The relevance of an argument to any subject of discussion can be evaluated when there is a clear statement of the issue. An issue-statement expresses a definite view upon a subject in question. It may take the form of a formal motion for a debate, a question to be subjected to rational evaluation or a plain statement of alleged fact that is to be judged as to tenability. As such, issue-statements set some clear limits upon the subject of discussion, providing a standard by which arguments for or against it can be judged relevant or irrelevant. As the motion for an orderly debate, the issue-statement must therefore be sufficiently clear and precise to avoid confusion as to the issue at hand, yet not so narrow and detailed as to exclude any exchange of views on the subject. This will be exemplified later under 'Ordered surveys of arguments on an issue'.

Since issue-statements can be of two main types, descriptive or prescriptive, the principle of relevance is formulated differently in each case.

The principle runs: An argument is relevant to a descriptive issue-statement if the argument's tenability would affect that of the issue-statement. If the argument has no consequences for the tenability of the issue-statement, it is irrelevant to the issue. Its relevance thus depends upon whether it lends support to the issue (in the case of a pro-argument) or weakens the issue (in the case of a contra-argument). If arguments in no way affect the tenability of the issue-statement, then they bear no pertinent relation to the question at hand and are thus irrelevant.

Let us suppose a discussion arises on the issue (I0) 'The United Nations is of little use for keeping world peace'. (Let issue-statements be symbolised by I0, I1 etc.)
This is a very broad or general issue-statement and is vaguely worded. It is hardly sufficiently precise to lead to an ordered debate as it could give rise to the discussion of many sub-issues. These could include for example, I1 'The U.N. is inadequate in solving world economic inequalities which are a cause of war", and I2 'The U.N. is not effective at the military organisation necessary to stop armed conflicts' and I3 'The U.N. is ineffective as an organisation for developing international understanding as an essential to avoidance of conflict'. If the context of the issue-statement is not such that makes it evident which interpretation applies, then a narrowing of the issue is required by the introduction of a sufficiently-precise issue-statement. This must be general or broad enough for an intelligent and far-reaching exchange of views, yet precise enough for clarity about what is and is not under discussion. How broad or precise the issue-statement should be will depend, of course, upon the communication situation in which it is to be employed, which includes the purpose of the debate, the functions of those taking part and so on. Therefore, a moderately-broad and -precise issue-statement will be regarded here as follows:- .

Eg: A descriptive issue-statement 10: 'The U.N. has become ineffective in hindering international conflicts of arms during the last two decades.'

This issue is stated generally yet with sufficient clarity and precision to qualify which arguments may be relevant to it. Consider a pro-argument directly relating to the issue (symbolised P1):

P1 'Yes, because protracted wars have been waged in the Middle and Far East during the last two decades without direct U.N. intervention.'

If the argument is tenable it would tend to strengthen the issue-statement's livelihood of being true, in which case it would be judged relevant. However, if strong arguments are forwarded against the tenability of P1, these would have to be taken into account in judging P1's tenability. An argument of second-order (being directed at the 'first-order' argument P1 and thus relating to the issue indirectly at a second remove) could be made against P1. Being a contra-argument against PI (pro-argument) it would be symbolised c1P1 (where the small c indicates a sub-argument, in this case of second-order, directed against the first-order argument P1):

c1P1 'but those protracted wars were not waged without UN diplomatic Intervention which was eventually sometimes effective in bringing ceasefires and negotiations between the warring parties.'

If c1P1 is tenable, the tenability of P1 is reduced and c1P1 will thereby also be judged relevant to P1 and indirectly relevant to the issue-statement. Other arguments of second, third or any order may be forwarded both for and against P1, all of which would have to be accounted for in judging the degrees of tenability and relevance of P1.

Yet another sub-argument could be directed against P1. This would be symbolised as c2P1 where c2 represents the second argument forwarded contra P1, as follows: c2P1 'but U.N. organised, peace-keeping forces have been effective in reducing hostilities in the Middle East during the last two decades.'

If this is judged tenable it further weakens the tenability of P1. Before deciding on the tenability of P1, however, one must observe any further sub-arguments. Suppose the following third-order argument were forwarded against c2P1. It would be symbolised as c1c2P1 (which stands for 'the first argument contra the second argument contra the first argument pro the issue-statement'), as follows:-

c1c2P1'but this did not involve direct armed intervention during hostilities.'

If this third-order argument is regarded as relevant and tenable it then weakens the tenability of c2P1 and strengthens that of P1. This in turn would affect the degree of relevance that P1 has as an argument in support of the issue-statement. In the actual case of c1c2P1, however, it may well be tenable yet still not relevant, since it specifies 'armed' intervention, which is not specifically claimed in P1.

As an example of an irrelevant contra-argument of the first order (against 10) consider 01 'No, because Europeans fought each other during World War I and II'. Though the assertion is tenable it makes no difference to the tenability or untenability of I0. It is obviously so far removed from the issue as to make no relevant argument against I0.

An argument is relevant to a prescriptive issue-statement if the future state of affairs predicted by the argument as a consequence of the issue-statement being realised is judged either good or ill. If neither, it is irrelevant

Because a prescriptive issue-statement asserts a value, arguments for or against it cannot prove that value to be true or false, only whether it is acceptable (good) or unacceptable (ill). Value judgements are not empirical judgements, which is to- say that they do not assert any matters of fact. Instead they forward a norm, whether social, political, ethical or religious in nature. A norm can be evaluated as to its rationality, but not as to its truth or falsity. In making relevant arguments for or against a norm, the reasonability of the norm can be investigated by considering the consequences of accepting or rejecting the norm as desirable or undesirable.

In this we see that relevance of arguments to prescriptive issue-statements depends upon the individual's judgement of the value that individual attaches to the consequential state of affairs argued for relevance is here therefore 'attaching importance to a consequence'.

If an argument for the norm is judged both to be tenable (i.e. likely to follow from accepting the norm) and to be either a good or an ill consequence, it is thereby judged relevant. If neither good nor ill it is judged irrelevant. Though its tenability nay be uncertain (i.e. whether it would follow from acceptance of the norm) an argument may still be judged relevant. Its relevance ultimately depends upon how important it is to those who accept it, whether or not they can forward grounds to convince others of its tenability.
Example; Prescriptive issue-statement 10 "Human beings have no right to kill any other animals."

This statement appears to be descriptive, but is in fact prescriptive in its assertion. It could be more clearly formulated as a prescriptive expression by:
I1 "Human beings ought never kill any other animals."

As an argument supporting the issue, a first pro-argument (P1) could be:-
P1 "because then the earth's natural profusion of species would ensure environmental ecological balance for the maximum security of all animals, including humans." (Note: Use of the word 'then' indicate a consequence argument.)

The problem here is that there are no adequate means of judging the tenability of the argument as a consequence of the issue-statement's norm being observed. It may be tenable or it may be untenable, because available observations of such a state of affairs will be insufficient either to prove or disprove the assertion. Nonetheless, there are those who strongly believe in and attempt to follow the norm, partly for the reason stated by the argument P1. (The Hindu religion generally accepts ahimsa or 'non-killing of animals', particularly the Jain sect). The argument is relevant to the issue because it is accepted as a consequence to attempt to bring about, even though its tenability is uncertain.

If an argument against the norm is judged both to be tenable and to be a good or ill consequence, it is thereby judged relevant. Similarly to the above, if its tenability is uncertain, it may yet be regarded as relevant.
For example:
C1 'No, because then many humans would die of starvation.'

The tenability of this is highly uncertain, many secondary arguments could be forwarded both for and against the likelihood of C1 being a consequence of I1.

If, however, it were possible definitively to prove that the consequence forwarded by an argument, whether pro- or contra- the issue-statement, were untenable, then it would be irrelevant. Only this is very seldom the case where prescriptive issue-statements are concerned. Therefore, an argument is almost invariably only judged irrelevant when it is considered to make no difference to one's evaluation of the issue. With prescriptive issue-expressions, therefore, the relevance and tenability of arguments are more closely interdependent than with descriptive issues. Opinion plays a stronger role with prescriptive issues, relevance being an individual subjective judgement which may or may not be shared by others (i.e. be inter-subjectively valid). As an example of an irrelevant argument to support 11 above, consider:
P2 'because then nobody could even be a vegetarian'.

This clearly does not follow as a consequence of the issue-statement. On the contrary, some form of vegetarianism would be necessary - apart from eating animals that have died naturally. It would be futile to assert the relevance of the argument because of its importance to be able to be vegetarian, or not to be a vegetarian because it is not a tenable consequence of I1. It could equally well be forwarded as a contra-argument, without increasing its tenability or relevance. Therefore, it does not make a clear argument on the issue at all.

An argument which is clear and yet evidently not in accordance with the facts - i.e. a false statement - may in some situations be regarded as relevant to the issue because it may be held to be tenable by those who know no better, or who lie about the facts. Tenability is after all only a judgement about the likelihood of truth or falsity which rests ultimately upon personal opinion and private tastes or values. Though a great majority may agree on the facts in some case, the individual can differ in opinion and may subsequently be proven right. For example, those who hold that cigarette smoking is not injurious to health because 'ill health always arises only of other causes' are in a minority and their argument is not in accordance with all the scientific evidence that has been amassed internationally. Nonetheless, though informed people would judge the argument untenable, it is a view held by enough people to justify including under an issue as peripherally relevant.

Evading an issue through introduction of side-issues

A special case of irrelevance occurs when side-issues are introduced into an argument. A 'side-issue', or any term or expression that has no cognitive relevance for the issue, should be eliminated from otherwise rational arguments.

This extends the principle of relevance to cases where any part of a statement or entire statement does not keep to the point. It applies with equal force to any arguments in serious discussion where the issue is sufficiently stated.

Referring to the issue-statement discussed above (i.e. I0 "Human beings ought never to kill any other animals") the following arguments would be irrelevant evasions of the issue by introduction of side-issues;-

Eg: P2: because cats always keep themselves very clean.
or P3: because there are many enjoyable things to do on a holiday.
or P4: because human beings are not really animals,
These 'arguments' are hardly arguments at all because they are not to the point of the issue. They do not express likely consequences of the actualisation of the issue prescription, neither good nor bad ones.
Emotive terms and expressions, which also occur in the above examples, are invariably irrelevant and constitute side-issues. Completely untenable statements that could serve only to confuse an issue nay be regarded as introduction of side-issues, as in:-
P5: because those who kill animals must always feel haunted by animals afterwards.
The principle may also be applied in exchanges of views where a fairly well-defined issue has been decided.