Not all science is created equal. Every scientific discipline has core ideas, but not every one ranks them unambiguously. This distinction is crucial for two reasons.
The first is that not all claims are equally reliable. One might argue about the results of a survey or the meaning of an experiment, but few are likely to argue about 2+2=4. So ranking one's principles is a clear way of communicating the strength of confidence one has in them, in the statistical sense of Bayesian priors.
The other reason for ranking principles is that claims sometimes collide. In neuroscience, for example, some models claim their stability as an advantage, while others advertise their sensitivity...but stability and sensitivity are functionally opposite. Likewise, some models value generality and some specificity, which come at the expense of one another. A field without ranked principles could never decide between such competing claims. At the other extreme, math is entirely self-consistent (with the well-known singular exception of Goedel's paradox), as are certain mathematical physics disciplines, like thermodynamics. In general disciplines like physics which most rely on mathematics are the most principled, and those which rely on experiment (like psychology) the least.
Principles provide a huge advantage in conflict resolution. If principles are arranged hierarchically, with undisputed math at the top, accepted experiment in the middle, and hearsay at the bottom, disagreements can be identified separately by likelihood ("Is this conflict real?") and severity ("How much theory does this conflict undermine?"). For a theory to inspire confidence, it should not be shaken whenever someone disputes part of it. By this standard, a theory like this one which claims to principled should not contain contradictions, and should be revised if they are found.