RELEVANCE
IGNORATIO ELENCHI
1. “Ignorance of refutation”, a fallacy of method
The fallacy of “ignorance of refutation” (Latin ignoratio elenchi [1]) is defined in relation to the dialectical game. In this game,
– One participant, the respondent (or proponent), is committed to a proposition P.
– His partner, the questioner (or opponent), tries to make him, the respondent, to assert not-P, i.e. to lead him into a contradiction, in order to refute the proposition he had previously accepted.
In this game, only contradictory propositions are considered (one and only one of them is true). The opponent must follow the rules of the dialectical method in order to refute the primitive proposition in reality (and not apparently as the Sophists do).
In the Aristotle’s catalog of fallacies 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).
In other words, the misconception of refutation is a general term that covers all methodological errors that may occur in a dialectical game.
This concept can be extended to the argumentative language game: “the arguer argues and does not know how to argue; thinks something is being proved or successfully refuted, when it is not; his practical concept of argument is flawed, etc.”
Basically this happens 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 an answer to the argumentative question that organizes the debate (external relevance).
2. Relevance of the Argument to the Conclusion
In the context of a dialectic game, the respondent asserts P. Starting from P, the questioner deductively constructs a chain of propositions that ends with the proposition not-P, and that P is false. Seemingly, the respondent has been refuted, and the questioner has won the game. But the respondent claims that the chain of evidence supporting not-P is not valid because the arguments presented do not actually support that conclusion. Thus, the respondent claims that the questioner has actually failed to prove 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 that the opponent supposedly admits. The opponent can resist the refutation by breaking the chain of inferences leading to the conclusive step he is supposedly forced to concede. In other words, the opponent argues that the arguments are not relevant to the conclusion.
In fact, this point actually involves the whole program of argumentation criticism.
3. Relevance of the Conclusion as an Answer to the Question
In the general case, the proponent commits himself to P, the opponent constructs a chain of propositions from P , at the end of which the proposition Q is reached. The proponent claims that “Q = not-P”.
The proponent replies that proposition Q is not equivalent to not-P, and that, therefore P has not been refuted.
In other words, the proponent claims that the opponent’s argument may be relevant to the conclusion Q, but that this conclusion does not disprove the original proposition to which he is committed.
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 lead the opponent down a false path (red herring); the charge of paralogism is reinforced by the suspicion of sophistry.
The criticisms of internal relevance and external relevance are cumulative. They invalidate an argument by saying that it does not support the conclusion, and that, moreover, the conclusion has nothing to do with the question.
4. The question is not relevant to the “real debate”
The dialectical framework is binary, the proposition to be discussed 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?”, to claim 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 debate. A student disputes, that is, wants to “disprove” the grade he has received:
If you don’t raise my grade, I’ll fail the exam; please, I desperately need just three more points!
The argument from consequences is quite valid, but the negative consequences of the bad grade are irrelevant to the determination of the grade (at least according to the classical scientific and educational regimes). The student’s conclusion is irrelevant, because it fails to recognize the real question: “What grade does my work deserve in itself?”. The student’s question is different from the teacher’s question, and the teacher is the master of the question.
Things can 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 is actually saying may be difficult to pin down, and may be constantly reformulated and reinterpreted see reformulation of speech. On the other hand, even when the original claim and its intended refutation have been previously written down, the connection between the two does not necessarily have the clarity of the binary contradiction. For example, does S2 refute S1, or does it merely show that the issue is complex:
S1: — Speculators buy commodities in advance just to speculate on future price fluctuations. Such operations with commodities should be prohibited by law.
S2: — However, it is essential for companies to buy the raw materials they need in advance to protect 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, accordingly, will, reject the opponent’s answer as irrelevant to the real question:
S1: — That’s not the question!
S2: — That’s is my answer to the problems that really arise. You’re not asking the right question.
The charge of fallacy of conclusion irrelevant to the question under debate can be answered by a counter-charge of a fallacious, wrongly formulated 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.
[1] Latin 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).