Existential Fallacy

One interesting fallacy that is rarely discussed is the existential fallacy.  It is a fallacy in formal logic, specifically Syllogistic (or Categorical) Logic, that provides, in essence that a universal statement such as “all X” doesn’t imply that there actually are (exist) any X.   In a syllogism, it means that you can’t conclude from all “Ss are Ms” and all “Ms are Ps” that there exists any Ss that are Ps, only that if there were any Ss, they’d also be Ps.

In the book’s entry for existential fallacy , there was one line that I think needed clarification:  

Given this example:

Example #1:

All babysitters have pimples.  All babysitter club members are babysitters.    Therefore, some babysitter club members have pimples.

The entry states:  “technically in the above example, all babysitter club members have pimples, not just some.”

This implies that the fallacy was that the Conclusion wasn’t saying 100% of the babysitter club members have pimples, but only some.   Actually, as is clear from the rest of the article's discussion, the fallacy is that it implies at least one such person actually exists, which is fallacious since the statement could be true even if there are no such persons.  Example:  “All trespassers will be prosecuted” doesn’t imply there actually are any trespassers, only that if there are any trespassers, they’ll be prosecuted.**

By the way, with regard to another example for this fallacy:

Example #2:

All forest creatures live in the woods.  All leprechauns are forest creatures.  Therefore, some leprechauns live in the woods.

Even Aristotle, whose system did not generally recognize the Existential Fallacy (as mentioned in the book), recognized that there may be a fallacy when talking about things that don’t exist like leprechauns.  As stand in Patrick Hurley’s logic textbook A Brief Introduction To Logic, in a syllogism such as Example 2 above, since leprechauns do not exist “the premises have no existential import from the Aristotelian standpoint.  Thus the syllogism is invalid…(even)… from the Aristotelian standpoint and commits the existential fallacy from that standpoint.”

———

** except in Los Angeles, San Francisco or New York