> But towards the end he backs away from that claim, and makes the claim I described:
> "[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.
If you want to go around calling things basic math, maybe you should actually do the math. You're not going to impress anyone by just parroting the idea that you're an idiot.
I can do it for you:
+----------+--------+
| eloquent | clumsy |
+-------+----------+--------+
| true | A | B |
+-------+----------+--------+
| false | C | D |
+-------+----------+--------+
Imagine there are A papers that are eloquent and true, B papers that are badly worded and true, C papers that are eloquent and false, and D papers that are badly worded and false. We'll also assume none of these values are 0.
For convenience, I'll use the lowercase letters to refer to probabilities rather than counts: a = A / (A + B + C + D), b = B / (A + B + C + D), etc.
We are given the postulate "papers that sound bad [in our terminology, "clumsy"] are less likely to be true". There are two possible interpretations of this:
1. Clumsy papers are less likely to be true than the average of all papers.
2. Clumsy papers are less likely to be true than eloquent papers.
Fortunately for us, each of these implies the other, so I'll use interpretation (1), again for convenience.
We can now define our postulate precisely:
b / (b + d) < (a + b) / (a + b + c + d)
Observe here that the four values a, b, c, and d are all positive and their sum is 1.
We can use basic algebra to rearrange the postulate:
b / (b + d) < (a + b) [because a + b + c + d = 1]
b < (a + b)(b + d) [because (b + d) is positive]
b < (ab + ad + b^2 + bd) [algebra]
b < b(a + b + d) + ad [algebra]
b < b(1 - c) + ad [because a + b + c + d = 1]
b < b - bc + ad [algebra]
0 < 0 - bc + ad [algebra]
bc < ad [algebra]
Let's examine whether eloquent papers are more likely to be true. As an algebraic statement, this is:
a / (a + c) > (a + b) / (a + b + c + d)
Same process:
a / (a + c) > (a + b)
a > (a + b)(a + c)
a > a^2 + ac + ab + bc
a > a(a + c + b) + bc
a > a(1 - d) + bc
a > a - ad + bc
0 > 0 - ad + bc
ad > bc
We have now proven that eloquent papers are more likely to be true if and only if ad > bc. We've also proven that, if clumsy papers are less likely to be true, bc < ad. I'm really, really hoping you can fill in the rest of the proof.
Why did you insist - repeatedly - that a very basic and obvious fact was false? What were you thinking?
> 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).
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.
> I think you are taking "less likely" too literally.
> I am simply pointing out that it is perfectly possible for both percentages to be the same
Come on. If you believe those percentages are the same, what's left of PG's claim?
> , so that whether or not the writing sounds bad gives no useful information about whether it's right or wrong.
He notes, and you stipulate, that if the writing sounds bad, that gives useful information about whether it's right or wrong.
> His intent is much better captured by treating the statements as logical implications, as I and others have been doing.
I have been treating them as logical implications. The difference is that I actually know what the implications are.
How do you think the argument "assuming badly worded papers are no more likely to be wrong than any other papers, it isn't necessarily the case that if badly worded papers are more likely to be wrong than other papers, conclusion X would follow" works? You want to use logic instead of algebra? Every conclusion follows from a contradiction.
No, it is not.
If A -> B is Not logically equivalent as If Not A -> Not B. Many make this mistake.
It is equivalent to If Not B -> Not A.
In this case, if a writing that sounds bad is less likely to be right - leads to - if the writing is right the writing is likely to sound good, (and only that).
> If A -> B is Not logically equivalent as If Not A -> Not B. Many make this mistake.
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".
> "[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.