Does the phrase "brief developing history of psychology" exist?
Does the phrase "brief developing history of psychology" exist? Or could it be "brief history of the development of psychology"

Question

Answer

It depends on how you use the adjective "brief."

In the first sentence, "brief" modifies  "developing history..."  That means a snapshot in time of an ongoing process--history.

In the second sentence, "brief" modifies "history of..." Which means a summary of.

Grammatically, the first sentence does not make sense since you do not know the duration of an ongoing action/process, therefore you cannot call it brief.

For more technical  information, search "Using Gerunds & Infinitives."
http://www.englishteachermelanie.com/grammar-gerunds-and-infinitives-for-purpose/

Answer

"brief developing history of psychology" works but not the best. 
"brief history of the development of psychology" sounds a lot better than the first one.

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