If "keen" refers to sharpness or intensity:
* Keenness: This is the most direct and common abstract noun for "keen" in this context.
* Acuity: This implies a sharpness of perception or intellect.
* Intensity: This emphasizes the strength or force of something.
If "keen" refers to enthusiasm or eagerness:
* Eagerness: This emphasizes a strong desire or anticipation.
* Zeal: This implies a strong passion or fervor.
* Enthusiasm: This refers to a feeling of excitement and interest.
If "keen" refers to a sharp edge or point:
* Sharpness: This refers to the quality of being pointed or having a cutting edge.
The best abstract noun to use will depend on the specific meaning of "keen" in the context.