Relevance and Sufficiency

The relevance and sufficiency conditions of a good argument appears to be an expansion of the validity concept in classical logic. Splitting the validity condition provides the benefit of allowing the making of nuanced judgement about the level of premise support.(1)

I. Relevance

Relevance refers to premises that provide some evidence or offer reasons that support the conclusion or can be arranged in a way from which the conclusion can be derived. Relevance can be categorized as positive relevance, negative relevance and irrelevance.

A. Positive Relevance, Negative Relevance & Irrelevance

1. Positive Relevance
When assessing an argument we would say that statement A is positively relevant to statement B if the truth of A counts in favor of the truth of B. In other words, A provides some evidence or reason to believe that B is true.

In each of the following cases, the first statement is positively relevant to the second:

P. Smith has appendicitis, gout, and cancer of the bladder.
C. Smith is not healthy enough to run the 26-mile Boston Marathon.

Here the first statement provides evidence for the second statement, because it describes adverse aspects of Smith’s health, and good health is required to run a marathon.(2)

2. Negative Relevance
Statement A is negatively relevant to statement B if the truth of A counts against the truth of B. So if A is true, it provides some evidence or reason to believe that B is not true.

Consider the following examples of negative relevance:

P. Jogging often results in knee injuries.
C. Jogging improves a person’s general health.

In (d), the first statement is negatively relevant to the second, because having knee injuries counts against having good general health.(2)

3. Irrelevance

Statement A is irrelevant to statement B if it is neither positively relevant nor negatively relevant to B. In other words, when statement A does not logically support or logically undermine statement B, we would say it is irrelevant.

P. Natural catastrophes such as earthquakes are beyond human control.
C. Human beings have no freedom of choice concerning their actions.

Here, the first statement cites some natural events that are beyond human control and the second statement is about human choices about their own action. The truth of the first statement would not count as any reason to accept or reject the second statement, which is why (f) exemplifies irrelevance.(2)

B. Argument Analysis
If the premises of an argument, considered together, are irrelevant to its conclusion, or are negatively relevant, the argument is not cogent. Any case in which the relevancy condition of argument adequacy is not satisfied will be a case in which sufficiency is not satisfied either. (If premises are not even relevant to the conclusion, they cannot provide sufficient support for it.)(2)


II. Sufficiency
Sufficiency refers to the degree of support provided by the premises to support the conclusion. Whereas relevance is a property of individual premises, sufficiency is a judgement made about all the premises that support the conclusion. Hence, to be considered sufficient, the premises must provide enough support to reasonably accept the conclusion. 

This is perhaps the most difficult principle to apply because we have no clear guidelines to help us determine what constitutes sufficient grounds for the truth or merit of a conclusion. Most argumentative contexts are different and thus create different sufficiency demands. 

The feature of the sufficiency principle that is most difficult to apply is the assignment of weight to each piece of supporting evidence.  Some sciences have well-developed sufficiency criteria in place. Statisticians, for example, have determined what constitutes a proper sample from which to draw defensible conclusions. But in informal discussion, it is usually very difficult to determine when enough evidence or evidence of the appropriate kind has been presented.

(1)Stanford Encyclopedia of Philosophy: Fallacies
(2)A Practical Study of Argument: Grover
Informal Logic and logic: Blair
Attacking Faulty Reasoning: Damer