Linked (or coordinate) argumentation is defined in relation with two different issues, as:
(i) An argumentation whose conclusion is based on several statements combining to produce an argument (whose conclusion is supported by a set of interrelated premises). The issue is about the link between statements, the sum of which constitutes a single argument; the notion of link being then constitutive of that of argument.
(ii) An argumentation whose arguments are sufficient for the conclusion only if they are taken jointly. The issue is about the mode of combining arguments so as to produce a conclusive conclusion. The notion of link is then constitutive of that of conclusive argumentation.
1. Statements combined so as to build an argument
A linked argumentation is defined as an argumentation based on linked premises. A premise (major, minor, S. Syllogism) is defined in relation to a conclusion:
Logic. a proposition supporting or helping to support a conclusion (Dic., Premise)
The expression “linked premises” can therefore sound pleonastic. In reality, propositions or statements are linked so as to function as premises supporting a conclusion.
Syllogistic reasoning has a linked structure: “all members of this Society are more than 30 years old”, is an argument in favor of “Peter is more than 30 years old” only when combined with the proposition “Peter is a member of this Society”.
Similarly, according to Toulmin’s representation the assertive component has a linked structure. The “data” statement becomes an argument only insofar as it combines with “warranting” and “backing” statements. S. Layout.
2. Convergent and linked argumentation
The concepts of link and convergence do not describe same-level phenomena: several arguments converge to (point to) the same conclusion, whilst several statements are linked in order to build an argument for a given conclusion.
Convergent arguments are made of two or more co-oriented arguments, each of them having, by definition a linked structure, as shown in the preceding paragraph. The complete schema of convergent argumentation therefore looks as follows:
2.1 Arguments linked to produce a conclusive conclusion
The linking effect also affects convergent argumentation, the strength of which is not just in the addition of the individual strength of the added arguments. For example, an argument from necessary signs can combine necessary indices into a necessary and sufficient bundle. Likewise, case-by-case arguments, when exhaustive, benefit from a binding effect, giving to the whole greater strength than would be achieved by the mere addition of each of the parts. S. Signs; Case-by-case.
2.2 Convergent or linked argumentation?
The technique used to answer this question is a) consider a conclusion supported by a set of statements, b) consider a particular statement, c) look what happens if it is false or suppressed (Bassham 2003):
— If what remains is still an argumentation, we are dealing with a convergent argumentation:
Peter is clever and personable, he will be a great negotiator
Peter is clever, he will be a great negotiator
Peter is personable, he will be a great negotiator
All these argumentations are admissible; “Peter is clever” and “Peter is personable” are two convergent, co-oriented arguments giving rise to the same conclusion “ Peter will be a great negotiator”.
— If what remains is not an argumentation, we are dealing with a linked argumentation:
(1) It rained and the temperature is below 0°C, there should be black ice on the road.
(2) It rained, there should be black ice on the road (wrong)
(3) The temperature is below 0°C, there should be black ice on the road (wrong, unless one adds the premise “low temperatures generally goes with wet roads”).
Discourse (1) is an explicit, valid and sound argumentation. Discourses (2) and (3) are still argumentations, but they are not valid and sound as they are. To make them sound, missing premises, corresponding precisely to the suppressed statements, must be added.
The usefulness and practicability of the convergent / linked distinction is challenged (Goddu, 2007). Walton considers that its merit lies in its ability to capture the different conditions of the refutation for the two constructions. To refute a linked argumentation, one must simply show that one of the premises is false or inadmissible; to refute the conclusion of a convergent argumentation, each converging argument must be tested separately (Walton on 1996, p. 175). The arguer can grant one of the arguments in the case of convergent argumentation, but cannot give up a premise in the case of linked argumentation.
Basically, one must decide whether one or more good reasons are involved in the argumentation, that is to say, one must structure the verbal flow by proposing coherent semantic blocks supporting the conclusion.