An intuitive way to think about "Unless" "Until"?

dcdcdcdcdc

I'm curious if anyone has a good way to handle group 3 indicators "unless" or "until." In English these are often used to heavily imply an EXCLUSIVE or relationship, but in logic they only give us an inclusive or.

Example: I will go golfing (G) unless it rains (R).

Applying our group 3 translation rules strictly, we arrive at: "/R --> G" and the contrapositive "/G-->R"

Translating the above statements back into English,
"If it is not raining, I will go golfing," and "If I am not golfing then it is raining."

That is fine. The trouble comes when you try to reason from the fact that it is raining. In our common understanding of the above original statement if we knew it was raining, then we would be inclined to say the person is not golfing. However, that is not correct based on our translations.

More frustrating is the idea that this person could be golfing in the rain as nothing prevents R AND G from being together. That is the essence of inclusive or and is the possibility that is implicitly ruled out in our natural reading of the statement. Obviously, we can't apply a conversational implicature on the LSAT and we have to obey a strict logical understanding. I can easily imagine a question giving us the original statement and then supplying an answer choice that says "It is raining, therefore you are not golfing."

I would be grateful if anyone has a way to explain the possibility of the inclusive or outcome in the original statement by giving an example in which this person could be golfing in the rain and such outcome is acceptable.

Logically I understand the possibility, but making it more intuitive by having an example in mind would greatly help.

--
It's interesting to note that the implicature of exclusive or seems to be most strong in statements of "until" involving time and "unless" involving things such as the weather. The possibility of an inclusive outcome is easier to understand on a different example.

I will be angry (A) with you unless you clean your room (CR).

/A --> CR "If I am not angry with you, then you cleaned your room"
/CR-->A "If you did not clean your room, then I am angry"

I believe we all still see the possibility that I could be angry with you and you cleaned your room. Maybe you didn't do your homework, etc. That makes it fairly obvious that we can't conclude the condition of your room from my anger. I'm wondering what that "other 'cause'" might be for the golfing example.

Thanks!

MrSamIam

You might be overthinking it.
Take your final example, for example. Yes, given the principle one can still be angry at someone who did in fact clean their room. However, logically speaking they would not be angry with them for cleaning their room.
Correct me if I'm wrong, but your main concern is that even given the principle (/A --> CR) it's still possible to have CR and A (since CR as a sufficient condition is not covered by the principle, and is therefore fair game).
You're not incorrect in thinking that. However, if someone is angry and the other individual cleaned their room, they are not angry at them for cleaning their room. They could be angry at them for something that is totally unrelated to a messy room.

So, A and CR can coexist, but it wouldn't be because CR --> A.

I would just try to think of it intuitively and trust the system.

"Jim won't go out unless Mike goes out." If someone were to say this to me, I would think, "Okay, so if Jim does go out then obviously Mike is also going out." In lawgic: JGO --> MGO.
Or, /MGO --> /JGO

Note: Just be wary of making faulty negations or reversing the variables incorrectly.

quinnxzhang

@dcdcdcdcdc, There are two senses of "unless". There's a weak sense of "unless", which uses the inclusive-or, and there's a strong sense of "unless", which uses the exclusive-or. For LSAT purposes, I've never seen the strong sense show up. If you see "unless" on the LSAT, I'm almost certain you'd be safe translating it using the weak sense (inclusive-or).

But outside of the LSAT, there *is* a strong sense, where "unless" is used to mean something closer to "except for". So your golfing example means something like "I will go golfing in all cases except for the case where it rains tomorrow". And this equivalent to "Golfing <--> ~Rain", with the biconditional, which is equivalent to the exclusive-or. See here (p. 22 - 23): http://courses.umass.edu/phil110-gmh/text/c04_3-99.pdf

@dcdcdcdcdc said:Obviously, we can't apply a conversational implicature on the LSAT

I don't think we should be so quick to chalk the strong sense of "unless" up to conversational implicature. Which maxim would you be violating in your golfing example? The strongest candidate is the maxim of quantity, but then you'd have to make a lot of assumptions -- e.g. it must be common knowledge between speaker and audience that if it does rain, I won't go golfing. But it seems like if I get rid of this assumption, the sense of "unless" remains the stronger one.

runiggyrun

Yeah, this is an interesting dilemma. I think sometimes we make things trickier by infusing some of our real life biases to sentences, which muddies what should be crystal clear logic.
Think about these two sentences:
I will go golfing unless it's raining
/golf--> rain
I won't go golfing unless it stops raining
golf-->STOP rain

Is it just me, or is it easier to intuitively believe that in the second case it's possible that it's stopped raining and I'm still at home sitting on my behind vs. believing that in the first case it's possible that I'm out there teeing in the rain?

And yet, logically the constructions are exactly the same....