The meaning of "unless"
Posted: Tue Nov 01, 2016 5:59 pm
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.
"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.