Statistical Determinism:

The Odds get Odder and Necessity gets Even

 

Paul Saka

University of Houston

 

Abstract. Libertarians claim that we do or might have free will because determinism is wrong, and that determinism is wrong because of indeterminacy at the quantum level, or because laws in the human sciences are fundamentally statistical.  It is my thesis, however, that determinism is entailed not only by classical laws of physics but by statistical laws as well.

            Statistical laws, interpreted extensionally and combined with facts about other people having actual existence, entail unique outcomes in personal behavior.  Statistical laws, interpreted intensionally and combined with facts about other people having counterfactual existence, also entail unique outcomes.  In order to make my case, I discuss possible interpretations of probability, confidence intervals and levels, the nomic status of statistical generalizations, and the gambler's fallacy.  Finally, aside from arguing that probabilistic laws do not provide for branching possibilities as libertarianism requires, I argue that even where branching possibilities exist they do not ground freedom. 

 

            My thesis is that fundamentally probabilistic laws, be they in quantum physics or the human sciences, entail a certain kind of determinism.  This kind of determinism contradicts libertarianism, which is entertained by numerous philosophers, is scattered through the physics and neuroscience literature, and is found among jurists and the lay population.[1]  In establishing determinism, my argument outstrips the standard objection to libertarianism, that indeterminacy amounts to mere randomness, and mere randomness is not sufficient for free will.[2]

Glymour 1971 distinguishes two features that are often regarded as standing or falling together: the determinateness of quantities and the impossibility of forks in history.  Kane 1996 observes that they pull apart in Epicureanism, according to which laws and physical magnitudes are exact (and hence quantities are determinate), but not all events are subsumed by law (because of the swerve), thus allowing for divergent possible histories.  Kane develops this point, citing Earman's 1986 argument that strict Newtonian laws may issue in indeterminism, but he overlooks another logically possible option.  Perhaps a physical system may be indeterminate in its present properties and regularities, while closed to all but one way of unfolding.  My work may thus also be seen as a contribution to the project of disentangling the strictness of laws from determinism proper.

            After presenting definitions and my basic argument for statistical determinism, the bulk of my paper turns to forestalling objections.  The concluding section sketches independent considerations against libertarianism.

 

1.  The Basic Argument

We can say that condition or fact P determines or necessitates condition or fact Q so long as the proposition that-Q necessarily follows from, or is a consequence of, the proposition that-P (cp. Earman 1986).  This characterization may fail to get at the heart of determinism – I think James 1884 and Kane 1996 do better – and it certainly fails to get at a number of complexities.  Nonetheless I believe it is fairly safe in that many competing accounts of determinism would agree to it, and more to the point it is what's relevant to the question of libertarianism since it feeds into the Consequence Argument (see van Inwagen 1983).

My version of the Consequence Argument relies on two principles [semantic turnstile represented by |=]:

  (α)     If P|=Q then N(P®Q), where "N" means "it's not up to one to decide";

  (β)     If NP and N(P®Q) then NQ.

According to (α) and (β), if P determines Q and if P is not up to us then Q is not up to us.  The threat to free will thus emerges without our having to suppose or establish that Q is categorically and metaphysically necessary, only that it is necessitated by events beyond our control.

            It is because of the Consequence Argument that libertarians deny classical determinism.  According to classical determinism, the laws of nature are all strict rather than statistical, and they are sufficient to determine, given conditions that are beyond our control, all of our actions: strict laws & independent conditions |= personal actions.  Yet events obviously happen according to patterns, even if the patterns do not conform to strict laws.  For this reason opponents of classical determinism point to the statistical laws of contemporary physics and of the human sciences.

However, I shall argue that statistical laws necessitate morally fraught outcomes, at least in "pivotal" cases: statistical laws & independent conditions |= personal actions.  To begin, consider statement (G), a generalization about gluttony:

  (G)    For all human subjects S under some particular condition C, the probability that S will overeat is .6.

The libertarian's idea here is that we have various causal factors implicated in eating habits (who could deny that?), and hence we have a derived law (G), but it does not necessitate any one individual's behavior, thus leaving room for free will.  The question arises, however: What does such a probability statement mean?

            According to one interpretation, probability means relative frequency (actual and finite).  To say that there is a 20% chance of rain tomorrow, given current conditions, is to say that in 20% of all cases matching current conditions, it rains on the subsequent day.

            Now take a scenario where condition C refers exclusively to a certain cafeteria on a certain day.  A total of 100 customers will go through it, 40 have already done so without overindulging, and next you step up.  Will you overindulge?  According to (G), you have to.  For if you do not, then at least 41% of the customers will not overindulge, and (G) would be false, contrary to hypothesis.  Indeed, the argument applies to each customer, even the earliest.  Given (G), which refers to C, and given that C involves some specified number of subjects, and given the actions of all subjects other than S, we can deduce S's exact behavior, for any subject S in C.

            My argument invites some obvious objections which I will address one by one. They involve alternative interpretations of probability, confidence intervals and levels, innumerate probability, the gambler's fallacy, and the nomic status of (G). [3]

 

2.  Rival Interpretations

My basic argument invokes one particular interpretation of probability, that of finite relative frequency.  There are, however, other possible interpretations.

            Sometimes probability is said to be the limit of relative frequency in a random infinite series.  If we think of an infinite series as an actual series, however, there may be precious few probabilities in the universe.  Although we might be able to speak of the probability of a random number being prime, for instance, we could not speak of the probability of any physical event, assuming that there are only finitely many physical particles and events in the universe.

So let us think instead of infinities as hypothetical.  Does it make sense to say that (G) is best interpreted as (G')?

  (G)    For all human subjects S in condition C, the probability that S will overeat is .6.

  (G')   If there were infinitely many human subjects in condition C, then the proportion of those who overeat to the total number of those who do not would approach .6.

The truth-conditions of (G) cannot be explicated by those of (G'), for the fantasy depicted by statement (G') is too indeterminate to have truth-conditions.  Nor does it do any good to replace our infinite series with an arbitrarily large one.  For no matter how large a series is, if it is finite then my original argument applies.

            Instead of invoking one hypothetical infinity as in (G'), perhaps we should invoke an infinite number of hypotheticals as in (G"):

  (G")   For all of the infinitely many possible human subjects S in condition C, the proportion of those who overeat to the total number of those who do not approaches .6.

This admits two interpretations.  According to the doctrine of counterparts, an individual S1 exists in only one possible world, though there be counterparts S2, S3... each separately existing in other worlds.  To say that S1 acts but could abstain is to say that at least one counterpart does abstain.  According to the doctrine of transworld identity, an individual may exist in many possible worlds, and to say that S acts but could abstain is to say that in some other world S herself does abstain.  Now both theses can be turned around: to enumerate the doings of all the counterparts is to say what S1 can do and it is to entail what S1 does do; to enumerate the goings on in all non-actual possible worlds is to say what can actually go on and it is to entail what does go on.

For example, suppose that there exists exactly one possible agent and one degree of freedom, to do A or not, for a total of two possible worlds. Then this proposition combined with the proposition that S1 does A entails that S2 does not do A.  More generally, the actual world wi (more precisely, the proposition that a given world is actual) necessarily follows from the facts that (i) w1wn exhaust all possible worlds, (ii) there exists exactly one actual world, and (iii) all but wi are mere possibilities.  To put the matter more abstractly, in my original argument a statistical law, interpreted extensionally, is combined with facts about other people, having actual existence; and from this combination we can deduce a given person's behavior.  In my new argument a statistical law, interpreted intensionally, is combined with facts about other people, having counterfactual existence; and from this combination follows a given person's actual behavior.  Either way, probability-governed behavior is necessitated by facts outside one's control.

            The libertarian might reply: "Granted that my counterpart S' and I are in a complementary relation inasmuch as we make exactly the same choices and act alike except when it comes to decision F, whereupon I choose +F and S' chooses –F.  But perhaps the symmetry breaks down inasmuch as free will is all located in the actual world; perhaps subjects do not enjoy equal status; perhaps, in order to be in control of myself, I am the puppetmaster of all my counterparts: I freely choose +F, which forces S' to choose –F; S' chooses -F, but without freedom and without forcing my choice."  This suggestion, however, is untenable.  If all free will is located in the actual world then it would not make sense to say, "under other circumstances I could have freely acted."  If there is no possible world in which I both perform –F and enjoy free will, then in order for my action to be free I must perform +F.  But to say I must perform +F in order to be free is, by libertarian lights, self-defeating.

            Technicalities aside, the idea that the actual world is the only one that counts for moral reckoning appears to introduce a double standard.  Why would the libertarian insist on the relevance, to moral accountability, of alternate possibilities, only to pooh-pooh it in the next breath?  I conclude that infinitary interpretations, as much as finite-frequency interpretations, spell trouble for libertarians and indeed indeterminists generally.

            According to the subjectivist view, probability is degree of belief, or better yet degree of rational belief, an epistemic notion.  For me to rightfully say that the probability of an event's happening is .5 is just for me to be rationally willing to bet, at even odds, that it will happen; and that is controlled by the body of evidence that is available to me.

            Although many who debate determinism speak of predictability, that is simply because epistemic discourse (a) entails ontic discourse (b), which is the real issue at stake (as noted by many others, for instance Garson 1995).

  (a)     We know or can know that, because of laws L and initial condition P, Q ensues.

  (b)     Because of laws L and initial condition P, Q ensues.

However, for all sorts of reasons (a) might be false while (b) is true.[4]  If external nature necessitates your actions, then regardless of whether anyone knows it or even could know it, your actions would not be up to you, which is all that the libertarian's Consequence Argument requires.[5]

            Finally, probability is sometimes understood as propensity.  The intuition is that individual events possess objective probability (this coin at the last toss had a 50% chance of landing heads, even though we now know it landed tails).  This means, in terms of (G), that even if all among the first 60 of the 100 diners overeat, there is still a 60% chance that the next diner will overeat.

Unfortunately, propensity is a contested notion even among those who believe in it.  For long-run propensity theories, as found in Popper's classic 1959 work and more recently Gillies 2000, propensities apply to collections and never to individuals.  This obviously offers no escape from the basic argument.  Single-case propensity theories, on the other hand, come with unacceptable costs.  Because the versions due to Popper 1990 and Miller 1996 define propensity in terms of unrepeatable conditions, basic propensities are admittedly "not open to empirical evaluation" (Miller, 139; compare Popper): there can be no evidence for asserting a probabilistic law, for denying it, for revising it, or even for entertaining it in the first place; no conceivable experience whatsoever.  (The same applies to Giere 1973 according to Howson & Urbach 1989.)  Meanwhile Levi 1980 and Lewis 1981 forge a connection between probability and empirical fact by sheer stipulation (Howson & Urbach 1989).  Their theories are completely arbitrary and could just as well be replaced by diametrically opposed ones.  Finally, the version due to Fetzer 1981, to avoid running afoul of Humphrey's paradox, desperately abandons the standard probability axioms as used by all other probability theorists.

More fundamentally, the postulation of propensity hardly averts the argument to statistical determinism.  After all, the guiding intuition behind single-case propensity involves the relative frequency of a singular event's being repeated in other possible worlds; and frequencies across possible worlds, as already indicated, yield the same deterministic results that extensional frequencies do

To sum up, I have surveyed prominent interpretations of probability.  Subjective probabilities and actual infinite frequencies are irrelevant to the matter at hand.  Propensities are variously irrelevant, eccentric, and occult, and moreover they feed determinism, as do fantasy frequencies generally. 

 

3.  Margins of Error

While our statistical law (G) cites a single exact probability, laws more realistic state ranges of probability as in (H).

  (G)    For all subjects S in condition C, there is a 60% chance that S will overeat.

  (H)    For all subjects S in condition C, there is a 60% chance, +10%, that S will overeat.

Such ranges are usually known as "confidence intervals" or "margins of error," but both labels are misleading.  They sound epistemic, yet they need not be: instead of expressing imprecise knowledge they might refer to imprecise facts of the matter.

            Recall our original story: in a certain cafeteria on a certain day, exactly 100 customers will go through, and 40 have already done so, without having overindulged.  Now you step up as customer #41; will you overindulge?  According to (G), you have to, but not according to (H).  For (H) asserts that anywhere from 50% to 70% of the customers will overeat – that 30-50% will not – so in this case whether you overeat or not is open to you.

            However, suppose that our cafeteria again has 100 customers, and this time 50 have gone through without overeating.  Then given law (H), even though it has a margin of error built in, it necessarily follows that the next customer overeats.  In short, under some conditions introducing a second level of indeterminacy fails to block the inference to determinism.

            The scenario just sketched presents a pivotal case inasmuch as the validity of the law hinges on the action of just one agent.  If all events are pivotal, or none, then we have either universal statistical determinism or the failure of statistical determinism; otherwise we have partial statistical determinism.  I imagine that partial statistical determinism holds, which suffices to invalidate libertarianism.  If the behavior of even one subject S is determined then, by libertarian lights, S is unfree in the moral sense (S is not responsible, S is not to be praised or blamed); and if S is morally unfree then, by common acclaim – libertarian, compatibilist, and hard determinist alike – everyone who is relevantly like S is unfree.  (By relevant similarity I mean to exclude comparing someone who has been ordered to overeat by gunpoint with one who has not; the point is to compare, for instance, two subjects who are identical except that one happens to eat in a cafeteria where less than 30% of the previous customers chose to overeat while the other eats in a cafeteria where more than 30% of the previous customers chose to overeat.)  To summarize, in only some cases does a statistical law (plus ancillary conditions) determine a unique outcome; but this suffices to make all actions covered by statistical laws unfree, if freedom requires indeterminism.

            Even if there are no actual pivotal events, their very epistemic possibility subverts libertarianism.  Applying modal logic as articulated in ____ 2000 we get the Epistemic Statistical Determinism Argument, where premise (a) is supported by everything I've been arguing:

  (a)     For all we know, John Hancock's signing of the Declaration of Independence was a pivotal event and thus necessitated. 

  (b)     If an event is necessitated then it is morally unfree.  [libertarian premise]

  (c)     Hence, for all we know, Hancock's signing was unfree.  [from (a), (b)]

  (d)     But we know Hancock's signing was free. [by common acclaim]

  (e)     Therefore libertarianism is false.  [by reductio]

For comparison, consider the Epistemic Strict Determinism Argument, which retains lines (b)-(e) and replaces (a) by:

  (a')     For all we know, Hancock's signing was classically determined and thus necessitated. 

Libertarians could reject this modified argument by denying (a').  They could claim that we know that classical determinism is false, and in support they could invoke quantum physics.  Denying the original line (a), however, seems not to be an option.  Statistical laws do threaten to create pivotal cases, the only question being whether such contingencies are actualized, and to recognize this is to say that, for all we know, they exist.  But the upshot of this, as we have seen, is that libertarianism is false.

 

4.  Levels of Confidence

Although statements (G) and (H) differ in exactitude, both are definite: (G) is true if and only if the actual frequency is exactly 60%, (H) is true if and only if the actual frequency falls between 50% and 70%.  In contrast, the indefinite statements (G*, H*) could be true regardless of what the actual frequencies are.

  (G*)  For all S in condition C there is a 20% probability ("confidence level") that 60% (+0%) of S will overeat.

  (H*)  For all S in condition C there is a 95% probability ("confidence level") that 60% +10% of S will overeat.

Notice that as exactitude grows (as interval shrinks), confidence level tends to diminish.  At one extreme we have 100% confidence in predicting that 60% of anything, +60%, has a given property F; that is, we can be utterly certain that some percentage of x's, from 0 to 100, is F.  At the other extreme, if we say that precisely n% of x's are F, no more and no less, then we run considerable risk of being wrong.

            I have said that the actual frequency of events does not determine the truth or falsity of statements like (G*, H*).  This means that you could overeat or not overeat without violating (G*) or (H*), regardless of the behavior of other diners.  But if neither your behavior nor that of anyone else affects the truth of general laws, what then does?

            One possibility is that confidence levels mark the epistemic reliability of a system.  For example, suppose that over the course of your lifetime you issue one hundred statements at a confidence-level of 95%.  Then if your statements were all true, 95 of their object clauses should be true.  (In a statement like "There is an n% chance that P", I call P the object clause.)  Alternatively, instead of taking a cognitive system to be an individual over a lifetime, we might take it to be an institution, method, discipline, school of thought, intellectual tradition, or body of data and/or doctrine.  At any rate, after delineating some collection of statements issued at a confidence level of 95%, we can say that they are all true if and only if 95% of their object clauses are true.

            Although this epistemological approach primarily concerns the truth-conducive reliability of cognitive systems (however they be identified), it has ontological implications.  For suppose that, of the object clauses you hold at the 20% confidence level, 80% are false, not counting that of (G*).  Then the object clause of (G*) must be true, in which case the basic argument runs as before.

Although the very term "level of confidence" suggests level of subjective certainty, it could also be taken as a brute indeterminacy, as an absence of a strict fact of the matter.  This ontological construal might be developed in terms of possible worlds.  To say (H*) is to say that, in 95% of all possible worlds, 60% +10% of the diners will overeat.  However, this interpretation too fails to save the indeterminist.  To begin with, suppose that the number of possible worlds is finite; indeed, for the sake of simplicity let us suppose that there are 100 possible worlds, including the actual world and 99 non-actual worlds.  Suppose furthermore that, in 5 non-actual worlds, the number of diners who overeat falls outside the 50%-70% interval.  Then law (H*) entails that, in the actual world, the number of diners who overeat falls inside the 50%-70% interval.  It now follows, precisely as before, that the diners in the actual world are determined to act as they do.

Alternatively, let us suppose that there is an infinite number of possible worlds.  As you might extrapolate from my discussion of infinite hypotheticalities in section 2, this move too leads to determinism.  As before, a statistical law, interpreted intensionally, combines with intensional facts to provide conditions that sometimes necessitate a given person's behavior.  Probability-governed behavior remains determined.

 

5.  Innumerate Probabilities

So far I have considered simple probabilities, confidence intervals, and confidence levels, which all involve cardinal numbers.  But what if probability need not involve cardinal numbers, as argued by Keynes 1921?  Applying this idea to the free-will discussion, Nozick writes: "I am not suggesting... a well-defined probability distribution... there are not fixed factual probabilities for each action, there is no such dispositional propensity or limit of long-run frequencies or whatever" (1981, p. 302).  In the same vein Kane writes: "with indeterminate efforts, exact sameness is not defined; nor is exact difference either... That is what indeterminacy amounts to" (1996, p. 171).

            This approach might seem to derail my basic argument.  However, even if we cannot assign cardinal numbers to the probability of an event, we can always say something about its ordinal probability.  It is more probable that climatic changes will trigger another dark ages within the next two centuries than that they will within the next two decades.  This establishes that the innumeracy thesis is untenable; even when propositions lack absolute numerical values, it would make sense to assign some proposition an arbitrary value and then to assign commensurable propositions relative values.  Furthermore, while we cannot absolutely measure the probability of, say, someone's committing suicide, we can say that it is greater if they are socially isolated than if they enjoy caring human contact.  Indeed, if we could not affect the probability of human action by means of praising, censuring, modeling, and so forth, then attempts at moral education would be fruitless and would never be pursued.  Because even libertarians believe in the efficacy of suasion, they must admit that probability comes in amounts, and furthermore that laws of the following sort can be found.

 (6)      Under normal conditions, the probability that a child of white-collar workers will go to college is greater than the probability that a child of blue-collar workers will.

Now suppose that all white-collar children have had their chance to go to college or not, that a certain percentage have, that all blue-collar children except S have had their chance, and that the only way for law (6) to be true is for S to drop out of school.  Then given the assumption that (6) is a true law, it necessarily follows that S drops out of school, and this in spite of the fact that the law is formulated without any cardinal values whatsoever.

            In sum, the appeal to completely innumerate improbabilities is untenable while the appeal to ordinal probabilities still permits a deduction to determinism.

 

6.  The Gambler's Fallacy

Is my argument just a version of the gambler's fallacy?  According to the gambler's fallacy, it is a mistake to use prior outcomes of gambling devices to predict future outcomes.  First, it is a mistake to make the persistence assumption that dice that have always landed odds in the previous one hundred throws will land odds on the next throw, for there is no such thing as a lucky streak.  Second, it is equally a mistake to make the compensation assumption that said dice will probably land evens on the next throw, as a consequence of some law of averages.

            Both assumptions are indeed fallacious when misapplied.  For example, the persistence assumption is fallacious when we know that we are dealing with gambling devices that are truly random.  In practice, granted, were I to notice that a certain pair of dice always landed odds over an extensive history of throws, I would assume that the dice were loaded, and I would bet that the next throw would yield odds.  But this changes the topic from that of objective probability to justified belief.

            It is the compensation assumption that is at issue here.  Granted, track record is definitely sometimes irrelevant and should be ignored.  But when we speak of objective frequencies as I am doing, be they actual or forthright fantasy or cloaked as "propensity", then it is a simple mathematical truth that the values in one subsequence, combined with a statement about the whole sequence, necessitate the values in the complementary subsequence.  To put it another way, the correct analogy is to cards rather than dice.  If I know that there is generally a 4/52 chance of getting an ace in a given turn, and if I also know that all four aces have already appeared, then I do in fact know that on my next turn I will not get an ace.  The soundness of gambler reasoning all depends on the game one plays!

            Of course if I initially accept generalization (G) and thereupon learn that the first 60 out of 100 diners in C overeat, then in practice I would normally not deduce the behavior of diner #61.  The reason is that in practice I would normally take (G) as an approximation of the truth and as expressing mere subjective probability.  But this is irrelevant, for I have been asking you to imagine a case involving ontic probability.  If a law decrees that up to n% of a population shall do A, and if a given n% of the people do A, and if the law is true rather than just provisionally posited, then it necessarily follows that the remainder of the population does not do A.

            To summarize:  Human behavior that invites moral appraisal is systematic inasmuch as it exhibits recurring patterns.  Hence it is described by true generalizations and, inferring to the best explanation for why this should be so, it is governed by true nomic generalizations (laws).  For the sake of argument, I assume that the fundamental laws are ineliminably probabilistic in character, although it is possible that the probabilistic laws of the human sciences are merely corollaries of strict laws.  Without omniscient access to these true laws, we must make do with laws formulated in terms of epistemic probability, which have no bearing on determinism.  Nonetheless ontic laws are presumed to exist, and from these – even if we cannot know them well enough to identify what deductions necessarily follow – we know that deductions of morally appraisable human behavior do necessarily follow.

 

7.  Semantic Determinism

Some of my deductions refer to possible worlds.  But since possible worlds do not stand in any temporal order to each other, my counterparts in other worlds do not act before I do.  In what sense then do they cause me to act the way I act?  By the same token, if the early cafeteria diners cause me to overeat, and if we are all in symmetric situations, then I, in combination with others, cause them not to overeat.  But how can my eating after they do have such causal power?

            I concede that we are dealing with an unusual sense of the word "cause".  This makes my argument for determinism radically different from the classical accounts; it is more like semantic determinism.[6]  According to semantic determinism, (7) is derivable from (8) plus laws or facts of semantics; (8), a fact about the distant past and therefore apparently not up to me, necessitates (7).

  (7)     The statement "____ is typing now in 2003" is true today.

  (8)     The statement "____ will be typing in 2003" was true years ago, in fact it was true before I was ever born.

Similarly, according to statistical determinism, (9) follows from (10) plus law (G) and incidental facts; (10), a fact about other people and therefore apparently not up to me, necessitates (9).

  (9)     I do not overeat.

  (10)   The first 60 of those in condition C overeat.

However, there are differences between semantic and statistical determinism.  For one thing, (7) and (8) are formally symmetric – you can derive either one from the other (given semantic laws) – whereas (9) and (10) are not, even given (G) and background information.  For another, it seems intuitively clear that the truth of (8) depends on that of (7) and not the other way around, whereas (10) does not seem to depend on (9).  In other words, the postulation of backwards causation – whereby (8) makes (7) true – defuses the moral significance of semantic determinism but not of my own.  I conclude that statistical determinism is not just a variant of semantic determinism.

            It might be argued that while I am not in sole control of the truth or falsity of (9), the collectivity to which I belong is.  On this view, the agency involved in determining the distribution of over-eaters and under-eaters is holistic rather than individualistic; any one person's behavior is jointly a function of that of all others, and the collective behavior receives contributions from each individual member.  Accordingly, while I suffer diminished control of my own actions, I enjoy added control over the actions of others, the net result being that I have as much control over the future as libertarians ordinarily think.  However, if everyone has equal control over the totality of future outcomes then everyone is equally responsible for whatever good and whatever ill happen; genuine individual responsibility would not make sense.

            Supposing I am an agent who enjoys free will, can we say that I am, in part, freely responsible for whatever true generalizations there are that cover me?  I admit we can.  Can we, however, say that I am freely responsible for whatever true laws there are?  I think it is part of the concept of a law that it controls me, not the other way around.  In order to decide whether the likes of (G) are within my control, then, we need to decide whether probabilistic statements are always contingent reports or whether they ever express genuine laws.

 

8.  Do Statistical Laws Exist?         

Statistical determinism, if it is to threaten libertarianism, rests on the assumption that statistical generalizations such as (G) hold whether one wills them to or not.  They are not up to us.

My reason for thinking they are not up to us is that pure randomness does not exist.  At the quantum level, for instance, radioactivity is not purely random, for otherwise isotopes would not have distinctive half-lives.  The fact is, uranium-235 has a half-life of thousands years while strontium-100's half-life is measured in milliseconds.  My inference to the best explanation for this difference is that some objective feature of reality makes uranium and strontium decay at different rates.  Likewise in the human sciences, events exhibit enduring and pervasive regularities.  For instance, Emile Durkheim found that suicide rates – in generation after generation, in country after country – conforms to the following law:

  (11)   The likelihood that S will commit suicide is a function of S's social integration.

In short, if quantum and social-science "laws" were merely true generalizations, then they would serve only as descriptions of observed cases, and not as explanations or as inductions for and about the future.  The fact that statistical laws hold up over time, and are expected to hold up over time, means that some underlying feature of reality is presumed to support inductions, some feature that forces the statistics to hold as they do.  I conclude that the presupposition of statistical determinism is true, that statistical laws exist.  Though I use the frequency interpretation to find empirical meaning in probability statements, this is consistent with viewing them as having nomic content.

            What if statistical statements were never objective governing laws but rather descriptions attendant upon free choices?  Supposing this were so, then the first diner S1 in condition C would not be constrained by the .60 probability postulated earlier or by any other; S1 would either overeat or not according to no probability at all, and likewise for S2 and so forth.  The net result would not add up to any enduring and pervasive regularity.  Since we know that such regularities do exist, we know that there must be governing laws that are not up to us.

            One last note on the status of (G) as a law.  Because it refers by proper name ("C") to a particular condition (a certain cafeteria on a certain day), it is not an especially general law.  However, it can be seen as the corollary of some completely universal law, call it γ; and if γ has nomic force, all of its corollaries do too.  (If, as a matter of physical necessity, mass attracts mass, then the fact that Venus attracts Mars is a matter of physical necessity too.)  Besides which, my example refers to a particular condition merely as an expository aid.  Instead I could just as well have invoked a truly universal law along with an elaborate background scenario using clumsy large numbers, and the conclusion would have been the same.

To recapitulate, I have merely observed that simple probabilistic laws like (G), in combination with sufficient background conditions, always necessitate unique outcomes (sections 1, 2); and that bells-and-whistle probabilistic laws like (H, G*, H*), in combination with sufficient background conditions, necessitate unique outcomes in pivotal cases (sections 3, 4):

  (a)     (G & background conditions) |= I overeat.

From this and the Consequence Argument's principle α we get that it's not up to me that if said conditions hold then I overeat:

  (b)     N((G & background conditions) ® I overeat).

On pain of obliterating individual responsibility, the number of customers in C, and the choices made other than mine, are not up to me (section 7):

  (c)     N(background conditions).

Nor are the laws of nature up to me (section 8):

  (d)     N(G).

Since neither (G) nor background conditions are up to me then surely the combination of (G) and background conditions is not up to me:

  (e)     N(G & background conditions).

From (b), (e), and the Consequence Argument's principle β, we get that it's not up to me that I overeat:

  (f)      N(I overeat).

Hard determinism results from statistical determinism supplemented by the Consequence Argument while compatibilism remains an option for those who reject the Consequence Argument.  Libertarianism, however, is not viable.

 

9.  Additional Problems for Libertarianism

So far I have argued that (a) in some circumstances involving moral choices, laws of physical and human nature, even when fundamentally probabilistic, will necessitate a unique outcome, from which it follows that (b) probabilistic laws cannot underpin libertarian freedom.  Leaving now the question of (a), I turn to some of my initial motivations behind (b), motivations presented more as "intuition pumps" than as rigorously developed arguments.

the compulsion argument.  If N% of a population typically acts a certain way, and if this percentage jumps to N+x% when the conditions are altered, then at first appearance we have evidence that the altered conditions make x% of the people act as they do.  The new conditions may be indeterminate inasmuch as they leave open exactly which individuals act in the new way, and even exactly how many do, but nonetheless they are compelling for some minimum number.  Since it is compulsion of any sort that threatens free will according to the incompatibilist, and not just determination according to strict laws, a libertarian defense of free will must reject both strict determinism and statistical laws.

The libertarian will insist that statistical laws merely incline or influence and do not compel, but this is a false dichotomy.  If you exert an influence on me in the sense that you increase my likelihood of doing A then you have compelled a change in my character: I have transitioned from being the kind of person who is hardly likely to do A to being the kind of person who is quite likely to do A, the transition being in your control and not mine.  This point is made in a priceless story by Stanislaw Lem (1976).  In it, a mischievous character uses a probability amplifier to convert the existence of a dangerous dragon, which would otherwise be infinitesimally improbable, into a significant probability.  When the dragon pops into being and goes on a rampage, Lem observes, the mischief-maker is at criminal fault.

the proportionality argument.  If a strict law of nature causes 100% of a population to perform some base act A then, libertarians hold, 100% of the population is to be excused for doing A.  So by parity of reasoning, if a statistical law of nature causes 75% of the population to do A then 75% of the population ought to be excused for doing so.  Which 75% should be excused?  Precisely those who perform A (that is, none of those who do not perform A), for otherwise some of those who perform A will be excused while others will not, which would be arbitrary and unjust.

            the sorites argument.  Imagine that a new drug, amokerine, works well on animal subjects.  The developers then test it on a pool of 1000 normal human subjects, who all go on a murderous rampage.  At the criminal trial one of the defendants says, "I can't be held responsible; amokerine causes everyone who takes it to turn violent, and neither I nor the doctors who prescribed it had any way of knowing this beforehand."  The defense seems legitimate.  But now suppose that of the 1000 subjects, only 999 turned violent.  Although the original defense would be a lie, it would be fair for a defendant to say, "I can't be held responsible; amokerine causes 999 out of 1000 users to turn violent, it made me turn violent, it made me turn violent."  The single unaffected patient would be regarded as lucky, not as especially virtuous.  Since there is no moral difference between 100% causation and 99.9% causation, there can be none between 99.9% and 99.8%, and so on until there is no moral difference between 100% causation and .0001%: "I can't be held responsible; amokerine always causes 1 out of 1,000,000 users to turn violent, and I happen to be that one!"[7]

            This argument may be criticized for committing the slippery-slope fallacy.  However, not all arguments having the structure of a slippery slope are specious.  The reason that the Paradox of the Heap is paradoxical is that, though the conclusion is clearly unacceptable (a single grain of sand is not a heap), the reasoning that leads up to the conclusion appears to be sound (ten-thousand grains of sand, piled together, make a heap; and taking one grain of sand from a heap leaves a heap...).  This suggests that slippery-slope reasoning is defeasibly legitimate; until it leads to conclusions that we have independent reason for rejecting, it must provisionally be accepted.

The case of the Heap is interesting because, though there is no consensus on exactly how it goes wrong, it is clear to just about everyone that it does.  In contrast, we do not know whether my moral conclusion is wrong (that if a drug leads to .001% of its users going berserk then the affected patients are not morally responsible).  Some may be tempted to think that if the overwhelming majority of amokerine users never turn violent then those who do must have something wrong with them – perhaps pre-existing malice that gets magnified or released – and therefore do deserve blame.  To think this, however, is to adopt a deterministic view: if amokerine use plus other factors in a person's life determines whether that person turns violent, then amokerine's effects are not properly stochastic.  For the sake of argument, however, I have been assuming that genuinely probabilistic laws do exist (in contrast to laws that merely seem probabilistic because of hidden variables), and to illustrate the logic of such laws I stipulate that predisposing factors in the effects of amokerine do not exist.  In this case, I maintain, there is no defeater to my sorites deduction.

the irrelevance of forks.  My paper began by saying that probabilistic laws do not guarantee branching possibilities.  To this I would like to add that branching possibilities do not engender freedom.  If all possible worlds are on a par, if non-actual worlds exist, and if I choose to perform action A in this world, then necessarily it follows that my self in some other world chooses to do other than A.  Assuming transworld identity, I myself am doomed to perform all conceivable actions at all times, in one world or another; and assuming transworld counterparts, then although I personally might lead a virtuous life, it would be logically possible for me to do so only if my virtually indistinguishable counterparts do otherwise.  In that case, responsibility would have to be holistic rather than individual.

For this reason, libertarians cannot be complete realists about possibility.  But nor can they reject possible worlds in favor of linguistic or cognitive constructs as Carnap does.  For taking possible worlds as mere facons de parler, without real reference, annuls their objective existence, which is what's at issue in the debate over ontic determinism.  (Yes, we can imagine and talk about a criminal's doing otherwise, but there's no there there.)  Thus, libertarians appear to be committed to some kind of position between modal realism and modal nominalism.  Unless they can explain away such a commitment, they must acknowledge it, they must articulate and defend it, and moreover they must explain its relevance.  Why is it that I am responsible for performing an action A only if there semi-exists another realm in which my other self does not perform A?

Conclusion.  The traditional view is that probabilistic laws do not necessitate outcomes.  But of course strict laws never necessitate outcomes either.  Only when strict laws are supplemented by initial conditions are outcomes necessitated.  By the same token, just because laws are "loose" or probabilistic does not rule out the possibility that such laws, combined with appropriate background conditions, stand in a "tight" or deterministic relation to some outcome.[8]

 

References

Dennett, Daniel (1978) Brainstorms, MIT.

Earman, John (1986) A primer on determinism, Dordrecht: Reidel.

Eccles, John (1994) How the self controls its brain, Berlin: Springer-Verlag.

Ekstrom, Laura (2000) Free will, Boulder CO: Westview Press.

Fetzer, James (1981) Scientific knowledge, Dordrecht: Reidel.

Garson, James (1995) "Chaos and free will", Philosophical Psychology.

Gillies, Donald (2000) Philosophical theories of probability, Routledge.

Glymour, Clark (1971) "Determinism, ignorance, and quantum mechanics", JP.

Gribbin, John (1984) In search of Schrodinger's cat, Bantam.

Hobart, R.E. (1934) "Free will as involving determination and inconceivable without it", Mind 43:1-27.

Hodgson, David (2002) "Quantum physics, consciousness, and free will", in Kane 2002b.

Honderich, Ted (2002) How free are you? 2/e, Oxford University Press.

Howson, Colin & Peter Urbach (1989) Scientific reasoning, Open Court.

James, William (1884) "The dilemma of determinism", reprinted in The will to believe and other essays, Dover, 1956.

–– (1891) Principles of psychology, Henry Holt.

Kane, Robert (1986) Free will and values, SUNY.

–– (1996) The significance of free will, Oxford University Press.

––, ed. (2002a) Free will, Blackwell.

––, ed. (2002b) The Oxford handbook of free will, Oxford University Press.

Keynes, John Maynard (1921) A treatise on probability, Macmillan.

Leiber, Justin (1991) An invitation to cognitive science, Blackwell.

Lem, Stanislaw (1976) "The third sally", The cyberiad, Avon.

LeShan, L. & H. Margenau (1982) Einstein's space and van Gogh's sky, Macmillan.

Levi, Isaac (1980) The enterprise of knowledge, MIT.

Lewis, David (1981) "A subjectivist's guide to objective chance", Studies in inductive logic and probability (ed. R. Jeffrey), U. of California.

McCall, Storrs (1994) A model of the universe, Oxford University Press.

Mele, Alfred (1995) Autonomous agents, Oxford University Press.

Miller, D.W. (1996) "Propensities and indeterminism", in Karl Popper (ed. A. O'Hear), Cambridge University Press.

Nozick, Robert (1981) Philosophical explanations, ch. 5, Harvard University Press, reprinted in O'Connor.

O'Connor, Timothy, ed.  (1995) Agents, causes, and events, Oxford University Press.

Popper, Karl (1959) "The propensity interpretation of probability", British Journal for the Philosophy of Science 10:25-42.

–– (1990) A world of propensities, Thoemmes.

Van Inwagen, Peter (1983) An essay on free will, Oxford University Press, relevant excerpt reprinted in Kane 2002a.

Walter, Henrik (2001) Neurophilosophy of free will, MIT.

Weatherford, Roy (1991) The implications of determinism, London: Routledge.

 



[1] A small sampling: jurists include Hodgson 2002; scientists include Eccles 1994, Gribbin 1984, and LeShan & Margenau 1982; and philosophers include Ekstrom 2000, James 1884 & 1891, Kane 1986 & 1996, Mele 1995, Nozick 1981, van Inwagen 1983, and Walter 2001.

 

[2] What I call the Mere Randomness Argument can be found in Hobart 1934.

[3] The Basic Argument could equally well be cast in microphysical terms.  Instead of law (G), consider this law: "for all particles S in condition C, the probability that S will decay within period t is .5."  Supposing that in condition C there are 1010 particles and that, excluding particle p, 1010/2 of the particles decay within t, it necessarily follows that p does not decay within t.  Insofar as decisions hinge on a single quantum event or series of quantum events, they are determined to do so.

[4] Even if we knew the laws of nature, the precise initial conditions are beyond our ken and possibly non-existent, thanks to Heisenberg's uncertainty principle; and even if we knew both laws and initial conditions, they might not be computable or the material resources for implementing the algorithm might be unavailable (even "in principle"), as suggested by the chaos of complex systems (Garson 1995) and by reflexive paradoxes involved in any system's trying to comprehensively cognize itself (Leiber 1991:53, ____ 1998).

 

[5] In actuality, I regard the epistemic/ontic distinction as being more nuanced than indicated here; cp. ____ 1998.

[6] This kind of determinism is sometimes called logical determinism (though such a label better describes the thesis that events are necessitated by the laws of logic alone, as held by Spinoza), and it is sometimes said to be based on the argument from future contingents (though if it is sound then nothing is actually contingent).  The term "semantic determinism" is motivated by the fact that it relies on semantic principles of the following sort: "If a statement is true now then the corresponding statement formulated in the future tense was true in the past."

 

[7] To repeat, my concern is ontic rather than epistemic. Whether a defendant S can prove that S is "the" 1 out of a million whose behavior traces to amokerine is irrelevant; what matters is that if S is that one then S's behavior would seem to be excusable.

[8] This paper benefited from comments by Patrick Maher, John Perry, and especially Jim Garson. In addition I wish to thank Robert Kane for his encouragement.