On the Algebraic Structure of Lewis Carroll's Logic -- Behind the Looking Glass: A Mathematical Perspective
Abstract
Charles Ludwidge Dodgeson, better known by his literary pen name `Lewis Carroll', has a number of well known and cherished literary works to his credit, for example "Alice in Wonderland" and "Through the Looking Glass". Apart from this he is known to have a strong professional interest in mathematics and logic with an inclination towards an educational and recreational perspective. In this work we consider the algebraic structure behind Lewis Carroll's approach to classical logic and his logical puzzles. Starting with the arithmetic of $0$ and $1$, we develop the connections between Boolean-valued functions, sets and predicates, which we refer to as the "entangled trinity". This provides a common setting in which Carroll's approach and Boole's perspective can be understood. Particular attention is given to what is meant by "the conclusion" of a logical problem. We suggest a precise interpretation of a complete conclusion in terms of largest lower bounds involving only the predicates to be retained, thereby sharpening Carroll's approach. The role of natural language in choosing a suitable universe and identifying these predicates is discussed through a variety of examples. Finally, we present computerised solution methods, including the use of Boolean satisfiability solvers for larger puzzles.
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BibTeX
@misc{franz2026algebraic,
title = {{On the Algebraic Structure of Lewis Carroll's Logic -- Behind the Looking Glass: A Mathematical Perspective}},
author = {Sebastian Franz and Rainer Picard},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32273},
eprint = {2610.32273},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32273},
}
RIS
TY - UNPB
TI - On the Algebraic Structure of Lewis Carroll's Logic -- Behind the Looking Glass: A Mathematical Perspective
AU - Sebastian Franz
AU - Rainer Picard
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32273
UR - https://arxiv.org/abs/2610.32273
AB - Charles Ludwidge Dodgeson, better known by his literary pen name `Lewis Carroll', has a number of well known and cherished literary works to his credit, for example "Alice in Wonderland" and "Through the Looking Glass". Apart from this he is known to have a strong professional interest in mathematics and logic with an inclination towards an educational and recreational perspective. In this work we consider the algebraic structure behind Lewis Carroll's approach to classical logic and his logical puzzles. Starting with the arithmetic of $0$ and $1$, we develop the connections between Boolean-valued functions, sets and predicates, which we refer to as the "entangled trinity". This provides a common setting in which Carroll's approach and Boole's perspective can be understood. Particular attention is given to what is meant by "the conclusion" of a logical problem. We suggest a precise interpretation of a complete conclusion in terms of largest lower bounds involving only the predicates to be retained, thereby sharpening Carroll's approach. The role of natural language in choosing a suitable universe and identifying these predicates is discussed through a variety of examples. Finally, we present computerised solution methods, including the use of Boolean satisfiability solvers for larger puzzles.
ER -