6. CANONS OF THE SYLLOGISM.
The dictum of Aristotle is ostensibly a self-evident truth, and some logicians have put this truth in the form of three axiomatic statements which are known as the canons of the syllogism. These are as follows:
(1) “Two terms agreeing with one and the same third term agree with each other.”
(2) “Two terms of which one agrees and the other does not agree with one and the same third term, do not agree with each other.”
(3) “Two terms both disagreeing with one and the same third term may or may not agree with each other.”
Making use of the symbols as explained on a previous page of this chapter, it will be seen that the first canon conforms to this syllogistic type:
All M is G
All S is M
∴ All S is G
The two terms are S and G, while M is the third term.
The attending symbolizations illustrate, respectively, the second and third canons:
No M is G
All S is M
∴ No S is G
No M is G
No S is M
Conclusion indeterminate.