Relaxing Some Constraints of Syllogism

Aristotle and logic

Aristotle laid the foundations for the formal study of logic, but he scoped his study to categorical syllogismsA syllogism is a form of deductive reasoning that consists of two premises and a conclusion. It typically involves categorical statements about relationships between categories or classes of things.. Let’s review the following valid syllogistic argument carefully and then discuss if we felt any difficulties because of Aristotle’s choice of limiting his study of logic to syllogisms.

Restrictions while arguing in syllogisms

Imagine if we were restricted to always arguing in syllogisms. Wouldn’t we feel the following elements of the categorical syllogism restricting our expression and thought?

Only speaking in categories

Aristotelian syllogisms indeed focus on categorical statements, which can sometimes be limiting when trying to address complex arguments. Let’s consider a small example that illustrates the need for a valid argument without relying solely on categories.

In this reasonable argument, we don’t categorically define individuals as belonging to specific groups; instead, we make statements about the capacity for empathy and the effect of acts of kindness on fostering empathy. The conclusion is drawn based on these premises, illustrating how syllogistic reasoning can be applied beyond strict categorical statements.

Always arguing with three propositions and two premises

The preceding example also makes the case that not all natural language arguments need to artificially restrict the number of statements to three. This Aristotelian restriction can sometimes limit our ability to fully address multifaceted arguments and scenarios.

Always maintaining the order of premises

Aristotelian syllogism follows a specific structure in which the major premise, determined by the predicate term of the conclusion, the minor premise, determined by the subject term of the conclusion, and the conclusion statement always follow a predetermined sequence. In natural language expression, people usually don’t think about the predicate term of one’s conclusion or how their argument’s first sentence must mention that term.

Validation requiring linguistic expertise

The preceding example shows how an Aristotelian logician constantly needs to think in terms of subjects and predicates and their consistent ordering. This ordering, of course, helps compute the mood of the syllogism. The placement of the middle term determines the figure of the argument. Another level of linguistic expertise is required when the propositions aren’t in the standard categorical form and must be converted into one. For instance, the following sentence is a valid proposition, but it’s a proper linguistic challenge to convert this to any of the four standard forms ($A$, $E$, ...