If there is no logic, go back to the logic behind each theorem, starting with theorem 1, and show me how each successive theorem does not follow from the logic presented therein.
Learn what theorem means. Here's a link.
"show me how each successive theorem does not follow from the logic presented therein."
Theorems require proof, not strings of illogical, or unsubstantiated, or unrelated statements.
Lets grab the first pile of text and look at it.
"It should now be clear that information, being a fundamental entity, cannot be a property of matter, and its origin cannot be explained in terms of material processes.
This erroneous statement follows from a string of similar claims. It is neither a conclusion, nor is it axiomatic. It is simply a false assertion.
Now...
"We therefore formulate the following fundamental theorem:
Ridiculous! The word therefore is unwarranted, because no logical operations whatsoever were performed.
Let's see...
" Theorem 1: The fundamental quantity information is a non-material (mental) entity. It is not a property of matter, so that purely material processes are fundamentally precluded as sources of information."
The first sentence is a statement attaching a quantitative attribute to the word information. In otherwords, it's part of the definition of the word information. The second statement is false. There has been no complete definition of the word information given, so the first claim in the sentence is indeterminate. The second part of the sentence is false, because it relies on an indeterminate value to arrive at some stated conclusion.