Is there a semantic difference between relevance and pertinence?
Solution 1:
I think the difference is in degree. It's similar to the difference between large/huge/gigantic or small/tiny/miniscule. In some contexts, you may be able to substitute any of those words, but due to common usage or word origin or whatever other factors, there is an understood subtle scale.
So, if you have relevant facts to discuss, they may or not be important, but they are related to the matter at hand. But if you have pertinent facts to discuss, they have precise or logical relevance to the discussion. They absolutely should not be overlooked. Pertinent facts are always relevant, but relevant facts are not necessarily pertinent.
One reason why this may be the case is that pertinent could also be used as a synonym for apt (ie. strikingly appropriate) but relevant doesn't really have that meaning. If I said you wrote an "apt answer" to this question how would you feel? What if I said it was a "pertinent answer?" Or "relevant answer?"
I think most people would feel that calling it a relevant answer is nearly a mild insult. Oh yeah, it's related, but not close to perfect.
Solution 2:
I feel that pertinent may be slightly stronger, but the two are definitely synonyms. The major difference I see is that the negative forms can be quite different. When something is irrelevant it has no bearing on the topic at hand. Impertinent can mean the same thing, but is usually used to describe a person's rudeness or lack of proper respect: "You asked a very impertinent question" can either mean the question was entirely irrelevant or the person asking it was being discourteous by doing so.
Solution 3:
Perhaps examine the question by inverting it: impertinent vs. irrelevant.
This leads me to this differentiation:
pertinent questions SHOULD be asked; we suffer a loss if they are not. relevant questions CAN be asked; we do not waste time answering them.
Solution 4:
I see that relevant has come to be used (at least in technical discussions) just to divide things into what's relevant and what's irrelevant. As such, saying that something is relevant doesn't really stress it's importance, just that it's not irrelevant.
While pertinent should have the same meaning, it's not as frequently used, so it can function as an alternative to relevant when you want to point out the importance of something.