Making sentence into Conditional statement

[Smokyearlgrey]

Hi there,

I had some trouble conceptualizing re making general sentence into conditional structures.
I will greatly appreciate any input from you!

My friend gave me the inference as below:

"Only 50% has agreed" entails

"The other 50% has NOT agreed"

because:

Agreed -> 50%
(Contrapositive) NOT 50% -> NOT Agreed ("the other 50% has NOT agreed")

My friend said that NOT 50% indicates the other 50%.


However, I view NOT 50% as meaning anything from 1%,2%,3%,4,5,6,7,8,9,…..upto 100% EXCEPT 50%

To elaborate I regard the sentence and resultant contrapositive as:

If there’s an agreement, then the percentage of the agreement is 50%
If the percentage of the agreement is not 50% then there is NOT an agreement.


However, I do understand the inference of
"Only 50% has agreed" meaning "The other 50% has NOT agreed"
not by the reasoning of above conditional statement but rather with the two-group concept.


Please let me know any of your thoughts!
Thank you so much

[ohthatpatrick]

You're just getting confused because "only" has multiple definitions.

When we're seeing "only" in the context of conditional statements, it's talking about necessity.

Only people with LSAT scores can apply to law school. (LSAT scores are necessary)
Only people who are good at math can understand quantum mechanics. (Math skills are necessary)

The other usage of "only" is an adjective or adverb that conveys the idea of "a puny, insignificant amount or degree".

I asked her for some cash, and she gave me only a dollar. (A dollar is a puny, insignificant amount)
Only 50% of the respondents have agreed. (a 50% rate of agreement is surprisingly small)

There's no statistical difference between saying
50% of the respondents have agreed
and
only 50% of the respondents have agreed

The only difference in meaning between those two statements is that the second one as a little bit of attitude / tone, concerning the statistic.

Neither one is a conditional, unless you're really forcing every sentence to be a conditional for some misguided reason.

Similarly, "She only gave me a dollar" is not conditional, unless you're just really forcing every sentence to be a conditional.

Does that make sense?

[Smokyearlgrey]

You're just getting confused because "only" has multiple definitions.

When we're seeing "only" in the context of conditional statements, it's talking about necessity.

Only people with LSAT scores can apply to law school. (LSAT scores are necessary)
Only people who are good at math can understand quantum mechanics. (Math skills are necessary)

The other usage of "only" is an adjective or adverb that conveys the idea of "a puny, insignificant amount or degree".

I asked her for some cash, and she gave me only a dollar. (A dollar is a puny, insignificant amount)
Only 50% of the respondents have agreed. (a 50% rate of agreement is surprisingly small)

There's no statistical difference between saying
50% of the respondents have agreed
and
only 50% of the respondents have agreed

The only difference in meaning between those two statements is that the second one as a little bit of attitude / tone, concerning the statistic.

Neither one is a conditional, unless you're really forcing every sentence to be a conditional for some misguided reason.

Similarly, "She only gave me a dollar" is not conditional, unless you're just really forcing every sentence to be a conditional.

Does that make sense?

Thank you so much for your feedback! It makes total sense to view it as the non-conditional only.

Nevertheless, even without only, how can the sentence:
"50% of the respondents have agreed" be deduced into "other 50% of the respondents have not agreed" ?

Taking this as a two-group concept, it must be the case that the other 50% have not agreed, but; the part i am having difficulty understanding is when I covert this into a conditional statement and taking a contrapositive form.

After all, all sentences can be expressed into a conditional statement, am I right?

So,

"50% of the respondents have agreed"

ORIGINAL: If respondents have agreed -> then the turnout is 50%
CONTRA: If the turnout is NOT 50% -> then the respondents have NOT agreed

To me, the contrapositive above seems to suggest a different notion than "other 50% of the respondents have not agreed"
Rather than referring If the turnout is NOT 50% to "the other 50% group", I tend to view it as "any turnout other than 50%, such as 40%, or 60%"

Is it the case that "50% of the respondents have agreed" is little ambiguous and I misinterpreted the logic?

Thank you in advance for your follow-up.

[ohthatpatrick]

At the risk of sounding insulting, the sentence you're analyzing is nothing like a conditional. So why are you trying to turn it into one and contrapose it?

If I say there's a 70% chance of rain, then I can infer that there's a 30% chance of no rain.

But that 30% inference has nothing to do with conditional logic or contrapositives. There's no way I could ever write "There's a 70% chance of rain" as a conditional where it would somehow derive me the 30% as a contrapositive. It seems, though, like that's what you're looking for.

If we're forcing a conditional, we could write something dreadful like
"If it's rain we're talking about, there's a 70% chance.
If there's something other than a 70% chance of something, then it's not rain we're talking about."

Similarly, you'd be saying something like
"If it's this survey, then 50% of respondents agreed."
"If something other then 50% of respondents agreed, then it's not this survey."

Remember, contrapositives are just a different way of saying the same thing.

The 50% agreed / 50% did not agree are actually two different facts. We need a third fact, namely that 100% is the total of any group, to derive the 50% who didn't agree. Conditional logic would never give it to us.

If I say "Tony has three sisters", I can derive that "Tony is not an only child".
Again, that has nothing to do with conditional logic.

In short, don't try to make something conditional unless it's conditional (which that sentence was, due to the "unless").

[Smokyearlgrey]

At the risk of sounding insulting, the sentence you're analyzing is nothing like a conditional. So why are you trying to turn it into one and contrapose it?

If I say there's a 70% chance of rain, then I can infer that there's a 30% chance of no rain.

But that 30% inference has nothing to do with conditional logic or contrapositives. There's no way I could ever write "There's a 70% chance of rain" as a conditional where it would somehow derive me the 30% as a contrapositive. It seems, though, like that's what you're looking for.

If we're forcing a conditional, we could write something dreadful like
"If it's rain we're talking about, there's a 70% chance.
If there's something other than a 70% chance of something, then it's not rain we're talking about."

Similarly, you'd be saying something like
"If it's this survey, then 50% of respondents agreed."
"If something other then 50% of respondents agreed, then it's not this survey."

Remember, contrapositives are just a different way of saying the same thing.

The 50% agreed / 50% did not agree are actually two different facts. We need a third fact, namely that 100% is the total of any group, to derive the 50% who didn't agree. Conditional logic would never give it to us.

If I say "Tony has three sisters", I can derive that "Tony is not an only child".
Again, that has nothing to do with conditional logic.

In short, don't try to make something conditional unless it's conditional (which that sentence was, due to the "unless").

Greatly appreciate your feedback.
I was overly predisposed with conditionals...

Thank you very much!