counter-implication
This shift includes a conscious rejection of forms of legal reasoning that, with the absorption of Greek logic in law, were deemed questionable, such as the counter-implication (mafhum al-mukhalafa), and reflects the rising power of the 'ulama' in Islamic society.
http://www.princeton.edu/~pisc/archives.htm
'mafhum al-mukhalafa' (an interpretation which diverges from the obvious meaning of a given text).
http://www.ummah.com/forum/showthread.php?406011-The-Fundame...

Isn't it just contrasting درجة هذا الرضا with درجة السخط الشعبي ?

This legal term is sometimes called "Divergent meaning" or the Latin "argumentum a contrario"

IMO

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I would say,
as conversely implied

This concept originally belongs to the science of uṣūl (principles of Islamic jurisprudence).

Scholarly suggestions include:
"Negatively Implied Meaning" (by Prof. Jonathon Brown)
http://books.google.com/books?id=HTD4AwAAQBAJ&pg=PA38&dq=maf...

"expressio unius est exclusio alterius" (by Prof. Ahmad Atef)
http://books.google.com/books?id=O31DAQAAIAAJ&q=mafhum al-mu...

and, contrariwise, identify the degree of …
and, on the other hand, identify the degree of …

As long as it's never been too late to post an answer, I decide to participate in this dialogue after its start with 955 days.

I was looking for translation of this term on the web and got this page among the results. However, I could not find a decisive answer.

So, I searched again, and got the answer below. I would like to share my findings with you. It may be helpful for some one in the future.

Argumentum a contrario n.

“Argument from the contrary.”An argument for different treatment made by negative reasoning from another argument. An argumentum a contrario ...
http://www.oxfordreference.com/view/10.1093/acref/9780195369...


In logic, an argumentum a contrario (Latin: 'argument from the contrary'), also known as appeal from the contrary, denotes any proposition that is argued to be correct because it is not disproven by a certain case. It is the opposite of the analogy. Arguments a contrario are often used in the legal system as a way to solve problems not currently covered by a certain system of laws. Although it might be used as a logical fallacy, arguments a contrario are not by definition fallacies.
https://en.wikipedia.org/wiki/Argumentum_a_contrario

HTH
Regards,
Saleh