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However, taking that as understood, let us ask how a word can have a meaning. Some words can be defined in terms of other words: "square" for example means "four-sided equilateral equiangular plañe figure." And most of the terms in that definition can also be defined. But definitions can't be the basis of meaning for all words, or we'd go fore ver in a circle. Eventually we must get to some words which have meaning directly.

[Thomas Nagel, What does it all mean, p.39]

I don;t know the meaning of "taking that as understood". Could you help me please?

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    It refers to whatever immediately precedes the passage: "if we stipulate that [WHAT WAS JUST SAID] is true". – StoneyB on hiatus Mar 18 '18 at 18:00
  • In a mathematical or philosophical context, it's more or less synonymous with "take as given", e.g. "To illustrate the transitive property of equality, take as given that a=b, and b=c. We can then conclude a=c." "Take as understood" means that the associated statement is similarly a given fact. – Andrew Mar 18 '18 at 21:40
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"taking that as understood" is a polite way of saying:

I'm not going to talk about that topic anymore. Whether you understand it or not, I'm moving on with what I want or need to talk about.

Often this does not have a negative connotation. An author needs to move on with his or her subject and must eventually assume the reader understands the material. In this case, the phrase acknowledges the fact that there is more that could be said about the earlier subject, but time or opportunity will not permit it or discussing it in detail will distract from the more important subject that will be discussed next.

Where you will see this phrase used in a negative context is in journalism, where the reporter is suggesting someone intentionally left an issue unclear to avoid responsibility (e.g., "the councilman took it as understood that his unsanctioned actions were acceptable.").

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