If we have a statement of the form “If P then Q” (which could also be written “P → Q” or “P only if Q”), then the whole statement is called a “conditional”, P is called the “antecedent” and Q is called the “consequent”. Some examples:
“If Fred is a dog, then Fred is a mammal.” (This conditional is presumably true, regardless of whether Fred is in fact a dog.)
“If Fred is a dog, then Fred is a fish.” (This conditional is presumably false.)
The conditional “If Q then P” (which could also be written “P ← Q” or “Q → P” or “P if Q”) is called the converse of “If P then Q.” For example:
It should be intuitive that this says something different than the original conditional. Presumably the original conditional has to be true, since every dog is a mammal. But “If Fred is a mammal, then Fred is a dog” might or might not be correct. It’d be correct if, for example, we’re doing detective work on what kind of animal Fred is, and maybe he might be a mammal or a fish, but we’ve settled that if he’s a mammal, then the only species he could be is a dog. But more likely, this conditional would be false. In normal circumstances, the premise that Fred is a mammal leaves it open that he might be any number of species: a dog, a cat, a monkey, and so on…
So in general, a conditional and its converse say different things. They might both be true, or they might both be false, or it might be that one is true and the other is false. There might be special cases where if one of them is true, the other one has to be true too. But we shouldn’t in general expect claims of the form “If P then Q” and “If Q then P” to say equivalent things.
On the other hand, consider these two conditionals:
It should be intuitive that if either of these is true, the other will be true as well. The second conditional is called the contrapositive of the first. That’s a bit of technical logical jargon, but hopefully the basic idea here is clear enough without studying logic. Suppose that Fred is a dog. Then the first claim says that he has to be mammal, and the second implies this too, a bit indirectly, because if he weren’t a mammal, then he couldn’t be a dog. On the other hand, suppose that Fred isn’t a dog. Then the first claim is silent about whether Fred is or isn’t a mammal. And the second claim tells us only that if he isn’t a mammal, then he isn’t a dog, which we were already supposing. So in the case where Fred isn’t a dog, neither conditional adds any new constraints. It’s very natural then to take them to be saying the same thing. They just package it in a different form.
Summarizing:
There’s a principle very often appealed to in philosophy called “Leibniz’s Law”. The basic idea is this:
Sometimes this principle is called the Indiscernability of Identicals (because if the entities are identical, they’re indiscernible — that is, they have the same properties).
For any entities x and y, if there’s a property one of them has but the other lacks, then they’re not identical.
That’s roughly the contrapositive of the first claim, and so we can regard these claims as equivalent.
(I say “roughly” the contrapositive because these claims aren’t really conditionals of the form “If P then Q”; instead they have a more complex form “For any entities x and y, if … then …”)
Some comments and clarifications about this principle / law:
The kinds of entities we’re talking about aren’t just physical objects, but any kind of entity, including numbers, words, ghosts, and so on (if these things really exist).
Similarly, the kinds of properties we’re talking about aren’t just physical properties, but any kind of property.
Also, the kinds of properties we’re talking about aren’t just intrinsic properties (like being 70 inches tall); the principle is supposed to apply to extrinsic properties (like being shorter than Professor Worsnip) too. It’s also supposed to apply to properties like where the object is and has been located in space.
The kind of “identity” we’re talking about is being one and the same thing, what philosophers usually call “numerical identity.” Sometimes when we say that objects are “identical” or “the same”, we mean something weaker: just that the objects have many of the same (intrinsic) properties. For example, I might say that you and I bought identical laptops, meaning we have laptops of the same model. Still, we have two laptops. Philosophers usually call that “qualitative identity.” Leibniz’s Law isn’t talking about that kind of identity. Instead it’s talking about when it’s right to say that my laptop and your laptop is one and the same laptop. (Maybe someone stole it from me and then sold it to you…?)
What Leibniz’s Law says is that if our laptops are one and the same, then they have to have all the same properties. So if we find a property that one of them has and the other lacks, then we’ve established that the laptops are different.
Leibniz’s Law is not supposed to rule out the possibility of things changing their properties over time. Perhaps when I owned the laptop, it didn’t have any scratches on it. But when you purchased it, it had a St Pauli logo scratched into it. Leibniz’s Law is compatible with that. It doesn’t say we should argue “Prof Pryor’s laptop was unscratched, this laptop is scratched, so therefore they’re two different laptops.” Instead, it might be that Prof Pryor’s laptop was unscratched yesterday (but so too was your laptop), and your laptop is scratched today: but if they’re really the same laptop, then Prof Pryor’s laptop is scratched today too.
Leibniz’s Law is of the form:
Or taking the contrapositive:
The converse of Leibniz’s Law says instead:
Since “identical” here means “one and the same thing,” another way of saying this is that there can’t be two (or more) distinct objects that have all the same properties. This principle (called the Identity of Indiscernibles) was also favored by the philosopher Leibniz, and by other philosophers, but it is more controversial than the principle we’re calling Leibniz’s Law. It may or may not be true. That depends on answers to other subtle questions and what other metaphysical theories you accept.
Leibniz’s Law on the other hand seems to be a lot more straightforward. (As our discussion proceeds, though, we’ll see that things turn out to be somewhat complicated for Leibniz’s Law, too.)
In summary, Leibniz’s Law tells us that if x and y are one and the same thing, they have to have all the same properties. If they have different properties (at the same time), they can’t be one and the same thing. Here’s an example of using this principle in some natural reasoning:
Similarly:
These seem to be good pieces of reasoning. In other words, if the premises are true, it seems legitimate to infer that the conclusion will be true too. Of course, I might be fooled into accepting some of these premises when they’re not true. Maybe the butler is left-handed after all; he’s just managed to fool me into thinking he isn’t. Still, that wouldn’t show that the reasoning is bad. The reasoning wouldn’t have led me astray; it was my my being fooled into accepting the premise that did so.
Now we have to be careful when applying Leibniz’s Law. It doesn’t tell us we’re allowed to infer like this: “x is F, but y is G, so x isn’t identical to y.” Maybe x and y are both F and G. For example, suppose it’s the 1980s and I’ve just met President Reagan. Somebody asks me, Hey do you think he’s that same guy, Ronald Reagan, who acted in the old westerns we’ve been watching? I say “No way! Ronald Reagan is a famous actor. But President Reagan is a politician. So they can’t be identical.” Clearly my reasoning here is mistaken. After all, Ronald Reagan was both a famous actor and a politician. I must have been thinking that President Reagan was a politician instead of being a famous actor; that is, I must have been thinking it’s not possible for someone to be both a politician and a famous actor. But that’s wrong. This is possible. (And Reagan is not the only example.) The lesson here is that when we’re applying Leibniz’s Law, if x does have some property F, we should be checking whether y lacks that property F. The fact that y is G only helps here if its being G is incompatible with its being F.
Many arguments for dualism have the form of applying Leibniz’s Law. They say “minds can’t be physical because physical objects are … but minds are …”
The materialist will want to resist these arguments. I’ll sort the arguments for dualism into several different groups, differentiated by what kind of complaint the materialist will make about them.
First, the materialist is going to complain that some of these arguments have the same problem as our Ronald Reagan example discussed above. Here’s an example:
This argument can only succeed if being mental is incompatible with taking up space. And we haven’t yet settled that. That’s just what the dualist and the materialist are arguing about.
The dualist can attempt to argue, more explicitly:
This is an improvement, in that it’s a clear application of Leibniz’s Law. It does seem right that if the premises of this argument are true, the conclusion would have to be true too. The problem though is that the second premise is too controversial to be helpful to use in an argument for dualism. It’s similar to if I were trying to persuade you that God existed, and I argued: “God exists because the Bible says so; and nothing written in the Bible is false.” It may be that everything I’m saying is correct, but you probably wouldn’t be very impressed or moved by my argument. The premise “nothing written in the Bible is false” is just too controversial to appeal to when what we’re trying to establish is whether God exists. Only someone who was already persuaded of the conclusion we’re aiming for is likely to be ready to accept the premise. This is the kind of argument that philosophers call question-begging.
Some arguments are really obviously question-begging, in that you can just see the conclusion among the premises: “God exists, and wrote the Bible. So God exists.” In other arguments, like the one I described a moment ago with the premise “Nothing written in the Bible is false,” the conclusion might not explicitly be among the premises. Still, these arguments are going to be unpersuasive because they start from points which are argumentatively too close to the conclusions they’re trying to establish. A good, persuasive argument should instead have more of a surprising punch to it. It should make its audience see that premises that you’d think are uncontroversial, or at least much less controversial than your conclusion, when taken together in fact do force us to accept that conclusion, after all.
The “Nothing written in the Bible is false” argument wouldn’t do that. And neither would the “Minds do not take up space” argument.
Here are other arguments that have the same feel:
In each case, a materialist, or someone who was just trying to make up their mind whether to accept materialsm or dualism, wouldn’t be ready to accept the second premise. If the dualist wants to talk us into their view, they should try harder to find premises that seem plausible even to people who haven’t yet subscribed to dualism.
Another group of arguments for dualism at first seem like they might achieve that. Consider:
Here premise 1 seems to be true, at least as it’s most naturally understood. And premise 2 also seems to be true. And the rest seems to be just an application of Leibniz’s Law. So is this a good argument for dualism?
The problem here, as someone suggested in class, is that the sense of “in” where it seems to be clearly true that Aunt Lobelia is in my mind doesn’t seem to be the same sense of “in” where it seems to be clearly true that Aunt Lobelia is not in my brain. For the latter, let’s say “spatially inside.” Sure, Aunt Lobelia is not spatially inside my brain. But is she spatially inside my mind? Don’t think we want to say that. The sense in which she clearly seems to be “in” my mind is that I’m thinking about her, I have thoughts concerning her. It’s not at all clear that that means she is spatially inside my mind. (The dualist wouldn’t want to say she’s spatially inside my mind, anyway! Since they think minds don’t take up space.)
So this argument equivocates. Premise 1 seems plausible if we understand “in” with one meaning (“in my mind” = thinking about). Premise 2 seems plausible if we understand “in” with a second, different meaning (“in” = spatially inside). And if you don’t notice that “in” has changed meanings, it might look like the reasoning structure is correct. But for it really to be correct, we have to understand “in” consistently, with a single meaning.
The dualist may think that the argument is correct with “in” understood consistently in the sense of “thinking about her.” That is, they may accept all the premises and the conclusion of this argument:
But now we’d once again have an argument whose second premise is too controversial to be persuasive, in an inquiry about whether or not to be dualist.
Where have we gotten so far? The materialist complains that if the dualist makes sure to be explicit about what property it is that the mind has but that physical objects lack (or what property it is that physical objects have but the mind lacks), the argument is going to be question-begging. Nobody is going to find the argument persuasive unless they’ve already subscribed to dualism.
The only times so far when it’s seemed otherwise, it was because the dualist was equivocating, and switching the meaning of some word halfway through the argument. One premise sounded plausible with the word understood one way, and the other premise sounded plausible with the word understood the second way.
But it turns out there’s a group of arguments for dualism that seem to be vulnerable to neither of these complaints. These are arguments 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:
The specifics of these arguments will turn on how they unpack the notion of this “special access.” As we discussed in an earlier class, here are some things philosophers say to explain what they mean here. (Many philosophers would say we have special access to our own minds in several of these senses.)
As we said earlier, there are controversies about how “special” our access to our own minds is: in what ways it’s better and/or different from our access to facts about our brains or bodies or physical environments (and to other people’s minds). But many philosophers would agree that our access to (at least some parts of) our own minds is “special” in some of these ways. And perhaps this will support an argument by Leibniz’s Law that our minds aren’t identical to anything physical.
Other ways to formulate this strategy could look like this:
Or:
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?