Antinomies underlying naive set-theoretical considerations in everyday language:

If I write to you: ‘do not obey statements in text’, I have demonstrated a propositional aspect of language that, while here, relatively obvious, is elsewhere as common as it is invisible. We have problems with language and conception that remain from the history of its evolution, and where it stopped evolving and began becoming pathogenic…

This is a fundamentally paradoxical problem… that leads to an entirely reasonable, but unlikely resolution.

One resolution is asserting that that statements and frameworks shall not dominate the minds that employ and interpret them.

More simply, an axiom: Statements and frameworks are the produce of minds, rather than the implicit origins of facts. They must not supervene over their origins in cognition, therefrom ‘making declarations’. This idea is, itself, a flavor of antimony.

The statement, then, that ‘No statement shall, by self reference or other means, be interpreted to have precedence to the minds in which statements arise, are structured, and by which are interpreted.’ is an axiomatic rejection of the antinomies otherwise emergent from common relationships not merely in logic… but in everyday language, thought and media.

There’s a problem with making direct statements in general: the are fundamentally psygenic, which is to say… generative of mind-like states or behavior. And what I have just said is self-violating, as I am making statements here. Yet, if we are aware of this, we may contend with it intelligently…

Particularly when we conceive of norms. The most normal person is abnormal… because the extreme case of normality renders them unique…

“In point of fact, Bertrand Russell constructed a contradiction within the framework of elementary logic itself that is precisely analogous to the contradiction first developed in the Cantorian theory of infinite classes. Russell’s antimony can be stated as follows. Classes seem to be of two kinds: those which do not contain themselves as members, and those which do. A class will be called “normal” if, and only if, it does not contain itself as a member; otherwise it will be called “non-normal”. An example of a normal class is the class of mathematicians, for patently the class itself is not a mathematician and is therefore not a member of itself. An example of a non-normal class is the class of all thinkable things; for the class of all thinkable things is itself thinkable and is therefore a member of itself. Let ‘N’ by definition stand for the class of all normal classes. We ask whether N itself is a normal class. If N is normal, it is a member of itself (for by definition N contains all normal classes); but, in that case, N is non-normal, because by definition a class that contains itself as a member is non-normal. On the other hand, if N is non-normal, it is a member of itself (by definition of non-normal); but, in that case, Nis normal, because by definition the members of N are normal classes. In short, N is normal if, and only if, Nis non-normal. It follows that the statement ‘N is normal’ is both true and false. This fatal contradiction results from an uncritical use of the apparently pellucid notion of class. Other paradoxes were found later, each of them constructed by means of familiar and seemingly cogent modes of reasoning. Mathematicians came to realize that in developing consistent systems familiarity and intuitive clarity are weak reeds to lean on.[1]”

Jul 20, 2020

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