Phil 101: Limits to Leibniz’s Law

Where Leibniz’s Law Breaks Down

We left off considering arguments like this:

1. My mind is not publically accessible.
2. Physical objects are all publically accessible.
3. So my mind isn’t a physical object.

1. I can’t intelligibly doubt whether my mind exists right now.
2. I can intelligibly doubt whether physical objects exist right now.
3. So physical objects are such that I can intelligibly doubt their existence but my mind lacks that property.
4. So my mind can’t be identical to any physical object.

Being intelligibly doubtable means roughly that one imagines them not existing even though everything seems the same.

How should the materialist respond to these arguments?

Let’s consider a different example. Suppose Lex Luthor thinks he has succeeded in destroying Superman. In fact, Superman is alive and well, and is walking on the street below, dressed as Clark Kent.

Lex argues:

1. I have no doubt about whether that reporter exists. I have very good evidence that he does exist. I can see him right there.
2. I do have doubts about whether Superman still exists. I think he was destroyed last night in my clever death-trap. Some people claim to have seen him this morning, but so far these just seem to be unreliable rumors. I do not have very good evidence that Superman still exists.
3. So Superman and that reporter have different properties. They differ with respect to the quality of my evidence concerning them, and what sorts of doubts I have about their existence.
4. So Superman and that reporter must not be one and the same person.

All of the premises of this argument seem plausible. Yet its conclusion is false. Superman is one and the same person as the reporter Lex sees. So this argument seems to be invalid. Something about the reasoning here must be broken.

Here’s another example.

1. Right now, I think that reporter is wearing a gray suit.
2. Right now, I do not think that Superman is wearing a gray suit.
3. So that reporter has some property that Superman lack: namely, whether he is thought by me to be wearing a gray suit.

Note that the argument here is not about the property is in fact wearing a gray suit. If Lex ascribed that property to the reporter but denied it to Superman, he’d just be making a mistake. One of his premises — that Superman is not wearing a gray suit — would just, unbeknownst to him, be false. That would be like our use of Leibniz’s Law to argue that the butler is not the murderer, when the butler has tricked me into accepting the false premise that he’s not left-handed. The argument we’re considering now is supposed to be different. Here the property that the reporter and Superman are supposed to differ with respect to is not wearing a gray suit, but rather being thought by Lex to be wearing a gray suit. Even if Superman and the reporter Clark Kent are the same person, doesn’t it still seem right to say that Lex thinks that Clark is wearing a gray suit, but doesn’t think that Superman is wearing a gray suit? So here there is more intuitive pressure to say that both premises of the argument are really true. Here it looks like the reporter does have some property that Superman lacks! Even though, as we set the story up, the reporter is in fact just Superman in disguise.

Apparently, Leibniz’s Law is broken when we’re dealing with cases of this sort. This kind of reasoning, that has to do with what people think, or have evidence for believing, or doubt, and so on — cases that seem to

essentially involve people’s perspective on things — doesn’t seem like a place where Leibniz’s Law can be validly applied.

Here’s another example. Lex says:

1. I am afraid of Superman.
2. I am not afraid of that reporter, he looks like a nerd.
3. So Superman has some property that the reporter lacks: namely, the property of me being afraid of him.
4. So by Leibniz’s Law, that reporter must not be Superman.

Again, the premises seem true but the conclusion is false. This is another invalid application of Leibniz’s Law.

Other examples might use premises about being famous, or whether Lois hopes that he’ll kiss her, and so on.

There are big debates in contemporary philosophy about how we should explain these breakdowns of Leibniz’s Law. One strategy is to deny that being thought by me to be wearing a gray suit and the like are genuine properties. But other philosophers prefer different explanations. If you take more advanced classes in philosophy of mind or philosophy of language, you will definitely spend time studying those debates. All you need to know for now is that Leibniz’s Law does break down in some way when you’re dealing with these kinds of cases.

Now the arguments for dualism we were looking at at the top of this webpage seem to be of this problematic sort.

One of them had to do with when something’s existence can be doubted, just like the first of the clearly invalid arguments presented by Lex Luthor. Another had to do with the kind of access people have to their own minds versus physical objects. But that’s a matter of what kind of evidence and reasons they have for thinking things. It seems problematic to use considerations like that in Leibniz’s Law arguments too. After all, Lex would be making a mistake if he reasoned:

1. I have perceptual evidence about that reporter right now: I can see that he’s crossing the street.
2. I don’t have any perceptual evidence about Superman right now. It doesn’t look like Superman is anywhere around here.
3. So that reporter has a property that Superman lacks, namely whether I have perceptual evidence about them right now (for example, whether I seem to see him).
4. So that reporter is not identical to Superman.