I shall argue that a legal system itself —considered from an argumentation standpoint, and complemented with the relevant factual evidence— indeed appears to be an argumentation basis rather than a deductive system. In fact, if we accept that the legal system contains general rules and exceptions, conflicting norms, and principles expressing incompatible legal interests, then we must reject the traditional postulate of the consistency of the law, and consequently we must reject its image as an axiomatic base that, when combined with the relevant facts, yields conclusive deductive implications.
On the contrary, a legal system is a heterogeneous, stratified, and conflicting set of legal defaults (legal rules and principles, metarules, accepted argument schemes, etc.) which, when combined with the relevant facts, make it possible to derive presumptive conclusions. By complementing a legal system (the relevant portion of it) with the evidence establishing the operative facts of a case (facts that match the antecedents of some of the system’s norms), we obtain an argumentation basis from which competing presumptive arguments may possibly be constructed. To clarify this idea, let us assume, for simplicity’s sake, that the legal system \(\mathbb{L}\) in question only contains the three defeasible rules on civil liability included in the arguments in Figure 11 above:
\(D_{1}\): If one culpably damages another, one is liable: \(CulpablyDamages(x,\ y)\ \Rightarrow\ Liable(x)\).
\(D_{2}\): If one is incapable, one is not liable: \(Incapable(x)\ \Rightarrow\neg Liable\ (x)\).
\(D_{3}\): If one’s incapability is due to one’s fault, then it does not excuse, i.e., default \(D_{2}\) does not apply: \(IncapableByFault(x)\Rightarrow\ \neg D2(x)\).
The three factual propositions (possible operative facts) that match the antecedents of these three rules are the following:
\(P_{1}\): John culpably damages Tom: \(\text{CulpablyDamages}\left(John,\ Tom\right)\).
\(P_{2}\): John was incapable: \(Incapable(John)\).
\(P_{3}\): John’s incapability is due to his fault: \(IncapableByFault(John)\).
By complementing \(\mathbb{L}\) with appropriate facts (any combination of \(P_{1}\), \(P_{2}\)and \(P_{3}\)) we obtain argumentation basis that make it possible to construct any combinations of arguments A , B , and C (different facts being required for each of these arguments).
All these arguments are in principle defeasible, being susceptible to rebuttal or undercutting by appropriate counterarguments, should the latter become available. However, only A and B and can be defeated by counterarguments constructed with the norms in \(\mathbb{L}\), plus corresponding operative facts, since \(\mathbb{L}\) does not contain any default that may be used to build a defeater to C .
Let us consider, for instance, argument A in Figure 11. This argument can be constructed from \(\mathfrak{L}\), complemented by the factual proposition \(F_{1}\), since the premises for A are constituted by default \(D_{1}\), which belongs to \(\mathbb{L}\), and fact \(F_{1}\). We can say that argument A can be defeated in \(\mathbb{L}\), to mean that \(\mathbb{L,}\) complemented with appropriate facts, provides the resources for constructing a defeater to A. In fact, A is strictly defeated by B , which can be constructed from \(\mathbb{L}\), complemented with factual proposition \(P_{2}\). Also B can be defeated in \(\mathbb{L}\), since B is defeated by C , which can be constructed from \(\mathbb{L}\), complemented with the factual proposition \(P_{3}\). On the other hand, C , while also being a defeasible argument, cannot be defeated in \(\mathbb{L}\), since there is no operative fact that would make it possible to rebut or undercut C using only the rules in \(\mathbb{L}\).
Note that the fact that an argument can be defeated in \(\mathbb{L}\) does not mean that the argument fails to be justified in every argumentation basis obtainable by adding an appropriate set of operative facts to \(\mathbb{L}\). For instance, if only the fact that John culpably damaged Tom is added to \(\mathbb{L}\), we obtain the argumentation basis \(\mathbb{L}\cup\{P_{1}\}\), from which we can only build argument A . Since no counterargument to A can be constructed from \(\mathbb{L}\cup\{P_{1}\}\), A is justified relative to argumentation basis \(\mathbb{L}\cup\left\{P_{1}\right\}\) and so is his conclusion: John is liable. If we also add the fact that John was incapable, we obtain the argumentation basis \(\mathbb{L}\cup(P_{1},\ P_{2}\}\), relatively to which A is no longer justified, since A ’s strict defeater B can be constructed. Relatively to \(\mathbb{L}\cup{\{P}_{1},\ P_{2}\}\), \(B\) is justified and so is his conclusion: John is not liable. Similarly, A would again be justified, and B would be overruled, relatively to the argumentation basis \(\mathbb{L}\cup{\{P}_{1},\ P_{2},\ P_{3}\}\), which makes it possible to construct argument C . Thus, relatively to \(\mathbb{L}\cup{\{P}_{1},\ P_{2}\}\), which originates the argumentation framework \(\left\{A,\ B,\ C\right\}\), A ’s conclusion is justified: John is liable
An argument that cannot be defeated in a normative system \(\mathbb{L}\) may be defeated in larger normative system. Assume, for instance, that through a legislative act or through judicial interpretation, a new norm \(D_{4}\) is introduced, which is stronger than \(D_{3}\):
\(D_{4}\): If one’s incapacity is due to a chronic condition (alcoholism or drug addiction), then the incapacity excuse, i.e., default \(D_{2}\), does apply: \(\text{IncapableByChronicalCondition}\left(x\right)\Rightarrow\ D_{2}(x)\).
Then argument C , which could not be defeated in L, can be strictly defeated in \(\mathbb{L^{\prime}\ =L\cup\{}D_{4}\}\). In fact, \(\mathbb{L^{\prime}}\), in combination with the operative fact:
\(P_{4}\): John is incapable by a chronical condition (e.g.,alcoholism): \(\text{IncapableByChronicalCondition}\left(John)\right)\)
enables us to construct a further argument, let us call it \(G\), that strictly defeats C . Thus, relatively to the argumentation basis \(\mathbb{L}^{{}^{\prime}}\cup{\{P}_{1},\ P_{2},\ P_{3},\ P_{4}\}\), that originates the argumentation framework \(\left\{A,\ B,\ C,\ G\right\}\), argument \(A\) is overruled, while argument \(B\) is justified, and so is its conclusion that John is not liable. as shown in Figure 18.