Functionalism and multiple realizability

Functionalism holds that two (deterministic) minds think the same thoughts when they engage in the same computation and have the same inputs. What does it mean for them to engage in the same computation?

This is a hard question. Suppose two computers run programs that sort a series of names in alphabetical order, but they use different sorting algorithms. Given the same inputs, are the two computers engaging in the same computation?

If we say “no”, then functionalism doesn’t have the degree of multiple realizability that we thought it did. We have no guarantee that aliens who behave very much like us think very much like us, or even think at all, since the alien brains may have evolved to compute using different algorithms from us.

If we say “yes”, then it seems we are much better off with respect to multiple realizability. However, there is a tricky issue here: What counts as the inputs and outputs? We just said that the computers using different sorting algorithms engage in the same computation. But the computer using a quicksort typically returns an answer sooner than a computer using a bubble sort, and heats up less. In some cases, the time at which an output is produced itself counts as an output (think of a game where timing is everything). And heat is a kind of output, too.

In my toy sorting algorithm example, presumably we didn’t count the timing and the heat as features of the outputs because we assumed that to the human designers and/or users of the computers the timing and heat have no semantic value, but are merely matters of convenience (sooner and cooler are better). But when we don’t have a designer or user to define the outputs, as in the case where functionalism is applied to randomly evolved brains, things are much more difficult.

So, in practice, even if we answered “yes” in the toy sorting algorithm case, in a real-life case where we have evolved brains, it is far from clear what counts as an output, and hence far from clear what counts as “engaging in the same computation”. As a result, the degree to which functionalism yields multiple realizability is much less clear.

Restricted epistemic mysterianism

There are two forms of mysterianism about X (say, consciousness):

1. Conceptual: It would not be possible for us to even conceptualize the true theory of X.

2. Epistemic: It would not be possible for us to know the true theory of X.

Conceptual mysterianism about X entails epistemic mysterianism about X. In the case of typical Xs, like consciousness or intentionality or morality, epistemic mysterianism entails conceptual mysterianism. For if we could conceptualize the true theory of X, then God could reveal to us that that theory is true. (I restricted to “typical Xs”, for there are some truths that we could not know but which we could conceptualize. For instance, that the past existence of life on Mars is a reality unknown to me is something I can conceptualize, but I can’t possibly know it.)

However, one can weaken epistemic mysterianism to:

3. Restricted Epistemic: It would not be possible for us to know the true theory of X merely by human epistemic resources.

Consider the following interesting conditional:

4. If physicalism is true about consciousness, then restricted epistemic mysterianism is true about it.

Here is an argument against 4. Imagine that we find a new physics in the brains of precisely those organisms that it is plausible to think of as conscious (maybe cephalopods and higher vertebrates). For instance, maybe there is a new particle type that is only found in those brains, or perhaps some already known particle type behaves differently in those brains. Moreover, there is a close correlation between the behavior of the new physics and plausible things to say about consciousness in these critters. And when make a sophisticated enough AI, surprisingly that new physics also shows up in it. Given this, it would be reasonable to say that consciousness is to be identified with the behavior of that new physics.

But I think the following is true:

5. If physicalism is true about consciousness and there is no new physics in the brains of conscious beings, then restricted epistemic mysterianism is true.

Here’s why. Assume physicalism. Some degree of multiple realizability of consciousness is true since cephalopods and mammals are both conscious, even though our brains are quite different—assuming the “new physics in brains” hypothesis is false (if it were true, the structural differences between cephalopod and mammal brains could be relevantly outbalanced by the similarities with respect to the “new physics”). Multiple realizability requires that consciousness be abstracted to some degree from the particular details of its embodiment in us. But there is no way of knowing how far it is to be abstracted. And without knowing that, we won’t know the true theory of consciousness.

If this is right, the true view of mind must be found among these three:

• non-physicalism

• restricted epistemic mysterianism (with or without conceptual mysterianism)

• new physics.

On each of them, mind is mysterious. :-)

Swapping ones and zeroes

Decimal addition can be done by a computer using infinitely many algorithms. Here are two:

1. Convert decimal to binary. Add the binary. Convert binary to decimal.

2. Convert decimal to inverted binary. Inv-add the binary. Convert inverted binary to decimal.

By conversion between decimal and inverted binary, I mean this conversion (in the 8-bit case):

• 0↔11111111, 1↔11111110, 2↔11111101, …, 255↔00000000.

By inv-add, I mean an odd operation that is equivalent to bitwise inverting, adding, and bitwise inverting again.

You probably thought (or would have thought had you thought about it) that your computer does decimal addition using algorithm (1).

Now, here’s the fun. We can reinterpret all the physical functioning of a digital computer in a way that reverses the 0s and 1s. Let’s say that normally 0.63V or less counts as zero and 1.17V or higher counts as one. But “zero” or “one” are our interpretation of analog physical states that in themselves do not have such meanings. So, we could deem 0.63V or less to be one and 1.17V or higher to be zero. With such a reinterpretation, logic gates change their semantics: OR and AND swap, NAND and NOR swap, while NOT remains NOT. Arithmetical operations change more weirdly: for instance, the circuit that we thought of as implementing an add should now be thought of as implementing what I earlier called an inv-add. (I am inspired here by Gerry Massey’s variant on Putnam reinterpretation arguments.)

And if before the reinterpretation your computer counted as doing decimal addition using algorithm (1), after the reinterpretation your computer uses algorithm (2).

So which algorithm is being used by a computer depends on the interpretation of the computer’s functioning. This is a kind of flip side to multiple realizability: multiple realizability talks of how the same algorithm can be implemented in physically very different ways; here, the same physical system implements many algorithms.

There is nothing really new here, though I think much of the time in the past when people have discussed the interpretation problem for a computer’s functioning, they talked of how the inputs and outputs can be variously interpreted. But the above example shows that we can keep fixed our interpretation of the inputs and outputs, and still have a lot of flexibility as to what algorithm is running “below the hood”.

Note that normally in practice we resolve the question of which algorithm is running by adverting to the programmers’ intentions. But we can imagine a case where an eccentric engineer builds a simple calculator without ever settling in her own mind how to interpret the voltages and whether the relevant circuit is an add or an inv-add, and hence without settling in her own mind whether algorithm (1) or (2) is used, knowing well that either one (as well as many others!) is a possible interpretation of the system’s functioning.

Multiple levels of multiple realizability

We could have sophisticated beings who reason about the world via numerical Bayesian credences. But we could also have sophisticated beings who reason in some other way—indeed, we are such beings. And there is one sophisticated being who reasons about the world via omniscience. This suggests that reasoning and agency are multiply realizable at multiple levels, including:

1. brain/mind architecture

2. algorithms implementing general reasoning and representation strategy

3. general reasoning and representation strategy.

Each level is an abstraction from the previous. So now we have a very deep question: Is there a fourth level that abstracts from the third, to get the concept of reasoning as such? Or are the various general reasoning and representation strategies unified analogically, say by similarity to some primary case? And if so, what is the primary case? Omniscience? Logical omniscience plus numerical Bayesianism?

Two problems of multiple realizability for functionalists

Problem 1

Functionalism can best be seen as a response to the multiple realizability argument against physicalism: the same kinds of mental events can happen in carbon-based brains, silicon-based chips, plasma-based alien minds, etc., but if a belief that 2+2=4 is a particular configuration of neurons in a brain, then no critter without neurons could believe that 2+2=4. So the functionalist says that there is a functional isomorphism between states that all of these could have, and that's all that's needed for mental sameness. At the same time, the functionalist, unlike the behaviorist, is interested in lower-level functional states than just inputs and dispositions to outputs.

I am now thinking that functionalism is subject to a higher level multiple-realizability worry. Start with the intuition that the same computational results can be obtained through different, non-isomorphic algorithms (think of insertion sort and quick sort algorithms). Very plausibly, the same behavioristic states—relations between inputs and dispositions to outputs—can be obtained through different, non-isomorphic functional arrangements. Imagine, then, an alien being, a product of natural selection in a different environment from ours, that has a mind that is not functionally isomorphic to ourself, but where the alien is basically behavioristically isomorphic to us. Why wouldn't this be possible? (That question is not much of an argument, I know.) We would, I think, rightly assume that this being is in fact a person, and has beliefs, feelings, etc., despite the lack of functional isomorphism. But the functionalist must deny that such an alien would have beliefs, feelings, etc. since those kinds of states are defined by their functional connections, and the alien doesn't have those functional connections.

Epistemically, we seem to be behaviorists. Maybe this is only pragmatic—we don't want to mistreat someone who might turn out to be a person (this suggestion is due to Todd Buras). But suppose it's more than that. Then functionalism is in trouble, unless it can supply an argument that only systems that are (approximately?) functionally isomorphic to us could be (approximately?) behavioristically isomorphic to us.

The theistic dualist can do well here. Because of the great value in rational beings, there is good reason that God bestows souls on any natural kind of being whose behavior is sufficiently sophisticated to be compatible with a mental life.

Problem 2

Two states are functionally isomorphic provided that they give the same map between inputs and outputs. In particular, the states must be connected up with isomorphically corresponding modules. But it is very unlikely that a pain in a mouse and a pain in a human are functionally isomorphic. The pain in the human is probably connected into modules (such as higher level judgment modules) that have no corresponding modules in the mouse. Consequently, if functionalism holds, it is improbable that mice feel pain. The non-naturalist theist can get a nice disjunction out of this: Either functionalism is false (in which case, probably, some form of dualism is true, since I think that's the best alternative to functionalism), or else the problem of animal pain is not a problem at least in regard to less smart mammals.