Re: "a premise which maintains that…" Can a premise maintain?
Solution 1:
Can a premise maintain? I'm not sure that a premise can maintain anything,
Yes, it most certainly can.
Consider
"The kettle boiled". Clearly kettles do not boil - but we all know that the meaning is "The water in the kettle boiled."
A premise [which maintains] is therefore an example of (probably) metonymy and perfectly valid, and means "The bloke who wrote the premise maintains..."
Solution 2:
Anthropomorphisms such as this are generally discouraged in academic works unless they are already in wide usage and do not cause confusion. "These results suggest ..." is generally accepted. "This premise maintains ..." who knows?
Solution 3:
Judging by usage (Google Books), using maintains after premise appears to be acceptable. It's not ambiguous or confusing and provides an alternative to the usual verbs like assert, say, affirm, hold, state, etc. While I probably wouldn't have thought to use maintains after premise, when I read it in these examples, it doesn't strike me as too unusual or out of place. (In one of the works below I came across "this premise claims", which could be the subject of another ELU question.)
...it was found advisable to set up a premise in the nature of a definition of vocational education at the junior college level. This premise maintains that the expression vocational education refers to ... California Journal of Secondary Education, vol. 16 (1941)
The argument's first premise maintains that it is possible for an act to harm a person while they are alive even if the act has no effect on that person's conscious experience. The argument's second premise maintains that if it is possible for an act to harm a person while they are alive even if the act has no effect on that person's conscious experiences, then frustrating a person's desires is at least one way to harm a person. ... The argument's third premise maintains that if frustrating a person's desires is at least one to harm a person, then it is possible for an act to harm a person even if the act takes place after the person is dead. David Boonin; Dead Wrong: The Ethics of Posthumous Harm
The minor premise maintains that P does occur. W. Clark et al.; Principles of Comparative Politics
This premise maintains two things. Emanuel Rutten; A Critical Assessment of Contemporary Cosmological Arguments
... but the strong version of the premise maintains that the net flow of environmental goods (e.g. food) and bads (e.g. pollution) across either... D. Mollica and T. Campbell; Sustainability
The second premise maintains that if a proposition is epistemically justified a priori, then its justification depends on intuition. Steven Hales; Relativism and the Foundations of Philosophy
But then, if moral reasons are non-instrumental, as Joyce's first premise maintains, it is at best doubtful that moral reasons are authoritative, as Joyce's second premise maintains. R. Joyce and S. Kirchen; A World Without Values
The first premise of the argument maintains that commonsense mental states like beliefs and desires can be viewed as... The second premise maintains that ... D. Murphy and M. Bishop; Stich and His Critics
Folk psychology, the First Premise maintains, underlies our everyday discourse about mental states and processes, and terms like "belief" and "desire" can be viewed as theoretical terms in this folk theory. Stephen Stich; Deconstructing the Mind
Blumer's third premise maintains that all meanings for individuals and groups "occur through a process of interpretation." Doreen Anderson-Facile; Dueling Identities: The Christian Biker
This premise maintains that the private decision to authorize military force does impose risk ... William Feldman; Privatizing War: A Moral Theory