# Aristotelian vs Boolean, trying to determine the exact difference [duplicate]

Good afternoon,

I've looked at some other answers and I feel those don't quite answer what I'm trying to ask, so I'll just ask it here.

I'm in a logic course and I'm either misunderstanding something or my teacher said something wrong.

The example given was: All cats are animals

Some cats are animals

He argued this was valid from the Aristotelian stand point, as cats really do exists, but invalid from the Boolean stand point (as an existential fallacy) because "All cats are animals" doesn't imply existence, so we can't conclude that "some cats are animals".

The next example was:

All unicorns are animals

Some unicorns are animals.

He argued this was invalid from both the Aristotelian and Boolean stand points because, for the Aristotelian, unicorns don't exist and therefore it commits an existential fallacy. But that it's also invalid from the Boolean stand point because of the same reasons the previous example was invalid.

My confusion comes from the fact that I thought the only difference between Boolean and Aristotelian stand points, for these examples, would be whether the subject (either cats or unicorns) actually existed.

I would have figured the first example would be valid from both Aristotelian and Boolean view points, and the second would be only invalid to the Aristotelian view point.

Thank you!

• Whether the subject (cats or unicorns) actually exists is not the only difference. In the modern logic ("Boolean", actually it is Fregean-Peircean since quantification is involved) "Some X are Y" has the so-called existential import (implies that X-s exist), and "All X are Y" does not. So "All X are Y" never validly implies "Some X are Y". Oct 17, 2019 at 19:35
• Oct 17, 2019 at 19:39