The Evolution of Modern Metaphysics: Making Sense of Things (21 page)

At this point there arises a particularly difficult exegetical question. Call the relation that obtains between two possible monads when their representations of the world cohere
harmony
. The question is this: what is the relation between harmony and compossibility?

We might think that they must be different relations. In particular, we might think that there must be instances of compossibility that are not instances of harmony. For, although it is impossible for two conflicting stories both to be true, it is not impossible for two conflicting stories both to be told. There is corroboration for this in Leibniz’ definition of the compossible as ‘that which, with another, does not imply a contradiction’ (
Textes Inédits
, p. 325). For there is surely no contradiction in two monads’ failing to be in harmony with each other. Furthermore, unless there were instances of compossibility that were not instances of harmony, either God would not after all be required to ensure that all monads are in harmony with one another, for it would be impossible for them not to be, or God would be required to ensure that the world is so much as possible. Either of these alternatives would be contrary to what Leibniz actually says. The former would be contrary to his insistence that ‘it is God alone … who is the cause of [harmony]’ (‘Discourse’, §14). The latter would be contrary to his denial that ‘the eternal truths of metaphysics … are only the effects of God’s will’ (‘Discourse’, §2; cf. IV, 344). (It is surely an eternal truth of metaphysics that the world is possible.)
²³

On the other hand, as against all of that, unless compossibility just
is
harmony, then it is hard to see what else it can be. What else, given the windowlessness of monads, might be thought to explain why not every set of possible monads constitutes a possible world? What, other than disharmony, might be thought to prevent any pair of possible monads from existing in the same possible world, or any one possible monad from existing in two different possible worlds?

These are genuine questions, not rhetorical questions. I raise them just to signal the exegetical difficulty. We could not accede to the suggestion that compossibility is the same as harmony without dismissing some of the quotations above as aberrations on Leibniz’ part. And in any case there are all sorts of further complications that I have not considered. (Here is one. I said earlier that there is surely no contradiction in two monads’ failing to be in harmony with each other. But if God necessarily creates everything for the best, and if the best necessarily requires harmony, perhaps disharmony does imply a contradiction? Here is another. It may be a basic error in the first place to think of possible worlds combinatorially. Perhaps each possible monad is just an aspect of some possible world, the worlds being ontologically more fundamental than the monads, so that the question whether a possible monad can exist in more than one possible world trivially receives the answer no.
²⁴
But then, to complicate this complication, how would that consist with the monads’ windowlessness?
²⁵
) All that matters for our purposes is that somewhere in the process of determining which of all the arbitrary sets of possible monads is to constitute this world there is a benevolent decree on the part of God that prohibits any whose monads are not in harmony with one another.
²⁶

But harmony is not the only desideratum. If it were, there would be no reason for God to create anything at all. For in a world with no created monads, it would be vacuously true that every monad was in harmony with every other. So, by the principle of sufficient reason, there must be something else guiding God’s creative act (‘Nature and Grace’, §7; cf. ‘Monadology’, §53).

What there is, Leibniz urges, is the value of sheer existence. The more that exists, the better. God’s own necessary existence serves as a ground for this desideratum, which Leibniz expresses as follows: ‘
everything possible demands existence
’ (‘Résumé’, §6, emphasis in original).
²⁷
So God actualizes as much as He can, subject to the constraint that there should still be harmony.

But subject only to that constraint? Or are there yet further desiderata besides these two? Leibniz does sometimes write as though harmony and plenitude were the only two desiderata. Indeed, in one striking passage he combines that suggestion with the suggestion – which, if it were intended, would settle the question we have just been considering about the relation between compossibility and harmony – that compossibility is indeed tantamount to harmony. He writes, ‘It does not follow from this [sc. that everything possible demands existence] that all possibles exist; though this would follow if all possibles were compossible’ (‘Résumé’, §7; cf. ‘The Ultimate Origination’, p. 139). Elsewhere, however, he seems to acknowledge beauty, order, and their perception by intelligent beings as further determinants of creation (e.g. ‘Résumé’, §§17 and 18). The issue is whether they really are
further
determinants. There is certainly more to beauty and order than harmony. But is there more to them than plenitude? Leibniz glosses plenitude in such a way as to make clear that there is more to
it
than sheer population size. Form and variety also count (e.g. ‘Résumé’, §12). And indeed he explicitly relates form and variety to beauty and order (ibid., §§13–15). But does he relate them tightly enough to derive the value of the latter from the value of the former? And what about the value of their perception by intelligent beings? Once again, the exegetical waters are deep. Once again, we do not need to wade through them. All that matters for our purposes is that there are, if not two desiderata influencing God’s creative act, then two broad categories of desiderata, one essentially quantitative and the other essentially qualitative, and these are in conflict with each other, so that what God needs to achieve in creation is a balance between the two, maximizing
each to the least detriment of the other.
²⁸
This world is the possible world in which that balance is struck. Or, as Leibniz himself puts it, this world is that which is ‘most perfect, that is to say that which is simultaneously simplest in theories and the richest in phenomena’ (‘Discourse’, §6; cf. ‘The Ultimate Origination’, p. 138, and ‘Monadology’, §58). In sum, this world is the best of all possible worlds.

4. Leibniz’ Various Modal Distinctions

Before we turn to Leibniz’ account of how this world appears not to be the best of all possible worlds, we should note an important implication of the story so far concerning the contingency of how things are. If, per impossible, we had an infinite intellect, and were thereby able to perform the infinitely complex calculations necessary to determine how things must be for the balance referred to at the end of the previous section to be struck, then we would be in a position to determine
a priori
how things in fact are. For in Leibniz’ view we have an
a priori
guarantee that there is an omniscient, omnipotent, perfectly good God, who ensures that things are just how they must be for that balance to be struck. That it would be possible in this way to determine
a priori
how things are is not however supposed to impugn our conviction that this world is just one of a range of possible worlds, in other words that it is contingent that things are the way they are.

How comfortable should we be with this? For any positivistically minded philosopher there is a harsh dissonance in the idea of determining
a priori
how, among all the ways things could have been, they are. If things could have been otherwise, such a philosopher will say, then nothing short of experiential contact with things can rule out their actually being otherwise.
²⁹

Three points can be made straight away, each of which should make Leibniz’ idea sound a little easier on the positivist ear. First, there is always
some
sense, if only an epistemic sense indicating a prior ignorance, in which determining
a priori
how things are means ruling out other possibilities. It is not obvious that what would be ruled out in the Leibnizian story need be possible in a sense that would be any more awkward to accommodate, positivistically, than that. (We shall return to this point.) Second, Leibniz’ conception of the
a priori
is in any case somewhat different from the positivist conception. It is closer to the original conception, which applied to
reasoning from explicans to explicandum. Roughly, on Leibniz’ conception, to determine
a priori
how things are is to determine how they are in a way that explains why they are that way.
³⁰
And third, there is of course the very grossness of the counterpossibility signalled in the phrase ‘
per impossible
’. Small wonder if the posit that we have an infinite intellect has such strange consequences!
³¹

This third point can be helpfully reinforced by looking at one familiar aspect of the Leibnizian idea of determining
a priori
how things are. Leibniz writes, ‘In every true affirmative proposition, necessary or contingent, universal or particular, the notion of the predicate is in some way contained in the notion of the subject’ (‘Necessary and Contingent’, p. 96).
³²
Thus suppose that Adam sins. Then the ‘notion’ of sinning must be contained in the ‘notion’ of Adam. This makes it sound as if Adam could not have failed to sin, and indeed, strictly speaking, Leibniz thinks, he could not. For strictly speaking there is only one possible world, namely this world, in which Adam, this actual man, this very monad, so much as exists, and that is a world in which he sins (cf. ‘Discourse’, §31). But it remains contingent that Adam sins, because it is contingent that Adam exists at all. The point about his notion containing the notion of sinning is just that a full infinite grasp of what it takes to be Adam must include a grasp of all that is involved in the possible world in which he exists, including his sinning. And that grasp would be part of the
a priori
exercise of determining that the world in question was the best, thereby inferring that the world in question was this world, thereby inferring that Adam exists, and thereby inferring that Adam sins (cf. ‘Letter to Arnauld’, dated 4–14 July 1686, in ‘Correspondence with Arnauld’).

We
, however, have only a partial, finite grasp of what it takes to be Adam. We cannot determine
a priori
that Adam sins. The only truths that
we
can determine
a priori
, which Leibniz calls ‘truths of reasoning’ (‘Monadology’, §§33–35), are those whose denial can, by a finite process of analysis, be reduced to absurdity.
³³
(A simple example might be that any father who sins
is a parent who sins – fathers being by definition male parents.) And the distinction between truths of reasoning and all other truths, the latter of which Leibniz calls ‘truths of fact’ (ibid.), just is the distinction between what is necessarily true, or true in all possible worlds, and what is contingently true, or true merely in this world (‘Necessary and Contingent’, esp. pp. 96–98; cf. ‘Discourse’, §13, and ‘On Freedom’, pp. 108–109). So once the counterpossible presumption of our infinite intellect has been dropped, Leibniz’ view is not so different from what a positivistically minded philosopher might choose to say after all.

That Leibniz talks about the notion of the predicate being contained in the notion of the subject has led some commentators, notably Bertrand Russell, to compare his idea to Kant’s idea of analyticity, which he (Kant) defines in a superficially very similar way. Kant calls a judgment analytic when ‘the predicate
B
belongs to the subject
A
as something that is (covertly) contained in the concept
A
’ (Kant (
1998
), A6/B10). Having made this comparison, Russell struggles with Leibniz’ claim, quoted above, that ‘in
every
true affirmative proposition … the notion of the predicate is in some way contained in the notion of the subject’ (emphasis added). For on even a remotely Kantian understanding of this, there is one kind of proposition, namely an existential proposition such as the proposition that Adam exists, which
must
be an exception (ibid., A225/B272–273 and A592–602/B620–630). And Russell, accordingly, does not see how it can fail to be an exception for Leibniz too (Russell (
1992a
), pp. 9–10).
³⁴
Russell does not see how even a full infinite grasp of what it takes to be Adam can suffice for seeing that anyone actually fills the bill. But in fact, once we realize that Leibniz’ idea allows for appeal to what would be visible to an infinite intellect ca- pable of seeing
a priori
how this world qualifies as the best of all possible worlds, and that Kant’s idea allows for appeal to nothing save what would be visible to a finite intellect trying to make sense of what is given to it in experience (ibid., B145), so that Kant’s idea, if it corresponds to anything in
Leibniz, corresponds to Leibniz’ idea of a truth of reasoning,
³⁵
then there is no obstacle to our accepting that Leibniz really does mean
every
true affirmative proposition, including the proposition that Adam exists.
³⁶
And if we insist on using the Kantian label ‘analytic’ for Leibniz’ much broader idea, however foreign that may be to Kant’s own use of the label, then we can say, with Louis Couturat, that just as part of the purport of the principle of contradiction is that every analytic proposition is true, so too part of the purport of the principle of sufficient reason is that every true proposition is analytic (Couturat (
1901
), pp. 214–221).