"primary premises" is a correct and usable phrase in written English.
You can use it to describe the essential parts of an argument or the most important facts a speaker is trying to prove. For example, "The debater used primary premises from scientific research to support their argument."
It is not necessary that the primary premises of an a priori science should in fact be truths; for the purposes of the system they need only be taken as true, or postulated as such.
The primary premises must, of course, be consistent one with another, and they may be chosen, as in fact happened with Euclidean geometry, because they are thought to have evident application in the real world.
(1) Those that begin from true and primary premises, or are owed to such, are demonstrations.
What this classification leaves out is (6) the arguments that do start from true and primary premises but then fail to necessitate their conclusions; two of these, begging the question and non-cause are discussed in Prior Analytics (II, 16, 17).
That's all before the programme's primary premise: climbing the most forbidding (and hitherto unconquered) mountain Venezuela can offer.
An arche is something from which an argument proceeds it can be either a primary premise or an ultimate presupposition.
The primary premise of hate-crime law, Levin explained, is determined by a "difference" between the victim and the suspect – by the very lack of a relationship.
Christianity's primary premise is that the incarnation and sacrificial death of Jesus Christ formed the climax of a divine plan for humanity's salvation.
A primary premise of evolutionary theory is that individuals behave in ways that maximize individual reproductive success, relative to other individuals within a population.
It is not hyperbole to say that the sentiment expressed by Cooke is the overarching belief system of the US political and media class, the primary premise shaping political discourse.
As regards mathematics, for example, it might be said that mathematicians could be uncritical about the first principles of their science in the following ways: (1) They might take as self-evidently true or universally applicable some axiom or primary premise that turned out later not to possess this property.
