefore be no accident that almost all of

the texts we have been examining come from a relatively

short period in Leibniz’ career, the mid-1680s to the mid-

1690s. Catherine Wilson has shown that Leibniz’ use of the

fruitfulness criterion owes much to Malebranche.43 From what

we have seen, Leibniz did not have any very good

philosophical reason for holding it, and his own

philosophical principles actually preclude him from having

such a reason. It seems reasonable to suppose, then, that he

held it because he was impressed by the way Malebranche used

it in his theodicy to explain natural evil (it was, in other

43 Wilson (1983) p. 774. See also Strickland (2006) pp.67-68, and p. 87

n. 1 – Strickland agrees with Wilson that Leibniz derived the idea from

Malebranche, but disagrees over which texts of Malebranche’s he first

found it in. See also n. 25 above.

57

words, a fruitful principle from that point of view). In his

later writings, the fruitfulness criterion drops somewhat

out of view.44 We have noted passages in the Theodicy where it

remains, but there it has a rather vestigial character. It

is not at all central to Leibniz’ argument in that book,

something which is striking when one bears in mind that he

had presented it with such fanfare within the first couple

of pages of the Discourse on metaphysics. Neither does it make

much of an appearance in his other writings of the later

period. The notion that the universe is run in an orderly

fashion certainly remained central to his thought, but as I

have suggested, that belief is distinct from the more

specific claim that it has simple primary laws that bring

about complex phenomena. And even the claim that the actual

universe possesses this characteristic, as a matter of fact,

44 Strickland (2006) p. 3 suggests that “Leibniz’s optimism did not

undergo any radical revision throughout his lifetime”. If what I have

argued here is correct, then his use of the fruitfulness criterion, at

least, did vary, although he never repudiated it. Whether one regards

that as “radical revision” or not will depend upon how central to his

optimalism one regards that criterion.

58

is distinct from the claim that this is a feature that makes

this universe more desirable than those that lack it. So it

may well be that, consciously or unconsciously, Leibniz

recognised that the various philosophical reasons he had –

or thought he had – for holding the fruitfulness criterion

did not mesh well with the rest of his philosophy, and while

he never repudiated the principle, he no longer placed the

emphasis upon it that he had when he was writing the

Discourse and during the decade that followed.45

45 I would like to thank Jeffrey Tlumak for his helpful comments on an

earlier version of this paper, and also Nicholas Rescher for drawing my

attention to his 2005 paper, which stimulated my thinking on this topic.