5

I would like to express that somebody gives a reason to believe a claim. Something among the lines

  1. They fortify their claim by ...
  2. They back their claim up by ...
  3. They support their claim by ...

In German, I would say

Sie untermauern ihre Behauptung mit ...

How can I say this in English?

5

All of your choices work well in academic and technical settings. Support is by far the most applicable term and, as noted in a comment below, is preferred. If you want to take advantage of subtle differences in the meanings of these terms:

  • They support their claim by ...

    Support for a claim covers it all—the basis for a claim, the reasoning behind its conclusions, and evidence of its validity.

  • They back their claim by ...

    [No need to say "back their claim up by ...," as in your example, or "back up their claim by ...."]

    To back a claim is to provide reasoning and supporting evidence intended to withstand broad counterargument.

    The term bolster, as noted in another answer, is an excellent alternative to back.

    The term substantiate, a translation of your German word untermauern, is itself a common alternative to back when presenting supporting evidence.

  • They fortify their reasoning by ...

    To fortify a line of reasoning is to protect it against a specific anticipated counterargument.

    The term reinforce is preferred over fortify.

The distinctions made here are minor in most contexts.

  • 1
    +1. I believe the first is more common though. – onlyforthis Jan 12 '16 at 20:02
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    I disagree that "back up their claim" isn't acceptable (unless you were just objecting to the word order of "back their claim up"?): it's actually more common than just "back" – stangdon Jan 12 '16 at 20:43
  • Agreed and revised but not encouraged. – lauir Jan 12 '16 at 20:56
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    (Native AmE) I've never heard "fortify a claim" except in the sense of a legal claim. (I did just google and find an occurrence of it outside of law, though.) – Ben Kovitz Jan 12 '16 at 21:56
  • Noted well and revised to "fortify their reasoning." – lauir Jan 12 '16 at 22:25
2

Another word you might consider is bolster. It's a verb meaning "to strengthen or support."

This verb is often paired up with the noun claim, as in these news articles:

A number of studies published in reputable journals and backed by the beverage industry have sought to bolster the claim that artificially sweetened beverages can prevent a person from packing on extra pounds. (Newsweek)

He also claimed that notebooks were doctored to bolster the claim that Brown wrote the script. (Variety)

To bolster the claim that the "loss" wasn't that bad, The Times points out that Google sold Motorola Home for $2.4 billion and is keeping most of Motorola's patents. (Mashable)

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