The application of singular propositions in burhān (apodictic proof) and intellectual sciences

Several conditions are mentioned for the elements of burhān (apodictic proof). Being universal is one of them. On the other hand, at least some of the elements lack this condition in case of singular propositions. Therefore, it seems that the logicians have suffered some kind of contradiction. The question is, can this contradiction be resolved? If possible, how is it possible? To answer this question, initially the singular propositions and their referents are defined and finally, the conclusion is reached that the difference between the elements and the premises of burhān must be taken into consideration. The elements are the foundations and used in a broader sense than the premises. Therefore, the elements include the premises of burhān as well as those propositions that the arguments ultimately lead to. Different names used for the elements of proposition by the logicians is an evidence to this claim that the elements are those propositions that are the result of proofs, and not necessarily the propositions that are used in the premises of burhān. Another evidence of this claim is that the vicious circle, the infinite regress and the law of non-contradiction are also, sometimes, considered as the elements of burhān, alongside the axioms.