The natural numbers are mental constructions, the real numbers are mental constructions, proofs and theorems are mental constructions, mathematical meaning is a mental construction… Mathematical constructions are produced by the ideal mathematician, i.e., abstraction is made from contingent, physical limitations of the real life mathematician.
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.
Any topos may be conceived as possible "universe of discourse" in which mathematical assertions may be interpreted and mathematical constructions may be performed.
But if a certain mathematical construction can be constructed out of another one, this is a purely mathematical fact, and as such independent of logic.
All mathematical constructions which can be carried out in TST can be carried out in NF.
From a devious, melting cube straight out of Hellraiser, to alien planet-worthy landscapes, and even a Middle-Earth-inspired techno-sojourn, it's a look inside mathematical constructions as divisible as they are mutable, mobile, and magical.
"But they are not purely mathematical constructions, either".
Some new methods are motivated by mathematical constructions such as tree metrics, while the rest employ tree concepts which work well in practice.
The orderliness, the elegant patterns, the neat categories and the mathematical expressions are constructions of scientists.
Evaluating several dispersal functions was necessary because these mathematical constructions behave differently across dispersal distances.
In particular, it would seem that if we construct the mathematical objects, for example, if the mathematical objects are mental constructions of some kind, then resorting to impredicative definitions would produce an undesirable form of circularity.
