I have two sentences:
- We experiment on both cases.
- We experiment with both cases.
The different preposition will change the meaning. But it's difficult to find such nuances in a dictionary. What are the subtleties here, if there are any?
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The main nuance is that using "on" makes the cases the subjects of the experiment; they are the things upon which you are experimenting. Using "with" makes the cases instrumental; they are the things you are using to conduct the experiment. From a literal standpoint they pretty much mean the same thing, but there's a subtly different emphasis on the role the cases are playing in the experiment.
Consider the following:
We experimented on a number of different people.
This implies a less consensual situation where the people didn't really have much say in whether the experiment happened or not. They're subjects rather than being involved directly.
We experimented with a number of different people.
This gives a connotation of mutual interest in the experiment; the people were willing participants.
My context is medicine. A commonly used phrase in medical history is that "physicians have experimented ON their patients since their profession began". The art of medicine began with empirical testing of techniques and natural chemicals ON patients. There was no science involved. Successes were reported, failures buried. Empirical testing still occurs today. A physician may try a drug not accepted as "standard of care" because she has a hunch it will work. She is experimenting on her patient. An experiment that is scientific has to conform to scientific methodologies (valid sample size, controls etc.). One can perform an experiment WITH a patient by following protocols consistent with such methodologies (including consent).