illuminati confirmed?

Sometimes, I like to think about how things are labeled as true or false and good or bad. It is very easy to decide whether statements are true. I could say that I am wearing a blue sweater, for example, and this statement would be true or false in the world that we are in. Since I am not wearing a blue sweatshirt, this sentence would be false. It is much harder to define what it means for an argument to be good. If I say: “All bananas are yellow. I am holding a banana. Therefore, I am holding a yellow banana,” intuitively, you would call this a good argument, but why? Is it because we know that it is, indeed, true that if I were holding a banana it would be yellow? If this were the way in which we define whether an argument is good, we could run into some problems. Consider the following argument: “All bananas are blue. Therefore, all bananas are yellow.”  Here, our conclusion is true in our world, but it’s hard to say that the argument is a good one. Thus, I like to evaluate arguments as being good if and only if they are “truth-preserving”. If we define an argument as a collection of ideas that forms a conclusion based on a set of “premises”, an argument is “truth-preserving” if, when we assume that the premises are true, the conclusion must be true (or it has at least a 50% of being true). This might sound weird at first, because if we define a good argument in this way we don’t actually care whether the premises of our argument are true—the premises of our argument could be false, while the argument itself is good. For example, we have the argument: “All bananas are blue. I am holding a banana. Therefore, I am holding a blue banana”. Even though our premise that “all bananas are blue” is false in our world, this argument is good. In other words, in every world where all bananas are blue and I am holding a banana, I must be holding a blue banana. 

Now there is a complication to consider. It is possible that an argument has premises that are contradictory (they can’t be simultaneously true). For example, there is the argument: “There exists an apple that is blue. All apples are red. Therefore, the Illuminati exists.” For this argument, it is not possible that both of our premises are true; there is no world in which they are simultaneously true. Thus, in every world in which our premises are true, the conclusion is true (since one does not exist), making this a good argument. Therefore, if our premises can never be simultaneously true (including, but not limited to contradictory sentences) then we can prove anything and our argument would be good, even if we are proving the existence of the illuminati.