I don't know what to say to this. They are exactly the same. It's not a controversial point. You could write an article on the theme "why apples fall upward in the winter", but that wouldn't make apples fall upward in the winter.
Perhaps you two are not using precise enough language?
The common definitions for 'all' and 'any' as used in math are certainly on thaumasiotes' side. But English as a natural, every-day language is a bit more fuzzy.
Correct. That is the point this article is making.
"all in the array are true" is not specific about how the empty case ought to be interpreted. That's not at all to say all([]) ought to be False; the wording is simply under-specified.
Where as "there is none in the array that is false" is clearly True when all([]) is encountered.
Thus the statement cannot be simplified to the English statement "all in the array are true", without introducing ambiguities.
As a general rule, this is why we don't perform mathematics (or programming) in English.
EDIT: Just to clarify why this is ambiguous, in case anyone reading is still not following (although I'd suggest reading the article!)
English is an (informally) consensus based language. Understanding boolean logic is not a precursor to being able to interpret common language, in particular English. Just because one has knowledge of logic (mathematics) and we happen to have given some operation the English name "all", that does not mean the English word "all" in general speech refers to this logical operation. Especially since, as the article describes, the mathematical consensus for this logic has only largely shifted to be interpreted this way in the last several hundred years. The English word "all" predates the current mathematical consensus (which isn't even universal) by thousands of years.
Additionally, if for some reason you are interpreting the written word "all" (no matter the context) as the logical operation, then "all in the array are true" is not a viable definition for this word, it's self-referential and thus ambiguous. "there is none in the array that is false" on the other hand is clear in its meaning (if not slightly grammatically incorrect).
> The English word "all" predates the current mathematical consensus (which isn't even universal) by thousands of years.
This is at the edge of possibility, but it's certainly not a slam dunk. "All" is not an indo-european word; it's restricted to Germanic languages.
> Just because one has knowledge of logic (mathematics) and we happen to have given some operation the English name "all", that does not mean the English word "all" in general speech refers to this logical operation.
This isn't a good argument; all you and the article are saying is that people have vocally objected to the meaning of "all" for a long time. They still do. But this isn't sufficient to claim that the objections reflect a disagreement over the meaning of "all". If you carefully explain to people how you want them to interpret sentences like "every cat is in a box", and then you show them pictures and ask them whether or not every cat is in a box, most people will screw it up. That's not because they didn't understand you; it's because they are very bad at the task.
It is quite clear that the vernacular meaning of the English word "all" coincides with the formal meaning of the logical universal quantifier. You can poll any number of people and they'll give you a definition that just so happens to match the logical quantifier. People don't object to all([]) being true after thinking about what "all" means to them -- they object before thinking about it.
If you poll people asking for a definition of "all", you're doing it wrong. Instead, you should ask them to use the word to describe various cases, and derive the actual definition from that.
Mostly agreed about the vernacular. Though a minor nitpick: mathematics has been around for longer than English.
As for eg Python: when in doubt, going with the mathematical usage of the term is the Right Choice here.
For another interesting example: the negation of must and may in English vs their German equivalents.
In English 'You must not do X.' means that refraining from X is obligatory. In German the equivalent 'Du musst nicht X-en.' means that engaging in X is not obligatory.
Both usages make sense in their respective languages. And both usages have translations into formal logic. Just different ones.
