Predictability, Computability, and Free Will
<p>I&#8217;ve been reading some philosophical discussion of the free-will/determism question recently.  Quite a number of years ago I discovered a resolution of this question, but never did anything with it because I assumed I had simply reinvented a well-known position and could not really contribute anything to the debate.  However, the research I&#8217;ve done recently suggests that my resolution of the question is actually a novel one.</p>
<p>Like a lot of philosophy, the discussion of free will and determinism I&#8217;ve seen founders on two errors.  One of this is Aristotelianism, an attachment to observer-independent two-valued logic in a system of universal categories as the only sort of truth. The other is a tendency to get snarled up in meaningless categories that are artifacts of language rather than useful abstractions from observed reality.</p>
<p>In this essay, I hope to show that, if one can avoid these errors, the underlying question can be reduced to a non-problem. More generally, I hope to show how ideas from computability and complexity  theory can be used to gain some purchase on problems in the philosophy of mind that have previously seemed intractable.</p>
<h3>Formulating The Problem</h3>
<p>The free-will question is classically put thus: do we really have choices, or are our actions and behavior at any given time entirely determined by previous states of the universe?  Are we autonomous beings, who ourselves cause our future actions, or meat robots?</p>
<p>The second way of forming the question gets at the reason most philosophers have for finding it interesting.  What they really want to know is whether we cause our own actions and are responsible for them, or whether praise, blame, and punishment are pointless because our choices are predestined.</p>
<p>Thus the free-will question, which is traditionally considered part of metaphysics or the philosophy of mind, is actually motivated by central issues in moral philosophy.  At the end of this essay, we will consider the implications of my proposal for moral philosophy.</p>
<h3>Classical Determinism And Its Problems</h3>
<p>The ways philosophers have traditionally asked these questions conceal assumptions that are false in fact and logic.  First, the evidence says we do not live in the kind of universe where classical determinism is an option.  In almost all current versions of physical theory there is an irreducible randomness to the universe at the quantum level.  Thus, even if we knew the entire state of the universe at any given moment, its future states would not be determined; we can at best predict the probability distribution of those states.</p>
<p>Another characteristic of quantum theory is that observation perturbs the system being observed.  Let&#8217;s sidestep that for the moment and introduce the concept of a perfect observer, with infinite computational capacity and the ability to take infinitely precise measurements in zero time without perturbing the system under observation.  In a universe with quantum randomness, even this perfect observer cannot know the future.</p>
<p>Matters are worse for imperfect observers, who have only finite computational capacity, can take only finitely accurate measurements, and perturb what they measure when they measure it.  Even in theories that preserve physical determinism, imperfect observers have two additional problems.  One is that they perturb what they observe; the other is sensitive dependence on initial conditions.</p>
<p>Two physical systems that are measurably identical to an imperfect observer and evolve by the same deterministic laws can have different futures because unmeasurably small differences between their present states are chaotically amplified over time &mdash; and some of those unmeasurable differences may be produced by the act of observation!</p>
<p>Even in the absence of sensitive dependence on initial conditions, though, an imperfect observer&#8217;s attempt to predict the future may fail without warning because his finite computer loses information to round-off errors (there are more subtle limits arising from finite storage capacity, but round-off errors will stand as a readily comprehensible representative of them).  And like it or not, human beings are imperfect observers.  So even without quantum indeterminacy, we cannot know the future with certainty.  </p>
<p>For philosophical purposes, quantum indeterminacy and sensitive dependence on initial conditions in classical (non-quantum) systems have nearly indistinguishable effects.  Together, they imply that classical determinism is not an option for imperfect observers, even in the unlikely case that quantum reality is not actually rolling dice.</p>
<h3>Non-Classical Determinism and Irreducible Randomness</h3>
<p>Philosophers have tended to make a fast leap from the above insight to the conclusion that humans do in fact have free will &mdash; but this conclusion is a logic error brought on by Aristotelian thinking. There is an unexcluded middle here: we may be meat robots in a universe that rolls dice, both non-determined and non-autonomous.</p>
<p>Most people (even most philosophers) find the idea that we are puppets on random strings even more repugnant than classical determinism.  In classical determinism there is at least a perfect-observer view from which the story makes sense.  The religiously inclined can believe in that perfect observer and identify it with God, and the rest of us can take some sort of fatalistic comfort in the face of our adversities that things could not after all have been any different.</p>
<p>In the indeterminate universe we seem to inhabit, the only way for even a god to know the future would be for it to intervene in every single collapse of a quantum state vector, and thereby to create that future by a continuous act of will. But if that were so, the behavior of all the matter in our bodies could be nothing but the god&#8217;s will. We&#8217;re back to determinism here, but it&#8217;s one in which a god is the sole causal agent of <emphasis>everything</emphasis> &mdash; good, evil, and apparent randomness.  Some varieties of Hindu theology actually read like this; one rather lovely version has it that the entire universe is simply the vibration of the voice of the god Atman (or Brahman) chanting a giant &#8220;OM!&#8221; and will end untold eons in the future when He next draws breath. In the West this position has been called &#8220;occasionalism&#8221;.</p>
<p>The trouble with occasionalism is that it&#8217;s untestable.  There is no observation we can make from within the universe to establish causal intervention from outside it.  If we could do so, we would simply extend our conception of &#8220;the universe&#8221; to the larger domain within which causality operates &mdash; including the mind of Atman. The testability problem would immediately re-present itself.  (This, of course, is a slightly subtler version of the standard rebuttal to the &#8220;First Cause&#8221; argument for the existence of a creator-God.)</p>
<p>For those of us unwilling to take occasionalism on pure faith, then, free will is about the only comfort an indeterminate universe can offer.  Our experience of being human beings is that some of the time our behavior is forced by factors beyond our control (for example, if we fall off a cliff we will accelerate at a rate independent of our desire or will about the matter), but that at other times we make unforced choices that at least seem to causally originate within our own minds and not elsewhere.</p>
<p>To carry the discussion further, we need to decide what the term &#8220;free will&#8221; means.  Our challenge is to interpret this term in a way that both consistent with its ordinary use and fits into a larger picture that is rationally consistent with physical theory. Try as I might, I can only see two possible ways to accomplish this. One has to do with autonomy, the other with unpredictability.</p>
<h3>The Autonomy Interpretation of &#8220;Free Will&#8221;, And Its Problems</h3>
<p>Most people, if pressed, would probably come up with some version of the autonomy interpretation.  All the philosophical accounts of &#8220;free will&#8221; I&#8217;ve ever seen are based on it. We have no problem with the idea that our choices are caused, or even determined by, our previous thoughts, but the intuitive notion of free will is that our thoughts themselves are free. This implies that the measure of a human&#8217;s degree of &#8220;free will&#8221; is the degree to each human being&#8217;s history of mental states is autonomous from the rest of the universe &mdash; not caused by it, but capable of causing changes in it.</p>
<p>There are several problems with this account.  The most obvious one is that we can often locate causal influences from the rest of the universe into our mental states.  To anyone who doubts this, I recommend the experience of extreme hunger, or (better) of nearly drowning. These are quite enlightening, and philosophers would probably talk less nonsense if they retained a clearer grasp of what such experiences are like.</p>
<p>Less extremely, evidence from sensory-deprivation experiments suggests that a mind deprived of sensory input for too long disintegrates.  Not only does the rest of the universe have causal power over our mental states, but we cannot maintain anything recognizable as a coherent mental state without that input.  Which makes sense; evolutionary biology tells us that we are survival machines shaped by natural selection to cope with a reality exterior to our minds.  Consciousness, reasoning, and introspection &mdash; the &#8220;higher&#8221; aspects of human mental activity that mostly concern philosophers &mdash; are recent add-ons.</p>
<p>None of this evidence outright excludes the possibility that there is some part or aspect of our normal mental activity that is autonomous, uncaused but causal.  The real problem, the problem of logic and principle, is that we don&#8217;t know how the autonomously &#8220;free-willing&#8221; part of the mind (if it exists) can be isolated from the part that is causally driven by sensory stimuli and normal physical laws.</p>
<p>For materialists like myself who model the mind as a kind of software or information pattern that happens to run on an organic substrate, this is an impossible problem.  We have no warrant to believe that <em>any</em> part of that system is causally autonomous from the rest of the universe.  In fact, on functional grounds it seems quite unlikely such a part would ever evolve &mdash; what would it be good for?</p>
<p>But the problem is not really any simpler for dualists or mysterians, those who hold that minds have some &#8220;soul&#8221; attached that is non-physical or inaccessible to observation.  That &#8220;soul&#8221; has to interact with the mind somehow.  If the interaction is one-way (soul affects mind, but mind does not effect soul) then the soul is simply a sort of blind pattern- or noise-generator with no access to reality. On the other hand, if mind affects soul we are right back to the beginning of the problem &mdash; is there anything in &#8220;soul&#8221; that is neither random nor causally driven by &#8220;mind&#8221;, which we already understand to be either random or causally driven by the rest of the universe?</p>
<p>The basic problem here is the same as the basic problem with occasionalism.  Define the &#8220;causal universe&#8221; as all phenomena with observable consequences, whether those phenomena are material or &#8220;soul&#8221; or the voice of Atman.  Unless the occasionalists are right and it is all just Atman saying a trillion-year &#8220;OM!&#8221;, the concept of &#8220;soul&#8221; does not actually in itself make us any space between determinism and chance.  The autonomy account of free will leaves us finally unable to locate anywhere autonomy can live.</p>
<h3>The Predictability Account Of Free Will</h3>
<p>I have invented a predictability account of free will which is quite different. Instead of struggling with the limits of imperfect observation, I consider them definitional.  I say human beings (or any other entity to which we ascribe possession of a mind) have &#8220;free will&#8221; relative to any given observer if that observer cannot effectively predict their future mental states.</p>
<p>By &#8220;effectively predict&#8221; I mean that the observer, given a  complete description of the mind&#8217;s state and a set of stimuli  applied to that state, can predict the state of the mind after those stimuli.</p>
<p>Since we have access to mental states only by observing the behaviors they generate, this is arguably equivalent to saying that an entity with a mind has free will with respect to an observer if the observer cannot predict its behavior.  However, I specify the term &#8220;mental state&#8221; because I think the natural-language use of the term &#8220;free will&#8221; requires that we limit the candidates for it to entities which we believe to have minds and to which we thus attribute mental states.</p>
<p>I am deliberately not proposing a definition or theory of &#8220;mind&#8221; in this essay, because I intend my arguments to be independent of such theory.  All I require of the reader&#8217;s theory of mind is that  it not exclude human beings from having one.</p>
<h3>Can There Be Minds Without Free Will?</h3>
<p>The first thing we need to do is establish that this definition is not vacuous.  Are there <em>any</em> circumstances under which an entity to which we ascribe mental states can fail to have free will?</p>
<p>A psychologist friend of mine with whom I discussed the matter reports that the answer is &#8220;yes&#8221;.  The example case she reported is a bot (software agent) named Julia designed to fool people in Internet Relay Chat rooms into believing it was a person. Julia could be convincing for a few minutes, but human beings would eventually notice mechanical patterns as they came to the edge of her functional envelope.  Studies of humans interacting with Julia showed that they continued to ascribe intentions and mental states to the bot even after noticing the determinism of its behavior.  The study evidence suggests that they went from modeling Julia as being like a normal adult human to being like a child or a retardate.</p>
<p>This was not even the first such result.  The AI literature reports humans projecting personhood even on much cruder early bots such as the famous ELIZA simulation of a Rogerian psychotherapist &mdash; and not giving up that attachment even after the shallow and mechanical algorithms used to generate responses were explained to them.</p>
<p>The reader may object, based on some theory of &#8220;mind&#8221;, that Julia did not actually have one.  But it is possible that we are all Julia. Suppose that the human mind is a deterministic machine with a very large but finite number of states; suppose further that the logic of the mind has no sensitive dependence on initial conditions (that is, its states are coarse enough for us to measure accurately).  This simplest-possible model we&#8217;ll call the &#8220;clockwork mind&#8221;.  If Julia has a mind, this is the kind of mind she has.</p>
<p>In principle, any clockwork mind can be perfectly simulated on a computer.  The computer would have to be more complex than the clockwork mind itself.  To predict the state of the clockwork mind, just run the simulation faster than the original.  But &mdash; and this is an important point &mdash; a clockwork mind cannot be predicted by itself, or by any clockwork mind of comparable power to itself.  Thus, whatever viewpoint a hypothetical perfect observer or god might have, human beings have free will with respect to each other.</p>
<p>It is also worth noting that human beings could have clockwork minds even in a universe of chaotic or quantum indeterminacy.  If you put enough atoms together, the Law of Large Numbers will normally swamp quantum effects.  If you make the states of a finite-state machine sufficiently coarse, there won&#8217;t be unmeasurable initial-condition differences to be amplified. After all, clockwork does tick!</p>
<h3>The Indeterminate Mind</h3>
<p>It is unlikely that humans have clockwork minds.  The anatomy and physiology of the brain suggests strongly that it has chaotic indeterminacy.  It may have quantum indeterminacy as well (the mathematician Roger Penrose suggested this in his book <cite>The Emperor&#8217;s New Mind</cite>, one of the favored texts of the new mysterians).  It is possible that the mind cannot be modeled as a finite-state machine at all.</p>
<p>These distinctions make little difference, because what they all have in common is that that they make the prediction problem far less tractable than for a clockwork mind.  Thus, they widen the class of observers with respect to which a non-clockwork mind would have free will.</p>
<p>At the extreme, if human minds have intrinsic quantum uncertainty then even a perfect observer could not predict their future mental states, unless it happens to be an occasionalist god and the only cause of everything.</p>
<p>The most likely intermediate case is that the mind is a finite-state  machine with sensitive dependence on initial conditions and an intractably large state space.  In that case it might fail to have free will with respect to a perfect observer, but will have free will with respect to any imperfect observer.</p>
<h3>Implications for Moral Philosophy</h3>
<p>The binding I have proposed for the term &#8220;free will&#8221; does not  rely on any supposed autonomy of the mind or self from external causes. From the perspective of traditional moral philosophy, it combines the worst of both worlds &mdash; a non-autonomous mind in an indeterminate universe. How, then, can humans being be appropriate subjects of praise, blame, or punishment?  In what sense, if any, can human beings be said to be responsible for their actions?</p>
<p>The first step towards solving this problem is to realize that these questions are separable.  Because we ascribe intention and autonomy to human beings and believe their future behavior is controlled primarily by those intentions, we explain acts of praise, blame, and punishment directed at human beings in terms of the supposed effects on their mental states. But this is where remembering that we have no direct access to mental states is useful; what we are actually after when we praise, blame and punish is to <em>change observable future behaviors</em>.</p>
<p>Thus, we also praise and blame and punish animals without much regard to whether they have mental states or free will.  When training a kitten it is of little interest to us in what sense it might be <em>choosing</em> to crap on the rug; what matters is getting it to use the litterbox.  Humans, like animals, are appropriate subjects of praise and blame and punishment to the extent that those communications effectively alter their behavior.  The attribution of &#8220;responsibility&#8221; is at best a sort of convenient shorthand, and at worst a red herring.</p>
<p>In any case the question of &#8220;responsibility&#8221; is simply the question of free will in another guise, and admits the same answer within a predictive account.  An observer may hold a mind &#8220;responsible&#8221; for the actions it initiates to the extent that the observer is unable to identify external causes of those actions.</p>
<p>This accords well with the way people normally reason about responsibility. If all we know of a man is that he murdered someone in a fit of rage, our inclination is to hold him responsible.  But if we then learn that he was unwittingly dosed with PCP, we have an external cause for the rage and can no longer consider him fully responsible.</p>
<h3>Conclusion</h3>
<p>The predictivist account of free will I have proposed here solves the classical problems with the autonomy account of free will, accords with natural-language use of the term &#8220;free will&#8221;, and is consilient with physical theory.  It does so at the cost of making the ascription of free will dependent on the computational and measurement capacity of the observer.</p>
<p>The parallel with the way &#8220;space&#8221; and &#8220;time&#8221; are redefined in Relativity Theory is obvious.  As in that theory, our intuitions about &#8220;free will&#8221; are largely valid in human-observable ranges but tend to break down at extremes. Relativity had to abandon the idea of absolute space/time; in our context, we need to abandon the ideal of the perfect observer and accept that finite computational capacity is yet another fundamental limit on theory-building.</p>
<p>I believe a similar change in stance is likely to prove essential to the solution of other outstanding problems in philosophy.</p>
