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"You could say they're whingeing or you could say what you like but the bottom line is they were playing under an English referee and under English interpretations," he said.
In this case, then, differences in the ways the model-theoretic and ordinary English interpretations of Ω x) handle the quantifiers provide a perfectly natural explanation of what's going on in Skolem's Paradox.
First, in order to get a better feel for how the differences between the model-theoretic and the ordinary English interpretations of Ω x) actually give rise to Skolem's Paradox, it's worth tracking these differences through a slightly more refined version of the paradox.
First, it ensures that the model-theoretic and the ordinary English interpretations of Ω x) agree on the interpretation of "∈": for m1, m2 ∈ M, M ⊨ m1 ∈ m2 if and only if m1 really is a member of m2.[21] In this case, therefore, the explanation of Skolem's Paradox has to involve the interpretation of the quantifiers.
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One is an English interpretation by David Greenspan and features six Western actors.
This description highlights two immediate differences between the model-theoretic interpretation and the ordinary English interpretation.
The answer is that there is a dangerous ambiguity in the English interpretation of A→□◊A.
On its ordinary English interpretation, this sentence says that R contains all the real numbers.
On the ordinary English interpretation of Ω(mˆ), the quantifiers "see" these bijections, and so Ω(mˆ) comes out false.
On the one hand, we could start with the formula Ω x), and give this formula what we might call its "ordinary English" interpretation.
Arguably we do not trust speakers who utter very long sentences to have uttered truths, under the ordinary English interpretation of their sentences.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com