The distinction between linked arguments and convergent argument
structures enables us to address more clearly two important concepts:
the concept of a contributory condition and the concept of a
contributory reason.
A contributory condition , relatively to a conclusion, is a
necessary element of a (presumably or conclusively) sufficient condition
of conclusion. This concept applies to the (unconditional) premises that
concur in matching the conjunctive antecedent of the warrant in a linked
argument, such as premises \(P_{1}\) and \(P_{2}\) in Figure 2
A contributory reason , relatively to a conclusion, is a
presumably sufficient condition of that conclusion. This concept applies
to each (unconditional) conjunction of premises that contributes, by
triggering the corresponding warrant, to one of the defeasible arguments
that are merged in a convergent argument. This is the case for premises
\(P_{1}\) and \(P_{2}\) in Figure 3 and Figure 4.
Thus, premises \(P_{1}\) and \(P_{2}\)in Figure 2 are contributory
conditions, but fail to qualify as contributory reasons, since neither
of them separately supports the conclusion of the argument including
both of them. Therefore, neither of them can be properly characterised
as a reason for that conclusion. On the other hand, premises \(P_{1}\)
and \(P_{2}\) in Figure 3 and Figure 4 do qualify as (contributory)
reasons for their common conclusion, since each of them (together with
the corresponding default warrant) independently supports that
conclusions, besides contributing to provide a stronger joint support to
that conclusion.
In the legal domain, the idea of a contributory reasons applies to the
domain of principles, understood as optimisation requirements (Alexy
2002, Ch. 4) or value-norms (Sartor 2013, Section D). The fact that a
choice advances a principle (a legal value) is a contributory reason for
adopting that choice (of for its constitutional legitimacy). When the
same choice advances multiple principles, this originates multiple
convergent arguments —the advancement of each principle being a
contributory reason— that join to provide a stronger support to that
choice. Similarly, the fact that a choice negatively affects the
realisation of a principle, is a contributory reason for not adopting
the choice or against its legitimacy. When multiple principles are
negatively affected this originates multiple convergent arguments
against that choice.
The idea of a contributory reason also applies to the antecedent
conditions of legal rules. As I shall argue in the following, the
antecedent of a legal rules usually only provides a presumably
sufficient condition for the conclusion of that rule to hold. For
instance, the driver exceeding the speed limit may not be subject to the
sanction in case his behaviour is justified by self-defence (he was
trying to escape from a killer) or state of necessity (he was running to
the hospital for an emergency). Rule-warranted arguments and
principle-warranted arguments, while sharing the same basic logical
structure, present some relevant differences. Firstly, rule-warranted
arguments may “exclude” (undercut, in our terminology, see Section 5),
rather than oppose (rebut), certain contrary arguments warranted by
principles (if we follow the idea of Raz 1985, also adopted by Hage
2000). Secondly, convergent rule-based argument structures usually do
not provide a stronger support to their conclusion than the constituting
arguments do. For instance, assume that a person has committed a
violation that triggers his or her liability both in contract and in
torts. This provides for a converging argument structure for the
liability of this person. However, this convergent argument structure
arguably does not provide a stronger support to the liability conclusion
than the strongest of the two separate arguments for that conclusion. I
have preferred to speak of a convergent argument structure, rather than
or a convergent argument, to denote the combination of arguments leading
to the same conclusions, to maintain the concept of an argument I
introduced above, that requires a single warrant linking premises and
conclusion.