Hobbes and geometry

I started off by trying to explain why Hobbes writes the way he does: he is trying to come up with a political philosophy that mirrors Euclid’s geometry. Euclid starts with definitions of the elements of geometry, like lines and circles. Then he adds postulates about making some of these elements. For instance, the first postulate, “to draw a straight line from any point to any point” means “I assume that it is possible to draw a straight line between any two points.” In practice, geometrical constructions are done using a straight edge for lines and a compass for circles, but you could do it by free hand too. The postulates allow us to assume that if you say that what you drew is a straight line, then it is a straight line.

As you can see on the handout, Euclid just proposes these definitions and postulates. He thought they were obvious. (There are also what Euclid calls “common notions,” such as that if line A is equal to line B and line B is equal to line C, then line A is equal to line C. I did not put those on the handout.)

The fun starts after these definitions, postulates, and common notions have been laid out. For instance, you can use these very simple, obvious propositions to make things like equilateral triangles.

You don’t have to measure the sides to know it’s an equilateral triangle. They are guaranteed to be equal by virtue of the steps we followed in constructing it.

I myself think that is too cool for words. Hobbes agrees. That is why he tries to model his philosophy on geometry. He starts with definitions of rights and tries to show how we can use them to make other things, like the state or having something as one’s “own” (justice, as traditionally understood).

One thing that we need to keep our eye on is whether Hobbes’s definitions are really as uncontroversial and obvious as Euclid’s definitions are. For instance, do you think it is obvious that people are allowed to do anything in order to preserve their own lives? I am not sure that I do.

We also need to look out for instances where Hobbes might be trying to force an argument to fit the geometrical model even when it really does not. I think that Hobbes is prone to claim that some things are logically necessary when, really, he has just shown that they are almost always the case as a matter of fact. (What’s the difference? Well, gravity always works, but it is logically possible that it could stop working tomorrow and we will all fly off the face of the Earth. By contrast, it is not even logically possible that 2 + 2 = 5.)

Rights

You have to understand the distinctions between claims, liberties, powers, and immunities on the handout.

A right is a liberty if it grants permission. Suppose you and I are running a race against one another. The following sentences are all equivalent to one another.

1. We each have the right to win the race.
2. We are each permitted to win the race.
3. Neither of us is obliged to let the other win the race.
4. Neither of us would do anything wrong by winning the race. More specifically, neither of us would injure the other (where “injure” means “treat unjustly”).²

Obviously, we cannot both win the race. That shows one important thing about liberties: they are compatible with competition. So when Hobbes says that everyone in the state of nature has the right to preserve their lives, he is not saying that they are forbidden from killing one another. Quite the contrary!

A right is a claim right if it grants an entitlement to something from someone else. For example, the following expressions concerning my physical security are all equivalent to one another.

1. I have a right not to be killed (unless I pose a threat to someone else or deserve to be killed for some reason)
2. No one else is permitted to kill me (unless, etc.)
3. Everyone else is obliged not to kill me (unless, etc.)
4. Anyone who does kill me would do something wrong (unless, etc.)

Claim rights are supposed to close off certain kinds of competition. If I have a claim right to my life, I do not have to compete with you to see if I “win” by staying alive or “lose” by doing the other thing. My claim right entitles me not to be killed by you.

Claims, liberties, powers, and immunities are elements of the rights that we talk about in everyday life. There are very few pure instances of one or the other. For instance, my property right in my pen can be analyzed as including:

1. Claims: everyone else has a duty not to interfere with the pen.
2. Liberties: I am permitted to use the pen as I like.
3. Powers: I can transfer my right to the pen by selling it or giving it away.
4. Immunities: no one else is capable of selling or giving away rights to the pen.

The reason why we bother with the elements is that they enable us to say more precisely exactly what an everyday right involves. They are especially useful in the law, where precision about rights is extremely important. That is why these elements were first identified by scholars interested in the analysis of legal rights (See Hohfeld 1913).

Back to Hobbes. Hobbes’s right of nature (see 14.1) is a liberty and not a claim right. What is shocking about Hobbes is that he says there are no claim rights in the state of nature. That means no human rights and nothing that anyone does to anyone else would be wrong, no matter how awful it is. That is hard to swallow.

It appears as though Hobbes rules out claim rights in the state of nature simply by not including them. If having a liberty right means you do not have obligations, having a claim right means that someone else does have an obligation, and the only rights in the state of nature are liberty rights, then it follows that there are no claim rights. Claim rights exist only if obligations exist and liberty rights are incompatible with obligations.

That is a plausible way of reading Hobbes. However, I think there is more going on there. I think he argues that there could not be claim rights in 14.4. That is the eight point argument in the sixth section of the handout. If I am right, that would be a more compelling reason for thinking that Hobbes is on to something. Without it, he is just saying “there are no claim rights” and, while that might be true, he would not have proven the point.

Powers

In 14.5 Hobbes introduces the idea of laying down rights. His idea is impeccable: there cannot be peace until people do not pose a threat to one another and the first step to achieving that is for people to give up the right to attack one another.

Of course, saying that you give up that right is one thing but actually convincing others that you won’t attack them is something else. By the standards Hobbes articulates in chapter 14, agreements not to attack others are invalid so long as some people suspect that others will not do their part. The point Hobbes is driving at is that the right to attack others cannot actually be surrendered until the state exists to ensure everyone’s safety.

But I want to go back to the first step, about what it would mean to lay down your rights at all, under even the most ideal circumstances or, say, in the social contract. Hobbes has a very basic problem: he has not explained how anyone is capable of laying down their rights even under the most perfect circumstances.

Hobbes defines rights as liberties: to have a right to do something is to have no obligation not to do it. So where does the ability to lay down the right come from? You can’t get it out of that definition because it simply describes a static condition of not having an obligation. It is as if Euclid had left out the postulates about making lines and circles. If the rules do not make any provision for drawing lines and circles, then they do not enable you to construct an equilateral triangle. Hobbes needs a definition of rights that enables those who have rights to do things with them.

In other words, he needs rights to be powers as well as liberties. When Hobbes says people have rights, he has to mean that they are capable of bringing about moral change with their rights.

A right is a power if it grants an ability to do something. When I say “I have the right to make a contractual agreement with you,” what I mean is that I am capable of doing so and that I will be bound by any agreement I make. So-called incompetents, such as children, are not capable of making contractual agreements and so do not have the right to do so. Note that this does not mean that they would do anything wrong if they tried to make a contractual agreement. Their efforts would fail and they would create a “nullity” rather than an actual contract.

For Hobbes, people with rights have to be able to be able to transfer them (he says “surrender” or “lay down” as well) and thereby create obligations. That is how they are capable of making contracts and covenants. In these agreements, one person agrees to give up their rights provided the other does the same. I give up my right to my pencil if you give up your right to your pen. Then I become obliged not to take the pencil from you and you become obliged not to take the pen from me. With our words alone we eliminate old rights and make new rights and obligations. As I said before: magic!

The other kind of change that have to be able to make is that they have to be able to authorize people to represent them (we talked about this in the next class, on the social contract). Before I authorized my lawyer to represent me, he could not sign contracts on my behalf. But after I authorized him to act as my representative, he gained that ability. And if a bunch of us all authorize the same person to act as our representative, we will become a corporate person, as our common representative will be able to speak for all of us. More magic!

So people with rights have at least two powers, according to Hobbes: the power of alienating or giving up their rights and the power of authorizing a representative. He will need them to have these two powers in order to agree to the two clauses of the social contract: one of which involves the alienation of the rights to govern themselves while the other authorizes the sovereign to act as their representative.

Key concepts

1. How did Hobbes support his contention that everyone has a right to everything in the state of nature?
2. The four meanings of “right” on the handout.
3. What authorization means.