The Fallacy of Nonsense
Lewis Carroll was a professor of logic, writing among his well known works of fiction, treatises on the subject of logic and even a textbook, Symbolic Logic. “It is the function of logic to classify and formulate fallacious forms of argument as well as valid ones.” (Burks 367) So is it some of the functions of Carroll’s tales of Alice’s Adventures in Wonderland and Through the Looking Glass. Presenting different puzzles, riddles, or what appears to be on the surface nonsense, Carroll in these books present many questions of logic and indirectly their solutions, challenging the ability of the reader to believe what has been presented. All his nonsensical puzzles can be either proved or disproved using some form of logic. “Not only is it not nonsense… it also contains, by implication, a great deal of excellent sense.” (Heath 51)
At one point in Alice’s Adventures in Wonderland, a pigeon claims Alice to be a serpent, because serpents eat eggs, and Alice eats eggs. (Carroll A/T 47) The propositions would be then what is quantified in symbolic logic as universal, with the functional word “all”. Using the notation AE to represent the proposition “Alice eats eggs”, SE to represent “Serpents eat eggs”, concluding AS, “Alice is a serpent”, and “” to mean “therefore”, the argument is represented in simple terms as:
In Symbolic Logic, Carroll represents this same argument as:
}(m being assumed to exist) x’y’1
(Carroll SL 261) where x would represent Alice, y would represent serpents, and m would represent eggs. He states this argument form to be a fallacy, or invalid by definition. Carroll may have chosen to use this particular example to demonstrate a fallacy due to the fact that the reader already knows that Alice is not a serpent, leaving it to logic to prove why.
Another fallacy is presented in Alice’s Adventures in Wonderland at the mad tea party. On the two propositions “I say what I mean” and “I mean what I say,” (Carroll A/T 61) Alice concludes equivalence, applying the symbolic logic rule of conversion. Translated into a form which can be applied, the first proposition becomes “All I say is what I mean”, notated “All S is M”, by definition a universal proposition. The second, assumedly a conversion of the first, is translated “All I mean is what I say” and is notated “All M is S”, also a universal proposition. However, the conversion is invalid, because a universal proposition converts to a particular proposition. The valid conversion would be “All S is M” to “Some M is S”, or “Some of what I mean is what I say”, according to the symbolic rules of conversion. (Copi 194) Now it is clear that the two propositions are not necessarily equivalent, and the following propositions...