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I read

Ordinary language, as most of us are at least vaguely aware, serves various functions in our day-to-day lives. The twentieth-century philosopher Ludwig Wittgenstein thought the number of these functions to be virtually unlimited.

Then I looked in the wiktionary

1 Almost but not quite.

With our medicare supplemental insurance plan, there are virtually no claim forms to fill out. (Advertisement)
Synonym: as good as

2 Without exaggeration.

3 In essence, but not in fact.

Which definition do I choose and why? How do I choose the right definition in general?

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    In your native language there are some words with more than one meaning or more than one sense. How do you choose the right definition when speaking your native language? – James K Mar 21 at 16:13
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The use in the passage is either 1 or 3.
Consider also the definitions from Merriam-Webster dictionary:
1 : almost entirely : nearly 2 : for all practical purposes, e.g. virtually unknown
M-W: "virtually"
Those definitions are about the same.

Either the author or Wittgenstein, whichever added the word "virtually", is being fussy, saying that the number of functions for language is very very many, though possibly not infinite in a mathematical sense. The word adds almost no meaning to the passage, and it could be removed without changing the overall meaning.

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