7.2 "How Syllogisms Work" - My Notes from "The Reasonable Person" by Mark Grannis

Finding the Middle Term Has the Power
7.2 expresses where the power of revelation lies in the categorical syllogism. "The fundamental strategy of the categorial syllogism is to relate the major term to the minor term by relating each of them to a middle term." 

One often starts in this process by beginning with a conclusion and then seeking justification for the conclusion. It is actually from the conclusion that the major and minor terms are acquired. Then by finding a third term to which one can relate both major and minor terms one can seek some elucidation or justification for their conclusion. 

Example

- Conclusion: Socrates is mortal 

- What can both Socrates and mortal relate to? The concept of man. 

- Setting up the syllogism now: 

All men are mortal. 

Socrates is a man. 

Therefore, Socrates is mortal. 

Why This Works

This particular syllogism works because it draws on two of the rules of the relations between categorical propositions, the "dictum de omni" and the "dictum de nullo" (explained in a previous chapter). 

Principles of Reciprocal Identity and Non-Identity

All syllogisms, though, rely on the first principles of logic, of which one of them was the "principle of identity" (again covered in a previous chapter). But from this first principle we can use two other principles which necessarily follow, "the principle of reciprocal identity" and the "principle of reciprocal non-identity." 

Principle of Reciprocal Identity - "Two things that are each identical with a third thing are identical with each other. ... Every single valid categorical syllogism relates S to P in the conclusion by relating them each to M in the premises." 

Principle of Reciprocal Non-Identity - "Two things, one of which is identical with a third thing and the other of which is non-identical with that third thing, are non identical with each other." 

Middle Term

"... the middle term mediates the inference from the two states premises to the desired conclusion." 

"The middle term, then, is supposed to function as sort of a bridge to get us over the gap between what we know and what we don't know."