we can get a Conclusion in Fresison, viz.
“No philosophers are conceited;
Some conceited persons are not-gamblers.
∴ Some not-gamblers are not philosophers”
This can be proved by reduction to Ferio, thus:—
“No conceited persons are philosophers;
Some not-gamblers are conceited.
∴ Some not-gamblers are not philosophers”.
The validity of Ferio follows directly from the Axiom ‘De Omni et Nullo’.
(2) Symbolic Representation.
Before proceeding to discuss other Methods of Solution, it is necessary to translate our Syllogism into an abstract form.
Let us take “persons” as our ‘Universe of Discourse’; and let x = “philosophers”, m = “conceited”, and y = “gamblers.”
Then the Syllogism may be written thus:—
“No x are m;
Some m are y′.
∴ Some y′ are x′.”