P: All leprechauns are shoemakers.P: No leprechauns are females.C: ?

Irina November 4, 2019

@nizhoni,

One of the rules of inference for categorical syllogisms tell us that two universal premises ("all"/ "none") can never have a particular ("some"/ "few") conclusion. Here we have two universal premises:

(1) L->S
(2) L -> ~F

(A) involves a "particular" conclusion S - some- ~F and commits what's known as an "existential fallacy." The issue with (A) is that it implies that a class has at least one member but the premises never tell us that L exist, merely that if there are any members of class L -then they are all shoemakers and not female. (A) and any "particular" conclusion would require us to assume that at least one member of the class exists, which is unsupported by the premises.

Another way to visualize this fallacy is to consider a Venn diagram where a circle representing leprechauns is entirely within the circle representing shoemakers. But since the circle representing leprechauns is empty - no leprechauns exist unless the premises tell us otherwise - the circle representing shoemakers could fit entirely in the circle representing females, thus proving (A) false.

Note that there are some difference between two systems of syllogistic logic in how this rule is applied (Aristotle vs Boole) when the premises involve real subjects but for purposes of this question, the answer would be the same because we know that leprechauns/ unicorns/ dragons etc do not exist.

Let me know if this helps and if you have any other questions.

Chase May 18, 2020

Okay but this displays that the correct answer is E, so can we please have some clarification?

Brett-Lindsay July 13, 2020

Thanks @nizhone - I fell into the existential fallacy trap, too.

It's really easy to do, especially when you're doing the quantifiers lesson, lol