Naked Science Forum
General Discussion & Feedback => Just Chat! => Topic started by: Jimbee on 01/05/2025 22:24:55
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"Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic."
From Through The Looking-Glass by Lewis Carroll.
Through The Looking-Glass was meant for children. But Carroll incorporated logic into his children's books like in Alice's Adventures in Wonderland and Through the Looking-Glass. He was also a mathematician and logician. In fact, my 8th teacher said some colleges have his children's novels as required reading for this reason.
What error in logic is Tweedledee making here? I took a community college logic class in 1998. And I found it very interesting. Everything that is written has an underlying logic to it. Also, we learned that statements can be logical even if their information is false. And they can be illogical even if their conclusions are correct. For example we learned
All Martians wear purple pajamas.
Stanley is a Martian.
Therefore Stanley wears purple pajamas.
Is logically correct, even if the information in it is all false. But
All presidents of the United States are or were Americans.
Donald Trump is an American.
Therefore Donald Trump is the president.
Is logically wrong. Donald Trump is just coincidentally president and an American. All Americans are not automatically president. (I said this on another message board and a poster said I was wrong. It has been a long time since I took that class. But I think I am correct with that.)
So what error did Tweedledee make? Inductive logic? I remember reading somewhere that is incorrect. But I forget the details.
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All Martians wear purple pajamas.
Stanley is a Martian.
Therefore Stanley wears purple pajamas.
Is logically correct, even if the information in it is all false. But
All presidents of the United States are or were Americans.
Donald Trump is an American.
Therefore Donald Trump is the president.
The mistake is not recognising that
"All presidents are Americans " is not the same as "All Americans are presidents".
The word order matters.
[ Invalid Attachment ]
All Martians wear purple pajamas.
"Martians" comes before "wearers of purple pjs."
But in
All presidents of the United States are or were Americans.
"Americans" comes after "presidents"
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The essence of the democratic process is that anyone can become president of the USA.
Der Furhrer Trumpf is living proof, though it could be argued that the effective POTUS is Vladimir Putin, who owns the majority of Trumpf.
However the logical fallacy is in confusing a subset with a superset. "A contains B" is clearly not equivalent to "B contains A".