Standards of Evaluation
What's the difference between fact and opinion? A standard of evaluation. When someone says "Sports team X scored the most points", it is a fact that everyone can go and verify. When someone says "Sports team X is the best", it is opinion because it's unclear what the standard is. Other people can't verify the results because there is no explicit method by which you came up with the result.
A standard of evaluation is a standard that you can measure against. It brings objectivity to a statement or idea by providing an explicit mechanism by which you make an evaluation. This is crucial when making comparisons. A comparison without a standard doesn't convey information. Without a standard of evaluation, statements about one would be unrelated to statements about another. There would be nothing to connect them.
A logical implication of this is that the two things being compared must have something in common. If they don't, there's no means by which they can be compared. Try comparing an apple to justice, or algebra with dirt. Can't happen.
A frequent problem is embodied in the phrase "Comparing apples to oranges." When you evaluate the two choices by different standards, the comparisons don't mean anything. If you compare two people, and you say one is nice, but the other is attractive, which is the "best"? We don't know. There isn't a proper comparison being made. If you want to compare them, you have to look at the same attributes in both. That's your standard of evaluation.
There's another problem that occurs frequently. I call it the fallacy of the second standard. The problem, essentially, is when you attempt to use more than one method of comparison at the same time. I mean that in a different way from the "apples to oranges" problem above. This one is when you use two different standards. For instance, for the sports teams, you could use points scored and rebounds. Maybe you think they're both important. But the problem is that if you use two different methods, you can end up with two different results. By points scored, Team X is the best. By rebounds, Team Y is the best. Which is the better team? You can't say at that point.
What happens if you say that one of the criteria is more important than the other. In other words, one has priority over the other. Say points scored is the more important of the two. In that case, the second criteria is almost useless. The answer always comes down to the first criteria, and only in cases of a tie would you even consider the second criteria. So in essence you're just picking one of the criteria over the other.
Another way to reconcile these problems would be to add some artificial weighting of the two criteria. You could produce some mathematical function to calculate something called a "Best Factor". Maybe points divided by 10 plus rebounds? But isn't it a bit arbitrary? You can assign it, and say "by this criteria, Team X is the winner", but unless that function makes a lot of sense, it's not going to be very useful.
A final way of reconciling the two standards is by picking a third standard that subsumes the first two. We don't really care who scored the most points in a season, or who gets the most rebounds, do we? What we really care about is who wins. And this is determined by a combination of the two, and a lot more factors.
Why is this important? It is very relevant in ethics, where you're making choices all the time. How do you choose between your different options? You have to have some standard by which you compare them. And that means you have to be able to evaluate all of your actions based on the same standard. In ethics, there's a concept called intrinsic values, which mean the values exist in the object itself, regardless of it's relationship to you. But can you see the consequence? If you're to choose between values, how do you compare these intrinsic values. Is one greater than another? If not, you have no means of choosing. If one is better than the other, what theory explains that? How do you compare values that have nothing in common? You can't.
You'll find this happening a lot in ethical theories, but it's primarily an epistemological problem. Without a single standard by which you compare things, you stop getting objective, rational results. Instead, you end up with more than one possible result, and you're left picking between them based on how you feel, which one sounds better, or any number of other methods. But then it goes back to mere opinion, since you're no longer making statements of fact.