Serial argumentation (Beardsley 1975, quoted in Wreen 1999, p. 886) also called subordinate argumentation (van Eemeren and Grootendorst 1992), is traditionally known as polysyllogism, S. Sorite; Epicheirema. A serial argumentation is an argumentation where an established conclusion is used as an argument for a new conclusion, up to an ultimate conclusion. Each argumentation which contributes to the global serial argumentation has its own structure, either simple or convergent. It might correspond to any kind of argument scheme.

Serial argumentation is schematized as follows:

Arg_1 => Concl_1 = Arg_2 => Concl_2 = Arg_3 => … Arg_n => Concl_n

Serial or convergent?

Difficulties can arise in the reconstruction of concrete argumentations, as shown in the following an example from Bassham (2003, p.72):

Peter is stubborn, he is a Taurus, he will not know how to negotiate.

1. First Interpretation, as a Serial Argumentation

(A) Peter is a Taurus so he is stubborn; (B) being stubborn, he will not know how to negotiate.

Peter is stubborn (indeed, since…) he is a Taurus; so, he will not know how to negotiate.

(A) First argumentation:
(1) Peter is a Taurus, so (2) he is stubborn

(Ai) — Technical definition of “being a Taurus”: “the Taurus sticks to his or her positions without being willing to change them”[1]
(A.ii) — Instantiation of the definition: “Peter remains on his positions without being willing to change” and conclusion of the first argumentation
(A.iii) — Lexical definition of stubborn: “who is obstinately attached to his opinions, and his decisions; which is insensitive to the reasons and arguments against it.”
(A.iv) — (A1) and (A.iii) are in a paraphrase relationship.
(A.v) — Conclusion: (2) Peter is stubborn.

(B) Second argumentation:
(2) Peter is stubborn; therefore (3) he will not know how to negotiate

(B.i) — Technical definition of negotiation “negotiation involves the confrontation of incompatible interests on various points that each interlocutor will attempt to make compatible by a set of mutual concessions.” (Wikipedia, [Negotiation])
(B.ii) — According to the above (A.iii) lexical definition, “being stubborn” and “making concession” are opposites.
(B.iii) — Opposites cannot be predicated upon the same subject, Peter.
(B.iv) — Conclusion: (3) Peter will not know how to negotiate.

This is a serial argumentation

Arg_1 => Concl_1; so [Concl_1=Arg_2] => Concl_2

2. Second Interpretation, as a Convergent Argumentation

In convergent argumentation, two arguments back the same conclusion.

(C) First argumentation (1) Peter is a Taurus, (3) he will not negotiate

(C.i) — The two technical definitions (A.i) and (B.i) are contradictory.
(C.ii) = (Biii)
(C.iii) — Conclusion: (3) Peter will not know how to negotiate.

Or:

(C.i’) — Technical definition: “the negotiator must remain flexible, calm, and exercise self-restraint.”[2]
(C.ii’) — “The Taurus’ promptness to accumulate feelings and grudges also makes him capable of strong anger”[3]
(C.iii’) — (C.i’) and C.ii’) are contradictory
(C.iv”) = (Biii)
(C.v’) — Conclusion: (3) Peter will not know how to negotiate.

(D) Second argument, (2) Peter is stubborn, (3) he will not negotiate

(D.i) — (A.iii) and (B.i) are opposites, see (B.ii).
(D.ii) = (Biii)
(D.ii) — Conclusion: (3) Peter will not know how to negotiate.

This is a convergent argumentation:

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[1] http://www.astrologie-pour-tous.com/taureau.html (09-20-2013)
[2] Jean-Paul Guedj, 50 Fiches pour négocier avec efficacité [50 leaflets to negotiate effectively], Paris: Bréal, 2010, p. 123.
[3] www.astronoo.com/zodiaque/zodiaqueTaureau.html (09-20-2013).