Abstract
Fallacies are logically false statements which are often considered to be true. In the “Sophistical Refutations”, the last of his six works on Logic, Aristotle identified the first thirteen of today’s many known fallacies and divided them into linguistic and non-linguistic ones. A serious problem with fallacies is that, due to their bivalent texture, they can under certain conditions disorient the nonexpert. It is, therefore, very useful to quantify each fallacy by determining the “gravity” of its consequences. This is the target of the present work, where for historical and practical reasons—the fallacies are too many to deal with all of them—our attention is restricted to Aristotle’s fallacies only. However, the tools (Probability, Statistics and Fuzzy Logic) and the methods that we use for quantifying Aristotle’s fallacies could be also used for quantifying any other fallacy, which gives the required generality to our study.
Highlights
Fallacies are logically false statements that are often considered to be true
A disadvantage of fuzzy logic (FL) is that the definition of the membership function of a fuzzy set (FS), it must always be based on logical arguments, is not uniquely determined depending on the observer’s personal criteria and goals
Statistical data or probability distributions can be used in certain cases to define membership degrees, but this is not the rule in general
Summary
Fallacies are logically false statements that are often considered to be true. The first fallacies appeared in the literature simultaneously with the generation of Aristotle’s bivalent Logic. A list of the most important of them is given in [2], while many fallacies are analyzed in the first of the present authors’ books [3] Because of their variety of structure and applications, it is difficult to classify the fallacies so as to satisfy all practitioners. A standard way of classifying them into formal (with deductive arguments that they are false) and informal fallacies is according to their structure or content [4] Another big problem with fallacies is that, due to their bivalent texture, they can under certain conditions disorient the nonexpert. This explains the frequent use of fallacies as rhetorical devices in the desire to persuade when the focus is more on communicating and gaining common agreement rather than on the correctness of reasoning.
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