The Purloined Letter by Edgar Allan Poe (Essay Example)

Mathematicians regard beautiful proofs as those which prove claims in the most economic fashion: minimize logical steps to reach the conclusion. While math and science seem to be greatly related, the scientific view on proofs is founded on a different nature, that of reality. Chemists, physicists, geologists, and biologists are not able to extract definite proofs simply because reality does not allow it. There exists a contradiction, a doubt, that, regardless of how we experience our world, can be applied to any realistic proposition. In Edgar Allan Poe’s adulthood, revolutionary strides were being made in math, physics, chemistry, biology, and geology as a result of a new wave of data educed from research and experimentation. Being an intellectual, Poe reflected society’s growing appreciation for the sciences and math through many of his works, especially in his proto-detective fiction story “The Purloined Letter.” The story centers around a private-detective-like Frenchman named C. Auguste Dupin who epitomizes the potency of cleverness and logic, however a further analysis of Dupin’s relationship with evidence reveals a subtle irony. Rather than wholly throning Dupin as a master of logic, Poe paints him as a jester who by happenstance can solve mysteries when the rational reader can not.

One indication of the sleuth’s satirical role lies in C. Auguste Dupin’s incompatible disapproval for mathematical reasoning and his reliance on it to solve crimes. The denouement of “The Purloined Letter” depends too much on mathematical reasoning that the amateur sleuth’s rejection of it implies his unawareness of his own investigative rationale. He expresses to the narrator his disbelief in “reason educed by mathematical study” (Poe 10). In the first few pages of the short story, Dupin demonstrates his logical prowess by concluding that the purloined letter must be in the Minister’s apartment. This conclusion itself can only be reached through the logical tool of implication that is embedded simultaneously within the structure of logic and thus the structure of mathematics. More specifically, Dupin and other detectives in the detective fiction genre seem to be masters of boolean algebra which deals with compound statements whose elements have true or false values. I will demonstrate how this works: each crime or mystery has a defining set of algebraic boolean equations whose variables are the true and falsehoods of evidence, and whose operations are the cause and effect relations amongst the pieces of evidence. Therefore, the inquiry process and the evidence gathering serve as evaluators of boolean variables of the investigation’s algebraic equation. Cause and effect relationships act as the logical operation of implications. While these equations exist for all crimes, it is up to the investigator to essentially discover the structure of the equation and the value of its variables. As shown, the nature of Dupin’s reasoning is highly mathematical when abstracted. While one can argue that logic precedes mathematics, the two simply coexist simultaneously with one another: logic exists, and math exists, and there is no ordering. Apart from Dupin’s misunderstanding of the structure of his logic, Dupin also demonstrates a veiled ignorance of formal logic. During the investigation process of “The Purloined Letter,” Dupin goes into painstaking thoroughness to explain his thought process, yet uses faulty logic to reach his conclusions. A serious analysis of Dupin’s deciphering process would reveal Poe’s layering of ornamental articulation to conceal his misunderstanding of logic’s, and thus mathematical, transitivity. For example, dominating his argument on the limitations of mathematics, Dupin incorrectly applies mathematical axioms to modes that are grossly inapplicable such as morals (Poe 10). The language of mathematics is extensively precise to avoid this exact fallacy of mis-applicability. Poe was noted for being a scholar of mathematics and as such, was well aware of the degree of precision exercised in theorems, axioms, and definitions. Therefore, Dupin’s application of the algebraic operation of addition under real numbers to the set of human morals is comically incorrect. Addition under the set of real numbers is defined precisely, and its effect on numbers has been diagrammed meticulously. Applying the operation to morals and expecting consistent results would be equivalent to adding the concept of vinegar to a slip of paper with “baking soda” written on it and expecting a chemical reaction to produce carbon dioxide gas. Morals simply aren’t defined under the operation of addition of the set of numbers. Taking in Dupin’s subtle misuse of logic and his misunderstanding of the structure of logic, it becomes clearer that Poe satirized the supernaturally gifted investigator to reflect a great movement of data-driven scientific investigation. In a century of the formulation of the theory of evolution, the discovery of radioactivity, and the formulation of the electro-magnetic relation, Dupin starkly contrasts the then-popular idea of thorough evidence gathering. Charles Darwin spent years on the HMS Beagle endlessly, carefully observing and documenting hundreds of finches. He did not observe a single mother finch and her daughter finch to form his theory of evolution. Dupin’s misinterpretation of the logical structure and his excessive deliberation of mathematical limitation using fallacies points to a contrasting impression of the sleuth than what a first reading of “The Purloined Letter” would suggest. Thus, Dupin plays a satirical role in the setting of extraordinary scientific transformations by being the investigator who fantastically solves mysteries from the most minute set of evidence. Nil sapientiae odiosus acumine nimio. The excess of cleverness has its role in spectacular showcases of wit, but is impractical in the realm of science and the nature of real mysteries of the world.