Well, I don’t want to take too much credit—it’s Gödel’s framework, not mine. I guess it would be the case that then it would not be a perfect property, since it is logically impossible to achieve. We just wouldn’t know that without doing a bunch of mathematics first, and might be confused to begin with. There’s many similar examples in this vein, for sure. But just because you don’t know something, doesn’t mean it’s not true or false. There either is a perfect property, or there is not.
I’m now going to address something that’s sort of irrelevant to your main point, but perhaps interesting:
It would seem strange to say that frequencies of music are inherently perfect. This seems to rely on a lot of contingent facts about how human ears work, why we like certain sounds and not other sounds. What is pleasant to us. So I wouldn’t call any property like this “perfect” in this sense. But I know it’s meant as an illustrative example, so this is not really to your point.
Wait, if we can be confused whether a property is perfect or imperfect—then why do we assert (in axioms 4 and 6) that some specific properties are perfect? What if they’re also impossible, like the perfect tuning?
For those ones we just say that they are, since we need those for the argument to hold logically. So we stipulate that for those properties there is no confusion, and they are perfect. You are totally allowed to say “hmm, seems suspicious,” but by the definition of these properties, there’s nothing contradictory about asserting that these properties are perfect.
But for a property like “is omniscient” or whatever, we could be more unsure. Since maybe “being omniscient” implies you also “know what it’s like to kick a baby.” And so it implies that you have a property that is not perfect, for example.
Well, I don’t want to take too much credit—it’s Gödel’s framework, not mine. I guess it would be the case that then it would not be a perfect property, since it is logically impossible to achieve. We just wouldn’t know that without doing a bunch of mathematics first, and might be confused to begin with. There’s many similar examples in this vein, for sure. But just because you don’t know something, doesn’t mean it’s not true or false. There either is a perfect property, or there is not.
I’m now going to address something that’s sort of irrelevant to your main point, but perhaps interesting:
It would seem strange to say that frequencies of music are inherently perfect. This seems to rely on a lot of contingent facts about how human ears work, why we like certain sounds and not other sounds. What is pleasant to us. So I wouldn’t call any property like this “perfect” in this sense. But I know it’s meant as an illustrative example, so this is not really to your point.
Wait, if we can be confused whether a property is perfect or imperfect—then why do we assert (in axioms 4 and 6) that some specific properties are perfect? What if they’re also impossible, like the perfect tuning?
For those ones we just say that they are, since we need those for the argument to hold logically. So we stipulate that for those properties there is no confusion, and they are perfect. You are totally allowed to say “hmm, seems suspicious,” but by the definition of these properties, there’s nothing contradictory about asserting that these properties are perfect.
But for a property like “is omniscient” or whatever, we could be more unsure. Since maybe “being omniscient” implies you also “know what it’s like to kick a baby.” And so it implies that you have a property that is not perfect, for example.