"Without" as a conditional indicator -- troubling issues

[PineapplePizza]

We all know that for "without" "unless" "except" and "until", we're supposed to negate one of the ideas and make that the sufficient.

"I will not get a scholarship without studying" = No study -> No scholarship

But there are situations where that translation method seems clearly incorrect. For example:

"I sleep without wearing a shirt."

Does this mean If No Shirt -> Sleep? Clearly not, yet that's what happens if we negate "wearing a shirt" and make it the sufficient. I submit that the correct way to diagram the sentence above is:

If Sleep -> Not wearing shirt.

This is the correct meaning of the sentence, and yet it is the reverse of what the ordinary method would produce. Why does the ordinary translation method fail in this example?

Also, consider the following sentence:

"I do not sleep without wearing an eyemask."

The ordinary translation method does work for this one: If not eyemask -> No sleep.

What explains why the ordinary method fails for "I sleep without wearing a shirt" but works for "I do not sleep without wearing an eyemask"?

Also, consider these examples.

"No one will become a great physicist without going to Harvard"

No Harvard -> Not great physicist

That one is pretty straightforward, and the ordinary method works.

"One can become great lawyer without getting a 180 on the LSAT.

This one does not appear to express a conditional relationship between "great lawyer" and "180", and in fact expresses the ABSENCE of a conditional relationship -- getting a 180 is not required to be a great lawyer. But the ordinary method would have us translate this to "Not 180 -> can become great lawyer." The contrapositive of that idea is "If one cannot become a great lawyer, then one got a 180." That seems very wrong.

What explains the different ways we treat the two examples above?

[ohthatpatrick]

Mostly, you're just highlighting the fact that our memorized conversion techniques are not bulletproof. We still need to use our wits to judge conditional logic.

FOR THIS ...
"One can become great lawyer without getting a 180 on the LSAT"
... we could never think to make it conditional in the first place, because it's not expressing some constant, timeless relationship. The only certainty it provides is that something is possible.

I could say, "It's possible to get a perfect score on your SAT and on the LSAT". And if we really wanted to, we could diagram that like
if you've gotten a perfect score on SAT --> possible you'll get one on LSAT

But that really defeats the point of conditional logic. We don't bother to symbolize statements that are saying something is POSSIBLE.

We're in the game of symbolizing certainty, whether that comes through:
RULES/CONDITIONS
UNIVERSALS
GUARANTEES
REQUIREMENTS

"Without" is only used on LSAT in a conditional way when it's conveying the idea of a requirement. Hence, you only see it with the other idea being negative as well (it's always in the form of Without this required thing, you can't be/do/have this second thing.)

The situations where the "Without" rule was working for you was sentences in which both ideas were negative:
"I will not get a scholarship without studying" = No study -> No scholarship
"I do not sleep without wearing an eyemask." = If not eyemask -> No sleep.
"No one will become a great physicist without going to Harvard" = No Harvard -> Not great physicist

The notion of saying "Without X, you can't have Y" is inherently stating a requirement.

The ones that weren't working were combining "without" with something positive.
"I sleep without wearing a shirt."
we could write many more
"I give to charity without publicizing it."
"I enjoy sandwiches without mayonnaise. "

It's actually not even clear with these phrasings whether we're implying certainty or not. Does that last claim mean that I ALWAYS enjoy a non-mayo sandwich. Does it mean that I NEVER enjoy a sandwich that has mayo?

LSAT isn't that vague or sloppy if they're testing conditional logic. The certainty would ring through.

I'd suggest you not worry about memorizing "an exception" or "sub-rule" to your current understanding of "without". It's a cool set of counterexamples you manufactured, but I think it's very safe to say that
if you see 'without' being used on LSAT in a conditional sentence, it will follow the rule you know


Hope this helps.

[YekaterinaW835]

Hi Patrick,

To continue this thread of without sometimes being confusing, I came upon the below on a practice drill, and I don’t understand the answer I saw.

Q: No one who really cares would ever just give to a charity without understanding how the charity operates.

They diagrammed it like this:

If really cares —> Does NOT give without understanding
Contra: If gives without understanding—>does NOT really care

How did they get this? It seems to me like the sufficient condition was all cut up, and that without was inserted as part of the necessary condition instead of becoming the necessary condition. Oh, and, the necessary condition was negated!

Do you have any idea what happened here? Thank you! Katya

[YiX773]

Hi Patrick,

To continue this thread of without sometimes being confusing, I came upon the below on a practice drill, and I don’t understand the answer I saw.

Q: No one who really cares would ever just give to a charity without understanding how the charity operates.

They diagrammed it like this:

If really cares —> Does NOT give without understanding
Contra: If gives without understanding—>does NOT really care

How did they get this? It seems to me like the sufficient condition was all cut up, and that without was inserted as part of the necessary condition instead of becoming the necessary condition. Oh, and, the necessary condition was negated!

Do you have any idea what happened here? Thank you! Katya

"No A would do B" means "If you are A, then you would NOT do B".

Q: No one who really cares would ever just give to a charity without understanding how the charity operates.
No ( A ) would ( B )

So, if one who really cares, then one would NOT ever just give to a charity without understanding how the charity operates.
That is: If really cares —> Does NOT give without understanding

BTW, I probably will continue to diagram this one like this:

Really cares —> (Give —> Understanding)

which actually means:

Really cares and Give —> Understanding
/Understanding —> /Really cares or /Give