Law School Discussion

"A unless B" question

Re: "A unless B" question
« Reply #10 on: July 21, 2004, 09:27:04 PM »
wow.  it makes sense when I diagram it, but in terms of semantics, the fact that those 2 are the same just creeps me out.  Wow.  Ok, they indeed are the same. 

You are probably thinking about the "unlesss" or "strictly unless" relationship.  "A strictly unless B" is equivalent to "~B->A and B->~A" which is also the "exclusive or" or the "xor" relationship.  Often, when speaking English, "or"/"unless" is actually used to mean "xor"/"unlesss".  For instance in the sentence: "You can have the cake or the pie."  There is an implied "but not both" at the end of this sentence which makes this an exclusive or.  When parsing these LR questions using symbolic logic, you need to be careful to figure out which "or" or "unless" they mean.

dta

Re: "A unless B" question
« Reply #11 on: July 21, 2004, 09:37:03 PM »
wow.  it makes sense when I diagram it, but in terms of semantics, the fact that those 2 are the same just creeps me out.  Wow.  Ok, they indeed are the same. 

wow.  it makes sense when I diagram it, but in terms of semantics, the fact that those 2 are the same just creeps me out.  Wow.  Ok, they indeed are the same. 

The reason it seems counter-intuitive is because people often 'say' A unless B when they really 'mean' A if and only if ~B. Example:

I am going to the police unless you give me $500.

Strictly translated:

If you do not give me $500 then I am going to the police.

But likely what the person *REALLY* means is a quid pro quo bargain. That is, according to the strict logical meaning above, the person could give you $500 and you could STILL go to the police and you will not have broken the strict meaning in the logic of your promise. You promised what you would do if you were NOT given $500. No assurances were given regarding what would occurr if you WERE given the $500.

What you likely intended when you said:

I am going to the police unless you give me $500.

is

I am going to the police IF-AND-ONLY-IF you do not give me $500.

This is often why the strict logical interpretation of "unless" seems funky. It's simply because people are using "unless" when they really mean "if and only if".

Re: "A unless B" question
« Reply #12 on: July 21, 2004, 11:28:20 PM »
Intuitively, I would think that A unless B would mean "A is the default state and will only cease to be the case if B is also the case" while B unless A seems to mean "B is the default state, and will only cease to be the case if A is also the case"

is this wrong, and why?

Re: "A unless B" question
« Reply #13 on: July 22, 2004, 04:08:28 AM »
Intuitively, I would think that A unless B would mean "A is the default state and will only cease to be the case if B is also the case" while B unless A seems to mean "B is the default state, and will only cease to be the case if A is also the case"

is this wrong, and why?

Because all that we know from "A unless B" is that A is true as long a B is not.  Once B becomes true, we know nothing, so we have vacuous truth.

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Re: "A unless B" question
« Reply #14 on: July 22, 2004, 10:41:44 AM »
So let me get this right... if the question says, "You will perform better on the LSAT unless you slack off" would be written as:
BL ---> ~S or S ---> ~BL
Where BL is Better LSAT and S is Slack Off...

dta

Re: "A unless B" question
« Reply #15 on: July 22, 2004, 10:57:28 AM »
So let me get this right... if the question says, "You will perform better on the LSAT unless you slack off" would be written as:
BL ---> ~S or S ---> ~BL
Where BL is Better LSAT and S is Slack Off...

No. The logical meaning of "You will perform better on the LSAT unless you slack off" is:

~S --> BL

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Re: "A unless B" question
« Reply #16 on: July 22, 2004, 11:40:16 AM »
Wow, so you guys should really teach logic or something because this is the first time im really understanding this stuff.

Here is another confusing one. What is the difference between "if and only if" and "only if"? Are they equivalent? And if not, what is the contrapositive of the two statements. I have a feeling that this may be too complicated to  discuss online but it is worth a shot.

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Re: "A unless B" question
« Reply #17 on: July 22, 2004, 12:43:32 PM »
Very good i was just testing you...  ;)

Mos

Re: "A unless B" question
« Reply #18 on: July 22, 2004, 09:34:59 PM »
Here is another confusing one. What is the difference between "if and only if" and "only if"? Are they equivalent? And if not, what is the contrapositive of the two statements. I have a feeling that this may be too complicated to  discuss online but it is worth a shot.

A only if B means: if A, then B.

A if and only if B means: if A, then B, and if B, then A.

Basically, the clause after "only if" will be your necessary condition that is required for the happening of whatever is being stated in the clause before "only if."

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Re: "A unless B" question
« Reply #19 on: July 22, 2004, 10:49:17 PM »
Thanks for the help

Here is another confusing one. What is the difference between "if and only if" and "only if"? Are they equivalent? And if not, what is the contrapositive of the two statements. I have a feeling that this may be too complicated to  discuss online but it is worth a shot.

A only if B means: if A, then B.

A if and only if B means: if A, then B, and if B, then A.

Basically, the clause after "only if" will be your necessary condition that is required for the happening of whatever is being stated in the clause before "only if."