Subject: If particles could be split up infinitely...

I've noticed that in physics, the existence of a fundamental level of particles 
is often assumed a priori, for simplicity and to avoid the paradox of an 
infinite regress of ever-smaller particles. Does this really remove the paradox 
in any way: why is this fundamental level non-divisible? 
   
If it were assumed that there is no fundamental level, or at least that we are 
a long way away from it at present, some interesting possibilities could arise. 
Say that an electron turned out to have an "internal structure" as complex as 
that of a cell appears to us now. 

Currently, the movement of electrons seems strange and unpredictable, and can 
only really be explained in terms of the probability of one thing or another 
happening. But if a culture of cells was examined under a microscope at a 
resolution where no internal structure could be seen, a similar situation would 
arise. You could make predictions about the probabilities of certain things 
happening, of the chance of a cell dividing in a given time interval, say. But 
with no idea of what the cells were composed of, predicting the behaviour of 
one specific cell would be an impossible task. 

Is it possible that nothing can be fully explained in terms of the scale level 
at which it appears, but only in terms of what it is made up of? 

Re: If particles could be split up infinitely...