From Logicism to Metatheory Final

CS Study Group FY 07 Phase 2 Machine - Checked Metatheory for Security - Oriented Languages Final Technical Report

Logicism, interpretability, and Knowledge of Arithmetic

A crucial part of the contemporary interest in logicism in the philosophy of mathematics resides in its idea that arithmetical knowledge may be based on logical knowledge. Here an implementation of this idea is considered that holds that knowledge of arithmetical principles may be based on two things: (i) knowledge of logical principles and (ii) knowledge that the arithmetical principles are re...

Russell’s Logicism

Logicism is typically de ned as the thesis that mathematics reduces to, or is an extension of, logic. Exactly what “reduces” means here is not always made entirely clear. (More de nite articulations of logicism are explored in section 5 below.) While something like this thesis had been articulated by others (e.g., Dedekind 1888 and arguably Leibniz 1666), logicism only became a widespread subje...

Toward a Science of Metatheory

In this article, I explore the field of metatheory with two goals. My first goal is to present a clear understanding of what metatheory “is” based on a collection of over twenty definitions of the term. My second goal is to present a preliminary investigation into how metatheory might be understood as a science. From that perspective, I present some strengths and weaknesses of our field and sug...

What is neologicism?

Logicism is a thesis about the foundations of mathematics, roughly, that mathematics is derivable from logic alone. It is now widely accepted that the thesis is false and that the logicist program of the early 20th century was unsuccessful. Frege’s (1893/1903) system was inconsistent and the Whitehead and Russell (1910–13) system was not thought to be logic, given its axioms of infinity, reduci...