Which are the major truths of paradigms on which the whole body of chemistry is built? For example, as evolutionary theory is fo biology or the existence of numbers for math, the existence of an independent reality for physics, etc.
Well the most important driving force I see in chemistry is for atoms and molecules to be most stable when the atoms have a noble gas electronic configeration. Many reactions will occur to try to reduce the energy of the atoms and molecules by gaining / losing or rearranging electrons to bring as many atoms as close as possible to a noble gas configeration.

Another important driving force is to reduce or avoid the mechanical strain in a molecule (Steric effects)

There are effects in pi systems such as aromaticness (4n + 2 pi electrons in rings)

There are entropy effects, by increasing the entropy of a system then an endothermic reaction can be made to occur. For example the dissolution of ammonium nitrate in water occurs with ease but this is an endothermic process.