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
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
"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.
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 of → which is
While 'that' has many meanings, the meaning here is defined by Merriam-Webster.com as:
that, pronoun
...
1c : the kind or thing specified as follows * the purest water is that produced by distillation
...
Using this definition, 'that' implies there is more than one kind or thing, and the phrase following 'that' will specify which kind or thing is being referred to. Recall the original sentence:
It is also extraordinarily difficult to meet the third criterion for causal studies, that of controlling for all other potential causal influences.
In the original sentence, 'that' is a pronoun in apposition with the preceding noun phrase 'the third criterion ...' This definition of 'that' implies that there is more than one criterion. The following phrase 'of controlling for...' specifies which criterion is being referred to.
A paraphrase could be:
It is also extraordinarily difficult to meet the third criterion for causal studies, which is the criterion of controlling for all other potential causal influences.
In this case, I believe that "that of" is the equivalent of "viz." [Latin videlicet] or "i.e."
