Arguing across Domains

First identified by Bill Joslin in response to Jay Dyer's attack on the trivium:

"If I remember correctly he argued 2 points.

1) Aristotelian logic is fundamentally tautological...

2) All "sets" ... this is the Godel argument. .. cannot be affirmed with in the set. That is to say the deductive logic of rational numbers are not able to affirm, completely, their validity.  It can only be affirmed from a super set of set outside of the original. So irrational numbers can affirm rational numbers. If you try to affirm rational numbers from with its own logic you end up with a tautology.

J. Dyer said, paraphrasing Godel, that the set need a "transcendental” argument (an argument from beyond the set). Jay asserts that the transcendental argument for reality is theism.

He also said Aristotle’s argument of affirming the consequent was a transcendental argument which affirmed "existence exists".

That I think is the gist of it.... others have argued that math, consciousness, and even fiction (mythology) fulfill the transcendental argument which Dyer says theism does.

Two thinks to note.

Godel's superset/transcendental argument was specific to math "sets" as in number sets. His argument is good, however it ignores that both the original set and the transcendent set are both part if a larger set. That being the set of quantities and the relationship of quantities.... short for... they are both contained with in math... each set had a common foundation and the transcendental set is derivative (dependent upon) the set which it affirms... each are of the sane category but of a different domain... a fallacy which I don't think has been identified yet, which I would call the fallacy of arguing across domains.

He is pointing at a real short coming if Aristotelian logic. The shortcoming though is not about this transcendental argument. It has to do with the distinction between fact and truth. We assume facts to imply truth, yet we can encounter truths which are not factual (as in fiction, empathy and mythology) these are meaningfully true assertions vs. factually true assertions. Without this distinction Aristotelian philosophy can result in an absolutist truth assertions which is unfounded (this is how the trivium was used by the Church for control or the Rhodes tables used it as a glue for English culture)... my opinion is this: The superset which affirms reality is consciousness (which is dependent on reality -biology, but is beyond mere biology) and the truth is not a rarefied ideal but rather is dependent upon our assertions... it is an artifact of language and has less to do with reality than it does with our claims about reality."