An Alternative Version of Categorical Logic

Main Author: Johnson, David
Format: Article eJournal
Terbitan: , 2019
Subjects:
Online Access: https://zenodo.org/record/3358400
ctrlnum 3358400
fullrecord <?xml version="1.0"?> <dc schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><creator>Johnson, David</creator><date>2019-08-02</date><description>Logicians have a very specialized definition of the word &#x2018;some&#x2019;: in logic it means &#x2018;at least one&#x2019;. But that is not how people outside of logic use the term at all. In other contexts &#x2018;some&#x2019; means &#x2018;at least one but not all&#x2019;, or &#x2018;not all and not none&#x2019;. In this work I explore how categorical logic is transformed with this new definition, which is more in harmony with how the word &#x2018;some&#x2019; is used outside of formal logic. This results in a more intuitive, and, I believe, more accurate version of categorical logic. Topics discussed: The proper definition of &#x2018;some&#x2019;, Aristotle&#x2019;s Square of Opposition, the Modern Square of Opposition, the &#x2018;Boolean interpretation&#x2019;, existential import, the Triangle of Opposition, categorical syllogisms, sorites arguments, conversion obversion and contraposition, modal logic (including the Modal Triangle of Opposition), the connection to propositional logic, and the connection to predicate logic.</description><identifier>https://zenodo.org/record/3358400</identifier><identifier>10.5281/zenodo.3358400</identifier><identifier>oai:zenodo.org:3358400</identifier><relation>doi:10.5281/zenodo.3358399</relation><rights>info:eu-repo/semantics/openAccess</rights><rights>https://creativecommons.org/licenses/by/4.0/legalcode</rights><subject>Categorical Logic, Aristotle, Modern Square of Opposition, Boolean Interpretation, Existential Import, Venn Diagrams, Predicate Logic, Propositional Logic</subject><title>An Alternative Version of Categorical Logic</title><type>Journal:Article</type><type>Journal:Article</type><recordID>3358400</recordID></dc>
format Journal:Article
Journal
Journal:eJournal
author Johnson, David
title An Alternative Version of Categorical Logic
publishDate 2019
topic Categorical Logic
Aristotle
Modern Square of Opposition
Boolean Interpretation
Existential Import
Venn Diagrams
Predicate Logic
Propositional Logic
url https://zenodo.org/record/3358400
contents Logicians have a very specialized definition of the word ‘some’: in logic it means ‘at least one’. But that is not how people outside of logic use the term at all. In other contexts ‘some’ means ‘at least one but not all’, or ‘not all and not none’. In this work I explore how categorical logic is transformed with this new definition, which is more in harmony with how the word ‘some’ is used outside of formal logic. This results in a more intuitive, and, I believe, more accurate version of categorical logic. Topics discussed: The proper definition of ‘some’, Aristotle’s Square of Opposition, the Modern Square of Opposition, the ‘Boolean interpretation’, existential import, the Triangle of Opposition, categorical syllogisms, sorites arguments, conversion obversion and contraposition, modal logic (including the Modal Triangle of Opposition), the connection to propositional logic, and the connection to predicate logic.
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