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Hi all,
Helpful insight would be appreciated; I am practicing my "translating" my Sufficient & Necessary conditional statements.
"Only" is a "group 2" operator that introduces the necessary condition, but I'm finding it difficult to figure out why this matters in certain simplistic contexts.
Consider the statement: "Only cats meow."
M --> C
/C --> /M
But with "only" sentences, it seems like the reverse logical operation is also true.
C --> M
/M --> /C
Am I simplifying it too much? In other words, is this logical reasoning or rule only relevant when ideas are more complex?
Thanks,
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3 comments
@gabeshelton3715 said:
@s00anderson268 said:
Let's look at the original statement first: "Only cats meow." Do Dogs meow? No. Do cows meow? No. Only cats meow.
Ok, so then we know if an animal is meows, it must be a cat. Hence, the translation rule:
M --> C (If meow, then cat).
Now looking at C --> M (if cat, then meow), we can't infer this from the statement "Only cats meow." For all we know, our particular cat could bark. Just because you are a cat, that doesn't mean you meow. We just know from our statement that Only cats meow, not dogs, not cows, only cats.
I hope that clarifies some confusion!
Was going to respond too, but this is a great explanation!
Thanks! Feel free to add on as well!
@s00anderson268 said:
Let's look at the original statement first: "Only cats meow." Do Dogs meow? No. Do cows meow? No. Only cats meow.
Ok, so then we know if an animal is meows, it must be a cat. Hence, the translation rule:
M --> C (If meow, then cat).
Now looking at C --> M (if cat, then meow), we can't infer this from the statement "Only cats meow." For all we know, our particular cat could bark. Just because you are a cat, that doesn't mean you meow. We just know from our statement that Only cats meow, not dogs, not cows, only cats.
I hope that clarifies some confusion!
Was going to respond too, but this is a great explanation!
Let's look at the original statement first: "Only cats meow." Do Dogs meow? No. Do cows meow? No. Only cats meow.
Ok, so then we know if an animal meows, it must be a cat. Hence, the translation rule:
M --> C (If meow, then cat).
Now looking at C --> M (if cat, then meow), we can't infer this from the statement "Only cats meow." For all we know, our particular cat could bark. Just because you are a cat, that doesn't mean you meow. We just know from our statement that Only cats meow, not dogs, not cows, only cats.
I hope that clarifies some confusion!