10 papers
Stoic Logic and Natural Term Logic
Clarence Lewis Protin
In this paper we propose a reconstruction of the theory of multiple generality in Stoic Logic using the Natural Term Logic (NTL) developped by the author in \cite{ntl}. Contrary to…
Hegel and Modern Topology
Clarence Protin
In this paper we sketch how some fundamental concepts of modern topology (as well as logic and category theory) can be understood philosophically in the light of Hegel's Science Lo…
Natural Term Logic
Clarence Protin
In this paper we develop a formal system called Natural Term Logic (NTL). NTL aims to represent key aspects of the logical and grammatical mechanisms of natural language as well as…
Introduction to Pylog
Clarence Lewis Protin
PyLog is a minimal experimental proof assistant based on linearised natural deduction for intuitionistic and classical first-order logic extended with a comprehension operator. PyL…
Aristotle's Second-Order Logic and Natural Deduction
Clarence Protin
This paper has two goals. The first goal is to show how an extension of second-order logic is a natural framework to formalize portions of Aristotle's \emph{Topics} and to bring to…
Modern Definition and Ancient Definition
Clarence Protin
In this essay we examine some aspects of the classical theory of definition as codified in Aristotle's \emph{Topics} and Porphyry's \emph{Eisagogê} in the light of the way definiti…
Quantifier Reasoning and Multiple Generality in Aristotle and Ancient Logic
Clarence Lewis Protin
Aristotelian logic and its related traditions in antiquity are often held to have been equivalent to monadic predicate logic and as such inadequate to formalize mathematics as well…
A Logic for Aristotle's Modal Syllogistic
Clarence Protin
We propose a new modal logic endowed with a simple deductive system to interpret Aristotle's theory of the modal syllogism. While being inspired by standard propositional modal log…
Modern incarnations of the Aristotelian concepts of Continuum and Topos
Clarence Protin
The aim of this paper is i) to argue for the feasibility and fruitfulness of a balance between the phenomenological method seeking intuitive evidence and the axiomatic-deductive me…
On the Soundness of Bealer's Logics
Clarence Protin
Bealer's intensional logics T1 and T2 were proposed and expounded most fully in his book \emph{Quality and Concept} (1982) \cite{QC} as well in \cite{C}. These logics are unique in…