SERIAL ARGUMENTATION

Serial argumentation (Beardsley 1975, cited in Wreen 1999, p. 886) is also called subordinate argumentation (van Eemeren and Grootendorst 1992).
In logic it corresponds to polysyllogism, see sorite; epicheirema.

A serial argumentation is an argumentation in which an established conclusion is used as an argument for a new conclusion, up to an ultimate conclusion.
Each argumentation that contributes to the global serial argumentation has its own structure, either simple or convergent. It can correspond to any kind of argument scheme.

A polysyllogism is represented as follows:

Arg_1 => Concl_1 = Arg_2 => Concl_2 = Arg_3 => …
Arg_n => Concl_n = Arg N+1 => …

The elementary serial argumentation is best represented as (see below, §1):

Arg_1 => Concl_1 = Arg_2 => Concl_2

1. Serial argumentation and polysyllogism

The critical problem with such chains of argumentations is the stability and reliability of the repeated underlying deduction principle
In the polysyllogism each step is governed by syllogistic laws and the transmission of the truth is flawless from the first argument to the final conclusion.
In a chain of arguments, there is no guarantee that the principle of inference, must remain the same at each step.

Consider an argument by analogy:

A is analogous to B, B is analogous to C, … and Y is analogous to Z
Is Z analogous to A?

Z would be analogous to A if the reason, that is, the element on which the analogy is based remained the same. But if it changes at each step, you can start with a shell and end up with a motorcycle.

The same is true for argumentative causality:

The following pragmatic argument develops a causal chain from an unusually dry spring to the resignation of the president.

The weather was hot, so there is a shortage of recolts (botanical causality)
— so the price of bread goes up (economic causality)
— so  social unrest increased (social causality)
— so the king had to resign (political causality).

Historians propose such plausible sequences, but only as one explanatory factor among others. The plausibility of the conclusions diminishes as the reasoning proceeds. In such a series, at each step, the weight of the refutations grows exponentially at each step, until the chain breaks and the domino effect stop.

Interpretive reasoning has the same problem

B is an interpretation of A, C is an interpretation of B, D is an interpretation of C.
Is D an interpretation of A?

This is why some Arabic schools of jurisprudence refuse to interpret the text of the Holy Qu’ran. They believe that only the starting point, the letter of the text can be considered certain, and that engaging in interpretation would trigger a slippery slope process, leading to an unpredictable result, that may contradict the original and undisputed content of the sacred text.

2. Serial or Convergent?

Difficulties can arise in reconstructing of concrete arguments, as the following example from Bassham (2003, p.72) shows:

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

1. First Interpretation, as a Serial Argumentation

In a serial argumentation, the conclusion of the first argumentation serves as an argument in the second argumentation:
(A) Peter is a Taurus so he is stubborn; (B) since he is stubborn, he will not know how to negotiate.
= Peter is stubborn (indeed, since…) he is a Taurus; therefore, he will not know how to negotiate.

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

(A.i) — Technical definition of “being a Taurus”: “the Taurus sticks to his positions without being willing to change them.”[1]
(A.ii) — Instantiation of the definition: “Peter sticks to his positions without being willing to change.”
(A.iii) — Lexical definition of stubborn: “who is obstinately attached to his opinions, and his decisions; who is insensitive to the reasons and arguments against them”
(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 at various points which each interlocutor attempts to make compatible through a series of mutual concessions.” (Wikipedia, [Negotiation])
(B.ii) — According to the lexical definition above (A.iii) , “being stubborn” and “making concessions” are opposites.
(B.iii) — Opposites cannot be predicated on the same subject, Peter.
(B.iv) — Conclusion: (3) Peter will not know how to negotiate.

The chain (A) + (B) is a serial argumentation:

Taurus, so stubborn; stubborn, so bad negotiator
Arg_1 => Concl_1; [Concl_1=Arg_2] => Concl_2

2. Second Interpretation, as Convergent Argumentation

In convergent argumentation, two arguments support the same conclusion.

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

(C.i) — The two technical definitions (Ai.) 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’) — “Taurus’ tendency to accumulate feelings and resentments 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 argumentation
(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 be able to negotiate.

The chain (A) + (B) is now a convergent argumentation:

Both constructions develop entirely on the basis of definitions. These reconstructions perfectly illustrate the central theme of the theory of argumentation in language: both constructions develop entirely on the basis of semantic content.

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[1] http://www.astrologie-pour-tous.com/taureau.html (20.09.2013)
[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 (20.09.2013).