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Dan E. Willard

Publications and source records attributed to Dan E. Willard.

6 recordsLinked to original sources
arXiv2020

How the Law of Excluded Middle Pertains to the Second Incompleteness Theorem and its Boundary-Case Exceptions

Our earlier publications showed semantic tableau admits partial exceptions to the Second Incompleteness Theorem where a formalism recognizes its self consistency and views multiplication as a 3-way relation (rather than as a total function). We now show these boundary-case evasions will collapse if the Law of the Excluded Middle is treated by tableau as a schema of logical axioms (instead of as derived theorems).

math.LO↗
arXiv2018

About the Chasm Separating the Goals of Hilbert's Consistency Program from the Second Incompletess Theorem

We have published several articles about generalizations and boundary-case exceptions to the Second Incompleteness Theorem during the last 25 years. The current paper will review some of our prior results and also introduce an `enriched' refinement of semantic tableaux deduction. While the Second Incompleteness Theorem is a strong result, we will emphasize its boundary-case exceptions are germane to Global Warming's threat because our systems can own a simultaneous knowledge about their own consistency, together with an understanding of the $Π_1$ implications of Peano Arithmetic.

math.LO↗
arXiv2017

On How the Introducing of a New $θ$ Function Symbol Into Arithmetic's Formalism Is Germane to Devising Axiom Systems that Can Appreciate Fragments of Their Own Hilbert Consistency

A new $θ$ function primitive is proposed that almost achieves the combined efficiency of the addition, multiplication and successor growth operations. This $θ$ function symbol enables the constructing of an "IQFS(PA+)" axiom system that can corroborate a fragmentary definition of its own Hilbert consistency, while it will simultaneously verify isomorphic counterparts of all Peano Arithmetic's $Π_1$ theorems. Many propositions and intermediate results are also established. Only one intermediate result, which most readers will intuit should be true, does remain formally unproven.

math.LO↗
arXiv2017

Implications of the Trivers-Willard Sex Ratio Hypothesis for Avian Species and Poultry Production, And a Summary of the Historic Context of this Research

At a theoretical level, the Trivers-Willard Sex Ratio Hypothesis applies to both avian species and mammals. This article, however, conjectures that at the statistical level, sex ratio effects are likely to produce sharper numerical variations among birds than among mammals. We explain this greater statistical variation should likely have beneficial implications for increasing the efficiency of world-wide poultry egg (and perhaps also meat) production.

q-bio.OT↗
arXiv2014

On the Significance of Self-Justifying Axiom Systems from the Perspective of Analytic Tableaux

This article will be a continuation of our research into self-justifying systems. It will introduce several new theorems and their applications. (One of these results will transform our previous infinite-sized self-verifying formalisms into tighter systems, with only a finite number of axioms.) It will explain how self-justification is useful, even when the Incompleteness Theorem limits its reach.

math.LO↗