I’ve thought about starting making videos on Youtube. I don’t know how to edit and I know making a “theatric” or visually appealing video is time consuming, but I think I might start just to make introduction to logic videos. My first idea was to explain a very basic concept in logic. And that is that every x and only x are very different things.
POP QUIZ: If I were, in theory, a racist, and as two Australian men walked by my house I remarked, “only Australian people are criminals.” Would this, were it to be true, be sufficient to know whether they were criminals?
A – Yes
B – No
The answer is No. For the statement, “only Australian people are criminals,” says nothing about these two Australian gentleman. It only indicates that they could be criminals. Not that they necessarily are. If I saw two Arabic gentlemen walk by my house, and if the proposition “only black people are criminals,” were true, then I knew they couldn’t be criminals because they weren’t black. In theory, there could be only one criminal in the world.
Now, remove the above statement and replace it with, “all black people are criminals.” If the statement were true then what would we know about a black man and a white man walking past us?
A – Neither are criminals
B – Both are criminals
C – We know the black man is a criminal but know nothing of the white man
D – We know the white man is a criminal but know nothing of the black man
The answer is C. For if the statement were true, and if the man is black, then to have the statement both be true and the black man not be a criminal is a logical impossibility. However, just knowing all black people to be criminals (in theory of course) says nothing about the criminality of people of different races. Every black and white person could be a criminal. Every black person and all white people save one could be criminals.
Now, take the statements above and combine them. All black people are criminals, and only black people are criminals. Apply this to the same scenario as above and answer the same question:
A – Both are criminals
B – We know the black person is a criminal but don’t know if the white person is
C – We don’t know if either are criminals
D – We know the black person is a criminal and the white person isn’t
The answer is D. For if both statements are true then we not only know that any black person is a criminal (from the all statement), we know that any other person who is non-black cannot be a criminal (from the only statement).
Adam from YMS, Ben from the Drunken Peasants and numerous others commit the logical error of mistaking “all” and “only” statements. Logic is important. Though I can’t ground that statement in pure logic to know that it’s necessarily true.