The term Conmathematics [ invented by Kedar Joshi (b.1979), Cambridge (England), i.e. myself ] means Conceptual Mathematics. It is a meta - mathematical system that defines structure of Superultramodern Mathematical Science. (Conmathematics means that modern/ultramodern mathematics is not as conceptual as it should be.)
It has four main components.
1. Conmathematical Definition of Mathematics :
a) Conmathematical definition of pure mathematics - Pure mathematics is a system of 100% precise propositions believed to be 99.999...% certain ( 0.00...1 % margin in belief being for sake of universal doubt : principle that 'anything may be possible.'). Precise means every term of a proposition is absolutely clarified, and every non - axiomatic proposition is supported on basis of axiomatic one/s leaving no doubt, except universal doubt. It is very possible that some of mathematical propositions are not clear ( or understandable ) to some persons. And, some of propositions are less than 99.999...% certain to some persons. This possibility effectively gives rise to possibility of multiple mathematical systems according to nature of individuals concerned, though truth is believed to be existing independent of individual minds. The principle of universal doubt makes it necessary to review mathematical systems continuously so that in future they may not be seen to be mathematical at all.
b) Conmathematical definition of applied mathematics - Applied mathematics is a system of propositions constructed by applying some or all of pure mathematical propositions to deal with ( i.e. to explain and / or predict ) phenomena that are believed to be less certain than phenomena expressed by pure mathematical propositions. For example, I cannot believe law of gravity ( law that every matter, in principle, attracts every matter out of some force or curvature of space - time ) to be 99.999...% certain, as I can imagine a universe where law of gravity is invalid ( i.e. where every matter distracts every matter out of some force or absence of space - time curvature ).
2. Philosophy as Mathematics :
According to conmathematical definition of mathematics, core ideas in ultramodern science / philosophy, though appearing to be philosophical, are, in fact, mathematical. For example, axiomatic component of NSTP ( Non - Spatial Thinking Process ) theory is pure mathematical, while its hypothetical component is applied mathematical.
3. Conceptual Reconstruction of Pure Mathematics :