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Legal Theory Lexicon 064: Possibility and Necessity

Introduction What policy choices are feasible and which options are "pie in the sky," "utopian," or "politically impossible"?  What is "necessary" and what is merely probable?  The Legal Theory Lexicon includes two entries that deal with aspects of these questons Legal Theory Lexicon 011: Second Best and Legal Theory Lexicon 062: Path Dependency.  In this post, we will investigate the concepts of "possibility" and "necessity."  These ideas are ubiquitious in theoretical discourse, but they are rarely defined or explicated.  One way to get clear about possibility and necessity is via the power philosophical idea of a possible world, made famous by Leibniz and deployed in contemporary metaphysics by Saul Kripke and others.

As always, the Legal Theory Lexicon is aimed at law students, especially first year law students with an interest in legal theory.  Although "possible worlds" talk may sound complex, the core ideas and terminology can easily be mastered.

Modality Before proceeding any further, we need to introduce an important term, the adjective "modal" and its noun form "modality."  These words are probably unfamiliar to anyone who wasn't a philosophy major, but you may dimly recall that "could" and "must" are called "modal verbs" in texts on English grammer.  "Could" is a modal verb because it expresses possibility: if something could happen, it is possible.  "Must" is a modal verby because it expresses necessity: if something must happen, it is necessary.  When I use the word "modality" in this post, I am simply referring to the general concept that includes both necessity and possibility in all their forms.

Possible Worlds Semantics  The phrase "possible worlds semantics" sounds pretty intimidating, but it is really based on a very intuitive and simple set of ideas.  Possible worlds talk translates talk about possibility and necessity into talk about possible worlds.

Begin with the notion of a possible world. This notion is similar to the notion of a "state of affairs," which may be familiar from economics. The philosophical idea of a "possible world," is understood as a complete history of a whole universe. If some thing is possible, say event X, we say that X occurs in some possible world. Complimentary to the concept of possibility is the concept of necessity. Let us say that an event Y is necessary if Y occurs in all possible worlds; a proposition, p, is a necessary truth if it is true in all possible worlds.

The next step is to add the notion of the "actual world," where actual is an indexical term that separates this world from all possible worlds.  You may not be familiar with the idea of indexical terms.  "Here" is an indexical: its meaning is indexed to the place where the word is uttered.  Likeise, "now" is an indexical: Its meaning is indexed to the time the word "now" uttered.  The actual world is the possible world that we inhabit.

Varities of Possibility  Now that we have the idea of a possible world in place, we can talk about different kinds of possibility.  For example, "logical possibility" requires only logical consistency, and, in the logical sense, possibility is rarely implicated by debates in normative legal theory.  That is because, almost anything that legal theorists would care to talk about is logically possible: it is logically possible that the Constitution will be amended next year to abolish the Electoral College and eliminate the Senate, but no one thinks that these possibilities are even worth discussing in that time frame.

Practical Possibility  The notion that there are different types of possibility can be made very precise by using the notion of a possible world.  Let's try to develop a concept of "practical possibility" that captures the claims made by legal theorists that same legal options are not in the feasible choice set.  We can do this by narrowing the set of possible worlds that are the domain of legal necessity in a series of steps.

Each step can be expressed in terms of the idea of an accessibility relation. The phrase "accessibility relation" may sound obscure, but an example will make it crystal clear. For practical purposes, normative constitutional theory may sometimes only be interested in those worlds that are possible future states of the actual world. Such worlds share the history of the actual world up to this moment, and we call worlds that have this property "historically accessible" from the actual world.  Notice that talk about historical accessibility frequently can be translated into talk about "path dependency."  The feasible choice set--the future choices that are possible--may be (or is) constrained by history.

But "historical accessibility" is not a sufficient limitation for the purposes of normative legal theory. Why not? Because it is logically possible that the future states of the actual world could be just about anything you can imagine; there is no logical contradiction in a possible world that shares the history of the world up until now but in which the United States instantly becomes a parliamentary democracy at the next snap of Jeremy Waldron's fingers. For the purposes of normative legal theory, we should restrict the domain of possible worlds to those that share the basic laws of nature (physics, etc.) with the actual world; these worlds are called "nomologically accessible."  In nomologically accessible worlds, Waldron's finger snaps do not produce constitutional revolutions. The historically and nomologically accessible worlds, then, are those that share the history of the actual world up to now and that share our laws of nature.

At this point it is useful to introduce the idea of "distance" between the actual world and some possible world. Adjacent possible worlds are "close" to the actual world. A possible world that was just like the actual world, except that this entry in the Legal Theory Lexicon was never written, would be very close, i.e., adjacent, to the actual world.  Remote worlds are "distant" from the actual world. A possible world in which complete essays appear without effort, simply by wishing upon a star would be more remote. Even more distant worlds are easy to imagine. In ascending degree of remoteness, we can imagine a world in which the Mongols conquered Europe and the Renaissance did not occur, a world in which humans never evolved, or a world in which subtle variations in physical laws made the evolution of carbon-based life impossible.

The possibilities that concern normative legal theory are primarily those that exist in historically and nomologically accessible possible worlds that are adjacent to the actual world. One set of accessibility relationships is especially relevant to legal discourse: these relationships concern human psychology, institutional capacities, social norms, and political attitudes. Some legal options will not work, given what is true about human psychology: they make unrealistic assumptions about what officials or citizens are capable of doing. Other legal options would require dramatic changes in social norms: their success relies on unrealistic assumptions about what citizens and officials believe is acceptable or unacceptable conduct. Some options make counterfactual assumptions about institutional capacities. And yet other constitutional options are politically infeasible: they presuppose political attitudes that only exist in possible worlds that are remote from the actual world.

But normative legal discourse requires what we might call "normative space."  That is, normative discourse assumes that minds can be changed and the attitudes are not entirely fixed. We can call worlds that conform to the laws of psychology and political science but in which attitudes and beliefs are not fixed "psychologically and politically accessible worlds."

Practically Accessible Possible Worlds Sometimes normative legal theory has practical aims: it is concerned with how we should act in the actual world. Let us call constitutional action in the actual world "legal practice."  Legal practice is not concerned with historically and nomologically accessible possible worlds that cannot come into being given the limits on human choices. If there is nothing that any agent (individual, institutional, or collective) does in any historically and nomologically accessible world that brings a future state of the world about, then the future state is outside the feasible choice set. Let us call the worlds that are open to human choice in the sense just specified "practically accessible."  A practically accessible world must be nomologically and historically accessible through human agency. Legal practice is, by stipulation, concerned with possible worlds that are practically accessible.

Epistemological Accessibility One final accessibility relation requires a brief mention. We can distinguish between those worlds that are consistent with our knowledge of the actual world and those which are inconsistent with such knowledge. We can use the phrase "epistemologically accessible" to capture this idea. Worlds that are consistent with everything we know about the actual world are epistemologically accessible. Worlds that have a feature contradicted by our knowledge of the actual world are epistemologically inaccessible. Not all epistemologically accessible worlds are nomologically and historically accessible; there may be historical facts or natural laws of which we are unaware.

The Feasible Choice Set  We are now in a position to define the notion of a feasible choice set. A claim that a given legal option is outside the feasible choice set is a claim about constitutional practice, and hence a claim about which possible worlds are practically accessible. Usually, a claim that a given legal option is infeasible will rest (either explicitly or implicitly) on a claim about human psychology, anthropology, economics, sociology, or political science.

For example, the claim that a constitutional amendment banning abortion is politically infeasible, if fully articulated, would rest on claims: (i) about the legal requirements for constitutional amendments, (ii) about beliefs and desires causally relevant to the motivations of constitutional actors such as congresspersons and state legislators, and (iii) about the beliefs and desires of citizens. Thus, the claim might be that, given the legal requirements, the motives of those whose assent is legally required for a constitutional amendment, and the attitudes of voters, a constitutional amendment banning abortion is impossible. In possible worlds talk, we might say that worlds in which such amendments become law are relatively remote from our own; in these worlds, political actors behave much differently or many citizens have different attitudes about abortion or the legal requirements for a constitutional amendment have been altered. This remoteness is the underlying reason for our judgment that such a constitutional amendment is outside the feasible choice set.

Legal options that exist only in possible worlds that are either historically or nomologically inaccessible are outside the feasible choice set in a very strong sense. They cannot come about in a future state of the actual world given the natural laws that govern this world. Legal options that exist in historically and nomologically accessible worlds may nonetheless be only remote possibilities: they may depend on changes in beliefs, desires, or institutions that depend on unlikely contingencies. When such possibilities are sufficiently remote, we may say they are outside the feasible choice set, but if we speak in this way, we are using "feasibility" in a sense that diverges from historical and nomological possibility.

Two Mistakes About Possibility

The Mistake of Reducing Possibility to Cost  Positive and normative law and economics provide powerful frameworks for thinking about the law and policy. Part of that power derives from a focus on costs and benefits. Frequently, we can understand and predict behavior by focusing on the expected costs and benefits of alternative actions. Sometimes, the action that is morally best is the action that accrues the greatest benefits or minimizes costs. If carried to an extreme, this focus on costs and benefits might lead to the conclusion that talk about possibility and feasibility can be reduced to talk about costs. We might come to believe that the sentence, “Outcome A is impossible,” can be reduced to, “Outcome A is too costly to be seriously considered.” Or “Choice B is not feasible,” might be equivalent to “Choice B is so costly that it should not be considered as an alternative.”

Possibility cannot be reduced to cost for several reasons. First, some kinds of impossibility are unrelated to cost (in even the broadest sense of that term). The number of Senators apportioned to each state cannot simultaneously be equal and proportionate to population; given unequal population size, this would be a logical impossibility. Second, the attribution of costs to options is dependent upon a prior notion of possibility. Thus, if we say that option A entails the accrual of cost n, that assertion depends on the prior assumption that a state of affairs in which option A is chosen, but cost n is not accrued is not a possible state. Third, even when costs play a causal role in establishing impossibility, agent relativity differentiates between costs as factors to be weighed in decisionmaking and costs that make certain outcomes practically impossible. For example, if respecting the freedom of speech is costly in cases involving advocacy of terrorism, the Supreme Court (as a relevant constitutional agent) might take that fact into account. And in some circumstances, high costs might lead the court to view a given constitutional rule as “infeasible.” But this is quite different from the court reaching the conclusion that compliance with a rule would be impossible, because the costs associated with compliance would be too large for the affected governmental entity to bear. In the first case, the costs are factors to be weighed in making the decision. In the second case, the costs are causal influences that determine which outcomes are possible from the point of view of the Court.

The Mistake of Reducing Possibility to Probability  Another tempting error is to equate possibility and probability. Possibility is normally understood as a binary function. An action, outcome, or event is either possible or impossible—once we specify the “sense of possibility” or, more technically, the accessibility relationships that define the relevant set of possible worlds. Probability, however, is a scalar: a given outcome may be “more or less likely” or, more formally, its probability may assume any real value from 0 to 1. The tempting mistake is to equate “possible” with “probability greater than zero” and “impossible” with “probability equal to zero.” Given this move, an even more serious error becomes tempting: one might then say that assertions of “impossibility” are actually assertions of “extreme improbability,” with the consequence that the concept of impossibility would turn out to be confused or mistaken. But the equation of possibility and probability is, in fact, based on conceptual confusion. The nature of the error is easiest to see in the case of logical possibility. It simply does not make sense to assert that it is merely improbable that the following two statements are both true: (1) this article was written entirely in the twenty-first century, and (2) this article was not written entirely in the twenty-first century. It is logically impossible that both statements are true, and the concept of improbability has no application to this kind of case. If someone were to assert the following: “The probability of both statements being true is zero,” we would understand that they were using probability in a figurative or metaphorical sense. There may be cases where “impossible” means “probability of zero,” but not all cases are like this. In some cases, talk of probabilities is simply inappropriate.

Avoiding Double Standards One last point before we conclude.  Arguments about legal possibility should avoid double standards. That is, if one argues against a legal alternative on the ground that it is outside the feasible choice set, then one is obligated to show that the preferred option or options are inside the set—on the basis of the same criteria and in light of available evidence. The possibility of a double standard can be illustrated by reference to a hypothetical dispute between advocates of constitutional originalism and Dworkin’s view of law as integrity. Originalists might claim that their approach is superior because it provides objective standards for correct constitutional interpretation. A Dworkinian might attempt to refute this claim by arguing actual judges are incapable of discerning the original public meaning of the Constitution; in the actual world, the argument might go, judges and justices lack both the historical chops and the capacity to set aside their own preferences. But if the Dworkinian (or quasi-Dworkinian) were then to appeal to Dworkin’s ideal judge, Hercules, when the feasibility of law as integrity was assessed, a double standard would have been imposed. In the actual world, the same judges who lack historical chops may lack Hercules’s capacity to construct the theory that best fits and justifies the law as a whole; in the actual world, the same biases that distort originalist judges could distort the method of law as integrity. Of course, we can easily imagine that the tables are turned and that it is the originalists who deploy a double standard.

Conclusion The concepts of "possibility" and "necessity" do a lot of work, but legal theorists frequently make arguments about feasibility without a theory.  This leads to confusion and creates the possibility of double standards.  The aim of this entry in the Legal Theory Lexicon has been to give you the tools to think clearly and consistently about legal possibilities.


John Divers, Possible Worlds (Rutledge 2002).

David Lewis, On the Plurality of Worlds (new ed. Wiley-Blackwell 2001).

Lawrence B. Solum, Constitutional Possibilities, 83 Indiana Law Journal 307 (2008).


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