Syllogism

(Greek: συλλογισμός syllogismos, “conclusion, inference”) is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.

In its earliest form, defined by Aristotle, from the combination of a general statement (the major premise) and a specific statement (the minor premise), a conclusion is deduced.

For example, knowing that all men are mortal (major premise) and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form:

• All men are mortal.
• Socrates is a man.
• Therefore Socrates is mortal.

We can now put this in an image:

	sig Men{}
	one sig Socrates {}

	check Correct {

		all mortal, men : some Men + Socrates {

			men in mortal
			and  
			Socrates in men 
			=> Socrates in mortal

		}
	} for 5 Men

Bad use of Syllogism

This is very error prone since the following is not correct:

• All men are mortal.
• Socrates is a mortal.
• Therefore Socrates is a man.

	
	check Wrong {
	
		all mortal, men : some Men + Socrates {
	
			men in mortal
			and  
			Socrates in mortal 
			=> Socrates in men
	
		}
	} for 5 Men
	

If you run the Wrong version then you’ll find that from the fact that Socrates is mortal it does not follow that Socrates is a man.