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.

Can someone please explain?

Thank you!


1 Answer 1


You are taking a logic class but did not specify which department in your school is doing the teaching. I mention this because there is a distinction between old school philosophy and what is taught under that concept and the modern Mathematical logic which is often today taught by staff in Mathematics or Philosophy.

First off I must point out most human beings that speak on the topic of alleged logic really mean "Mathematical Logic". That is the specific NAME -- just LOGIC. What do I mean? Well there are typically three periods of the history of deductive reasoning: Aristotelian logic, medevial logic, and Modern logic. The stand out point is Modern "Mathematical Logic" utilizes symbols in the reasoning that stand for logical operations like NOT, AND, OR, IMPLIES, EQUIVALENT, etc. None of the prior historic deductive reasoning points in -- this alleged logic -- had such symbolic representation. Aristotelian logic was closer to the subject of RHETORIC than Mathematics. No symbolic representation with the operations like in mathematics. Syllogisms were the primary tool to argue. There are rules for syllogisms which math does not cover. So there are parts of alleged logic that math does not cover. So math is not equal to deductive reasoning. Math utilizes some deductive reasoning techniques.

Existienal import did not become popular until modern logic aka "Mathematical Logic". It is true that one could trip and make a mistake in reasoning if we were to say All trespassers parked without a valid sticker will be towed that there were actually cars towed. Did we just BREAK LOGIC? It is possible there are no towed cars which makes the set empty. How do we fix this problem? We clearly see this is not 100 percent accurate. Let's really be honest here: existential import is BASED ON SENSE VERIFICATION. Mathematical logic or people who claim to study logic typically say "Logic is about FORM -- not content." Well my friend, that us your first QUESTION to the instructor of you logic class. We have a problem!!! If logic were JUST ABOUT FORM then how do you KNOW about existential import? How would you as you say LOGICALLY KNOW there are no unicorns? Existence is not a property of logic but of science. Science uses sense verification to justify its reasoning about existence or non existence. The Mathematical people who were interested in logic in the mid 1800s wanted logic to be LIKE SCIENCE and verifiable. That is how existential import arose in the first place. Aristotelian logic and medevial logic took the conceptual approach to deductive reasoning. They defined terms properly and tried to not violate concepts previously defined and accepted. The fundamental concept was "proposition" which seemed to have been watered down today. We all have likely heard something to the effect a proposition is true or false. If logic is about form there is no existence or sense verification on a conceptual level. A concept is in the mind. So originally this implies that in Aristotelian logic form was not All logic was about. The concept had to apply to REALITY. This implies that the concept had to apply to reality and then we could be certain the truth value of the propositions in question. Validity is trivial as we can have valid arguments with false premises involved. This implies SOUNDNESS was the primary concept to evaluate arguments. Sound arguments are arguments that MUST HAVE true propositions throughout and must be valid.

The proposition "All unicorns are white colored animals" would indeed necessitate that "Some unicorns are white colored animals" if the unicorns were sense verified already. What has happened in this generation is that You already came in with scientific knowledge and knowledge about logic as a topic. The proposition about all cats are animals is known from science which this magic math logician already knows as well. Then the magician aka math person waves his magic wand and says "IT's LOGIC!" No my man its Science with logic mixed in between! You already KNEW THE PROPOSITION about unicorns by science was FALSE which is how you came to the conclusion that the universal proposition does not always necessitate the particular proposition. Deductive reasoning FORM does not inform you there are no unicorns in existence in reality.

If the original proposition about unicorns is true and there is sense verification of unicorn there is no doubt that the concept of conversion of an A type proposition must also be true. Again to say that there are no x in existence is sense verification not logic. So the mathematicans seem to have a lie or a paradox on their hands to say "logic is about form --not content". Deductive reasoning uses BOTH content (pattern repetition) and sense verification. I would say Aristotelian logic used BOTH as well. The focus was not on validity but soundness. No false premises would be allowed.

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