Relevance: Some thing or fact P has relevance for some fact or thing Q, or is relevant for it, if the truth of P makes a difference to the truth or probability of Q.

The concept of relevance is very important, and often neglected. The reason that it is important is that anything whatsoever may be relevant to anything whatsoever, and we need to somehow settle what is and is not relevant for the theories and guesses we entertain or consider.

As stated, the definition conforms to the one that is used in standard probability theory - which implies that (i) P is relevant to itself (ii) P is relevant to ~P and (iii) P is relevant to Q if the probability of Q if P is not the same as the probability of Q if ~P.

There are more subtle definitions of irrelevance and independence in personal probability.

And in a wider sense, perhaps, also including desires, values or feelings, relevance is very important too for human reasoning, as is also wishful thinking, that tends to be caused by confusions of what is factually and what is personally and emotionally relevant.

A final remark that should be made is that the term "relevance" is much abused in political and bureaucratic rhetorics: One very common rhetorical move to avoid unpleasant questions or conclusions is to declare them "irrelevant" (as if the speaker has the divine right of deciding this); another common rhetorical move to plug plans and proposals that are useful only or mostly for those who propose them is to insist loudly on their "(social) relevance". One normally can see through this - just as with advertising phrasess like "X is more valuable" - by asking for what or for whom or by what standard?