Conditional Logic: Only vs. Any

[phil.ogea]

On Interact Lesson 3 for LR, we are asked to write out 2 conditional logic statements as follows:

"Any organism that can experience pain can be mistreated"
Pain -> Mistreatment

"Only organisms that can experience pain can be mistreated"
Mistreatment -> Pain

There is no further discussion on how the alteration of those two words (Only/Any) completely flips the logic of the statement. To me it seems like they are both identical as:
If the organism experiences pain -> then it can be mistreated.

Does anyone have an explanation for the reasoning behind the difference?

Thanks in advance.

[ohthatpatrick]

Do these seem like equivalent sentences:

1. Anyone who has taken the LSAT has planned to go to law school.

2. Only people who have taken the LSAT have planned to go to law school.

They shouldn't seem like the same.

To provide a counterexample to #1, you just need to find someone (like me) who took the LSAT but had no plans to go to law school.

To provide a counterexample to #2, you just need someone (like you, presumably) who plans to go to law school but has not yet taken the LSAT.

The way most students hear conditional statements is bi-conditionally, meaning, either both things apply or both things don't.

If you've taken LSAT, you planned to go to law school.
If you haven't taken it, you don't plan to go.

But conditional statements aren't like that. Only one of those two versions can be correct for a given conditional statement.

How about this one:
You can't have dessert unless you eat your veggies.

Is that saying that
IF you eat your veggies, you get dessert
or
IF you don't eat your veggies, you don't get dessert

To most people it sounds like either would be right, but only the second is correct.

Consider this pair:
Only people with four working limbs play in the NFL.
Any person with four working limbs plays in the NFL.

Do you hear the difference?

The first claim is true in the real world. The second one is crazy .. or else I'm late for training camp!

I encourage all my students to approach Conditional Logic with a very mechanical, robotic, memorized approach.

Although good intuition can often augment a mechanical understanding, there are so many cases where our intuition misleads us or where the given conditional statement we're examining doesn't have enough footing in a real world meaning to give us an intuitive approach.

Given the example you cited, I would want you to recognize that
if
when
whenever
any
each
all
every

are all Sufficient (left-side) keywords.

So if we see
"Any organism that can experience pain can be mistreated"
we know that "organism that can experience pain" goes on the LEFT.

Meanwhile
only
only if
unless
requires
ensures
guarantees
implies

all introduce NECESSARY (right-side ideas)

So seeing
"Only organisms that can experience pain can be mistreated"
tells us that "organisms that can experience pain" goes on the RIGHT side.

I'll attach a little cheat-sheet with conditional keywords if you wanna keep it handy while you work your way through more of these.

[chike_eze]

I always thought of UNLESS as negating a condition and making that condition sufficient.

e.g., X UNLESS Y is equivalent to saying X IF NOT Y, or more appropriately stated, IF NOT Y then X; the contrapositive of which is IF NOT X then Y.

Therefore, the rule is if you see UNLESS, just grab either condition, negate it, and make it the sufficient condition.

E.g., I will not fly to Glasgow unless my wife will come with me

Apply the formula:

IF NOT (I will not fly to Glasgow) then my wife will come with me

--> IF I will (NOT cancels not) fly to Glasgow then my wife will come with me

OKAY let's clean it up: IF I will fly to Glasgow, my wife will come with me.

Alternatively, we could have negated the other condition...
--> IF NOT (my wife will come with me) then I will not fly to Glasgow

Cleaned up: IF my wife will not come with me, I will not fly to Glasgow.

[ohthatpatrick]

You're exactly right, but it's also true to say that UNLESS always introduces a necessary condition.

As you wrote:
I will not fly to Glasgow unless my wife will come with me

And as one of our two valid conditionals would look:
Fly to Glasgow -> my wife will come with me

I think of Unless the way you do. Memorizing it as a Necessary trigger is not good enough; you need to realize that the OTHER idea must be negated.

I teach Unless as "Un-left", which is, as you were saying, the idea that you take either idea, negate it, and put it on the sufficient side.

But it is still true to list Unless as a trigger word for a necessary condition.

On the pdf I attached, I explain "Unless" our way, but since I was listing trigger words I threw it in on the Nec side, where it technically belongs.

So can I take a BOAT to Glasgow and leave my wife at home?

[chike_eze]

So can I take a BOAT to Glasgow and leave my wife at home?

The answer is No. If I did go to Glasgow then it must mean that my wife went with me. I agree with your analysis.

I think I would add an asterisk to "UNLESS" in the necessary list.

UNLESS*

* = UNLESS introduces the necessary condition (to the right) when the other condition (to the left) is no longer the case.

[SalmaC760]

So can I take a BOAT to Glasgow and leave my wife at home?

The answer is No. If I did go to Glasgow then it must mean that my wife went with me. I agree with your analysis.

I think I would add an asterisk to "UNLESS" in the necessary list.

UNLESS*

* = UNLESS introduces the necessary condition (to the right) when the other condition (to the left) is no longer the case.

Hi,

With the statement, "I will not fly to Glasgow unless my wife will come with me" tells us two things that are logically possible:

1. If his wife did not come with him, then he did not fly to Glasgow

2. If he did fly to Glasgow, then we know that his wife came with him

but if he takes a boat to Glasgow, isn't it possible for him to leave his wife at home? or for example, if we know he is in Glasgow, that doesn't necessarily mean that his wife came with him (i.e. he didn't fly, he took the boat).

I am confused as to why you sternly "The answer is No. If I did go to Glasgow then it must mean that my wife went with me."

[ohthatpatrick]

I was actually just making a stupid "Jeez, can I somehow get away from my wife?" joke when I said, "So can I take a BOAT and leave her?"

I wasn't trying to issue a follow-up challenge. But maybe that was good because the previous poster failed the 'quiz'.

YOU are correct that if I take a boat, then the rule doesn't tell us anything about whether or not my wife needs to come.
She could come or not come.

YOU are technically incorrect in thinking that conditional statements give you two options. Conditionals actually give you 3 out of 4 options.

GIVEN:
if A, then B

POSSIBLE:
A, B
~A, B
~A, ~B

IMPOSSIBLE:
A, ~B

You said:

With the statement, "I will not fly to Glasgow unless my wife will come with me" tells us two things that are logically possible:

1. If his wife did not come with him, then he did not fly to Glasgow
2. If he did fly to Glasgow, then we know that his wife came with him


You're right that the statement gives us those two conditionals, but it's not quite true to say that those are the only two things that are logically possible.

[stockshellish]

Good question, but I don't know why.