Here is a private question to the paper The Finitist Completeness Theorem (FCT): No Gödel's Uncertainties by Ed Gerck at ResearchGate.
The paper presents a rigorously motivated departure from the traditional framework of mathematical logic. It claims that Gödel’s incompleteness theorems, long considered insurmountable limitations on formal systems, are not intrinsic to logic but instead emerge from the assumption of infinite domains.
Gerck proposes that when logic is restricted to explicitly bounded, finite domains of arbitrary-length integers (up to a fixed N), the resulting system becomes complete, consistent, and decidable -- Distinguished in the DAOF method cited.
The author's invitation to feedback is welcomed, and this response aims to contribute constructively to that dialogue.
What is your qualified opinion?
Parenthetically, per the manuscript, arbitrary-length integers of length N means integers of any size up to a fixed integer upper bound N, not infinitely extensible, irrational, or undefined and first-order logic over said finite domains.
To question this definition seems like an AI hallucination that FCT combats.
Dear Ed Gerck I've briefly read the document and generally support the direction. I'd also like to emphasize, from a different perspective, the absolute necessity of abandoning real numbers in mathematics and physics.
I think, however, that to reject real and complex numbers in physics, you also need a consistent and well-founded physical derivation.
My work is concerned with excluding real numbers from physics and mathematics based on fundamentally new first axioms. A major role in this is the analysis of how irrational and real numbers made their way into physics—historically speaking. In my opinion, the events surrounding the definition of physical units during the French Revolution play a central role.
Perhaps some aspects of my work can be helpful in underscoring the significance of your work.
I wish you all the best and success with your paper.
- Badges
- Science topic
- Similar topics
- Linguistics
- Composition Studies
- Publication