ISSA Proceedings 2006 – The A Contrario Argument: A Scorekeeping Model

• by: Damiano Canale & Giovanni Tuzet - Bocconi University, Milan

1. Is There a Gap in the Law?
Traditionally, the legal literature describes the A Contrario argument as an ambiguous technique of justification. On the one hand, the A Contrario argument can be used to justify a creative interpretation of a normative sentence, namely the interpretation that produces a norm that is implicit in the sentence, although it does not correspond to its literal formulation. In this sense the A Contrario argument is used to claim that the case is regulated by the law: there is no gap in the law relatively to the case. On the other hand, it can be used to justify a literal interpretation of a normative sentence, so as to exclude from the application of the norm the cases that do not correspond to its formulation. In this sense the A Contrario argument is used to claim that the case is not regulated by the law: there is a gap in the law relatively to the case.

It is possible to give an example of this ambiguity drawn from the Italian Constitution (see Guastini 1998, pp. 265-267)[i]. Article 18 of the Italian Constitution states: ‘Citizens have the right to form associations freely’. Now, can foreigners and stateless persons claim they have the same right? Two different answers can be justified by means of the A Contrario argument. The first is: according to the Constitution, only citizens have the right to form associations freely, so foreigners and stateless persons do not have such a right. The second is: the Constitution does not regulate the position of foreigners and stateless persons in this respect.
In order to clarify the ambiguous character of the A Contrario argument, first in this paper we consider some interesting logical features of it, then we propose an inferential analysis thereof based on the scorekeeping practice as described by Robert Brandom. Our aim is not to justify one use of the argument over another, but to clarify the pragmatic structure of the ways it is used. What is at stake is not only a more rigorous use of the argument, but also a better understanding of what the argument depends on.

2. Strong and Weak Pragmatic Negation
The A Contrario argument is also traditionally called A Silentio argument (cf. Jansen 2003b, p. 44 ff.). The subject of this argumentative technique is what a text does not say, not what a text says. It aims at discovering what the silence of the law means for the law, and for the legal regulation of a case in particular.

In this sense, the A Contrario argument is a general practical inference that we often use in our everyday life. In particular, such an inference is used when silence seems to signify, for what is not said, the contrary of what is said. From the normative sentence ‘No smoking in the public area’ we usually infer that smoking is allowed at home; from the normative sentence ‘Driving is permitted at 18’ we infer that driving is not permitted to those who are not in the majority age; etc. The description of the standard use of this inference seems to be the following (where ‘p’ and ‘q’ stand for propositional contents and ‘P’ is the deontic operator for permission[ii]):

If p then Pq
—————
If r then ~Pq.

It is easy to show that this use is logically incorrect. First, at least a further premise is necessary to draw the conclusion: a premise excluding other cases from the regulation stated by the legal sentence. In particular, if the conditional is intended as a material implication, the inference is an instance of the fallacy called “denying the antecedent” (cf. Henket 1992, Kaptein 1993 and 2005, Jansen 2003a). To avoid the fallacy, one should point out that there are no other legal grounds on which the consequence should follow. Second, the A Contrario argument is a de dicto argument and not a de re argument: it concerns what is (not) said by the text, not what is the case as a matter of fact[iii]. A description of a logically correct use of it could be the following:

(1) The text T states ‘if p then Pq’
(2) ‘If p then Pq’ means that iff p then Pq
—————————————————
(3) If ~p then ~Pq.

Premise (2) is normally the conclusion of other inferences, whose premises are legal norms or practical principles of communication[iv]. In the first case, such premises are contingent: they depend on the legal system the argument is referring to. In the second case, such premises are not contingent: they do not depend on the considered legal system. In both cases, however, the normative text is interpreted as stating that iff p then Pq.

But one may challenge such a use, claiming that the A Contrario argument could justify a different interpretation of the text, namely the interpretation that excludes from the application of the norm the cases that do not correspond to its literal formulation[v]. In this sense, ‘if p then Pq’ is taken to mean that if p then Pq (and nothing else). If ~p is the case, therefore, the conclusion will be that it is not determined whether q is permitted, because the circumstance is not regulated by the interpreted legal sentence. This different use of the argument could be described as follows:

(1) The text T states ‘if p then Pq’
(2′) ‘If p then Pq’ means that if p then Pq
—————————————————
(3′) ~ (if ~p then Pq)[vi].

So, assuming that r is ~p, the two uses of the argument bring to the following normative conclusions:

(3) If r then ~Pq,
(3′) ~ (if r then Pq).

On the one hand, (3) and (3′) might seem to be logically equivalent and to have the same semantic content[vii]. On the other, the pragmatic content of (3) and (3′) is quite different. If the conclusion is (3), the A Contrario argument justifies the claim that r is regulated by the law. In this case, the regulation of r (i.e. ~Pq) will be opposite to the regulation of p (i.e. Pq). If the conclusion is (3′) the A Contrario argument justifies indeed the claim that r is not regulated by the law. There is a gap in the law, which has to be filled by means of analogy.

To resume, the A Contrario argument is an interpretive argument (see Alexy 1978, p. 342). It justifies the semantic content of a legal sentence relatively to the case in hand. But the semantic content of the legal sentence depends on the use we make of the argument in the context of our legal practice, namely on the speech acts performed by the speakers in order to justify their interpretation of the sentence.
The different speech acts performed by uttering (3) and (3′) can be clarified by means of the distinction between strong pragmatic negation and weak pragmatic negation. Speech act (3) is an instance of strong pragmatic negation. When a judge performs (3) in a trial, he determines not only the semantic content of T (i.e. if r then ~Pq), but he also decides that the case is regulated by the norm so stated. When a judge performs (3′), on the contrary, he determines the semantic content of T (i.e. ~ (if r then Pq)), but in such a way he decides that the case is not regulated by the law. This is an instance of weak pragmatic negation, a negation which does not determine the legal regulation of the case: it determines that the case has no regulation according to the law[viii].

3. A Scorekeeping Model of Legal Argumentation
What we have observed so far about the A Contrario argument suggests to overcome the standard description of the argument adopting a different style of analysis in order to clarify its ambiguous character. The different uses of the argument and their justification depend on some pragmatic conditions governing the interaction of the speakers in a legal context. In this sense, it is useful to consider this argument as a standard model of pragmatic interaction, which aims at determining and justifying what a legal sentence means, or does not mean, for the case in hand.
Robert Brandom has recently set out a theoretical framework permitting an analysis of this kind (cf. Brandom 1994, 2000, 2002, 2006). This framework is based on an inferentialist theory of meaning, which explains the semantic content of a sentence in a genuine pragmatic way. In Brandom’s picture, the conceptual content of a sentence is its inferential role as premise or conclusion within an exchange of reasons. The rules governing an exchange of reasons are not a priori determined. Their determination is a result of the exchange of reasons itself. And a genuine pragmatic explanation of inferential roles is possible if we consider the steps of the argumentation, i.e. the speech acts it is composed of, moving from the normative attitudes of the speakers. From the inferentialist point of view, to be a participant within an argumentative practice is to be responsible for the claims one makes. And to be responsible is to be taken to be responsible by the other participants within the practice. In the context of legal argumentation, for example, to take another’s utterance as a claim about the facts, or as a prescription drawn from a legal text, is to attribute inferential commitments and entitlements to the speaker: the duty to accept the consequences one is committed to, and the authority to claim the consequences one is entitled to.
Saying or thinking that things are thus-and-so is undertaking a distinctive kind of inferentially articulated commitment: putting it forward as a fit premise for further inferences, that is, authorizing its use as such a premise, and undertaking responsibility to entitle oneself to that commitment, to vindicate one’s authority, under suitable circumstances, paradigmatically exhibiting it as the conclusion of an inference from other such commitments to which one is or can become entitled (Brandom 2000, p. 11).

By virtue of this theoretical approach, the meaning of a sentence, that is the set of the correct inferences it can be involved in, is instituted by the practice consisting in keeping score of discursive duties (commitments) and authorities (entitlements) of the participants within the practice. Furthermore, the use of a standard set of inferences, such as the A Contrario argument, and the legal conclusions it justifies, depends on the normative attitudes of the speakers. On the basis of considerations such as these, Brandom identifies three fundamental structures of commitment and entitlement that explain, from a pragmatic point of view, how an argument is inferentially articulated (Brandom 2002, pp. 7-8):
1. Commitment-preserving relations. These are a pragmatic description of standard deductive relations. For example, since the Italian Constitution states that citizens have the right to form associations freely, anyone who is committed to the claim that Theodore is an Italian citizen is also committed to the claim that Theodore has such a right. This kind of relation can be schematized as follows: if S is committed to p, then S is committed to q.
2. Entitlement-preserving relations. These are pragmatic generalizations of standard inductive (or abductive) relations. For instance, since the legal position of stateless persons is normally not regulated by the state law, anyone who is entitled to the claim that Anastasia is a stateless person has a reason prima facie entitling him to the claim that the Italian Constitution does not state if Anastasia has the right to form associations freely. This kind of relation can be schematized as follows: if S is entitled to p, then S is prima facie entitled to q.
3. Incompatibility relations. These are a generalization of “modally robust relations” (Brandom 2002, p. 8)[ix]. Two claims are incompatible if commitment to the one precludes entitlement to the other. For instance, as far as everything incompatible with being a citizen is incompatible with having a citizen’s right, anyone who is committed to the claim that Anastasia is not a citizen is not entitled to the claim that she has the right to form associations freely. This kind of relation can be schematized as follows: if S is committed to p, then S is not entitled to q.

To clarify whether the conclusion of the A Contrario argument instantiates a strong or a weak pragmatic negation, we have to analyze which normative attitudes the speakers undertake and attribute using this argumentative technique. In particular, we shall try to answer the following question: What kind of inference leads to conclusion (3) and what kind to (3′)? A commitment-preserving, an entitlement-preserving, or an incompatibility relation? In order to answer this question, we propose in the next section an example of exchange of reasons within legal argumentation, focusing on the different uses of the A Contrario argument considered above.

4. The A Contrario Argument in the Exchange of Reasons
We sketch in this section the pragmatic interaction between lawyer L and lawyer M within an exchange of reasons concerning the right of Anastasia to form associations freely[x]. As we said, the structure of the interaction attributing commitments and entitlements is described by Brandom through a deontic scorekeeping model of semantic determination. Competent practitioners keep track of their own and each other’s linguistic actions: they “keep score” of commitments and entitlements by attributing those deontic statuses to others and undertaking them themselves. The score is fixed from the point of view of each of the participants, and not from outside the practice. In our example, each speaker uses the A Contrario argument but draws a different normative conclusion from the same legal sentence. Through the linguistic interaction between L and M, it is also possible to make explicit the pragmatic structure of these different uses of the argument at stake.
At the beginning of the exchange of reasons, imagine that lawyer L performs the following speech act:

(L1) Since the Italian Constitution states ‘citizens have the right to form associations freely’, then the Italian Constitution states that only the citizens have such a right, and then Anastasia does not have it.

L1 is an example of application of the A Contrario argument whose conclusion instantiates a strong negation. Through speech act L1, L undertakes in particular the following inferential commitments (c) from the point of view of M:

(c1) the Italian Constitution states ‘citizens have the right to form associations freely’;
(c2) only citizens have the right to form associations freely;
(c3) Anastasia has not the right to form associations freely.

In countering L, M might say:

(M1) Since the Italian Constitution states ‘citizens have the right to form associations freely’, and the Italian Constitution does not regulate the position of foreigners and stateless persons in this respect, then the Italian Constitution does not regulate the position of Anastasia in this respect.

M1 is an example of application of the A Contrario argument whose conclusion instantiates a weak negation. Performing M1, in an inferentialist picture, M attributes one entitlement (e) to L:

(e1) the Italian Constitution states ‘citizen have the right to form associations freely’.

This means that L assumes the authority to perform c1, because M treats such a commitment as fulfilled assuming it himself: this claim of L is justified from the point of view of M. But, from the point of view of L, M undertakes two further commitments which are in conflict with c2 and c3:

(c4) the Italian Constitution does not regulate the position of foreigners and stateless persons in this respect;
(c5) the sentence ‘citizens have the right to form associations freely’ does not regulate Anastasia’s position.

Because of this conflict, L and M are requested to give further reasons in order to justify their different conclusions. L might add:

(L2) Since stateless persons do not have citizen’s rights, then Anastasia does not have the right to form associations freely.

Performing L2, L undertakes a new commitment within the argumentative practice here considered:

(c6) stateless persons do not have citizen’s rights.

This is an important step in the argumentation of L, because it shows that the inference to (3) has, from his point of view, the structure of the incompatibility relation described by Brandom. On the basis of c6, the property of being a stateless person is claimed to be incompatible with the property of having the citizen’s rights. Those who have the former cannot have the latter and the other way round. But if being a stateless person is incompatible (in Brandom’s sense) with having the citizen’s rights, it follows that anyone who is committed to the claim that Anastasia is a stateless person is not entitled to the claim that she has the right to form associations freely. Then the legal sentence ‘citizens have the right to form associations freely’ regulates the case through a norm which does not correspond to the literal formulation of the text, but which is implicit in the sentence by virtue of the incompatibility relation between the property of being a stateless person and the property of having the citizen’s rights. From the point of view of L, therefore, if M is committed to the claim that Anastasia is a stateless person, he cannot be entitled to c4 and c5, i.e. to the conclusion that the legal sentence does not regulate Anastasia’s position. Since Anastasia is a stateless person and the right at stake is a citizen’s right, the law regulates the case and Anastasia does not have such a right. We can thus remark that a strong negation instance is the pragmatic consequence of an incompatibility relation: if the inference from the premises to the conclusion is an incompatibility relation, such as the inferential relation to (3), the A Contrario argument leads to a strong negation instance[xi].

But imagine that M, at this point of the argumentation, performs a further speech act:
(M2) Since being a stateless person implies prima facie not being subjected to the state law, and also to the sentence ‘citizens have the right to form associations freely’, then this sentence does not regulate Anastasia’s position.

The new relevant commitment undertaken by M is the following:
(c7) being a stateless person implies prima facie not being subjected to the state law.

This new commitment makes explicit the pragmatic structure of the A Contrario argument whose conclusion is a weak negation instance. In M2 the inference from the premises to the conclusion has the structure of an entitlement-preserving relation. If one is entitled to the claim that citizens have the right to form associations freely, one is also prima facie entitled to the claim that such a norm applies only to citizens: now, since Anastasia is not a citizen, she seems not to be subjected to the state law. What does ‘prima facie entitled’ mean here? The conclusion of M is not a necessary one, i.e. it is not resulting from a deductive relation (a commitment-preserving relation, using Brandom’s vocabulary). It is a hypothetical claim, which produces two different pragmatic consequences: on the one hand, M claims that the normative sentence does not regulate Anastasia’s position; on the other, he claims that there could be another norm regulating the case within the considered legal system. Using this version of the A Contrario argument, therefore, M discovers the existence of a gap in the law, but he also opens the possibility to fill such a gap by means of analogy.

In this sense, we can point out that a weak negation instance is the pragmatic conclusion of an entitlement-preserving relation: if the inference from the premises to the conclusion is an entitlement-preserving relation, such as the inference to (3′), the A Contrario argument leads to a weak negation instance.
There is one more question to be answered at the conclusion of our imaginary exchange of reasons between L and M. Which conclusion of the scorekeeping practice is the right one? Is it the strong negation of L or the weak negation of M?
The answer to this question depends on the context, i.e. on the other reasons the speakers are giving and asking for within the argumentation (cf. Jansen 2003b and 2005). Apart from the contextual background of the argumentation, anyway, our point here is that a strong use of the A Contrario argument is inferentially justified if and only if the properties qualifying the regulated subject are modally incompatible. On the other hand, a weak use of the A Contrario argument is inferentially justified if and only if such an incompatibility does not hold. There could be a legally relevant relation between the regulated subject and the present case; if so, there is a gap in the law to be filled by means of analogical reasoning. Considered in his weak form, the A Contrario argument is not an autonomous argument. It is only the first step of the A Simili argument.
To conclude, it is possible to point out that what justifies the claim that there is a gap in the law is not the literal formulation of a normative sentence, but rather the deontic commitments and entitlements undertaken by the speakers. Gaps are not properties of texts. They depend on the interpretation of texts and on the different normative attitudes one attributes and assumes within the argumentative practice.

NOTES
[i] In Guastini’s account the A Contrario argument always deals with a gap: either, as a productive argument, it fills a gap or, as an interpretive argument, it remarks a gap to be filled. Contra, see García Amado (2001). For a more detailed analysis of the relation between the problem of gap-filling and the use of the A Contrario argument, see Carcaterra (1994). Note however, for the sake of the example here considered, that it is conceptually incorrect to qualify a constitutional right or a liberty as a simple permission (Mazzarese 2000, pp. 123-124).
[ii] But note that what we sketch is a general description of the A Contrario argument considering its different uses, not a particular description applying uniquely to permissions.
[iii] This use of de dicto and de re specifications is somewhat different from the standard use in modal logic. Cf. Carcaterra (1994, p. 180 ff.). On de dicto and de re modalities in deontic logic, see Rossetti (1999).
[iv] Cf. Carcaterra (1994, pp. 222-230), referring to the cooperation principle formulated by Grice (1975).
[v] Two types of A Contrario reasoning are also distinguished in Jansen (2003a) and (2003b).
[vi] And logically, since it is not determined whether q is permitted, ~ (if ~p then ~Pq).
[vii] They are not logically equivalent if one assumes a verifunctional point of view; cf. von Wright (1959).
[viii] Note that the notions of strong and weak negation have been used, for different purposes, by von Wright (1959) (cf. Mazzarese 2000, p. 115). Furthermore, they are used in contemporary nonmonotonic logic: strong negation captures the presence of explicit negative information, weak negation captures the absence of positive information.
[ix] Brandom points out that incompatibility is a modal notion which makes explicit some important relations between properties: “To say that one way things could be entails another is to say that it is not possible that the first obtain and the second not – that if the first obtains, then the second necessarily does. And to say that one way things could be is incompatible with another is to say that it is not possible that the second obtain if the first does – that if the first does, it is necessary that the second does not” (Brandom 2006, p. 11). For instance, ‘Charlie is a donkey’ entails ‘Charlie is a mammal’, for everything incompatible with Charlie’s being a mammal (Charlie’s being an invertebrate, an electronic apparatus, a prime number…) is incompatible with Charlie’s being a donkey. However, one might reply that every kind of inferential relation involves some modal relation (think of the standard definitions of deduction, for instance, as the inference drawing necessary conclusions).
[x] For a more detailed example, see Canale and Tuzet (2005).
[xi]. From a logical point of view, however, one might claim that the inference to (3) is a deductive inference, that is to say, using Brandom’s vocabulary, that the incompatibility relations are not something separate from deductive relations.

REFERENCES
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