?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.title=Counting+Distinctions%3A+On+the+Conceptual+Foundations+of+Shannon's+Information+Theory&rft.creator=Ellerman%2C+David&rft.subject=Computation%2FInformation&rft.subject=History+of+Philosophy+of+Science&rft.subject=Mathematics&rft.subject=Probability%2FStatistics&rft.description=Categorical+logic+has+shown+that+modern+logic+is+essentially+the+logic+of+subsets+(or+%22subobjects%22).+Partitions+are+dual+to+subsets+so+there+is+a+dual+logic+of+partitions+where+a+%22distinction%22+[an+ordered+pair+of+distinct+elements+(u%2Cu%E2%80%B2)+from+the+universe+U+]+is+dual+to+an+%22element%22.+An+element+being+in+a+subset+is+analogous+to+a+partition+%CF%80+on+U+making+a+distinction%2C+i.e.%2C+if+u+and+u%E2%80%B2+were+in+different+blocks+of+%CF%80.+Subset+logic+leads+to+finite+probability+theory+by+taking+the+(Laplacian)+probability+as+the+normalized+size+of+each+subset-event+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+%7CU%7C%C2%B2+from+the+finite+universe.+That+yields+a+notion+of+%22logical+entropy%22+for+partitions+and+a+%22logical+information+theory.%22+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+%22distinctions.%22&rft.publisher=Springer+(Springer+Science%2BBusiness+Media+B.V.)&rft.date=2009-05&rft.type=Published+Article&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.identifier=http%3A%2F%2Fphilsci-archive.pitt.edu%2F8967%2F1%2FCounting%252DDistinctions%252D3.pdf&rft.identifier=Ellerman%2C+David+(2009)+Counting+Distinctions%3A+On+the+Conceptual+Foundations+of+Shannon's+Information+Theory.+[Published+Article]&rft.relation=http%3A%2F%2Fphilsci-archive.pitt.edu%2F8967%2