> "[W]hile we can't safely conclude that beautiful writing is true, it's usually safe to conclude the converse: something that seems clumsily written will usually have gotten the ideas wrong too."
What do you mean, backs away? Those aren't different claims. If writing that sounds bad is less likely to be right, it is necessarily the case that writing that doesn't sound bad is more likely to be right.
Yes, they are. The first claim (the one he backs away from) is A implies B, where A = "this writing is beautiful" and B is "this writing is true". The second claim is Not A implies Not B. Those are not logically equivalent. The second claim is logically equivalent to B implies A, i.e., "this writing is true" implies "this writing is beautiful". But B implies A is not equivalent to A implies B.
> If writing that sounds bad is less likely to be right, it is necessarily the case that writing that doesn't sound bad is more likely to be right.
No, it isn't. It could also be the case that both types of writing, sounding bad and not sounding bad, are less likely to be right (because, say, sophistry is very prevalent).
What is necessarily the case is that, if writing that sounds bad is less likely to be right, writing that is right is less likely to sound bad. Which, as above, is not logically equivalent to "writing that doesn't sound bad is more likely to be right".
> What is necessarily the case is that, if writing that sounds bad is less likely to be right, writing that is right is less likely to sound bad.
That's true. You're 100% right about this.
But if you're able to prove it, you should be well aware that exactly the same proof will quickly show that writing that doesn't sound bad is more likely to be right.
> Which, as above, is not logically equivalent to "writing that doesn't sound bad is more likely to be right".
And that, obviously, is false. They are the same statement; either is sufficient to prove the other. I don't know what happened in your comment.
It's a logical tautology, at least if we make the implications definite (i.e., "sounds bad" necessarily implies "not right", and therefore "right" necessarily implies "does not sound bad"). In other words, "A implies B" is logically equivalent to "Not B implies Not A". There's no need to give any further proof.
> you should be well aware that exactly the same proof will quickly show that writing that doesn't sound bad is more likely to be right.
No, it won't. You really need to learn some basic logic.
> They are the same statement
No, they're not. Again, please learn some basic logic. "A implies B" is not logically equivalent to "B implies A". You are claiming that it is. Any basic textbook on logic will tell you that you are wrong.
No, it cannot be the case that every type of writing is less likely to be right. Less likely than what?
Think of it this way: some percentage of writing that sounds bad is wrong, and some percentage of writing that does not sound bad is wrong. I am simply pointing out that it is perfectly possible for both percentages to be the same, so that whether or not the writing sounds bad gives no useful information about whether it's right or wrong.
I think you are taking "less likely" too literally. PG makes it clear that he is not talking about exact mathematical functions. His intent is much better captured by treating the statements as logical implications, as I and others have been doing.
But many people making a mistake won't show that everything anyone says is an example of that mistake. Your observation isn't relevant here, because a claim of that form hasn't been made. We don't have "not", we have "less", which behaves differently.
For the claim "f(a) > f(b) -> g(a) > g(b)", it is trivial to show that "f(a) < f(b) -> g(a) < g(b)". These two claims are identical to each other. The proof is one step long.
In the present context, we have f(x) representing "quality of the writing in x" and g(x) representing "likelihood that the ideas in x are correct".
