Conditional Logic Paradox - Help pls!

[PineapplePizza]

A -> B.

In this world, it is a could be true that /A --> B. And yet, the contrapositive of this is /B --> A...which contradicts the initial claim, because according to the contrapositive of the initial claim, /B -> /A. Aren't contrapositives supposed to be expressing the exact same logical relationships? Why does the initial statement seem possible but the contrapositive impossible?

All Dogs are Cute = All things that are Not Cute are Not Dogs.

In this world, it's theoretically possible that All things that are NOT Dogs are Cute. But the contrapositive of that idea is All things that are NOT Cute ARE Dogs, which contradicts the initial sentence. This doesn't make sense!

[ohthatpatrick]

Stop writing everything with arrows and then you'll wriggle out of your paradox.

Write CONDITIONAL statements with arrows, but nothing else.

You said:
GIVEN: A -> B.

In this world, it is a could be true that /A --> B.


If you just meant "it's possible that something that is ~A could be B", you're right, but we wouldn't write that as a conditional, since it's not a permanent inflexible piece of certainty that "being ~A implies you are B".

If you meant that "It's possible for something and its logical opposite to both lead to the same idea", those are hard to come up with. That only works if everything in the universe is B.

So you could say something like
"If a physical object is in my house, it exists"
but also say
"If a physical object is not in my house, it exists".

Those contrapositives WOULD contradict
"If a physical object doesn't exist, then it's not in my house"
and
"If a physical object doesn't exist, then it's in my house"

Obviously, someone sane should step in here and remind us, "Hey, dorks, why are you guys worrying about this? The only time it would ever be true that A --> B and that ~A --> B is when everything in the universe is B. Do we really have to worry about that contingency?"

No, we definitely don't. Thank you, Rhetorical device.

You were worried:
And yet, the contrapositive of this is /B --> A...which contradicts the initial claim, because according to the contrapositive of the initial claim, /B -> /A. Aren't contrapositives supposed to be expressing the exact same logical relationships? Why does the initial statement seem possible but the contrapositive impossible?


Contrapositives and initial claims are saying the same thing.

You created a paradox by adding a 2nd conditional, which contradicted the 1st one.
The initial statement AND the contrapositive are impossible.

You gave us:
A --> B
(~B --> ~A)

Then you gave us:
~A --> B
(~B --> A)

So your 2nd conditional contradicts both the initial statement and the contrapositive of the initial statement.