Ellerman, David (2009) Counting Distinctions: On the Conceptual Foundations of Shannon's Information Theory. Synthese, 168 (1). pp. 119149. ISSN 15730964

PDF (Edited version of Synthese article)
CountingDistinctions3.pdf  Updated Version Download (285kB) 
Abstract
Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u′) from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition π on U making a distinction, i.e., if u and u′ were in different blocks of π. Subset logic leads to finite probability theory by taking the (Laplacian) probability as the normalized size of each subsetevent of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs U² from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions."
Export/Citation:  EndNote  BibTeX  Dublin Core  ASCII/Text Citation (Chicago)  HTML Citation  OpenURL 
Social Networking: 
Item Type:  Published Article or Volume  

Creators: 


Keywords:  logical entropy, distinctions, Shannon entropy, logical information theory  
Subjects:  Specific Sciences > Computation/Information General Issues > History of Philosophy of Science Specific Sciences > Mathematics Specific Sciences > Probability/Statistics 

Depositing User:  David Ellerman  
Date Deposited:  23 Dec 2011 00:46  
Last Modified:  23 Dec 2011 00:46  
Item ID:  8967  
Journal or Publication Title:  Synthese  
Publisher:  Springer (Springer Science+Business Media B.V.)  
Subjects:  Specific Sciences > Computation/Information General Issues > History of Philosophy of Science Specific Sciences > Mathematics Specific Sciences > Probability/Statistics 

Date:  May 2009  
Page Range:  pp. 119149  
Volume:  168  
Number:  1  
ISSN:  15730964  
URI:  http://philsciarchive.pitt.edu/id/eprint/8967 
Monthly Views for the past 3 years
Monthly Downloads for the past 3 years
Plum Analytics
Actions (login required)
View Item 