For the third blank H and I are out for the logic above. ....................how ?

Till the first clause, we understand the argument that Hopkin’s extensive anthropological fieldwork led to a unified theory may seem plausible, but there is something wrong (specious).

Then a close examination is done - it should be to justify why this argument is wrong. (we dont have context indicating a shift)
2 factors are cited as reasons for this:
1. "hodgepodge of observations" - a mere collection of observations - this one is subtle and may not be a factor from a certain perspective. It gave me an indication that the observations were merely gathered, and in a way lacked some kind of logical coherence.
2. Nature of these observations - a mere mixture of observations is fine, but many a times they even seemed to contradict each other (or something -ve)

For blank (2) I got confused with the option "a coherent system of observations" - which could have been continued with "at times, even inimical to each other" => but later refuted this, as it made no sense. How can a coherent system been contradicting ? This could have been possible had there been some kind of shift or word meaning dubious, specious etc.

Sir Carcass,

If the contentious is specious, how could it lead to a unified theory? Please help.

Regards

sometime is better to rearrange the sentence.

he made an extensive work in a specific field of studies.

Now, this work , in its argumentation os reasons, is specious or well-reasoned.

therefore, all this massive job led to a unified theory

Hope this helps