Noun – A syllogism is a deductively based three-part logical argument in which two assumptions are joined to get a conclusion. The conclusion will be true if the syllogism’s premises are true and the syllogism is appropriately organized.

I’ve encountered this word from “Bad Ideas About Writing” Edited by Cheryl E. Ball & Drew M. Loewe.

*badideasaboutwriting-book.pdf (wvu.edu)

Quote from the passage :

“Aristotle loved syllogisms and seems to have believed that all
reasoning could be done through them. In philosophy, to get to
the truth, you try to begin with a universally valid major premise
(e.g., all men are mortal). Then you have a more specific proposition related to that premise (e.g., Socrates is a man) that enables
you to conclude (e.g., Socrates is mortal).”

The quote itself gives a slight idea of what syllogisms mean and how Aristotle used them as a way of communication with people and for reasoning. But does not always work for large assemblies because some topics cant be universally valid and can be controversial.

To further understand the Glossary word: Syllogism | Definition of Syllogism by Merriam-Webster

Basic Logic, Propositions and Syllogisms (Aristotle’s Logic) – YouTube