Logical conditional statements -- confusion about the word "only"

BBNinetyOne

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,

_megana_

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!

gabes900-1

@s00anderson 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!

_megana_

@gabes900 said:

@s00anderson 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!