Standard archaeological techniques make it possible to determine the age of anything containing vegetable matter, but only if the object is free of minerals containing carbon.
Conclusion (therefore)
It is not possible to determine the age of prehistoric paintings on limestone using standard archaeological techniques.
Evidence
Prehistoric paintings on limestone were painted with vegetable matter.
Standard techniques for determining the age of vegetable matter require that it is free of minerals containing carbon.
It is impossible to collect samples or prehistoric paint without removing limestone (which has carbon) with the paint.
Evaluate
Since the Anti-Conclusion is that , we need to think of a way around this roadblock.
We have to collect samples in order to analyze them for age, and any sample we collect will also contain limestone, which is a mineral containing carbon.
Standard techniques require that an object is free of minerals containing carbon.
Is there any way for this to work?
Maybe every sample will contain some limestone, but not spread the entire sample? In other words, maybe every 4 oz sample of paint will have 1 oz of limestone, but perhaps it's all located on one side of the sample and we can grab a "clean" oz or two of pure paint from the other side.
Maybe we can separate out the limestone from the paint? Is there a centrifuge that could send the limestone to one end and the vegetable matter to the other?
Goal
Look for an answer that helps us argue, .