Method for translating "without" into lawgic seems to run into problems in some situations

lsat4life

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?

akistotle

This is interesting because "it gets into the weeds of how ambiguous English is" (quoting @"J.Y. Ping").

"I sleep without wearing a shirt" is not a conditional statement because we know from our common sense that it means "I sometimes sleep without wearing a shirt."

But I'm tagging @"Cant Get Right" because I'm sure he can explain better than I do!

Related discussion:
https://7sage.com/discussion/#/discussion/14942/until-as-a-logical-indicator

Seeking Perfection

This is sort of a question dodge, but I never bought into that part of lawgic all that much.

What I found more useful was to turn the sentence into a conditional not based on a rule, but on understanding.

"I sleep without wearing a shirt." could be rephrased to "If I'm sleeping, then I'm not wearing a shirt."
Sleep-->¬Shirt
Now language is ambiguous so its not clear that this is a good translation.
Does "I sleep without wearing a shirt." actually mean "I always sleep without wearing a shirt." or "I usually sleep without wearing a shirt" or "I sometimes sleep without wearing a shirt."? This translation would only work if we meant always. We probably actually mean sometimes. Thankfully, language on the actual LSAT is never or almost never written in ambiguous fashion.

"I do not sleep without wearing an eye mask." doesn't suffer from this ambiguity. We kind of negated it away. I sleep without wearing an eye mask is ambiguous. Does he always sleep that way or only sometimes? But when we negate it, we end up with clarity. The sentence "I do not sometimes sleep without wearing an eye mask" does not actually change the meaning. The sentence "I do not always sleep without an eye mask" does evidently change the meaning entirely.

Lawgic translations assumes we are using sometimes in boththis negated case where it is clear and the ambiguous case which is why we get what feels like the wrong translation in the other case.

Hence, we can translate this clear sentence either using the rule or a more intuitive approach.
If he is not wearing an eye mask then he doesn't sleep.
¬Wearing Mask --> ¬Sleep
Consequently, Sleep --> Wearing Mask

@thrillhouse said:
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.

Its not that wrong. If we said a specific person say Sally instead of one to make it clearer will either get a 180 or a 179 on the LSAT.

If we then had the statement, "Sally can become a great lawyer without getting a 180 on the LSAT" your application would make sense.

If Sally gets a 179 she can still become a great lawyer. That's what our statement tells us.
Sally Gets a 179--> Sally can become a great lawyer.

So if Sally cannot become a great lawyer which of the two possible scores could she have gotten? It has to be the 180.
Therefore
Sally Cannot Become a Great Lawyer --> Sally got a 180

Of course it's possible that there is no way for Sally to be made unable to become a great lawyer simply by virtue of her LSAT. In which case the sufficient condition (Sally Cannot Become a Great Lawyer) will never be triggered.

The logic actually works the same if you can keep the options at 180 or Not 180.

Not having a 180 won't prevent Sally from becoming a great lawyer. (A 120 might, but then it won't be not having a 180 that stops her. We have to avoid subdividing out the other 39 options.)
Could having a 180 prevent Sally(or one) from being a good lawyer. As far as we know it could. There are two options one not having the 180 which won't stop her; the other having it which might. Therefore if she is stopped by one of the two options, it will be having the 180.

Maybe the 180 makes Sally arrogant or turns her into an LSAT tutor.

Most likely though it is just true that neither getting nor not getting the 180 can stop Sally from having the possibility of being a good lawyer. If she'll never (based on getting or not getting the 180) not be able to be a good lawyer then we can but anything as the neccessary condition and still be correct.

Sally cannot become a good lawyer (based on whether her LSAT score is 180) --> Earth will explode tomorrow and no one will survive

This would be valid if the sufficient condition is never fulfilled.

I hope that helped a little. Sorry for the repetition.

lsat4life

@"Seeking Perfection" said:
This is sort of a question dodge, but I never bought into that part of lawgic all that much.

What I found more useful was to turn the sentence into a conditional not based on a rule, but on understanding.

"I sleep without wearing a shirt." could be rephrased to "If I'm sleeping, then I'm not wearing a shirt."
Sleep-->¬Shirt
Now language is ambiguous so its not clear that this is a good translation.
Does "I sleep without wearing a shirt." actually mean "I always sleep without wearing a shirt." or "I usually sleep without wearing a shirt" or "I sometimes sleep without wearing a shirt."? This translation would only work if we meant always. We probably actually mean sometimes. Thankfully, language on the actual LSAT is never or almost never written in ambiguous fashion.

"I do not sleep without wearing an eye mask." doesn't suffer from this ambiguity. We kind of negated it away. I sleep without wearing an eye mask is ambiguous. Does he always sleep that way or only sometimes? But when we negate it, we end up with clarity. The sentence "I do not sometimes sleep without wearing an eye mask" does not actually change the meaning. The sentence "I do not always sleep without an eye mask" does evidently change the meaning entirely.

Lawgic translations assumes we are using sometimes in boththis negated case where it is clear and the ambiguous case which is why we get what feels like the wrong translation in the other case.

Hence, we can translate this clear sentence either using the rule or a more intuitive approach.
If he is not wearing an eye mask then he doesn't sleep.
¬Wearing Mask --> ¬Sleep
Consequently, Sleep --> Wearing Mask

@thrillhouse said:
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.

Its not that wrong. If we said a specific person say Sally instead of one to make it clearer will either get a 180 or a 179 on the LSAT.

If we then had the statement, "Sally can become a great lawyer without getting a 180 on the LSAT" your application would make sense.

If Sally gets a 179 she can still become a great lawyer. That's what our statement tells us.
Sally Gets a 179--> Sally can become a great lawyer.

So if Sally cannot become a great lawyer which of the two possible scores could she have gotten? It has to be the 180.
Therefore
Sally Cannot Become a Great Lawyer --> Sally got a 180

Of course it's possible that there is no way for Sally to be made unable to become a great lawyer simply by virtue of her LSAT. In which case the sufficient condition (Sally Cannot Become a Great Lawyer) will never be triggered.

The logic actually works the same if you can keep the options at 180 or Not 180.

Not having a 180 won't prevent Sally from becoming a great lawyer. (A 120 might, but then it won't be not having a 180 that stops her. We have to avoid subdividing out the other 39 options.)
Could having a 180 prevent Sally(or one) from being a good lawyer. As far as we know it could. There are two options one not having the 180 which won't stop her; the other having it which might. Therefore if she is stopped by one of the two options, it will be having the 180.

Maybe the 180 makes Sally arrogant or turns her into an LSAT tutor.

Most likely though it is just true that neither getting nor not getting the 180 can stop Sally from having the possibility of being a good lawyer. If she'll never (based on getting or not getting the 180) not be able to be a good lawyer then we can but anything as the neccessary condition and still be correct.

Sally cannot become a good lawyer (based on whether her LSAT score is 180) --> Earth will explode tomorrow and no one will survive

This would be valid if the sufficient condition is never fulfilled.

I hope that helped a little. Sorry for the repetition.

Thanks for the response everyone.

Seeking Perfection, your discussion of the "I sleep without wearing a shirt" and how that differs from a sentence beginning with a negation - "I never sleep without wearing an eyemask" makes a lot of sense. But I would like to push for rules that help us in these situations -- I understand your recommendation to think about the meaning of the sentence and avoid "lawgic" rules, but that position seems counter to the way that language works. And it is often a source of frustration when we LSAT students encounter tough issues! The idea that language depends on context is true, yet there must be rules to that context, no? It doesn't make any sense to me for some aspect of language to turn on "context" without being susceptible to a rule. That rule may be one that is hard to articulate precisely, but there IS a rule, even if one would call it a "contextual" rule.

"I always sleep without wearing a shirt." I see that if we add "always", it adds clarity. This sentence means "If I'm sleeping -> Not wearing a shirt." And it does not follow the ordinary rule for "without" (where without introduces a necessary condition and we negate the other part of the sentence and make it the sufficient.)

I wonder if that is because there are 2 meanings of without? In the example immediately above, "without" is being used to describe the lack of a particular thing in a particular situation. But perhaps that is a different use of "without" than when the sentence begins with a negative:

"I never sleep without wearing an eyemask." Could this use of "without" be a conditional use, which is distinct from the meaning of "without" in the sense of lacking a particular thing in a particular circumstance? Maybe this is exactly what you were getting at? I wonder if the rule we can derive is that when without is paired with a positive in the other part of the sentence, it does not introduce a requirement, whereas if without is paired with a negative, then the ordinary "lawgic" rule applies.

For the other statement - "One can become a great lawyer without getting a 180" - I am not entirely persuaded by your explanation. This sentence seems to be something that we would not view as a conditional, because it is stating that getting a 180 is not required to become a great lawyer. "Sally can become a great lawyer without getting a 180." Is this truly asserting that if Sally cannot become a great lawyer, she must have gotten a 180? Consider the situation where Sally can become a great lawyer without getting a 180, as long as she studies hard in law school and gets lucky in her career. In this situation, if Sally cannot become a great lawyer, then it doesn't have to mean she got a 180, because she may have failed to become a great lawyer from lacking luck in her career or from failing to study. The original sentence is not expressing that there is nothing else that is required in order to be a great lawyer; but your reading of it seems to turn on that interpretation. Rather than reading it as "If she does not get a 180, she can become a great lawyer," I still think it should be read as "Getting a 180 is not required to become a great lawyer." (I also wonder whether specifying "Sally" changes the meaning from the original, more general statement.)

Thanks for any insight into these issues.

Seeking Perfection

@thrillhouse said:

@"Seeking Perfection" said:
This is sort of a question dodge, but I never bought into that part of lawgic all that much.

What I found more useful was to turn the sentence into a conditional not based on a rule, but on understanding.

"I sleep without wearing a shirt." could be rephrased to "If I'm sleeping, then I'm not wearing a shirt."
Sleep-->¬Shirt
Now language is ambiguous so its not clear that this is a good translation.
Does "I sleep without wearing a shirt." actually mean "I always sleep without wearing a shirt." or "I usually sleep without wearing a shirt" or "I sometimes sleep without wearing a shirt."? This translation would only work if we meant always. We probably actually mean sometimes. Thankfully, language on the actual LSAT is never or almost never written in ambiguous fashion.

"I do not sleep without wearing an eye mask." doesn't suffer from this ambiguity. We kind of negated it away. I sleep without wearing an eye mask is ambiguous. Does he always sleep that way or only sometimes? But when we negate it, we end up with clarity. The sentence "I do not sometimes sleep without wearing an eye mask" does not actually change the meaning. The sentence "I do not always sleep without an eye mask" does evidently change the meaning entirely.

Lawgic translations assumes we are using sometimes in boththis negated case where it is clear and the ambiguous case which is why we get what feels like the wrong translation in the other case.

Hence, we can translate this clear sentence either using the rule or a more intuitive approach.
If he is not wearing an eye mask then he doesn't sleep.
¬Wearing Mask --> ¬Sleep
Consequently, Sleep --> Wearing Mask

@thrillhouse said:
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.

Its not that wrong. If we said a specific person say Sally instead of one to make it clearer will either get a 180 or a 179 on the LSAT.

If we then had the statement, "Sally can become a great lawyer without getting a 180 on the LSAT" your application would make sense.

If Sally gets a 179 she can still become a great lawyer. That's what our statement tells us.
Sally Gets a 179--> Sally can become a great lawyer.

So if Sally cannot become a great lawyer which of the two possible scores could she have gotten? It has to be the 180.
Therefore
Sally Cannot Become a Great Lawyer --> Sally got a 180

Of course it's possible that there is no way for Sally to be made unable to become a great lawyer simply by virtue of her LSAT. In which case the sufficient condition (Sally Cannot Become a Great Lawyer) will never be triggered.

The logic actually works the same if you can keep the options at 180 or Not 180.

Not having a 180 won't prevent Sally from becoming a great lawyer. (A 120 might, but then it won't be not having a 180 that stops her. We have to avoid subdividing out the other 39 options.)
Could having a 180 prevent Sally(or one) from being a good lawyer. As far as we know it could. There are two options one not having the 180 which won't stop her; the other having it which might. Therefore if she is stopped by one of the two options, it will be having the 180.

Maybe the 180 makes Sally arrogant or turns her into an LSAT tutor.

Most likely though it is just true that neither getting nor not getting the 180 can stop Sally from having the possibility of being a good lawyer. If she'll never (based on getting or not getting the 180) not be able to be a good lawyer then we can but anything as the neccessary condition and still be correct.

Sally cannot become a good lawyer (based on whether her LSAT score is 180) --> Earth will explode tomorrow and no one will survive

This would be valid if the sufficient condition is never fulfilled.

I hope that helped a little. Sorry for the repetition.

Thanks for the response everyone.

Seeking Perfection, your discussion of the "I sleep without wearing a shirt" and how that differs from a sentence beginning with a negation - "I never sleep without wearing an eyemask" makes a lot of sense. But I would like to push for rules that help us in these situations -- I understand your recommendation to think about the meaning of the sentence and avoid "lawgic" rules, but that position seems counter to the way that language works. And it is often a source of frustration when we LSAT students encounter tough issues! The idea that language depends on context is true, yet there must be rules to that context, no? It doesn't make any sense to me for some aspect of language to turn on "context" without being susceptible to a rule. That rule may be one that is hard to articulate precisely, but there IS a rule, even if one would call it a "contextual" rule.

"I always sleep without wearing a shirt." I see that if we add "always", it adds clarity. This sentence means "If I'm sleeping -> Not wearing a shirt." And it does not follow the ordinary rule for "without" (where without introduces a necessary condition and we negate the other part of the sentence and make it the sufficient.)

I wonder if that is because there are 2 meanings of without? In the example immediately above, "without" is being used to describe the lack of a particular thing in a particular situation. But perhaps that is a different use of "without" than when the sentence begins with a negative:

"I never sleep without wearing an eyemask." Could this use of "without" be a conditional use, which is distinct from the meaning of "without" in the sense of lacking a particular thing in a particular circumstance? Maybe this is exactly what you were getting at? I wonder if the rule we can derive is that when without is paired with a positive in the other part of the sentence, it does not introduce a requirement, whereas if without is paired with a negative, then the ordinary "lawgic" rule applies.

For the other statement - "One can become a great lawyer without getting a 180" - I am not entirely persuaded by your explanation. This sentence seems to be something that we would not view as a conditional, because it is stating that getting a 180 is not required to become a great lawyer. "Sally can become a great lawyer without getting a 180." Is this truly asserting that if Sally cannot become a great lawyer, she must have gotten a 180? Consider the situation where Sally can become a great lawyer without getting a 180, as long as she studies hard in law school and gets lucky in her career. In this situation, if Sally cannot become a great lawyer, then it doesn't have to mean she got a 180, because she may have failed to become a great lawyer from lacking luck in her career or from failing to study. The original sentence is not expressing that there is nothing else that is required in order to be a great lawyer; but your reading of it seems to turn on that interpretation. Rather than reading it as "If she does not get a 180, she can become a great lawyer," I still think it should be read as "Getting a 180 is not required to become a great lawyer." (I also wonder whether specifying "Sally" changes the meaning from the original, more general statement.)

Thanks for any insight into these issues.

Not sure I have anything more to offer on the eyemask thing. I think you can get therewith or without lawgic, but I just didn't find it very helpful in these types of cases. Sometimes our language is ambiguous, but thankfully it isn't on the LSAT.

Getting a 180 is not required to be a great lawyer is indeed a valid way of restating the sentence. It is still a conditional statement.

We know...

Not getting a 180 --> is possible to be a Good Lawyer as far as LSAT performance is concerned.

And consequently...

¬ Possible to be a Good Lawyer as far as LSAT Performance is Concerned --> Got a 180

Is this truly asserting that if Sally cannot become a great lawyer, she must have gotten a 180?

No it means if she cannot become a great lawyer because of whether or not she got a 180, then she must have got a 180. Certainly other thibgs like not trying could prevent Sally from becoming a great lawyer. However, we have to keep them outside the scope. Otherwise for some people it may not be possible to be a great lawyer without getting a 180(or with getting a 180 although that doesn't matter to our original sentence) since they won't put in the needed effort. For these people a 180 would be required to succeed along with anything else you can name since they will never be grest lawyers and consequently anything can be in the neccessary condition. This wrecks both are original sentence and our negated lawgic version. It is attacking the premise.

lsat4life

@"Seeking Perfection" said:

Getting a 180 is not required to be a great lawyer is indeed a valid way of restating the sentence. It is still a conditional statement.

We know...

Not getting a 180 --> is possible to be a Good Lawyer as far as LSAT performance is concerned.

And consequently...

¬ Possible to be a Good Lawyer as far as LSAT Performance is Concerned --> Got a 180

Is this truly asserting that if Sally cannot become a great lawyer, she must have gotten a 180?

No it means if she cannot become a great lawyer because of whether or not she got a 180, then she must have got a 180. Certainly other thibgs like not trying could prevent Sally from becoming a great lawyer. However, we have to keep them outside the scope. Otherwise for some people it may not be possible to be a great lawyer without getting a 180(or with getting a 180 although that doesn't matter to our original sentence) since they won't put in the needed effort. For these people a 180 would be required to succeed along with anything else you can name since they will never be grest lawyers and consequently anything can be in the neccessary condition. This wrecks both are original sentence and our negated lawgic version. It is attacking the premise.

Thank you for responding.

I don't understand the idea of adding "as far as LSAT performance is concerned." Didn't you originally say that "Sally can become a great lawyer without getting a 180" = "Sally Cannot Become a Great Lawyer --> Sally got a 180"??

Imagine that these are true facts about the world: Getting a 180 is not required to be a great lawyer. However, hard work and luck are required in order to become a great lawyer.

Now, within this world, we are examining the following statement: "Sally can become a great lawyer without getting a 180." That statement is true given the facts above. You seemed to agree that that statement means "Getting a 180 is not required for Sally to be great lawyer." With that understanding, if Sally cannot become a great lawyer, I don't see why that necessarily means she got a 180, because she may have lacked the other things. I don't see why those other requirements would be out of scope.

You seem to be reading the statement "Sally can become a great lawyer without getting a 180" and ""Getting a 180 is not required for Sally to be great lawyer" as including the assertion "Sally definitely has the ability to become a great lawyer." That seems to be why you view a world in which Sally could not become a great lawyer for lack of the other requirements as attacking a premise. However, I am reading that statement as not expressing whether or not Sally has the ability to become a great lawyer. It is merely saying whether she can become a great lawyer is unrelated in a conditional manner to getting a 180. We still do not know whether she in fact can become great lawyer.

This is related to why I wonder whether turning "One can become a great lawyer without getting a 180" into a statement about a specific person, Sally, changes the meaning. The more general statement I do not read as asserting that every single person in the world definitely has the ability to become a great lawyer -- only that getting a 180 is not required to be a great lawyer. It seems plain to me that in that world one can fail to be a great lawyer for other reasons besides anything relating to the LSAT, which is why it does not imply that if one cannot become a great lawyer, they must have gotten a 180.

I read the Sally statement in the exact same way. But if one were to read that Sally statement as saying she definitely can become a great lawyer, I think we run into the issue we are debating.

Seeking Perfection

I don't understand the idea of adding "as far as LSAT performance is concerned." Didn't you originally say that "Sally can become a great lawyer without getting a 180" = "Sally Cannot Become a Great Lawyer --> Sally got a 180"??

Imagine that these are true facts about the world: Getting a 180 is not required to be a great lawyer. However, hard work and luck are required in order to become a great lawyer.

If these are true facts about the world Sally might not be able to become a great lawyer(if she wasn't going to put in the work or wasn't lucky) in which case she also wouldn't be able to become a great lawyer without getting a 180. The premise would therefore be false.

One is a specific person, every specific person for the purposes of logic so it is valid to make it a specific person.

I might not be explaining it very well, but if there is someone who cannot become a great lawyer at all, then we can't say one can become a great lawyer and then also can't say that one can become a great lawyer without getting a 180.

The more general statement I do not read as asserting that every single person in the world definitely has the ability to become a great lawyer -- only that getting a 180 is not required to be a great lawyer.

But it does. What if it just said "One can become a great lawyer." or "One can accomplish his/her dreams."
That's not saying there is at least a single person who can do whatever the task is. It is saying everyone can do the thing. In our case the thing is "become a great lawyer without getting a 180".

If a person on the street told me "One can become a great lawyer without getting a 180" I wouldn't bat an eye. I would assume they mean exactly what you think and they undoubtedly would. But, the logical meaning of what they said is different.

lsat4life

@"Seeking Perfection" said:

I don't understand the idea of adding "as far as LSAT performance is concerned." Didn't you originally say that "Sally can become a great lawyer without getting a 180" = "Sally Cannot Become a Great Lawyer --> Sally got a 180"??

Imagine that these are true facts about the world: Getting a 180 is not required to be a great lawyer. However, hard work and luck are required in order to become a great lawyer.

If these are true facts about the world Sally might not be able to become a great lawyer(if she wasn't going to put in the work or wasn't lucky) in which case she also wouldn't be able to become a great lawyer without getting a 180. The premise would therefore be false.

One is a specific person, every specific person for the purposes of logic so it is valid to make it a specific person.

I might not be explaining it very well, but if there is someone who cannot become a great lawyer at all, then we can't say one can become a great lawyer and then also can't say that one can become a great lawyer without getting a 180.

The more general statement I do not read as asserting that every single person in the world definitely has the ability to become a great lawyer -- only that getting a 180 is not required to be a great lawyer.

But it does. What if it just said "One can become a great lawyer." or "One can accomplish his/her dreams."
That's not saying there is at least a single person who can do whatever the task is. It is saying everyone can do the thing. In our case the thing is "become a great lawyer without getting a 180".

If a person on the street told me "One can become a great lawyer without getting a 180" I wouldn't bat an eye. I would assume they mean exactly what you think and they undoubtedly would. But, the logical meaning of what they said is different.

I think I understand what you're getting at, you are clarifying well. But my question now then is how you would express the idea that I had in mind (besides turning "one" into "at least one person").

In particular what about "People can become a great lawyer without getting a 180." Do you view that as different in meaning from "One can become a great lawyer without getting a 180."? Couldn't there be a difference in meaning in that a statement about "people" isn't always a statement about every single person but can be statement about the group generally? (And if so, is "one" EVER susceptible to that same interpretation?)

I also am curious how one would express the idea that getting a 180 is not required to be a great lawyer without also asserting that there are any individuals out there who in fact have such ability. For example, in the world I described earlier -- where getting a 180 is not required to be a great lawyer, but luck and hard work are -- could it be impossible for anyone in the world to be a great lawyer because nobody happens to have the requisite luck and hard work, and yet the idea that "a 180 is not required to be a great lawyer" still be true? How would one express the idea there is no conditional relationship between a 180 and great lawyer without asserting that there are at least some people who can become a great lawyer?

EDIT:

What about this:

"One can become a unicorn without having red skin." Do you view that statement as also implying that if one cannot become a unicorn, then one must have red skin? If I'm understanding you correctly, if it were not possible for Sally to become a unicorn, then you would say that the statement "One can become a unicorn without having red skin" is a contradiction of that fact about Sally?

Seeking Perfection

@thrillhouse said:

@"Seeking Perfection" said:

I don't understand the idea of adding "as far as LSAT performance is concerned." Didn't you originally say that "Sally can become a great lawyer without getting a 180" = "Sally Cannot Become a Great Lawyer --> Sally got a 180"??

Imagine that these are true facts about the world: Getting a 180 is not required to be a great lawyer. However, hard work and luck are required in order to become a great lawyer.

If these are true facts about the world Sally might not be able to become a great lawyer(if she wasn't going to put in the work or wasn't lucky) in which case she also wouldn't be able to become a great lawyer without getting a 180. The premise would therefore be false.

One is a specific person, every specific person for the purposes of logic so it is valid to make it a specific person.

I might not be explaining it very well, but if there is someone who cannot become a great lawyer at all, then we can't say one can become a great lawyer and then also can't say that one can become a great lawyer without getting a 180.

The more general statement I do not read as asserting that every single person in the world definitely has the ability to become a great lawyer -- only that getting a 180 is not required to be a great lawyer.

But it does. What if it just said "One can become a great lawyer." or "One can accomplish his/her dreams."
That's not saying there is at least a single person who can do whatever the task is. It is saying everyone can do the thing. In our case the thing is "become a great lawyer without getting a 180".

If a person on the street told me "One can become a great lawyer without getting a 180" I wouldn't bat an eye. I would assume they mean exactly what you think and they undoubtedly would. But, the logical meaning of what they said is different.

I think I understand what you're getting at, you are clarifying well. But my question now then is how you would express the idea that I had in mind (besides turning "one" into "at least one person").

In particular what about "People can become a great lawyer without getting a 180." Do you view that as different in meaning from "One can become a great lawyer without getting a 180."? Couldn't there be a difference in meaning in that a statement about "people" isn't always a statement about every single person but can be statement about the group generally? (And if so, is "one" EVER susceptible to that same interpretation?)

I also am curious how one would express the idea that getting a 180 is not required to be a great lawyer without also asserting that there are any individuals out there who in fact have such ability. For example, in the world I described earlier -- where getting a 180 is not required to be a great lawyer, but luck and hard work are -- could it be impossible for anyone in the world to be a great lawyer because nobody happens to have the requisite luck and hard work, and yet the idea that "a 180 is not required to be a great lawyer" still be true? How would one express the idea there is no conditional relationship between a 180 and great lawyer without asserting that there are at least some people who can become a great lawyer?

EDIT:

Yes people can become great lawyers without getting a 180 would be closer to what you are trying to say. Even clearer would probably be to say that some people can become great lawyers without scoring a 180. However, that might sound like(though not logically mean) that 180 scorers had some advantage in becoming great lawyers.

What about this:

"One can become a unicorn without having red skin." Do you view that statement as also implying that if one cannot become a unicorn, then one must have red skin? If I'm understanding you correctly, if it were not possible for Sally to become a unicorn, then you would say that the statement "One can become a unicorn without having red skin" is a contradiction of that fact about Sally?

That sounds right to me. As long as Sally doesn't have red skin it should be possible for her to be a unicorn.