How to write conditionals with "without"?

lawgical error

Hi guys!

I am a bit confused on how to use "without" when writing out conditionals. I understand that you negate the sufficient when you see the word without, but what if the statement says:

John always sleeps without socks.

Isn't "always" a necessary indicator?

Would it be diagrammed as:

sleep -> /socks (this one makes more sense to me)

or

/socks -> sleep

Another example, I know that if the statement says: You can't come home without making money, the conditional would be written out as:

come home -> made money.

Just a bit confused with the "always... without..." statement I mentioned initially.

Thanks!

cdot9000

sleep -> /socks

Translation: If sleep then no socks.

or

/socks -> sleep

Translation: If no socks then sleep.
This would be incorrect to me because it seems to confuse sufficient and necessary (someone correct me if I am wrong) bc its like, the rule is only for when he sleeps he isn't wearing socks NOT when he isn't wearing socks he is sleeping.

For certain indicators, they are not always actively being an indicator - which is what makes this hard. in that sentence it seems that the indicator is always.

romanbahadursingh

I think cdot9000 has a good grasp but the small error here is that the contra positive of that statement is not correctly translated

alvinsunmerfeild

You are right, I agree with you.

KevinLin7Sage

OP, good question. The issue is that "without" is sometimes used to indicate conditionality, and sometimes used simply to mean the absence of something.

"I always sleep without wearing a shirt."

Here, the "without" is simply part of a description of something that is true when I sleep. When I sleep, my shirt is absent from my body. But "without" is not establishing that "wearing a shirt" is necessary for something else.

"You can't enter the restaurant without wearing a shirt."

Here, the "without" does introduce conditionality. "Cannot ... without" establishes that "wearing a shirt" is necessary for entering the restaurant.

I'm pretty sure the different uses of "without" boil down to whether the the other part of the sentence asserts that something cannot happen without something else (in which case "without" is used just like the Group 3 conditional indicators), or whether it says that something can/does happen without something else. (in which case "without" operates as the negation of a concept, but not as a conditional indicator).