A mistake the book?

Philosophical, mathematical and computational logic, linguistics, formal argument, game theory, fallacies, paradoxes, puzzles and other related issues.

A mistake the book?

Postby BadgerJelly on March 8th, 2018, 1:47 am 

I have just read something from "The Cave and The Light" by Arthur Herman and I am taking the firm stance that it is a horrible mistake.

Sorry, on phone so "quoting" is an issue:

"All human beings are rational.
Some human beings are American.
Therefore, some Americans are rational."

And the funny thing is ... now that I've just typed this out I now see that it is actually correct! Haha!

The problem is what we understand an American to be. I am assuming all Americans are human, but the logical statements are arbitrary, in the sense that we come to the statement with semantic knowledge, so whilst we can say that the statement is "true" in a purely logical sense (ignoring the semantic weight of particular terms of category) it is also contradictory because we know well enough that Americans are all human so all Americans must be rational according the first statement.

I think this example show well the easy misconceptions that pop up in logic. The first two statements must be taken together and bracketed out from any other inference. The problem then is the value of the statement becomes completely mute.

What the statements really say, ignoring the American/human issue, is that some Americans are definitely rational and the rest of the Americans we cannot comment on and that can wrongly be taken to insinuate that the "other" Americans are not rational when in fact no such conclusion is apparent and we merely fall prey to our automatic bias of placing every item of experience into direct polar opposition.

I found this interesting, yet all too obvious.

Note: I did not make up the start for effect. I literally thought it was wrong! Haha!
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