There is no mathematical need for the devious interpretation: this theory proves the existence of n-Mahlo cardinals and supports all mathematical constructions at that level of consistency strength in its own terms without any need to refer to the theory of well-founded extensional relations.
In doing so, we argue on pragmatic grounds against mathematical literalism as an appropriate constraint to mathematical constructions: such literalism would allow mathematics to constrain biology when the biology ought to be constraining mathematics.
The mathematical constructions that are readily accessible to this author are simply carried over from ZF or ZFC; the well-founded sets are considered within the world of positive set theory, and we find that they have exactly the properties we expect them to have from the usual viewpoint.
Historians of science observe that the astronomy of the earliest civilizations, although astonishing and incorporating mathematical constructions far in excess of any practical value, proved to be misdirected and of little importance to the development of science because they failed to inquire more carefully into the mechanisms that drove the heavenly bodies across the sky.
The efficiency in conceptualizing whole numbers as iterations of a single iterable unit is thought to allow many of these more advanced mathematical constructions students make after construction of an ENS.
The device of associating mechanical properties with the fields, which up to this point had appeared merely as convenient mathematical constructions, has even greater implications when conservation of energy is considered.
The idea of energy as a real constituent of matter has, however, become too deeply rooted to be abandoned lightly, and most physicists find it useful to continue treating electric and magnetic fields as more than mathematical constructions.
But then no contact at all is made with the concepts that figure in meaning explanations, which have to do with our cognitive capacities, such as those of effecting mathematical constructions or those of understanding, learning, and using a language.
"But they are not purely mathematical constructions, either".
All mathematical constructions which can be carried out in TST can be carried out in NF.
