1. “Ignorance of refutation”, a fallacy of method

Lat. ignoratio elenchi. The Greek word [elenkhos] means: “1. Argument to refute … 2. Proof in general” (Bailly, [elenkhos])”. The Latin title of Aristotle’s Sophistical Refutations is De Sophisticis elenchi (Hamblin 1970, 305).

The fallacy of “ignorance of refutation” (ignoratio elenchi) is defined in the context of the dialectical game, where a participant, the Respondent (or Proponent), is committed to a statement, and the partner, the Questioner (or Opponent), tries to lead the Respondent to a contradiction, to thus refute the statement he or she (the Respondent) had previously accepted. The dialectical game considers only contradictory propositions (one and only one of them is true). The opponent must conform to the rules of the method in order to truly refute (and not in appearance) the primitive affirmation, S. Dialectic. The fallacy of ignorance of refutation is independent of language, it occurs “because the terms ‘proof’ or ‘refutation’ have not been defined, and because something is left out in their definition”. (Aristotle, R. S., 167a20, §5), S. Fallacy: Aristotle. In other words, the misconception of refutation is a general term covering all methodological errors occurring in a dialectical game.

This concept may be extended to any argumentative language game: “the arguer argues and does not know how to argue; thinks something is being proven or successfully refuted, when this is not the case; his or her practical concept of argument is flawed, etc.” This basically occurs when the argument does not respect the principles of relevance: on the one hand, the argument must be relevant to the conclusion (internal relevance) and, on the other hand, the conclusion must be relevant as a reply to the question (external relevance), S. Argumentative question.

2. Relevance of the argument for the conclusion

In the context of a dialectic game, the Respondent asserts P. Starting from P, the Questioner deductively constructs a chain of propositions ending with proposition not-P. So, the Questioner claims that this chain proves proposition not-P. Apparently, the Respondent has been refuted, and the Questioner has won the game. But the Respondent claims that the chain of proofs backing not-P is not valid because the arguments put forward do not actually support this conclusion; so, the Respondent claims that the Questioner actually failed to demonstrate not-P.

This schematizes the general situation when an arguer claims to have refuted the opponent ex datis, that is using only beliefs and modes of inference supposedly admitted by the opponent. In the same way, in an ex datis or ad hominem procedure, the opponent can resist the refutation by breaking the inference chain leading to the conclusive step s/he is supposedly compelled to concede. In other words, he or she argues that the arguments are not relevant to the conclusion. This issue actually involves all the program of criticism of argumentation.

3. Relevance of the conclusion as a reply to the Question

In the general case, the proponent commits himself to P, the opponent constructs from P a chain of propositions, at the end of which the proposition Q is reached. The proponent therefore claims that “Q = Not-P”. The proponent argues that proposition Q is not contradictory to P, and that, accordingly, it has not been rebutted. The arguments may be relevant to the conclusion, but the conclusion does not disprove the original thesis.

To argue that an intervention is externally irrelevant is to argue that it misses the point, is off-topic, etc. It may also be denounced as an attempt to put the adversary on a false trail, S. Red herring; the accusation of paralogism is reinforced by a suspicion of sophistry.

Criticisms of internal relevance and external relevance are cumulative. They invalidate a speech by saying that it does not back its conclusion, and that, besides, the conclusion has nothing to do with the issue.

4. The question is not relevant to the “real debate”

The dialectical framework is binary, the proposition to discuss is expressed in a simple and explicit proposition, and the methodology of a refutative discussion is well defined. Since the question is “P or not-P?”, claiming that the opponent’s conclusion does not logically contradict P, is to claim that it is not relevant to the debate.

The situation can be equally clear in an ordinary discussion. A student contests, that is, wants to “refute” the grade he has received: “if you don’t up my grade, I’ll fail the exam; please, I badly need just three extra points!”. The argumentation by the consequences is quite valid, but the negative consequences of the bad grade are irrelevant to the determination of the grade (according to the classical scientific and educational regimes at least). The student’s conclusion is irrelevant, failing to acknowledge the real issue: “what mark does my assignment deserve in itself?”. The student’s question is different from the teacher’s question, and the teacher is the master of the question.

Things may be more complicated. When the proponent refutes the rebuttal by saying, “what you disagree with has nothing to do with what I am saying”, what he actually says can be difficult to pin down, and may be constantly reformulated and reinterpreted S. Resumption of speech. On the other hand, even when the original claim and its intended rebuttal have been previously set down in writing, the link between the two does not necessarily have the clarity of the binary contradiction. For example, does S2 refute S1, or merely show that the issue is complex:

S1: — Speculators buy raw material in advance just to speculate on future price variations. Such operations on raw material should be banned by law.
S2: — Nonetheless, it is essential for companies to purchase in advance the raw materials they need, to cover themselves against price fluctuations.

Finally, in ordinary argumentation, the issue itself may be controversial. When none of the participants is the (natural or conventional) master of the question, each key participant will be tempted to give a definition of the question, and, will, accordingly reject the opponent’s answer as irrelevant to the real issue:

S1: — That’s not the question!
S2: — This is my answer to the problems that really arise. You’re not asking the right question.

The accusation of fallacy of conclusion irrelevant to the question under debate can be answered by a counter accusation of a fallacious, wrongly framed question, irrelevant to the “real” debate.

The function of the participating third party, be it the judge, the (universal) audience or the informed participants, is to construct, manage and decide upon the question, and accordingly, to determine what is or is not relevant in the debate.