Contingency

G. W. Leibniz

(1646-1716)

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HOW TO READ THE TEXT

Contingency

© Jonathan Bennett 2017

Contingency

G. W. Leibniz

1686

Early Modern Texts, 2017

COPYRIGHT

Contingency

© Jonathan Bennett, 2017. All rights reserved.

Early Modern Texts

First launched: September 2004

Last amended: June 2006

Contact: earlymodern31@gmail.com

www.earlymoderntexts.com

HOW TO READ THE TEXT

[Brackets] enclose editorial explanations. Small ·dots· enclose material that has been added, but can be read as though it were part of the original text. Occasional •bullets, and also indenting of passages that are not quotations, are meant as aids to grasping the structure of a sentence or a thought.

Contingency

In God existence is the same as essence; or—the same thing ·put differently·—it is essential for God to exist. So God is a necessary being, ·a being who exists necessarily·.x

Created things are contingent, i.e. their existence doesn’t follow from their essence.

Necessary truths are ones that can be demonstrated through an analysis of terms, so that they end up as identities. ·For example, square analyses into figure that is plane, closed, equilateral, and has four sides. Apply this analysis to the necessary truth

A square has four sides

and you get

A figure that is plane, closed, equilateral, and has four sides has four sides,

which is an identity·. Similarly, in algebra when in a correct equation you substitute values ·for the variables· you get an identity. ·For example, in the equation

(x × y)2 = x2 + 2xy + y^2

if we put 2 for x and 3 for y we get

(2 + 3)2 = 2^2 + 2(2 × 3) + 3^2

which comes to

25 = 4 + 12 + 9

which comes to 25 = 25, which is an identity·. Thus, necessary truths depend upon the principle of contradiction, ·which says that the denial of an identity is never true·.

Contingent truths can’t be reduced to the principle of contradiction. If they could, ·they wouldn’t be contingent, and· everything would be necessary and nothing would be possible except what actually exists.

Nevertheless, since we say that both God and creatures •exist and that necessary propositions and ·some· contingent ones are •true, there must be a notion of •existence and one of •truth that can be applied both to what is contingent and what is necessary.

What is common to every •truth, in my view, is that one can always give a reason for a true proposition unless it is an identity. In necessary propositions the reason necessitates, whereas in contingent ones it inclines. ·Identical propositions· are, as I have said, the rock-bottom reasons for all necessary truths; we don’t have reasons why they are true·.

And it seems to be common to things that •exist, whether necessarily or contingently, that there is more reason for their existing than there is for any others to exist in their place.

Every true universal affirmative proposition, whether necessary or contingent, has some connection between subject and predicate. In identities this connection is self-evident; in other propositions it has to be brought out through the analysis of terms.

This little-known fact reveals the distinction between necessary and contingent truths. It is hard to grasp unless one has some knowledge of mathematics, ·because it goes like this·. When the analysis of a necessary proposition is continued far enough it arrives at an identical equation; that’s what it is to demonstrate a truth with geometrical rigour. But the analysis of a contingent proposition continues to infinity, giving reasons (and reasons for the reasons (and reasons for those reasons. . . )), so that one never has a complete demonstration. There is always an underlying ·complete and final· reason for the truth of the proposition, but only God completely grasps it, he being the only one who can whip through the infinite series in one stroke of the mind.

[This paragraph expands Leibniz’s compact formulation in ways that can’t be flagged by ·dots·. For more on ‘incommensurables’, see pages 4–5 of his Dialogue on human freedom.] I can illustrate this with a good example from geometry and numbers. In •necessary propositions, ·as I have said·, a continual analysis of the predicate and the subject can eventually get us to the point where we can see that the notion of the predicate is in the subject. For a •numerical analogue of this, consider the process of getting an exact comparison between two numbers: we repeatedly divide each until we arrive at a common measure. For example, wanting to compare 24,219 with 12,558, we find that each can be divided by 3 then by 13 then by 23, giving us the more graspable relationship of 27 to 14. But that doesn’t work with an •incommensurable pair of numbers such as any whole number and √2: as Euclid has clearly demonstrated, there is no fraction F such that (F × F) = 2. We can work along a series of fractions, squaring as we go, and get ever nearer to 2, but it is mathematically impossible for us to end the series by finding a fraction whose square exactly equals 2. Still, there is a proportion or relation between (say) 3 and √2; we can’t express it exactly in terms of fractions, but we know that it exists: 3 is a certain determinate definite amount larger than √2. I offer this as analogous to the situation with •contingent truths: in them there is a connection between the terms—i.e. there is truth—even if that truth can’t be reduced to the principle of contradiction or necessity through an analysis into identities.

·Here are two questions that can be asked about the necessity of certain propositions·. Is this proposition:

•God chooses the best

necessary? Or is it one—indeed, the first—of his free decrees? Again, is this proposition:

•Whatever exists, there is a greater reason for it to exist than for it not to exist

necessary? ·I answer that the •former proposition is not necessary: God always chooses the best because he decrees that that’s what he’ll do. It follows that the •latter proposition is not necessary either: there is always a greater reason for the existence of an actual thing than for any possible rival to it, but only because God has freely decided always to choose the best·.

It is certain that there is a connection between subject and predicate in every truth. So the truth of Adam, who sins, exists requires that the possible notion of Adam, who sins involves something by virtue of which he is said to exist.

It seems that we must concede that God always acts wisely, i.e. in such a way that anyone who knew his reasons would know and worship his supreme justice, goodness, and wisdom. And it seems that God never acts in a certain way just because it pleases him to act in this way, unless there is a good reason why it is pleasing. ·Thus, something may be done ‘at God’s pleasure’ (as we say), but that is never an alternative to its being done for a reason·.

Since we can’t know the true formal reason for the existence of any particular thing, because that would involve an infinite series ·of reasons·, we have to settle for knowing contingent truths a posteriori, i.e. through experience. But we must at the same time hold the general principle, implanted by God in our minds and confirmed by both reason and experience, that nothing happens without a reason, as well as the principle of opposites, that ·of rival possibilities· the one for which there is more reason always happens. (I said ‘confirmed by experience’, but ·treat that cautiously. I meant only that experience confirms the principle· to the extent that we can discover reasons through experience.)

And just as God decreed that he would always act in accordance with true reasons of wisdom, so too he created rational creatures in such a way that they act in accordance with prevailing or inclining reasons—reasons that are true or, failing that, seem to them to be true.

Unless there were such a principle ·as this one about reasons·, there would be no principle of truth in contingent things, because to them the principle of contradiction is certainly irrelevant.

Not all possibles come to exist—we have to accept that, because if it were false you couldn’t think up any story that wasn’t actually true somewhere at some time! Anyway, it doesn’t seem possible for all possible things to exist, because they would get in one another’s way. There are, in fact, infinitely many series of possible things, no one of which can be contained within any other, because each of them is complete.

From the following two principles, the others follow:

(1) Whatever God does bears the mark of perfection or wisdom.

(2) Not every possible thing comes to exist.

To these one can add:

(3) In every true universal affirmative proposition the predicate is in the subject, i.e. there is a connection between predicate and subject.

[In this next paragraph, Leibniz wrote of a proposition’s existing, apparently meaning its being true.] Assuming that this proposition:

The proposition P that has the greater reason for being true is true

is necessary, we must see whether it then follows that P itself is necessary. It isn’t. If by definition a necessary proposition is one whose truth can be demonstrated with geometrical rigour, then indeed it could be the case that these two propositions are demonstrable ·and thus necessary·:

•A proposition is true if and only if there is greater reason for it to be true than for it to be false.

•God always acts with the highest wisdom.

But from these one can’t demonstrate any proposition of the form Contingent proposition P has greater reason ·for being true than for being false· or of the form Contingent proposition P is in conformity with divine wisdom. So it doesn’t follow from the above two displayed propositions that any contingent proposition P is necessary. Thus, although one can concede that it is necessary for God to choose the best, or that the best is necessary, it doesn’t follow that P is necessary, where P is something that has been chosen; for there is no demonstration that P is the best. This can be put in terms of the ·technical· distinction between •necessity of the consequence and •necessity of the consequent—that is, between •P necessarily follows from Q and •P is itself necessary. Assuming that the best is necessarily chosen, we have

From P is the best it follows necessarily that P is true,

but we do not have

Necessarily P is true,

because we have no demonstration that P is the best.

·Though I have been exploring the implications of the thesis that necessarily God always chooses the best, I don’t assert it. I say only that· it seems safer to attribute to God the most perfect way possible of operating. When it comes to creatures, one can’t be as sure ·as we can with God· that they will act in accordance with even the most obvious reason; with respect to creatures, this proposition—·that they will always so act·—can’t be demonstrated.