Putnam’s multiple-realizability argument against the identity theory is unsound by the fact that the mental states that arise from separate physical phenomena are just as distinct as the physical phenomena themselves; that is, the relationship of mental states to brain states is a bijection. Anything that can be in a mental state must be in a unique corresponding brain state; therefore, the first premise of Putnam’s argument is false.

Putnam’s reasoning for arriving at his multiple-realizability argument follows from his consideration of the question “is pain a brain state?” Putnam doesn’t think so, and uses the octopus as a counterexample. Because the octopus has a very different brain from people, and because the octopus can feel pain, it must follow that the property of pain is not reducible to a human brain state: something can be in pain without being in a human brain state. This works for the human brain as well as it can feel pain without being in the brain state of an octopus. So, Putnam argues, something can be in the state of pain without being in an arbitrary physical state of pain.

If something can be in one state without being in another state, Putnam reasons, then it must follow that the two states are distinct. Since pain is an arbitrary mental state, it follows that mental states cannot be reducible to brain states, as the counterexample of the octopus shows. So mental states are not brain states, hence, physicalism is flawed.

However, this argument is unsound as it assumes a universalisable mental state.

While it is true that if something can be in one state without being in another state then the states are distinct, it is not true that something can be in a mental state without being in some brain state. The relationship of mental states to brain states is a bijection. This is best illustrated through analogy.

Instead of humans and octopi, let’s consider a butterfly can-opener and a church key can-opener. Just as the human and octopus brain can realize pain, so too can the butterfly and church key open a can; just as the human and octopus brain realize pain in different ways, the butterfly and church key open cans in different ways. The butterfly can-opener will clamp onto the sides of the can and the sharp wheel will be turned around the circumference of the can until the top can be popped off. The church key, on the other hand, will be used to apply enough pressure to the top of the can until it punctures right through. Observe that in both cases, we have the same end result: an opened can. In the case of the human and octopus brain, the end result is pain. But notice that the opened cans in the cases of the butterfly and church key are different. In fact, you could point to the differences and tell which can was opened by which can-opener. While the can opened with the butterfly has no lid, the can opened with the church key has a lid with large holes poked through it.

Observing these cans being opened by different can-openers could prompt us to note that something can be a can-opener without being in the state of a butterfly can-opener, namely, the church key. Note that this holds for any can-opener. The butterfly can be a can-opener without being a church key can-opener. Then, we can say something can be a can-opener without being in a physical state of a can-opener. We might then also note that, if something can be in one state without being in another state, then the two states are different. Then, following Putnam’s reasoning, the state of being a can-opener is different from being a physical can-opener. But this seems absurd. Why?

The can-openers in this example both realize different states of being a can-opener. The butterfly can-opener realizes the state of being a butterfly can-opener while the church key can-opener realizes the state of a church key can-opener. Just as the human brain realizes the mental state of human pain and the octopus brain realizes the mental state of octopus pain. So, the state of being a can opener is not a state but a set of states where each set corresponds to exactly one kind of can opener that opens cans in it’s own unique way. For the nature of mental states, this means that the state of being in pain is a set of states each of which corresponds to exactly one kind of brain that realizes pain in a unique way. Therefore, something cannot be in a mental state without being in the unique corresponding brain state.

Putnam might disagree here and say that, if this were true, then it would necessitate that not only pain but every mental state is distinct, even between people or organisms with the same evolved brain structures and how could that be? This seems like a very unlikely ad hoc explanation for an identity theorist grasping at straws as he’s backed into a corner. But I disagree. As complicated as the corollaries to this theory might seem to be, it’s actually the simplest, most reasonable explanation for mental states there is.

To return to the can-opener analogy. What if we have two of the same butterfly can-openers? If we let each butterfly open a can, the cans are still opened in different ways. No matter how similarly the butterfly can-openers are manufactured, there will still be small differences in them and, therefore, how the can is opened. One of them, for example, may have a slightly duller wheel resulting in a jagged opening which can be examined under a microscope if need be. This holds true for every type of can-opener: the manufacturing can only be so precise. In fact, this works in exactly the same way as the evolution of the human brain. Evolution, like the manufacturing of can-openers, can have remarkably similar results, but it is imperfect. The result in the case of the human brain is that every person has a very similar, but unique experience of pain and there’s no reason not to assume the same is true for any other organism or being that can feel pain.

The evidence of differing pain tolerances seems to support this theory. The range of responses people have to getting pinched implies that the same stimulus puts them in slightly different brain states. Probabalistically, these states are single-realizable. If the firing of nerve fibers is sufficient to give rise to the mental state of pain, we must ask who’s nerve fibers and what is the exact strength of the electrical impulses fired by each axon? In the case of other beings, even cockroaches have hundreds of thousands of neurons: it doesn’t seem that there is a simple enough biological basis for the realization of pain such that multiple beings can be in the exact same mental state.

But what if we simplify this argument. Is something as simple as experiencing the colour orange really a unique, single-realizable state? If we take the set of all the organisms or beings that can be in the state of experiencing orange, will the state of their physical phenomena really necessitate different mental states? I think so.

Consider if every being capable of being in the physical state of experiencing the colour orange could occupy the same very large room where the colour orange is projected onto a space on one of the walls. Let’s also assume that every being could be told to sit and look at the projection through some universal language. Would they be in the same mental state of experiencing orange? It seems very unlikely. First, the fact that the beings cannot occupy the same spatial-temporal region means they are all experiencing the colour differently in that the projection occupies a different part of their perspective. Perspective is unavoidable and the state of any brain will certainly be aware of it in any case. Even if we somehow were able to wave the issue of perspective and beam the colour directly into their perceptual senses, what of the beings whose favourite colour is orange – Would they not have a different experience of it? And even further, if orange is their favourite colour, which hue, saturation, and brightness is their exact preferred orange? What is their brain or related phenomena doing at the time that it is viewing the colour? With all of these variables, it seems to be a serious kind of empirical reduction to assume that the mental state of experiencing orange is the same state between all of these beings. Even though we can define what experiencing orange entails, and we can talk about it as if it were the same for all beings, the smaller details simply cannot be ignored or willed away in favour of a simpler explanation. Hence, the mental state of being in pain, or experiencing a colour, or any “multiple-realizable” mental state is actually a set of mental states; and every individual brain, or related physical phenomena capable of being somewhere in that set, is in it’s own distinct mental state strongly related to, but not equivalent to, the others within that set.

Putnam might say, couldn’t we take that which is the same between the brains and run the argument again? If there are so many differences in the brain states of the same species, then we can take that which remains the same and re-apply the argument. But then we must ask – by which criteria? This would necessitate drawing an arbitrary line over what is and isn’t necessary for pain which seems like an empirical reduction in favour of a simpler explanation.