Define Categorical Syllogism.

A categorical syllogism is a form of deductive reasoning that consists of three categorical propositions arranged in a specific structure to draw a conclusion. Each proposition in a categorical syllogism belongs to one of the four standard forms: A (universal affirmative), E (universal negative), I (particular affirmative), or O (particular negative). The structure of a categorical syllogism is defined by its three propositions, each having a subject, a predicate, and a quantifier (universal or particular).

The standard structure of a categorical syllogism is as follows:

1. Major Premise: A statement that makes a broad claim about a class or category.
2. Minor Premise: A statement that provides specific information about a subset of the category mentioned in the major premise.
3. Conclusion: A statement that logically follows from the major and minor premises, revealing a relationship between the subjects and predicates.

An example of a categorical syllogism is:

1. All humans are mortal. (Major Premise – A type)
2. Socrates is a human. (Minor Premise – I type)
3. Therefore, Socrates is mortal. (Conclusion – I type)

Categorical syllogisms play a fundamental role in traditional logic and are essential for analyzing the validity of arguments based on categorical propositions.