“Bestimmungsgrund” is a Kantian term.
http://shortify.com/10252

The standard translation is ” ground of determination”.

http://shortify.com/10254
http://www.bu.edu/wcp/Papers/Mode/ModeFilh.htm


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Note added at 9 hrs (2010-05-05 22:57:50 GMT)
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In response to Helen's query as to why I chose this particular translation-- here is a quote from my 3rd reference:

"The strongest argument is based on the very nature of free-will in the "Metaphysic of Morals." There is a definition of free-will (freie Willkür) and its freedom. The faculty of desire (Begehrungsvermögen) is defined as "the faculty of being, through its representations, the cause of the objects of these representations." (9) On the other hand, "the faculty of desiring according to concepts, to the extent that its (of this faculty) ground of determination (Bestimmungsgrund) lies in itself rather than in the object is called the faculty of doing or omitting to do arbitrarily (nach Belieben zu tun oder zu lassen). To the extent that this faculty is joined to the consciousness of its capacity of action towards the production of its object, it is called will (Willkür)." (10)

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Note added at 9 hrs (2010-05-05 23:08:58 GMT)
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"Determining ground" or "det. principle" are alternative options;
http://shortify.com/10255.
Whichever term you may choose in the end - it is crucial to identify the term (and thought process described in your paragraph) as "Kantian" and to then look for an established translation in scholarly works.

Did you try to find it? It is a scholarly term.
It is included in the title of one of Kant's sub-sections of Kritik der Urteilskraft, which makes it very easy to find.
I don't have an English translation available, so I had to use Project Gutenberg. That means that the translation may very well be dated or unusual, but it also comes up in current secondary literature (google).
Theoretically, the translation could also be specific to Kant, but that doesn't seem very likely.
Because the translation is so old and I don't have any way to check for alternatives, I only gave it a "middle". But it has a chance of being correct in contrast to (admittedly much more attractive) translations 'from the hip'.


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Note added at 20 Stunden (2010-05-06 10:01:18 GMT)
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Please ignore my answer; I did the same to the above answers. I am not a philosopher and my philosophical dictionary is too small to help with this kind of question. I don't know what the current standard term is, but you need to find it, because it is a technical term. And I confused the source title in my text above: It is the "Critique of Pure Reason". Doesn't anyone have a recognized and up-to-date translation on their shelf?