## 5 Citations

The Use of Trustworthy Principles in a Revised Hilbert’s Program

- Mathematics
- 2015

After the failure of Hilbert’s original program due to Godel’s second incompleteness theorem, relativized Hilbert’s programs have been suggested. While most metamathematical investigations are…

Hilberťs Programme and Gödel's Theorems

- Mathematics, Philosophy
- 2005

In this paper, we attempt to show that a weak version of Hilberťs metamathematics is compatible with Godel's Incompleteness Theorems by employing only what are clearly natural provability predicates.…

Proof Theory

- Mathematics
- 2014

Proof theory began in the 1920’s as a part of Hilbert’s program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving…

A Gentle Introduction to Membrane Systems and Their Computational Properties

- Computer ScienceBio-Inspired Computing Models and Algorithms
- 2019

The theory of computation investigates the nature and properties of algorithmic procedures and the development of computational complexity theory, pioneered by Hartmanis and Stearns in the paper On the computational complexity of algorithms, that also gives the name to the field.

Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic

- Philosophy
- 2015

Hilbert’s choice operators τ and e, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker…

From Solvability to Formal Decidability: Revisiting Hilbert’s “Non-Ignorabimus”

- MathematicsJournal of Humanistic Mathematics
- 2019

The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of…

Anti-Foundational Categorical Structuralism

- Philosophy
- 2012

The aim of this dissertation is to outline and defend the view here dubbed “anti-foundational categorical structuralism” (henceforth AFCS). The program put forth is intended to provide an answer the…

Reconstructing Hilbert to Construct Category Theoretic Structuralism

- Philosophy
- 2009

This paper considers the nature and role of axioms from the point of view of the current debates about the status of category theory and, in particular, in relation to the “algebraic” approach to…

The Identity Problem: The Case of The Non-trivial Automorphism

- Philosophy
- 2010

This project describes a solution to a problem in Stewart Shapiro’s ante rem structural ism, a theory in the philosophy of mathematics. Shapiro’s theory proposes that the nature of mathematical…