Enthymeme-abridged Syllogism

A typical Syllogism is composed of two premises and a conclusion as follows:

All men are mortal

Socrates is man

Therefore, Socrates is mortal

However, this is not how we generally speak or write. Our discourse occurs in an abridged form where one of the propositions is missing. Such kind of abridged Syllogism is called Enthymeme. An Enthymeme where Major Premise is supressed is called First Order Enthymeme. Where Minor Premise is supressed is called Second Order Ethymeme. Where Conclusion is supressed is called Third Order Enthymeme.

Example of the above is as follows:

First Order Enthymeme:

Socrates is Man. Therefore, Socrates is mortal.

Second Order Enthymeme:

All men are mortal. Therefore, Socrates is mortal.

Third Order Enthymeme:

All men are mortal. Socrates is man.