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Please help me to understand the meaning of following paragraph; I'm having particular trouble with the part that reads "that of":

It is also extraordinarily difficult to meet the third criterion for causal studies, that of controlling for all other potential causal influences.

Please paraphrase it, many thanks

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3 Answers

The that here is not subordinating, but adjectival.

the third criterion for causal studies, that of controlling

is the same as

the third criterion for causal studies, that [criterion] of controlling

or

the third criterion for causal studies, [the criterion] of controlling

or

the third criterion for causal studies, [i.e. the criterion] of controlling

So, what the sentence says, is

  1. It is very difficult to meet the third criterion.
  2. The third criterion is "controlling for all other potential influences".
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2  
I like the way it's said in your fourth wording: It is also extraordinarily difficult to meet the third criterion for causal studies, that is, the criterion of controlling for all other potential causal influences. It's specifying which of the criteria is being referred to as the "third" one, sparing the reader the trouble of going back to an earlier paragraph where that information has been presumably specified. –  J.R. Jan 7 at 13:33
    
" that is" what I thought –  learner Jan 7 at 18:24
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"That of" is mostly used to compare two things (that is used as a pronoun).

Example:

The population of New York is greater than the population of San Diego.

Can be transformed to:

The population of New York is greater than that of San Diego.

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That's true, but that's not really the case in the O.P.'s sentence, I don't think. –  J.R. Jan 7 at 13:30
    
J.R.: I disagree. I think it is exactly the case in the OP's sentence, and I think Bala's "pronoun" is more accurate than Reg's "adjectival". –  Colin Fine Jan 7 at 16:35
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It is also extraordinarily difficult to meet the third criterion for causal studies, that of controlling for all other potential causal influences.

maps to

It is also extraordinarily difficult to meet the third criterion for causal studies, (which is) controlling for all other potential causal influences.

so

that ofwhich is

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