The meaning of "unless" Forum

[Rogah]

Background: "or" has two senses, inclusive and exclusive. So "X or Y" can mean either "X or Y or both", inclusive; or "X or Y but not both", exclusive. Multiple sources say that for LSAT purposes "or" denotes inclusive or.

"Unless" similarly can have two senses, strong and weak. Examples:

weak: Takers score under 170 unless they prepped; where "Takers score under 170" is X and "they prepped" is Y, we have: if takers score 170+ then they prepped (not-X --> Y), or if they didn't prep then takers score under 170 (not-Y --> X). Note that this is the same symbolic expression as for inclusive or, i.e., X or Y (or both) also becomes not-X --> Y. So both takers scoring under 170 and having prepped are logically possible, as there is no way to derive either not-X or not-Y as a necessary condition from the preceding conditional expressions. Logically, this "unless" statement says that prepping is necessary for scoring 170+, but not sufficient. We can't say it's unlikely that takers who prepped score under 170.

probably strong: I'll go out unless it rains; where "I'll go out" is X and "it rains" is Y, X <--> not-Y (biconditional). I'll go out, or it rains, but not both -- except in unusual circumstances; in other words, I'll go out if and only if it doesn't rain. After I've made this "unless" statement we can say it's quite unlikely that I'll go out in the rain.

infinitely strong: a mathematical definition such as: an integer is prime unless it's divisible by an integer other than 1 or itself. It's impossible for an integer to be both prime and divisible by .... .

In sum, just like "or", the English meaning of "unless" is contextual. I've seen a couple of sources say that for LSAT purposes "unless" -- and "except if", "without", "until" -- translates into conditional expressions in accord with the weak sense. But they don't mention, even to deny LSAT applicability, of the strong sense. So: does anyone want to deny that on the LSAT "unless" always means the weak sense that allows for both the consequent and the negation of the antecedent, i.e., for both Y and X?

Edit: as it happens, the "TLS1776's Thoughts on the LSAT" thread was bumped soon after this post, and I looked again at its original post which has an excellent discussion of my topic (scroll down a bit in TLS1776's post); it concludes that on the LSAT the weak sense of "unless" is used.

[HonestAdvice]

Unless = only if

I'll go out unless it rains if an if and only if statement. It's really just:

Go Out <-> No Rain

One of the great ways to understand the concept is Cricket's Law: https://www.youtube.com/watch?v=54GV2qS3tL4

"Hips and nips, otherwise I'm not eating". Otherwise and unless are equivalent. Cricket's Law can be reduced to "Eating -> H & N". If you're missing hips or nips then you're not eating.

[Rogah]

Unless = only if

...after a negation. Takers score under 170 unless they prepped; or, Takers score 170+ only if they prepped.

I'll go out unless it rains [is] an if and only if statement. It's really just:

Go Out <-> No Rain

Just so; the strong sense of "unless."

One of the great ways to understand the concept is Cricket's Law: https://www.youtube.com/watch?v=54GV2qS3tL4

"Hips and nips, otherwise I'm not eating". Otherwise and unless are equivalent. Cricket's Law can be reduced to "Eating -> H & N". If you're missing hips or nips then you're not eating.

"Unless hips and nips, I'm not eating." Yes, this is the weak sense of "unless." Anyone ever see the strong sense used on the LSAT?

[HonestAdvice]

Unless = only if

...after a negation. Takers score under 170 unless they prepped; or, Takers score 170+ only if they prepped.

I'll go out unless it rains [is] an if and only if statement. It's really just:

Go Out <-> No Rain

Just so; the strong sense of "unless."

One of the great ways to understand the concept is Cricket's Law: https://www.youtube.com/watch?v=54GV2qS3tL4

"Hips and nips, otherwise I'm not eating". Otherwise and unless are equivalent. Cricket's Law can be reduced to "Eating -> H & N". If you're missing hips or nips then you're not eating.

"Unless hips and nips, I'm not eating." Yes, this is the weak sense of "unless." Anyone ever see the strong sense used on the LSAT?

I don't understand the strong/weak distinction. Everything on the LSAT is literal. The literal translation of unless is the same as only. Unless signifies the necessary condition, and having the necessary condition doesn't mean you have the sufficient condition. This is confusing to read, which is the very reason why Cricket wrote Cricket's Law.

[Rogah]

Unless = only if

...after a negation. Takers score under 170 unless they prepped; or, Takers score 170+ only if they prepped.

I'll go out unless it rains [is] an if and only if statement. It's really just:

Go Out <-> No Rain

Just so; the strong sense of "unless."

One of the great ways to understand the concept is Cricket's Law: https://www.youtube.com/watch?v=54GV2qS3tL4

"Hips and nips, otherwise I'm not eating". Otherwise and unless are equivalent. Cricket's Law can be reduced to "Eating -> H & N". If you're missing hips or nips then you're not eating.

"Unless hips and nips, I'm not eating." Yes, this is the weak sense of "unless." Anyone ever see the strong sense used on the LSAT?

I don't understand the strong/weak distinction. Everything on the LSAT is literal. The literal translation of unless is the same as only. Unless signifies the necessary condition, and having the necessary condition doesn't mean you have the sufficient condition. This is confusing to read, which is the very reason why Cricket wrote Cricket's Law.

In one example you took "unless" to be logically equivalent to "only if" and in another to "if and only if". Do you see that "only if" or its equivalent "if only" is a different logical condition than "if and only if"? The former is "weak" and the latter is "strong". What you said in the most recent reply about necessary and sufficient conditions applies to the "weak" sense, which is represented by an ordinary conditional -- a one-way arrow. But it's not true for the "strong" sense which is represented by a biconditional; in a biconditional either side is sufficient, and both sides are necessary.

Edit: Yes, it can be confusing! TLS1776, in the post to which I linked in an edit of the OP here, said, "The word ['unless'] gave me a lot of grief when I first started studying because the definition that of the word that LSAC uses seemed to have counterintuitive implications in certain situations." And it gave me a lot of grief today until I understood the different meanings, weak or strong, which was the background of my question in this thread.

[Deardevil]

This is a good question.
Fortunately, the LSAT revolves around a "weak sense."
"Unless" definitely does not mean "only if." It is "if not."
Plainly said, you either have one side be the case or the other.
For example, I cannot watch television unless I finish doing the dishes.
That just means watching TV (negation of the sufficient side) implies me doing or having done dishes.
Similarly, not doing dishes (negating the necessary side) means I am unable to watch TV, leaving the original sufficient condition intact.

[Ilovemydogxo]

Full Definition of unless
1
: except on the condition that : under any other circumstance than
2
: without the accompanying circumstance or condition that : but that :




Source: http://www.merriam-webster.com/dictionary/unless

[Blueprint Mithun]

Background: "or" has two senses, inclusive and exclusive. So "X or Y" can mean either "X or Y or both", inclusive; or "X or Y but not both", exclusive. Multiple sources say that for LSAT purposes "or" denotes inclusive or.

"Unless" similarly can have two senses, strong and weak. Examples:

weak: Takers score under 170 unless they prepped; where "Takers score under 170" is X and "they prepped" is Y, we have: if takers score 170+ then they prepped (not-X --> Y), or if they didn't prep then takers score under 170 (not-Y --> X). Note that this is the same symbolic expression as for inclusive or, i.e., X or Y (or both) also becomes not-X --> Y. So both takers scoring under 170 and having prepped are logically possible, as there is no way to derive either not-X or not-Y as a necessary condition from the preceding conditional expressions. Logically, this "unless" statement says that prepping is necessary for scoring 170+, but not sufficient. We can't say it's unlikely that takers who prepped score under 170.

probably strong: I'll go out unless it rains; where "I'll go out" is X and "it rains" is Y, X <--> not-Y (biconditional). I'll go out, or it rains, but not both -- except in unusual circumstances; in other words, I'll go out if and only if it doesn't rain. After I've made this "unless" statement we can say it's quite unlikely that I'll go out in the rain.

infinitely strong: a mathematical definition such as: an integer is prime unless it's divisible by an integer other than 1 or itself. It's impossible for an integer to be both prime and divisible by .... .

In sum, just like "or", the English meaning of "unless" is contextual. I've seen a couple of sources say that for LSAT purposes "unless" -- and "except if", "without", "until" -- translates into conditional expressions in accord with the weak sense. But they don't mention, even to deny LSAT applicability, of the strong sense. So: does anyone want to deny that on the LSAT "unless" always means the weak sense that allows for both the consequent and the negation of the antecedent, i.e., for both Y and X?

Edit: as it happens, the "TLS1776's Thoughts on the LSAT" thread was bumped soon after this post, and I looked again at its original post which has an excellent discussion of my topic (scroll down a bit in TLS1776's post); it concludes that on the LSAT the weak sense of "unless" is used.

Based on your definitions, I think the LSAT 'unless' definitely lines up with the weak definition of the word. When I see it on a conditional statement, I replace it with "if not." The condition following unless is your sufficient condition, but you have to negate it, and the other condition is the necessary condition. This little strategy always works and makes it really easy to hand that keyword.