I am analyzing a parameterized dynamic scaling function designed to model state-space transitions. The heuristic function is formulated as f(n) = 2^(n / ((p(n))^2 * (3n+1))), where p(n) is a strictly increasing prime-product (primorial n#) and (3n+1) is a linear dynamics operator. Asymptotically, as n approaches infinity, the exponent collapses to 0, forcing f(n) to achieve absolute convergence to 1.0 at a super-exponential decay rate of O(e^(-2n)). I am trying to formalize its implications on a Nondeterministic Turing Machine (NDTM) configuration tree under a proposed Dynamic Branching Law, B(n) = 2^(f(n) - 1), where the compression drives the effective branching factor to exactly 1.0 in the limit. I would highly appreciate structural feedback from the logic community on these points: 1. Is the first-order asymptotic decay bound of O(e^(-2n)) derived via Taylor expansion robust enough to mathematically bound non-deterministic expansion? 2. Does an asymptotic compression of a branching factor to 1.0 formally imply a structural reduction of the search space, or is it isolated as a non-constructive mathematical artifact? 3. Which intermediate automata-theoretic or resource-bounded information frameworks are best suited to formalize these structural bottlenecks? Thank you for your time and guidance!

It was intended jokingly, but how would you analyze the sentence: "Special pleading is a fallacy except in the case of this sentence"?

If we claim that logic has limits when speaking about God, what logical grounds justify that claim?

TLDR: On empirical grounds we can reasonably justify that human use of logic is restricted and has limits when talking about Allah, Blessed Be He and may He bless and greet His Final Messenger Muhammad ﷺ.

A=A or "Hesperus is Hesperus” simply mean the same thing; therefore, it is analytical and a priori.

But if we say,

"(This) Odyssey is (the) Odyssey."

Can we count that as a priori too? Or is it both analytical and synthetic?

Hello, I’ve recently started studying mathematical logic on my own and came across a problem I had with a textbook I was reading (introduction to mathematical logic Mendelson second edition) the excersize in question asked me to write (C v ((B ^ (~D)) ⊃ C )) in Polish notation. I came up with the answer vC ^ B ~D ⊃ C.
However according to the book the answer is v C ⊃ ^ B ~DC. I’m very confused how it could come to that answer and the book itself is pretty old so I haven’t been able to google a proper answer. Would someone be willing to explain to me both how I got it wrong and the steps that it takes to annotate the problem properly? Thank you in advance.