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I have a quote by Marquise de Laplace:

It is remarkable that a science (Probability) which began with consideration of games of chance, should have become the most important object of human knowledge.

Why is should used in this quote? To me it reads as a mis-translation. Why is it not for example: ...became... or ...has become... in place of ...should have become.... Is the meaning same? Is it some archaic way of saying the same thing?

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    It's ok. it's + adjective + that ............>>> subjunctive. It's highly ironical that he should have said that.
    – Centaurus
    Apr 22, 2020 at 16:07
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    It's relatively common in formal written English.
    – Centaurus
    Apr 22, 2020 at 16:09
  • This would have been a translation from the French, n’est-ce pas? Sometimes the structure of French forces the translator to choose between an awkward-sounding English expression that closely follows the original, or a more idiomatic expression that may not accurately convey the tone of the original writer. Apr 26, 2020 at 17:44

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Both of your alternatives (became and has become) would also work and they wouldn't really change the meaning of the sentence.

Should has many uses as an auxiliary. This is not one of the most common, but it's not exactly rare:

used for describing a fact or event that someone has a particular feeling or opinion about

It’s hardly surprising that people should be suspicious of politicians’ promises.
How sad that she should have no one to comfort her.
Claudia was shocked that anyone should believe such a scandalous story.
It’s odd you should mention Ben – I was just thinking about him.

https://www.macmillandictionary.com/us/dictionary/american/should

It's interesting that that definition is in Macmillan's "American English" section. The Cambridge Dictionary marks this use as "mainly UK":

mainly UK

used after "that" and adjectives or nouns that show an opinion or feeling:

It's odd that she should think I would want to see her again.
It's so unfair that she should have died so young.

https://dictionary.cambridge.org/us/dictionary/english/should

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