A quick way to build your intuition that causal claims don't contrapose is to recognize that causation is time-bound -- the cause has to happen before the effect. "Contraposing" causal claims involves putting the effecty-thing before the causy-thing, which in most cases makes it clear even to the untrained ear that it's not a legit move. See the rooster example for instance -- the negation part of the contrapositive is whatever, but putting roosters on the "cause" side of the arrow is immediately ridiculous. Roosters doing or not-doing anything doesn't have any effect on the sun.
Semi-relatedly, I think there's a common confusion when describing real world situations that involve both conditional and causal elements. Situations like that are pretty common. For example, consider my morning yoga routine:
1: Every time I do yoga I feel good. (conditional)
2: Doing yoga causes me to feel good. (causal)
In conversational English we're likely to collapse those elements and say something like:
Conditiony-causy 1+2: Doing yoga always makes me feel good.
We can change the wording of that sentence in a way that seems likecontraposition:
1+2 (CP??): If I'm not feeling good, that's because I didn't do yoga.
But notice that the causal element doesn't actually switch direction there -- yoga is still the causy-thing and feeling good is still the effecty-thing. Really we're just leaning on the fact that we can validly contrapose the conditional element of the scenario...
1 (CP): If I'm not feeling good, I didn't do yoga.
...and then layering causation on top of that in a way that happens to match reality in this particular situation.
So the main takeaway is to just separate conditionality from causality in your head. They are two different things -- you should think about conditional stuff according to the rules of conditional logic, and you should think about causal stuff according to the rules of causation. Scenarios often involve both elements, which makes it super important not to conflate the two when thinking about those scenarios. Treat each element separately.
Can you clarify what you are asking? A contrapositive is a relationship between two formal logic statements - one is the contrapositive of the other. You can chain FL statements, and the fact that you got a FL statement by contraposing another FL statement doesn't change that it's a FL statement.
If you mean can you turn A -> B -> C into not C → not B → Not A, then yes, because you are just taking
A → B
B -> C
and turning them into
not B → not A
Not C → Not B
But I don't like big left to right chains. I like to keep each separate statement on its own in a list so I can scan the left column. That's just my preference based on how my brain works.
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5 comments
Short answer is no.
True: The sun coming up causes roosters to crow.
Not True: Roosters not crowing causes the sun to not come up.
@MichaelWright thank you! This is exactly what I needed. If you don’t mind my asking though, what is the long answer?
@sasquatch_believer haha okay okay
A quick way to build your intuition that causal claims don't contrapose is to recognize that causation is time-bound -- the cause has to happen before the effect. "Contraposing" causal claims involves putting the effecty-thing before the causy-thing, which in most cases makes it clear even to the untrained ear that it's not a legit move. See the rooster example for instance -- the negation part of the contrapositive is whatever, but putting roosters on the "cause" side of the arrow is immediately ridiculous. Roosters doing or not-doing anything doesn't have any effect on the sun.
Semi-relatedly, I think there's a common confusion when describing real world situations that involve both conditional and causal elements. Situations like that are pretty common. For example, consider my morning yoga routine:
In conversational English we're likely to collapse those elements and say something like:
We can change the wording of that sentence in a way that seems like contraposition:
But notice that the causal element doesn't actually switch direction there -- yoga is still the causy-thing and feeling good is still the effecty-thing. Really we're just leaning on the fact that we can validly contrapose the conditional element of the scenario...
...and then layering causation on top of that in a way that happens to match reality in this particular situation.
So the main takeaway is to just separate conditionality from causality in your head. They are two different things -- you should think about conditional stuff according to the rules of conditional logic, and you should think about causal stuff according to the rules of causation. Scenarios often involve both elements, which makes it super important not to conflate the two when thinking about those scenarios. Treat each element separately.
@MichaelWright Thank you!!!
Can you clarify what you are asking? A contrapositive is a relationship between two formal logic statements - one is the contrapositive of the other. You can chain FL statements, and the fact that you got a FL statement by contraposing another FL statement doesn't change that it's a FL statement.
If you mean can you turn A -> B -> C into not C → not B → Not A, then yes, because you are just taking
A → B
B -> C
and turning them into
not B → not A
Not C → Not B
But I don't like big left to right chains. I like to keep each separate statement on its own in a list so I can scan the left column. That's just my preference based on how my brain works.