There are 719 errors in this sentence

Here’s a famous paradox (or a variant of it at least):

• There are two errers in this sentence.

The only visible error is the misspelt “errers”. But if the sentence claims to have two errors while having only one, that is another error and there are two errors after all.

Now for another variant. I’m not sure if I’ve thought this up for myself, but try this sentence:

• There are three errors in this sentence.

There are no visible errors in the sentence. Therefore it has one error: the claim that it has three errors when there is in fact no error. But if it has one error, it’s in error to claim that it has three errors. Therefore the sentence has two errors. And if it has two errors, again it’s in error, because it claims to have three errors while having only two. Therefore it has three errors after all.

The same reasoning can be applied to any integral number of errors:

• There are five errors in this sentence.
• There are 719 errors in this sentence.
• There are 1,000,000 errors in this sentence.
• There are 1,000,000,000 errors in this sentence.

No matter how large the number of errors, the sentence becomes true instantly, because each time the sentence makes a false claim, it makes another error. But those “times of error” don’t take place in time, any more than this equation does:

• 2 = 1 + 1/2 + 1/4 + 1/8 + 1/16…

So I think these sentences are instantly true:

• There are infinitely many errors in this sentence.
• There are ∞ errors in this sentence.

But there are infinitely many infinities. Ordinary infinity, the infinity of 1,2,3…, is called ℵ0 or aleph-zero. It’s a countable infinity. Above that comes ℵ1, an uncountable infinity. So does this sentence instantly become true?

• There are ℵ1 errors in this sentence.

I’m not sure. But I think I can argue for the validity of sentences claiming fractional or irrational number of errors:

• There is 1.5 errors in this sentence.
• There are π errors in this sentence.

Let’s have a look at “There is 1.5 errors in this sentence”. There are no visible errors, so there’s one error: the claim that sentence contains 1.5 errors. So now there seems to be another error: the sentence has one error but claims to have 1.5 errors. But does it therefore have two errors? No, because if it has two errors, it’s still in error and has three errors. And that generates another error and another and another, and so on for ever. The sentence becomes unstoppably and infinitely false.

So let’s go back to the point at which the sentence contains one error. Now, the difference between 1 error and 1.5 errors is small — less than a full error. So how big is the error of claiming to have 1.5 errors when having 1 error? Well, it’s obviously 0.5 of an error. So the sentence contains 1.5 errors after all.

Now for “There are π errors in this sentence”. There are no visible errors, so there’s one error: the claim that the sentence contains π errors. Therefore it contains one error. But it claims to have π errors, so it has another error. And if it has 2 errors and claims to have π errors, it has another and third error. But if it has three errors and claims to have π error, it’s still in error. But only slightly — it’s now committing a small amount of an error. How much? It can only be 0.14159265… of an error. Therefore it’s committing 3.14159265… = π errors and is a true sentence.

Now try:

• There is -1 error in this sentence.

What is a negative error? A truth. So I think that sentence is valid too. But I can’t think of how to use i, or the square root of -1, in a sentence like that.

4 thoughts on “There are 719 errors in this sentence

  1. The only visible error is the misspelt “errers”. But if the sentence claims to have two errors while having only one, that is another error and there are two errors after all.

    …and then maybe a third? If the sentence is a paradox, it’s an error to have the correct number of errors.

    And since 3 errors != 2 errors, there’s 4 errors, and since 4 errors != 2, there’s 5 errors, and so on. It seems you can reach an infinite number of errors from any starting point.

    Although maybe considering the writer’s intent is cheating: we could just as easily say the sentence has 0 errors, since it’s supposed to be a paradox and the “errer” mistake is intended…but if it has 0 errors it’s not paradoxical, just false. So it has 1 error again, and since 1 also isn’t paradoxical…

    • and then maybe a third? If the sentence is a paradox, it’s an error to have the correct number of errors.

      It’s not the definition of a paradox to be erroneous, so I don’t agree. A paradox seems erroneous, but is actually true. Or becomes erroneous because it’s true, true because it’s erroneous. Etc.

      Although maybe considering the writer’s intent is cheating: we could just as easily say the sentence has 0 errors, since it’s supposed to be a paradox and the “errer” mistake is intended

      It’s intended, but still an error. A Zen paradox might involve an unintentionally intentional or intentionally unintentional error.

      • It’s not the definition of a paradox to be erroneous

        You’re right – my mistake. The paradox doesn’t come from errors but from the fact that there’s an inconsistent number of them (if 2 there’s 1, if 1 there’s 2).

        It’s intended, but still an error. A Zen paradox might involve an unintentionally intentional or intentionally unintentional error.

        I find errors ontologically interesting – correctness, too, and how it exists by consensus. In biology, a strand of DNA that replicates differently is called a copy error, but all previous DNA strands were themselves errors: there’s no platonic perfect life-form being copied. Also, continuous values can only be approximated with numbers (meaning all clocks display the wrong time, all thermometers display the wrong temperature, pi = 3.14 is wrong, pi = its first trillion digits is still wrong, and so forth). Errors can be acceptably small for certain purposes that we consider them correct, but the boundary can still seem vague and arbitrary.

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