Phil 86: Limits to Leibniz’s Law

Using Leibniz’s Law, Part 3?

Last time, we left off saying there’s a group of arguments for dualism where the premises do all seem to be plausible, even to people who haven’t yet subscribed to dualism. And it’s not obvious that any words need to switch their meaning halfway through the argument, for the premises to seem obvious in this way.

The general flavor of these arguments can be summarized like this:

  1. I have some “special” or privileged access to my own mind.
  2. I don’t have that kind of access to anyone else’s mind, nor to facts about my brain or body or anything in my physical environment. My access to my own mind is better or different than to those other things.
  3. So my own mind has a property — being accessible to me in this special way — that physical objects lack.
  4. So my mind is not identical to any physical object.

The specifics of these arguments will turn on how they unpack the notion of this “special access.” Here are some things philosophers say to explain what they mean here: updated

  1. I can’t be mistaken about my own mind’s properties.
  2. I and only I can know my own mind’s properties without evidence, observation, or inference.
  3. I can’t intelligibly doubt whether my own mind exists: that is, I can’t imagine everything seeming the same right now, but my mind not existing.

The details are controversial: for example, some philosophers think you can’t make mistakes about the properties of your own mind. If you have a headache you’ll know you do and it won’t be possible for you to think you have one when you don’t. Other philosophers think you can make mistakes about at least some of your mind’s properties. You might think you’re happy for your friend’s success (and not envious), but in fact you’re envious (and not happy about it).

It’s enough for the purposes of this class just to know that there are some controversies here, especially concerning the first claim. But if you want to read more, here are some notes from another course:

See also the page on intensions that I mention below.

Despite those controversies, many philosophers would agree that our access to (at least some parts or aspects of) our own minds is “special” in one or more of the ways listed. (Especially the second and third way.) And we don’t seem to have that same special access to anyone else’s mind, nor to facts about our brains or bodies or things in our physical environments.

Perhaps this can be used in an argument by Leibniz’s Law that our minds aren’t identical to anything physical.

For example:

  1. My mind is not “publically accessible”: there are ways to know about it that are in principle only available to me.
  2. Physical objects are all publically accessible: in principle, anybody could get into the best positions to know about them.
  3. So my mind isn’t a physical object.

Here’s the argument that van Inwagen discusses, unpacking “specialness” in our sense (c):

  1. I can’t intelligibly doubt whether my own mind exists right now.
  2. I can intelligibly doubt whether physical objects exist right now. Maybe I’m in some kind of Matrix, and everything seems real, but it’s all an illusion. That at least makes sense.
  3. So physical objects are such that I can intelligibly doubt their existence — I can at least imagine them not existing even though everything seems the same — but my mind lacks that property.
  4. So my mind can’t be identical to any physical object.

As above, “intelligibly doubting” something here means roughly to imagine it not existing even though everything seems the same.

These applications of Leibniz’s Law are more challenging than the ones we considered before. It’s less clear how the materialist should respond here. What do you think?

How should the materialist respond to these arguments?

Where Leibniz’s Law Breaks Down

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 down there exists. I have very good evidence that he exists. 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 lacks: 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.

It may be useful to know that philosophers use the label intensional language for cases of this sort. There’s also another word philosophers use, “intentional” (with a t instead of an s) that has a connected meaning, but these aren’t exactly the same.

Philosophers sometime use "intentional" to mean something like "representational."

You don’t need to master this vocabulary in this course, but here are some notes on intensions if you want to read more about it.

Here’s another example. Lex says:

  1. I am afraid of Superman.
  2. I am not afraid of that reporter, he looks like a weak 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. This is the strategy van Inwagen takes when discussing these kinds of arguments. 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.

Summing Up

In response to the kinds of Leibniz’s-Law-based arguments for dualism we’ve seen so far, a materialist/physicalist would make one (or more) of these objections:

There are other, more promising strategies the dualist might appeal to, in support of their view. In this course, we’re not going to have the time to explore those arguments, or the different philosophical issues they raise. We’ll just note that there are other strategies for arguing for dualism than the ones we’ve looked at so far, which weren’t that successful.

And look, even if the dualist weren’t able to come up with a really compelling argument for their view, the view might nonetheless still be correct. Sometimes things are true even if nobody can prove—or even if nobody knows—that they are true. So materialists shouldn’t get too pleased with themselves if all they’ve managed to do is criticize some arguments for dualism. If they want to argue for their own view, and so against dualism being true, they’d have to do more work.