Significance of Proofs within Materialism and within Solipsism :
Mutual Interdependence of Materialism and of Solipsism
Such systems (materialism and solipsism) are so interrelated through aequivalencies in structures of the proofs generated within them, that the aequivalent structures of the proofs are such as to necessitate an aequivalency-relation between materialism and solipsism, such that proofs within materialism can hold true only if solipsism be praesumed, and vice versa.
Fundamentally, the aequivalencies are due to the two systems both belonging, in formal logic, to the same category of relationship to their corresponding enveloping meta-systems. The meta-levels of the meta-systems involved are necessarily more intricately than is usual in quantitative mathematics, and are capable of demonstating by their structure systematic shortcomings in quantitative mathematics -- such as of transfinite numbers, where the meaningfulness of numbers substantially exceeding the number of quanta (as known in quantum physics) in the universe can be established only through postulations in the meta-levels of the meta-system (though this objection can be easily evaded by postulating infinitely decreasing-and-increasing number of quanta projecting into an infinite past and and infinite future, respectively).
The most renowned deduction within materialism is the well-known proof of absence (or lack) of purposivity and (when the definition of "meaning" is considered as dependent on the definition of "purpose") of meaningfulness (that is, the absence of these within the scope of mere materiality). Without a purpose of construing (which is necessary to entail any system of logic) there can be no system (such as, a cohaerent "materialism"), and without meaning there can be no way of making sense of any of the words (or phrases, or clauses, or sentences) used in describing materialism or any of its congeners.
A more decisive way of depicting this situation is to assert that the entire logical apparatus for describing (and imparting meaning to the vocabulary of) materialism must lie outside the material universe. This situation is typical of (and, indeed, can be shewn to be logically restricted to) entirely hypothetical systems, which are mentally produced by being hypothecated from the substances of imaginal worlds.
But the whence, wherefore, and how of the existence of such imaginal worlds is highly relevant to the quaestions of solipsism. A pressing quaestion in solipsism is that of the source of contents of consciousness -- and, in particular, of purposivity (and of meanings definatory of the aspects of "purpose"). The strictest solipsism (which will not allow anything outside the self) must exclude existence of a material universe; while the looser form of solipsism (which will allow for a material universe outside the self) is nevertheless still tightly constrained by the proofs within materialism (of derivability from the material universe of neither purposivity nor meaningfulness).
So, much as the disproofs of purpose and of meaning within the material universe can be shewn logically to establish the existence of universes outside the material universe; analogously, solipsism's inability to find purpose and meaning within the isolated self can be demonstrated logically to establish the existence of selves outside one's own self.
Universality in application of the "laws" of logic and of physics is a strong indication of natural egalitarianism; and non-conflict among laws of logic (also, non-conflict among laws of physics) is a strong indication that socio-oikonomic systems based on conflict (such as capitalism, based on useless ploutokrats shamelessly extracting excessive profits from a subjugated working-class, with all manner of attendant social miseries) are entirely unnatural, essentially incompatible with logic, reason, and common decency.
Among the meta-constructs of universal applicability of the "laws" of logic and of physics is the actuality of beings and entities to whom such shared laws apply in egalitarian fashion being illusorily separate multiples of the same essence, such that on the meta-level of their own consciousness they can display their awareness of such shared essence by establishing a socio-oikonomic system of communism -- which system must, of course, be in practice guided by communication-networks of being-entities abiding on other meta-levels (the subtler planes-of-existence, commonly known as "heavens") of the universal consciousness, filtred through an adequate network of mortals receiving such guidance in their dreams, visions, intuitions, etc. Such divinely-guided mortals are conspicuous by combination of their generosity, their willingness for undergoing privations, their natural spiritual gifts with their proclivity for studies (including in history of religions) along the lines of theistic metaphysics, both traditional and innovative.
Incidentally, use of materialism's disproof of existence of purposivity and of meaningfulness to establish logically the existence of other universes (which we correlate with the meta-levels of formal logic), could be suggested [as was suggested in the authoring of this] by the fact that synaisthesia, which is usually used as a proof of materialism (on the basis that what is most visualized synaisthetically is something in the material world being then perceived), can even more decisively be used as a proof of immaterial parapsychology (on the basis that synaithetes themselves not only commonly undergo experiences in synchronicity, seeing auras, etc., but also highly esteem such experiences). Indeed, the very fact that synaisthesia is so often associated with meaningful symbolic forms (such as letters of the alphabet) would suggest (given materialism's own disproof of the existence of meaningfulness in the material universe) that the major factor in synaisthesia is something apart from, and countreposed to, the material universe.
[written Aug 18, 2014]