Discourse on Metaphysics

Section 13: The Problem of Free Will

As the individual concept of each person includes once for all everything which can ever happen to him, in it can be seen, a priori the evidences or the reasons for the reality of each event, and why one happened sooner than the other. But these events, however certain, are nevertheless contingent, being based on the free choice of God and of his creatures. It is true that their choices always have their reasons, but they incline to the choices under no compulsion of necessity.

Now we're up to section 13 of the Discourse -- personally my favorite section of the work. The issue is free will, namely the free will of God's creatures (although the subject of God's freedom comes up too). Section 13 was so disturbing to Arnauld that it sparked the whole content of the ever-interesting Leibniz-Arnauld correspondence, a series of letters between the two thinkers on the subject of free will. Arnauld thought that Leibniz's system clearly made the actions of all of God's creatures necessary, and so determined and hence not free. Leibniz thought that Arnauld wasn't really understanding his argument fully, since as far as Leibniz sees it, God's creatures are as free as they can be. With this background in mind, let's now turn to section 13 itself.

First, Leibniz starts with what he already knows is a problem that has been stirred in the mind of his reader (in fact, this is the very problem Arnauld is thinking of). So he states the problem, and suggests that he realizes the reader will be thinking this. He writes:

But before going further it is necessary to meet a difficulty which may arise regarding the principles which we have set forth in the preceding. We have said that the concept of an individual substance includes once for all everything which can ever happen to it and that in considering this concept one will be able to see everything which can truly be said concerning the individual, just as we are able to see in the nature of a circle all the properties which can be derived from it. But does it not seem that in this way the difference between contingent and necessary truths will be destroyed, that there will be no place for human liberty, and that an absolute fatality will rule as well over all our actions as over all the rest of the events of the world?

So Leibniz is suggesting that the reader will think:

1. The CIC of a substance includes all that has happened, is happening and will happen to it.
2. The CIC of a substance is the essence of the it, just as the nature of a circle reveals all properties proper to circles.
3. The nature of a thing belongs to it by necessity, and cannot be removed from the thing without destroying it.
4. There are only substances
5. Everything that has, is, or will happen is thus a truth of necessity.
6. Thus, there are no contingent truths.
7. Thus, human actions are necessary not contingent.
8. Thus, human action is not free.

Let's look at a few of the premises to make sense of them and as we do this reconstruct the argument that Leibniz thinks the reader will lodge against him.

First, premise (1) is assured in the Discourse as true. Leibniz has argued in section 8 that the CIC of a substance includes everything that ever has happened to it or that ever will happen to it. So if Judas's CIC includes the fact that Judas betrayed Jesus, then it is a fixed fact about the substance Judas that such an event will occur.  

Why is it fixed? It is fixed because premise (2) is true -- the CIC of a substance fixes the essence of that substance. So "betraying Jesus" is part of the essence of Judas. So just as knowing the properties of a right triangle reveals that the Pythagorean theorem must be true of it, knowing the properties of Judas reveals that betraying Jesus must be true of Judas.

Why? Because (3) is also true -- the essence of a thing belongs to it by necessity (by definition). So removing the fact about the Pythagorean theorem would assure that the notion of right triangle has similarly been destroyed. Similarly, removing the fact about the betrayal of Jesus would destroy the substance of Judas.

Now Leibniz has already argued that the world is simply composed of monads (minds, or substances). So that's premise (4).

Since all that exist are substances, premises (1) - (3) assure that everything that is true is true by necessity, since everything that is true must be an essential property of some substance.

Thus it seems as if (5) is true. If everything that is true is an essential property of some substance, it seems to follow from the definition of what it means to be an essential property of something that all truths are necessary truths.

If (5) is true, then (6) must be true, since contingent truths are unnecessary truths. So if all truths are necessary, then there are no contingent truths.

Since the existence of a human action is just a truth in the universe, it is no different than any other truth. So what is above must apply to it as well. So Judas's betrayal of Jesus -- a human action -- is an essential property of the substance Judas. As such, (7) follows: there are no contingent human actions and so all human action is necessary. So Judas's betrayal was necessary. 

If (7) is true, then human action is predetermined and thus (8) human actions are not free. Judas's betrayal was predetermined and as such the betrayal is not a free act.

So what does Leibniz say to this -- admittedly well reasoned -- argument?

To this I reply that a distinction must be made between that which is certain and that which is necessary.

Aha! So Leibniz will take aim at premise (5). All truths are not "necessary" truths just because they are all essential properties of some substance. Here Leibniz says that he will draw a distinction between "what is necessary" and "what is certain."

He continues:

Every one grants that future contingencies are assured since God foresees them, but we do not say just because of that that they are necessary.

First, Leibniz gets rid of a sort of "faux-objection" and to set up an analogy. The reader might assume that because God knows what will happen in "advance" that those events cannot freely occur.

This is an old objection one can find repeated in Aristotle and Hobbes. The first mention of this argument arises in Aristotle's Categories, where he talks of the "Sea Battle." Aristotle's thought experiment is this: it is either true or false that tomorrow there will be a sea battle on the Aegean. Once the time has passed, the proposition "There was a Sea Battle on the Aegean (on such an such a day)" will be either true or false. But what is the truth value of this proposition -- called a "future contingent" -- before the day in question? According to Aristotle, it must be "indeterminate" (neither true nor false) because to claim that it is true or false before the event actually occurs is to rob the actors of their free will. Essentially, Aristotle argues, we must "wait and see" what the free agents in the situation decide to do. Then the truth of the proposition will be fixed. According to Thomas Hobbes, writing on the same issue, the truth value of the proposition is fixed before the event happens. So the agents have no free will because the truth of the proposition "There will be a Sea Battle" is necessarily fixed one way or the other before it happens.

Leibniz is thinking of this sort of argument. He is, actually, disagreeing with both parties. He is suggesting here that future contingents are not necessary at all, although they are certain (they are "assured" he says). So their being "fixed" beforehand doesn't entail that they are necessarily true. One might think of the analogy this way: imagine that Aristotle is right -- agents freely decide what to do. So at the time of the day in question, many agents freely decide what to do and on the basis of these decisions a Sea Battle occurs. Would this mean that God could not know beforehand what they would do? Leibniz would say (for the sake of the analogy) that the answer is no -- God could have foreknowledge of what the agents will freely decide to do. This foreknowledge doesn't rob them of their freedom. (Note: this is not Leibniz's argument here in 13 in favor of free will; he is simply using this as a sort of analogy to make the reader see that there can be a difference between "fixed" and "necessary.")

Next he returns to the subject at hand:

But it will be objected, that if any conclusion can be deduced infallibly from some definition or concept, it is necessary; and now since we have maintained that everything which is to happen to anyone is already virtually included in his nature or concept, as all the properties are contained in the definition of a circle, therefore, the difficulty still remains.

Leibniz suggests that the reader will argue that the situations are different. Leibniz, they will argue, suggests that what happens to a person is a part of their concept (virtually) just as a conclusion can be infallibly deduced from a concept or definition. And essences are not "assured" of their concepts, but are rather "necessary" to them. In other words, we can know that the Pythagorean theorem is true of right triangles because it is necessary that it is true of them. So it's not a matter of our being "assured" or "certain" but rather of it being necessary. So, the argument will go, the situation is no different for human acts. They will follow necessarily from the substances to which they belong as essences.

Leibniz counters the phantom objector:

In order to meet the objection completely, I say that the connection or sequence is of two kinds; the one, absolutely necessary, whose contrary implies contradiction, occurs in the eternal verities like the truths of geometry; the other is necessary only ex hypothesi, and so to speak by accident, and in itself it is contingent since the contrary is not implied.

Leibniz returns to the distinction between what is "certain" and what is "necessary". He suggests that the two divisions can be understood as follows:

• Truths that are absolutely necessary. These truths are distinctive in that their contraries imply contradictions. For example, to claim that a triangle has four interior angles is a contradiction. So geometric truths belong in this category. 
• Truths that are necessary ex hypothesi. These are truths which are distinctive in that their contraries do not imply a contradiction. So "Judas did not betray Jesus" or "Caesar did not cross the Rubicon" are not contradictions. As such, Leibniz argues that they are really contingent truths.
  

At this point, the distinction is not entirely clear and moreover it seems as if Leibniz is not allowed to make this distinction. According to what he has already argued, all truths are analytic. So how can there be contingent accidental truths? He continues:

This latter sequence is not founded upon ideas wholly pure and upon the pure understanding of God, but upon his free decrees and upon the processes of the universe.

By "the latter sequence" Leibniz means the contingent truths. So he is expanding the meaning of the distinction a little more. Now we know that:

• The absolutely necessary (the really necessary truths) truths are not grounded in the understanding of God. 
• The necessary ex hypothesi truths (what Leibniz is calling the contingent truths) are grounded in the free decrees of God 

What does he mean, though, by God's "understanding" and God's "free decrees"? He gives an example:

Let us give an example. Since Julius Caesar will become perpetual Dictator and master of the Republic and will overthrow the liberty of Rome, this action is contained in his concept, for we have supposed that it is the nature of such a perfect concept of a subject to involve everything, in fact so that the predicate may be included in the subject ut possit inesse subjecto.

Okay, so far so good. Leibniz is just restating the "predicate in subject" position about substances. Caesar's actions are all contained within his concept. He continues:

We may say that it is not in virtue of this concept or idea that he is obliged to perform this action, since it pertains to him only because God knows everything. But it will be insisted in reply that his nature or form responds to this concept, and since God imposes upon him this personality, he is compelled henceforth to live up to it.

Leibniz is now thinking of how his objector will tend to think of why certain predicates (like "crossing the Rubicon" is part of the concept of Caesar) are in certain substances. The argument he thinks the objector will think of is:

P. God know (beforehand) that substance X will perform action Y (that predicate Y belongs to concept X).
---
C. Thus, it is not in virtue of concept X that Y happens, but rather due to God imposing that nature on X. 

Notice here that Leibniz is drawing a distinction between two ways to understand the situation of "Y being an action of X":

• Y belongs to X because Y is the nature of X itself
  

or

• Y belongs to X because God made Y to be a part of X

The objector will suggest that the latter explanation is really the case. Y belongs to X because God made Y to be a part of X. Is this Leibniz's way of understanding the issue? He continues:

I could reply by instancing the similar case of the future contingencies which as yet have no reality save in the understanding and will of God, and which, because God has given them in advance this form, must needs correspond to it. But I prefer to overcome a difficulty rather than to excuse it by instancing other difficulties, and what I am about to say will serve to clear up the one as well as the other.

Leibniz first says that he could reply to this argument by using the example he has already instanced above (the one where I discussed the Sea Battle). But he says that he doesn't want to reply to a difficulty by pointing out how a problem with an analogous case could be solved. He thinks that would be a weak reply. Instead, he says he will take on the objection directly, and that, once said, one can apply the answer to the earlier case (the Sea Battle) if one wishes to (since they really are analogous cases). So he turns directly to the problem:

It is here that must be applied the distinction in the kind of relation, and I say that that which happens conformably to these decrees is assured, but that it is not therefore necessary, and if anyone did the contrary, he would do nothing impossible in itself, although it is impossible ex hypothesi that that other happen.

Leibniz turns immediately to the question of "God's free decrees" and action in relation to it. He says that actions which are "conformable" to God's free decrees are "assured" (or necessary ex hypothesi). What are God's free decrees? Well, let's take a simple one. Let's say that out of the many possible worlds God could have actualized, one of them -- World A -- has the laws of physics we have in ours (so nothing can travel faster than the speed of light, say, because of certain ways in which the stuff of that universe was constituted). Another, World B, has different physical laws (say in this world it is possible to go faster than light -- because the stuff composing the universe is in some way different). Now let's further claim that God actualizes World A and not World B (because it turns out that World A is more perfect, or whatever). In actualizing World A, God will have to make some "Free Decrees." Firstly, he will have to make it such that the laws of World A obtain, such that nothing can go faster than light in that World. This decree is free because what it refers to does not exist before God actualizes it -- the choice of worlds is open to God before he makes the choice.

Now let's say that we are looking at the proposition

"Particle X cannot travel faster than the speed of light."

Now in World A the truth value of that proposition is "true." What is the metaphysical nature of that truth? Is it a necessary truth, or a contingent one?

Well, according to Leibniz (and the whole tradition before and after him), a contingent truth is one where its contrary does not imply a contradiction. Does "Particle X travels faster than the speed of light" imply some kind of logical impossibility? No. It would be the case that "Bachelor X is married" is a contradiction, so we know that propositions like "All bachelors are unmarried" are of a different type than propositions like "X cannot travel faster than light." So, Leibniz argues, "X cannot travel faster than light" it is actually contingently true. As Leibniz puts it, there is nothing "impossible in itself" about the contrary of the proposition.

However, he suggests that although it is contingent, it is necessary ex hypothesi. What does this mean? Well, essentially what he is saying is that given that God made the free decree to create World A, it is not possible for a particle to travel faster than light. But it is only impossible given that larger context -- that God has previously made a free decree. So it is not "impossible in itself" but rather "impossible given something prior to it". Once God makes it the case that particles are composed a certain way, it is impossible for something to go faster than light.

Returning to Leibniz's example, the proposition "Caesar crossed the Rubicon" is contingently true, or necessarily true ex hypothesi. He continues:

For if anyone were capable of carrying out a complete demonstration by virtue of which he could prove this connection of the subject, which is Caesar, with the predicate, which is his successful enterprise, he would bring us to see in fact that the future dictatorship of Caesar had its basis in his concept or nature, so that one would see there a reason why he resolved to cross the Rubicon rather than to stop, and why he gained instead of losing the day at Pharsalus, and that it was reasonable and by consequence assured that this would occur, but one would not prove that it was necessary in itself, nor that the contrary implied a contradiction, almost in the same way in which it is reasonable and assured that God will always do what is best although that which is less perfect is not thereby implied.

What Leibniz appears to be arguing here is that human actions are "certain" (because given God's free decrees, they must happen) but not "necessary" because there are clearly possible worlds in which those actions do not occur (and the only reason that those worlds were not actualized is because God made certain free decrees that limited his selection to a different world).

So what about these "free decrees"? Which decrees did God make that -- once made -- made it "certain" or "necessary ex hypothesi" that all human actions happen the way they do and will in the future?

Leibniz does hint at one of them: he says that statements like "Caesar crossed the Rubicon" are necessary ex hypothesi  in the same way that "God will always do what is best" is necessary ex hypothesi. In other words, it seems as if Leibniz is suggesting that the fact that God acts in accord with what is best is not necessary, but rather chosen freely by God. Once this choice is made, then it becomes the case that God must actualize the best possible world, and once that decision is made it becomes necessary that Caesar crossed the Rubicon. It is strange to think that God's action in accord with the principle of the best is contingent, but this seems to be what he is saying. Strange! (The Arnauld - Leibniz correspondence deals heavily with this issue, but unfortunately we cannot go further in this.)

Leibniz continues on the subject of the free decrees of God:

For it would be found that this demonstration of this predicate as belonging to Caesar is not as absolute as are those of numbers or of geometry, but that this predicate supposes a sequence of things which God has shown by his free will. This sequence is based on the first free decree of God which was to do always that which is the most perfect and upon the decree which God made following the first one, regarding human nature, which is that men should always do, although freely, that which appears to be the best.

Now notice that Leibniz makes the distinction between what is "absolutely necessary" and what is "contingent" here (as he already did earlier but now he can explain) as what is separate of God's free decrees. As it seems, Leibniz is arguing that numerical or geometrical propositions have their truth independently (and by necessity) of what God decrees. All other truths have their basis in the "sequence" of free decrees made by God.

Note here also that Leibniz says that the first free decree of God was to always do that which is in the most perfect. Following from this decree, obviously, is the principle of the best (and as such it follows that the principle of the best is necessary ex hypothesi as he had just stated earlier).

Leibniz continues regarding the truths dependent upon divine decree:

Now every truth which is founded upon this kind of decree is contingent, although certain, for the decrees of God do not change the possibilities of things and, as I have already said, although God assuredly chooses the best, this does not prevent that which is less perfect from being possible in itself.

So truths that are necessary ex hypothesi are all contingent because they rely upon a prior free decree by God. He moveover adds that the actualization of the perfect must be necessary ex hypothesi because that which is not perfect is still possible -- and the decrees of God do not change or in any way alter or even create what the nature of possibility is. So although God does in fact choose what is most perfect, it is a free action of God because it's opposite is still possible. 

Leibniz continues on the subject of God's free will in actualizing the most perfect:

Although it will never happen, it is not its impossibility but its imperfection which causes him to reject it. Now nothing is necessitated whose opposite is possible.

So again, God actualizes the most perfect not because the imperfect is impossible in itself, but because God has already made a free decree regarding perfection that makes it "certain" that he do so.

And thus Leibniz ends the passage:

One will then be in a position to satisfy these kinds of difficulties, however great they may appear (and in fact they have not been less vexing to all other thinkers who have ever treated this matter), provided that he considers well that all contingent propositions have reasons why they are thus, rather than otherwise, or indeed (what is the same thing) that they have proof a priori of their truth, which render them certain and show that the connection of the subject and predicate in these propositions has its basis in the nature of the one and of the other, but he must further remember that such contingent propositions have not the demonstrations of necessity, since their reasons are founded only on the principle of contingency or of the existence of things, that is to say, upon that which is, or which appears to be the best among several things equally possible. Necessary truths, on the other hand, are founded upon the principle of contradiction, and upon the possibility or impossibility of the essences themselves, without regard here to the free will of God or of creatures.