"No accident is too severe to ignore" vs "No accident is too trivial to ignore"

Question

etymology - How does a word come to have two completely opposite meanings? - English Language & Usage Stack Exchange

specifically with the case of words taking on their opposite meanings, a possible influence is that speakers appear to be quite bad at processing negatives. For example, speakers are liable to process pairs such as , or "No accident is too severe to ignore" vs "No accident is too trivial to ignore" as effectively meaning the same thing, even though "severe" and "trivial" have pretty much opposite meanings (this is similar to the "much to be desired" example, but specifically having a negative in the sentence appears to enhance the effect)

From this answer,

1. "No accident is too trivial to ignore"" means

2. Every accident is serious enough to pay attention to it.

But what means

3. "No accident is too severe to ignore"?

4. Every accident is ???WHAT DO I WRITE HERE??? enough to pay attention to it.

This isn't math class, but pls can you show all work and steps? How 3 turn into 4?

Answer 1

Further to Conrado's answer:

We can take Conrado's version:

1. Every accident is serious enough to be noticed.

If it's desired to convert that into a sentence which begins "No accident", then the above can be transformed into such a sentence by contraposition. Showing my working:

Every accident is serious enough to be noticed.

If X is an accident, X is serious enough to be noticed.

If X is not serious enough to be noticed, X is not an accident.

If X is so trivial as to be ignorable, X is not an accident.

which can be recast into something closer to idiomatic English as:

No accident is so trivial as to be ignorable.

A pertinent point here is that the notion of "too trivial" does not arise.

But what if you wanted a sentence which expressed Elaine's meaning using the word "too"? Then that would have to be something like

Every accident is too severe to ignore.

Answer 2

Not only speakers, but listeners or readers, often seem to be a bit weak this way. The "mental stack" (http://www.secretgeek.net/pushpop) required for proper parsing of this sort of sentence is mechanically simple, but apparently unsuited to human reason.

The two example sentences posted in the original answer play (or should we say prey?) on this debility, to the extent that one is left wondering afterwards what exactly the speaker meant to say.

Just because the speaker processes this pair of sentences to mean the same thing does not mean that they actually express the same meaning.

Here are the same sentences expressed in negatives of the negatives in the originals except for serious and trivial (that makes positives, you know)!

1. Every accident is serious enough to be noticed.

---

3. Every accident is trivial enough to be noticed.

Said this way, it is obvious that they have opposite meanings.

Sentence (4) should say: "Every accident is too trivial to ignore."

Or perhaps:

"Every accident is trivial enough to pay attention to it."

Which is an unusual construction; one is accustomed to positive threshold levels of severity as a go/no go gauge in most situations (most, because as Araucaria pointed out in the comments, an accident could be seen as desirable)