Metaphysical Vagueness, Identity of Legal Cases, and the Rule of Law

1. Introduction

One of the prominent themes in legal theory and philosophy is the exploration of inde terminacy in the domain of law. I believe that it is helpful to understand indeterminacy as an overarching concept2 and to distinguish between the various sources of indeterminacy. This allows for further differentiation of manifestations of indeterminacy in the domain of law, leading to a deeper understanding of the problem, but, if indeterminacy is seen as undesirable, this also makes it easier to find ways to avoid or deal with it. Among the sources of indeterminacy, we can include, for example, ambiguity, open texture, generi city, relativity, vagueness, but also, in a sense, generality, and so on. According to various theories, indeterminacy can manifest itself at the ontological, epistemological, logical or linguistic level. For example, what may be indeterminate (in different senses) is the law itself, the linguistic expression of the law, the world to which the law applies, the contents of the mind when we think of the law, the models representing the law, etc.

In a more specific context, when examining vagueness as a source of indeterminacy in the domain of law, these are the main topics discussed in literature: the impact of vagueness on the content of law and in the context of the application of the law, the nature of vagueness that is relevant to the domain of law, positive or negative effect of vagueness in the domain of law, philosophical theories of vagueness and their impact on theories of law and judicial decision-making, special legal mechanisms to deal with vagueness, and so on.3

Discussions focus mainly on so-called semantic and epistemic vagueness, including an analysis of the philosophical theories associated with these kinds of vagueness.4

The prevalence of theories focused on language and knowledge may be due to the widespread idea that the external world to which we apply law is definite and precisely circumscribed.5 The action or legally relevant state of the world that we legally qualify is most often understood as having certain properties, and we are fully or to some extent able to grasp these properties and possibly represent them in language. In case there is an error in this grasp or representation, there is a tendency to see the source of the error in an imperfection of language or knowledge. Less often do we find the view that vagueness at the metaphysical level is to blame, i.e. a situation in which the action itself or the legally relevant state of affairs is vague, so we can speak about epistemic vagueness or vagueness at the level of language only secondarily.

The potential impact of metaphysical vagueness in the domain of law is an under-ex plored area that I want to address, at least partially, in this article. It is a neglected area, although it may have important implications for the understanding of the concept of law, for the reception of law by the addressees, or perhaps for standards of proof, ques tions about the role of truth in legal theory and practice, etc. In this article, I discuss metaphysical vagueness in relation to legal cases and the rule of law.

In the second section of the text, I present the theory of Diana Raffman, who is a proponent of the idea that it is metaphysical vagueness that is problematic for law. Of particular relevance to the legal field is the challenge that metaphysical vagueness poses to the rule of law, which she argues in her article Vagueness in Law: Placing the Blame Where It’s Due.6 Therefore, in section three of the article I explore whether and in what sense metaphysical vagueness can be a problem for the rule of law, by applying Gareth Evans’s argument to legal cases understood as objects in the metaphysical sense. In the fourth section, I explore and evaluate perhaps the most familiar way of challenging Evans’s argument. This involves a refutation of one of the premises of Evans’s argu ment, which was proposed by Terence Parsons. I conclude with a brief analysis of the implications of the result that metaphysical vagueness as conceived by Raffman, with its possible use of Parsons’s challenge to Evans’s argument, is presumably not a threat to the rule of law after all. I also surmise that other avenues which Raffman leaves open, and whose analysis is beyond the scope of this article, need to be explored.

2. Metaphysical vagueness and law

Raffman holds an important role in the field of investigation of metaphysical vagueness. She understands it as the reason why it is impossible to establish sharp boundaries between cases within soritical series, which is a problem for law the moment it enco unters such a series.7

In the process of decision-making, if, because of metaphysical vagueness, a judge cannot draw a sharp boundary between the individual cases from which a soritical series is constructed, they must decide arbitrarily if they are not to decide absurdly. Arbitrariness poses a threat to the rule of law, with the result that the judge faces

a meta-decision in which they have a choice between two undesirable options. Either they can go against the rule of law, or they can decide absurdly, i.e., by deciding all cases in the soritical series the same way, even though it is obvious that a distinction must be made between the cases, and a situation where no distinction is made between them represents an absurd result.

2.1. What is vague?

In her article Vagueness in Law: Placing the Blame Where It’s Due, Raffman argues that it is the states of affairs and actions which are the subject of adjudication, not their linguistic representation, that are vague, and this vagueness, or more precisely the inde terminacy that results from it, renders arbitrary the decision about such vague actions or states of affairs. Raffman specifically states:

In what follows I will argue that in legal cases where soritical vagueness is present, specifically,

where the court appears obliged to draw arbitrary boundaries between cases that are only

incrementally different, the difficulty derives not from the vagueness of the language in which

the law is expressed, but rather from the relationship between the law and the continuous,

seamless character of the actions and states of affairs to which it is applied.8

I hold that it is legitimate to interpret the above to mean that, according to Raffman, we can characterize actions and states of affairs as legal cases if the law is applied to them. This definition can also be understood as an instance of the more general definition of legal cases as a set of facts which, as a whole, have legal significance, or as factual matters subsumable under the hypothesis of a legal norm.9 Thus, according to Raffman, vagueness in law relates directly to actions and states of affairs and is therefore a metaphysical vagueness. If it were a vagueness of description of these states and actions, it would be a linguistic vagueness.

The assumption of Raffman’s position relating to the role of metaphysical vagueness is also that these cases (i.e., actions or states of affairs) can be made into a metaphysical soritical series. In particular, this assumption is the focus of the critique of metaphysical vagueness. First, however, I will give an example of a soritical series to better illustrate the problem faced by those who apply the law.

2.2. Soritical series

We can use Timothy Endicott’s example of a soritical series:

The Criminal Justice and Public Order Act empowers the police to direct organizers of ‘raves’

to shut down their sound equipment [if] ‘amplified music is played during the night [and] is

likely to cause serious distress to the inhabitants of the locality’. [It is] easy to imagine clear

cases of a ‘rave’ as defined in the Act. It seems that there will also be borderline cases, chiefly

because of the vagueness of ‘serious distress’. Somewhere between the silent and the seismic,

there is music to which the police power is not clearly applicable, and not clearly inapplicable.

Imagine one million rave organizers charged with disobeying a police order to shut down their

music. All appear in the same court one after the other. The first defendant [played music]

at a deafening volume, and he is convicted. (...) [E]ach successive rave organizer played the

music at an imperceptibly lower volume— until the one millionth rave organizer played it at a hush that undeniably caused no distress to anyone. He will be acquitted. But if the decre ment in volume in each case is trivial, it seems that no particular conviction ought to be the last. (...) Finding the organizer guilty in one case and not in the next case seems arbitrary.¹⁰

In considering these cases, the court is obliged to convict whoever plays something and:

1) that something must be music,

2) that music must be amplified,

3) that music must be loud enough to cause a distress,

4) there must be certain degree of probability of causing distress,

5) that distress must be severe,

6) it must be caused to the inhabitants,

7) inhabitants must be from certain locality.

Each of these conditions can be understood as indeterminate. We can ask what is understood to be playing? What is understood as music? What music is considered amplified music? What music is deemed loud? What volume is needed to cause dis tress? With what degree of probability must distress be caused in order to impose liability? What distinguishes serious from ordinary distress that amplified music loud enough is likely to cause? What distinguishes residents from other people to whom serious distress is likely to be caused by amplified, sufficiently loud music? How is the locality (from which the affected residents must come) defined?¹¹ We may also ask whether the judge is able to distinguish when a condition is met and when it is not. We may also ask for reasons why they cannot distinguish between fulfil ment or non-fulfilment of a condition if we are convinced of that conclusion. We may also ask what is to blame: the vagueness of the language in which the conditions are stated, the lack of cognitive ability of the judges, or the fact that the world is itself indeterminate. If we are to speak of metaphysical vagueness and to give an example of a metaphysi cal soritical series, let us for the moment exclude the vagueness which may arise from the linguistic formulation and the inadequacy of cognitive faculties. Endicott himself notes in this regard that the problem of distinguishing between cases also poses a problem for Ronald Dworkin’s Judge Hercules,¹² who by definition is familiar with all the relevant facts, possesses superhuman intellectual abilities, and understands all the nuances of legal interpretation:

I propose that the case of the million raves would cause a crisis, in which Hercules would have to make decisions that he cannot justify in principle. (...) Why should an imperceptible difference in volume make a polar difference to the legal outcome?¹³

Let us also restrict ourselves, for simplicity,¹⁴ to treating only one condition as prob lematic for distinguishing between cases, namely the condition that the music must be

loud. Let’s presuppose that the other conditions have been met for each of the million organizers.¹⁵

If, as Raffman proposes, vagueness is to affect a state of affairs or action, it is appro priate to restrict oneself to the metaphysical aspect of the condition. The question, then, is whether the music in each case will have the property of “being loud” or whether the action will have the property of “being the playing of loud music”.

Let’s denote the property expressed by ‘being loud’ as F and the individual musics played by the organizers in Endicott’s example as x1, x2,..., x1,000,000. The metaphysical soritical series then corresponds to relations between x1, x2,..., x1,000,000 such that the following derivation using the modus ponens inference scheme holds:

1) x1 is F

2) If x1 is F, then x2 is F

3) If x2 is F, then x3 is F

4) …

5) x1,000,000 is F

Informally speaking, if the music played by the first organizer is qualified as loud, and this organizer is thus convicted, and at the same time the differences between the musics are merely incremental, i.e., so small that it does not allow to say that one of them has property F (being loud) and the adjacent one does not, which means that there are pre conditions for the construction of a metaphysical soritical series, then by repeated appli cation of the modus ponens scheme it is possible to conclude that the music played by the millionth organizer also has property F and this organizer should therefore be convicted.

In the following section, I will elaborate on the challenge that such a metaphysical soritical series poses to the rule of law, according to Raffman.

2.3. The challenge

Raffman’s idea is thus that there are metaphysically vague actions and states of affairs. If we make a soritical series of these candidates of metaphysical vagueness and decide them in terms of law, then this means that in deciding legal cases that differ only soriti cally, any judge, Dworkin’s Judge Hercules included, has to decide all of them equally.

Such a decision, however, would be absurd from Raffman’s perspective, because we can take it as obviously false that the music is still loud, for example, in the millionth case, i.e., after the millionth reduction in volume. But if we accept modus ponens as a valid inference scheme, and yet the judge does not make that decision and decides differently than in, say, the first case, then such decision will be arbitrary because the difference in decision is not based on any relevant distinction between the cases. The judge would draw an arbitrary sharp boundary between some pair of legal cases, where in one case it is decided that the music has property F and in the next one that it does not have it. Such an arbitrary decision presents a challenge to the rule of law, according to Raffman, because the decision is not made on the grounds of the facts of the case that could lead to a difference in legal consequence.

In order to reconstruct Raffman’s position in Vagueness in Law: Placing the Blame Where It’s Due adequately, it should be said that in her view, there is a way, based on the semantics of natural language, to avoid the arbitrary introduction of sharp boundaries, while effectively using vague language in the continuous environment of the external world, i.e., while preserving metaphysical vagueness. Nevertheless, this mechanism is accessible only to ordinary non-expert speakers and it renders a kind of semantic solu tion to the problem at hand.

The relevant semantic mechanism is described in more detail in her article, but its specifics are not immediately relevant to this paper, because Raffman simultaneously argues that the nature of law makes this mechanism, which is accessible to ordinary language users, inapplicable in the context of judicial decision-making. The nature of law here means precisely that it needs sharp boundaries, absurdity of adjudication. The premise is that law cannot get these sharp boundaries under metaphysical vagueness.

The absurdity of making decisions without installing a sharp boundary would be that intuitively different cases (always lying closer to one side of the soritical series, but far enough apart to be intuitively different)¹⁶ would be decided in the same way, because the soritical series does not allow for a different decision. The legal case that would be decided would have such characteristics that it could not be distinguished in relevant respects ontologically (and a fortiori, legally) from another case, sufficiently distant in the soritical series, that would be intuitively different enough to require a contrary decision.

Thus, the problem of arbitrary sharp boundaries that the judge must create to avoid absurdity (coupled with the impossibility of distinction due to vagueness), continues to exist for the law according to Raffman, and the semantic solution accessible to ordi nary speakers that she presents is not applicable in the realm of law.

Summarizing, the legal cases in the soritical series are themselves metaphysi cally vague and therefore indeterminate. Within the semantics of ordinary language, Raffman argues, we have the possibility of using certain mechanisms to avoid the prob lem of sharp boundaries, but she states that this semantic solution is inapplicable to law because its nature is such that it needs sharp boundaries, and so the problem remains unresolved for law. This is the challenge that metaphysical vagueness poses for law.

2.4. Escape route options

Raffman elaborates, inter alia, on the reason why it is impossible to apply her semantic solution to a vagueness caused metaphysically, not on the issue whether it is indeed metaphysical vagueness that causes the problem for which she proposes a solution, i.e., whether it is indeed possible to make a soritical series out of legal cases. This possibility is understood, as I have argued above, as a presupposition. However, this assumption is not, in my view, self-evident. It is based on a belief in the mandatory nature of the doctrine of the rule of law, specifically in the part stating that cases must be decided based on their facts.

This observation makes it possible to identify certain escape routes in relation to the challenge Raffman rises:

1) Argue for an interpretation of her semantic solution that would allow the judge

to use it, i.e., the judge would not have to install sharp boundaries between cases

within the soritical series, and yet could rule in a non-arbitrary and non-absurd way.

2) Argue against Raffman to the effect that some other type of vagueness (e.g.,

semantic or epistemic vagueness) is to blame for indistinguishability in the sori

tical series, regardless of whether or not metaphysical vagueness also exists.

3) Argue against Raffman to the effect that it is not metaphysical vagueness that

accounts for the absence of a non-arbitrary sharp boundary, since metaphysical

vagueness does not exist, or at least it is not possible to construct a soritical series

from metaphysically vague cases.

I will not address solutions (1) and (2) in this text, since I am not primarily con cerned with semantic vagueness or epistemic vagueness. I will therefore address the third escape route.

3. Metaphysical vagueness?

3.1. Legal cases as objects

From a metaphysical point of view, legal cases can be understood as objects having some properties that define their identity. Of these properties, only some are relevant to law. Which ones are is determined, for example, by the legal norm.¹⁷ Whether a given case actually exhibits the properties envisaged by the legal norm is a matter for adjudication, where, however, as a preliminary question, it is necessary to determine what properties the case has. If legal cases are understood in a metaphysical sense as objects of a soritical series, then this is standardly understood to mean that they indeterminately have a property that makes it indeterminate whether they have the property envisaged by the legal norm.

If such a case is indistinguishable from another case because of the metaphysical sor itical series, then in terms of properties they should be “the same legal cases”, different only soritically. For such cases, it should also be indeterminate (because of metaphysical vagueness) whether case a is identical to case b, and thus legal cases a and b should be vaguely identical.¹⁸ In what follows, then, I will examine the vague identity of legal cases.

3.2. Evans’ argument

One of the important arguments against vague identity in general, and when applied to legal cases, against vague identity of legal cases in particular, is Evans’

argument.¹⁹ Its conclusion, in short, is that cases a and b can always be distinguished by means of the property on which the metaphysical soritical series is constructed, with the result that the possibility of its construction is blocked. An informal reconstruction of this argument in its general form is as follows:

1) it is indeterminate that a is identical with b

2) a has the property of being indeterminately identical to b

3) it is not true that it is indeterminate that b is identical to b

4) it is not true that b has the property of being indeterminately identical to b

5) it is not true that a is identical to b

Formally, this argument can be rewritten as follows:

1) ∇ (a = b)

2) λx [∇ (x = b)] a

3) ¬ ∇ (b = b)

4) ¬ λx [∇ (x = b)] b

5) ¬ (a = b)

In order to understand this formal rewriting, it is necessary to know that “∇” repre sents the indeterminacy operator, furthermore, that by means of an abstraction oper ation referred to as “λx [...]” we can derive the predication of a predicate (e.g., “F”) about some object (e.g., a) in the term ““Fa” and from this term the predication of the property that is expressed by the given predicate, i.e. the predication of the property F of the object a, i.e., “λx [Fx] a”.

Evans’ argument is that from the given premise (1.), i.e., that a and b are indeter minately identical,²⁰ we arrive by further inferences at the negation of the identity of a and b, i.e., the conclusion (5.) that a and b are determinately distinct from each other. Clearly, this conclusion contradicts the given assumption.

The indeterminate identity of a and b, given by premise (1.), implies that cases a and b are neither determinately identical nor determinately distinct. However, this contra dicts the derived conclusion (5.) that a and b are determinately distinct from each other.

The principle we use for this derivation is the contrapositive of Leibniz’s law of the principle of indistinguishability of the identical, which is: if a has a property that b does not have, then a and b are distinct. The core of Evans’ argument is that the property that a has, by (2.), but b does not have, by (4.), is the property of “being indeterminately identical with b”, because b is not indeterminately identical with itself.

It should also be emphasized at this point that we can use the contraposed Leibniz law for inference within Evans’ argument only if the formulas for predicates are supple mented by abstraction steps (i.e., steps (2.) and (4.)) that allow us to infer from the use of a predicate that there is a property that corresponds to that predicate. If this were not the case, and we were therefore not assured that predicates express properties, we could not apply contraposed Leibniz’s law, which is based on attributing properties to objects, and we would lose the principle on which Evans’s argument operates.

This emphasis is important because it is the questioning of the existence of the properties necessary for the operation of the contraposed Leibniz law through which Parsons’ attack on Evans’ argument is conducted. I will discuss Parsons’ argument for challenging Evans’ argument in the following section.

On the reading of Evans’s argument presented above, we can see that even if we assume that cases a and b are indeterminately identical, they can ultimately always be distinguished as non-identical, because a has some property that b does not. This possibility accounts for the traditional reading of Evans’s argument, according to which vague identity is an incoherent concept, and this incoherence in turn implies the nonex istence of vague objects because vague identity is usually interpreted to be constitutive for them.²¹ If Evans’s argument is sound, this leads to the conclusion that Raffman is wrong and that it is not in fact possible to make a metaphysical soritical series of the required type out of legal cases.

If we want to take an example from legal theory to illustrate Evans’ argument, we can present it in the context of the theory of the degree of proof. For now, it suffices to say that the core of any theory of the degree of proof is that for a legal consequence (e.g., in the form of a conviction) to be materially valid, there must be a situation of a cer tain evidentiary quality or intensity. Let’s have a theory, e.g., in criminal law (but this is not necessary for the example): Enough pieces of indirect evidence are needed for a conviction. The pieces of indirect evidence are of equal weight, but the correct limit of the degree of proof is indeterminate for the court. Let’s have hypothetical offenders whose cases meet the same conditions, except that for one of them we have four pieces of indirect evidence and for the other – five pieces of indirect evidence to support a con viction. Call these case A and case B. Now we have a judge who is facing the question of what level of proof is sufficient in those cases. The situation for them is that in case A it is indeterminate whether there is a sufficient degree of proof, in case B it is also indeterminate whether there is a sufficient degree of proof (i.e., cases A and B are indeterminately identical). If the judge takes this feature into account, then both cases are identical in terms of the decision, i.e., it is indeterminate whether there is a sufficient degree of proof in both cases. This should imply the same decision for both, or rather, there is no substantive reason to draw a line between four and five pieces of indirect evidence, whatever that decision will ultimately be. If we extend the line of offenders, using soritical reasoning, we get by successive steps of application of modus ponens to the situation that there is no factual reason to draw a line even between five and six pieces of indirect evidence, etc. – to the absurd conclusion that there is no difference between, say, five and thirty pieces of indirect evidence.

A judge using Evans’s argument would say that the situation for cases A and B is not the same to begin with, because in fact the identity conditions of cases A and B are not the same, since, for example, case A does not have the property of being indeter minately identical to itself, while B has the property of being indeterminately identical to A. From this reasoning, he would infer that there is a difference between A and B, which is contrary to the original assumption. In principle, then, it is possible to somehow line up cases A and B in a meaningful way, draw a sharp boundary between them, and then combine this with the theory of a sufficient degree of evidence to say, for example, that four is not enough, but five or thirty is. It allows for a substantive discussion of sharp

boundaries at all, no matter what the reasons are why four or five or thirty, or any other number of pieces of indirect evidence is the correct degree of evidence.²²

In this way, the judge’s dilemma becomes more of an epistemic (or semantic) mat ter. However, at the outset, there is a direct normative implication of Evans’ argument for what judges are to do in their work. Some may say that they need not try very hard because the cases may be distinguishable in principle, but the truly relevant reasons are not after all distinguishable in epistemic terms (or because of language) from nonrele vant ones. Others may say that judges should try harder to find those relevant reasons because they know that there are some. A still others may argue that they should try to develop a methodology because, with the right (e.g., not yet discovered) methodol ogy, they can find that boundary they know exists but do not know where. Surely the reader can think of other paths that can be taken. A quite tangible real impact may be in the normative influence on what judges are supposed to do in their work, once metaphysical vagueness is ruled out by Evans’s argument and from that moment on judges cannot say that cases are indistinguishable in terms of metaphysical vagueness and decide completely arbitrarily or absurdly draw the line. From there, one can move on to what qualities should be subsequently required to justify such a decision. Should such a decision, for example, include a judge’s explicit statement of their view of met aphysical vagueness?

A corollary of the preliminary result that Raffman is wrong due to Evans’ argument should be a more careful examination of whether, and possibly how, Raffman can argue for a circumvention of Evans’s argument in order to preserve the possibility of constructing a metaphysical soritical series and its unfortunate effect on the law that causes a challenge to the rule of law. I will now turn to this examination. Note that in this paper I will limit my analysis to what is arguably the most famous challenge to Evans’s argument, however, I would like to point out that this is only one of many attempts.²³

4. How can Raffman argue for saving the metaphysical soritical series?

Parsons, in his Indeterminate Identity: Metaphysics and Semantics,²⁴ challenges Evans’ argument. Parsons’ counterargument has to do with the properties by which the iden tity of objects is conceived, and which are approved as to existence in the abstraction steps of Evans’ argument. Parsons’ proposed solution is that these properties will not be understood as properties.

Parsons interprets Evans’s argument as being enabled by defining identity by the properties that the objects being compared have,²⁵ and further by the fact that the problematic property (the property of “being indeterminately identical to x”) is itself defined by an abstraction step that uses quantification through the properties by which identity is defined. A condition in the abstraction step of Evans’ argument is, according to Parsons, set to conflict with some of the identity-defining properties of the objects, which then allows “it is certain that x is not indeterminately identical with itself” to be understood by Evans as valid.

In other words, if the abstraction step of Evans’ argument introduces a problematic property that is itself within the scope of its own variable for properties that can be used to distinguish a and b as to their identity, which Evans does, he can show that it is not true that it is indeterminate for all properties P that if a has property P, then it is equivalent to b having property P.²⁶

Parsons explicitly demonstrates what he understands to be Evans’s problem with abstraction steps by analysing Evans’s argument through replacing the concept of iden tity with its definition in terms of properties. This analysis can be paraphrased as fol lows:²⁷

If instead of the identity “b = a” we use the definition ⩝ P (Pb ⟺ Pa), i.e., the definition by properties, then we can introduce the indeterminate identity by inserting the indeterminacy operator “∇” before this identity definition:

∇⩝ P (Pb ⟺ Pa).

If we subsequently ask whether there is the problematic property of “being inde terminately identical with b”, which Evans claims there is, then we ask whether the following abstraction introduces the property:

λx [∇⩝ P (Pb ⟺ Px)].

If we assume with Evans that it does, then we can reject the indeterminate identity, i.e., ∇⩝ P (Pb ⟺ Pa), because:

1) b certainly does not have this property, which we can express as

¬ λx [∇⩝ P (Pb ⟺ Px)] b, and this is because it is certainly not indeterminate

that b has the property of “being indeterminately identical to b”, in other words

∇⩝ P (Pb ⟺ Pb) is false, and

2) a has this property, which can be written as λx [∇⩝ P (Pb ⟺ Px)] a, since a is

indeterminately identical to b, i.e., ∇⩝ P (Pb ⟺ Pa).

This puts us in a situation where a has this problematic property, i.e., the property λx [∇⩝ P (Pb ⟺ Px)] a ∧ ¬ λx [∇⩝ P (Pb ⟺ Px)] b. of “being indeterminately identical to b”, and b does not, which can be written as

By existential generalization, we can then infer that there exists a property that a has and b does not, which is Evans’ goal. We can state this conclusion as ∃ P (Pa ∧ ¬Pb).

According to Parsons, the goal can be avoided by not allowing the abstract λx  [∇⩝  P  (Pb  ⟺  Px)] to introduce a  property. In other words, neither λx [∇⩝ P (Pb ⟺ Px)] a nor λx [∇⩝ P (Pb ⟺ Px)] b would express properties, and so they could not be used by Evans in the definition of identity over properties.

To support his proposal not to understand Evans’ abstraction steps as introducing properties, Parsons uses a condition for a formula to express a property. If we have a formula Fx, then a necessary condition for Fx to express a property is that the sat isfaction or non-satisfaction of F by the objects represented by the variable x makes a definite difference to the identity of those objects.

The condition thus states that there are no objects y and z such that (a) y certainly satisfies F, (b) z certainly does not satisfy F, and (c) at the same time it is indeterminate whether y and z are identical. If Fx does not satisfy this condition, then it does not express the property.

Parsons’s counterargument rests on the claim that the problematic “property” of Evans’s argument, i.e., in the above reconstruction, the property of “being indetermi nately identical with b”, is such that it does not satisfy the given condition and therefore does not express property at all. This, in turn, is why the abstraction step of Evans’ argument, and hence the argument as a whole, cannot work.

Summarizing the above, we can say that Evans’s argument in Parsons’s interpreta tion introduces the existence of a problematic property, i.e., a property that ultimately allows us to understand cases a and b as non-identical, and it is this introduction that Parsons rules out, and therefore resists Evans’s argument.

5. Is Parsons’ challenge to Evans’ argument of assistance to Raffman?

Raffman might try, along with Parsons, to oppose Evans’s argument by claiming that what is supposed by Evans to lead to the non-identity of cases a and b, namely the problematic property, is actually not a property.

I suggest that Raffman cannot use this approach for her argument if my reconstruc tion of her idea of the composition of a metaphysical soritical series is correct. This composition is, as I demonstrate using the example in section 2.2, based on ascribing the property of “being loud” to the individual cases that are to form the metaphysical soritical series. The predication of this property is made possible in the series by the fact that the case to be decided (i.e., case a) has the property of “being indeterminately loud”. At the same time, I hold that it is justified to understand this property as “being indeterminately as loud as b”, since the indefinite identity in loudness is referentially related to the loudness of b.

If what is denoted by the predicate of “being indeterminately as loud as b” is not a property, as Parsons claims, neither a nor b can have it as a property. Further, if we know that b certainly has the property of “being as loud as b” there is nothing that would allow us to attribute to a the property of “being as loud as b” and to identify the cases with each other.

I point out that case a will have the property of “being as loud as a”. If the properties of “being as loud as b” and “being as loud as a” express accidentally the same loudness, then we can decide cases a and b in the same way, but they will not be identical.

In other words, in this case Raffman has no reason to claim that a metaphysical sorit ical series operates, because while there may be a property that would provide a soritical series, namely the property of “being as loud as b”, there would not be a property that would guarantee the transfer of this property to case a as well, namely the property of “being indeterminately as loud as b”.

If, despite Parsons’ suggestion, we were to assert that “being indeterminately as loud as b” is a property, then a and b will be distinct by virtue of Evans’ modified argument, which will show that a has the property “being indeterminately as loud as b” and b will not have this property, since it will certainly have the property of “being as loud as b”, and hence it will certainly not be true that b has the property of “being indeterminately as loud as b”.

Such a modified Evans argument would look like this:

1) it is indeterminate that a is identical with b

∇a = b

2) b is as loud as b

H(b)

3) it is not true that it is indeterminate that b is as loud as b

¬ ∇ H(b)

4) it is not true that b has property of being indeterminately

as loud as b

¬ λx[∇ H(x)] b

5) it is indeterminate that a is as loud as b

∇ H(a)

6) a has property being indeterminately as loud as b

λx[∇ H(x)] a

7) it is not true that a is identical to b

¬ a = b

In this second case, a and b will be different, because b will certainly have the property of “being as loud as b”, but it will certainly not have the property of “being indeterminately as loud as b”, which, on the other hand, case a will have.

Another reason for concluding that Raffman’s possible use of Parsons’s approach is ill- suited is that if my analysis is correct, namely if Raffman wants to support the claim of the existence of metaphysical vagueness by showing that it is possible to construct a metaphysi cal soritical series from legal cases, she does so very likely on the basis of the properties that are supposed to constitute the identity of legal cases (the property of “being loud” is, after all, an essential property for the fulfilment of the hypothesis of the rule used in our exam ple), which is the standard conception of legal cases. But applying Parsons’ solution without changing the theory of legal cases does not make good sense, because the properties needed to form a metaphysical soritical series are, according to Parsons, actually not properties.

In other words, in order for Raffman to use Parsons’ argument against Evans’, she would need to be able to construct a metaphysical soritical series on “properties” which, according to Parsons, are not properties. But if those are not properties, there can be no metaphysical soritical series construed on them.

If, however, Raffman could find a theory of legal cases that allows legal cases to be identified/constructed on what Parsons takes to be non-properties, then she could use Parsons’ argument against Evans to argue that the problematic property that makes Evans’ argument possible is not a property (and therefore block Evans’ argument), but that one can still construct a metaphysical soritical series on it.

6. Conclusion

With this result, further investigations are becoming more important. Other possible challenges to Evans’s argument need to be addressed and it needs to be determined whether these solutions may be more suitable for Raffman than Parson’s rejected

argument. In case other challenges to Evans’s argument prove unsuccessful, and in case there is no other account of metaphysical vagueness that would be problematic for law, then it is certainly appropriate to address the impact of vagueness at the level of semantics or epistemology. Here I leave unanswered the question whether there is a possibility left open for the construction of a semantic soritical series which would be just as devastating in terms of the application of law and the challenge to the rule of law as the metaphysical soritical series.

In this paper, I have addressed the challenge to the rule of law that Raffman raises when she argues that it is metaphysical vagueness that causes it. I have presented Evans’s argument, which, if it works as it is usually interpreted, provides the ever-present possi bility of distinguishing between cases and ultimately blocks the construction of a met aphysical soritical series, thereby at least limiting the potential impact of metaphysical vagueness in the field of law. In what follows, I have tried to find a way for Raffman to avoid the conclusion of Evans’ argument for legal cases, but Parsons’ solution, which I have analysed, has been judged inapplicable on the grounds that it would have to lead to a radical revision of the theory of legal cases, which Raffman does not pursue. The attack on the rule of law on the basis of metaphysical vagueness seems to be blocked as a result of Evans’ argument, or the modified Evans’ argument put forward in section 5. Thus, explorations of other ways to limit or refute Evans’s argument, whether from metaphysical, semantic or epistemic positions, become more relevant.

I have also illustrated the direct connection of Evans’s argument to the theory of the degree of proof, showing how a relatively formal argument from general philoso phy concerned with vagueness and identity can be used in the context of considering the preconditions necessary for a substantive discussion of the specific content of legal theories. And this was done in the context of questions that every judge has presumably at some point asked themselves: Is the degree of proof in this particular case before me sufficient compared to other cases that are different in terms of only one feature? Under what conditions am I in a position to try to answer that question? Should the results of my reasoning be somehow reflected in my communication with the addressees of the law? I believe that my text can also provide support for the metatheoretical positions of those authors who believe that philosophical theories can have important implications for arguments in legal theory.