RE: The Limits of Logic #3
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For the raining/cloudy example, try thinking about another one:
All triangles are 3-sided
Not a triangle -> not 3-sided
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You are viewing a single comment's thread:
For the raining/cloudy example, try thinking about another one:
All triangles are 3-sided
Not a triangle -> not 3-sided
Again, I think the order is critical and the correct statement would be:
All triangles are 3-sided
not 3-sided -> not a triangle
For instance, a shape with 3 curved sides is not a triangle, but it is 3-sided
Okay, so let's see:
All triangles are 3-sided
A -> B
not 3-sided -> not a triangle
~B -> ~A
squares are 4-sided
C -> D
not 4-sided -> not a square
~D -> ~C
A square -> not 3-sided
C -> ~B
a 4-sided object -> not a triangle
D -> ~A
So everytime we see a non 3-sided object (because it is 4-sided) it is reinforcing the idea that it is not a triangle (it is a square)
Then going further, we could say that a pentagon (which is non 3-sided) implies that it is not a triangle. But if that is true, it would be equivalent to saying that triangles imply they are pentagons, or all sorts of other crazy things.
Yes, absolutely, I agree the paradox is really quite interesting. By reasoning logically, one can end up with an obviously unrelated statement supposedly supporting the original statement. Like I said, I like these logic oddities. Thanks for writing about this paradox.