“Only” in conditional logic

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OVOXO
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“Only” in conditional logic

Postby OVOXO » Fri Nov 01, 2013 12:06 pm

I want to make sure my diagramming is correct.

If the statement is that “Only X’s understand Y”

Y —> X


If the statement is “…Only if X understands Y”

X —> Y

Is this correct?

Basically, the only vs only if threw me off on a question. Thanks!

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OVOXO
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Re: “Only” in conditional logic

Postby OVOXO » Fri Nov 01, 2013 12:16 pm

It’s basically the “the only” vs only/only if that’s stumping me.

ie. X goes to the movies only if Y does

Xm —> Ym

The only people who understand quantum mechanics are good at math

UQM —> GM

(reverse wouldnt be true GM —> UQM because this would mean being good at math is sufficient for understanding QM).

So does “the only” part go into the sufficient while “only if” part goes into the necessary?

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SecondWind
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Re: “Only” in conditional logic

Postby SecondWind » Fri Nov 01, 2013 4:48 pm

Edit: My explanation was completely off the mark, so I deleted it. I always assumed that, no matter what, "Only" signified the necessary condition which is incorrect. I'm inherently glad I tried and failed at answering this question because I learned something out of it. I appreciate you both, neprep and bee, for correcting before I lead too many people astray.
Last edited by SecondWind on Fri Nov 01, 2013 5:44 pm, edited 1 time in total.

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neprep
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Re: “Only” in conditional logic

Postby neprep » Fri Nov 01, 2013 5:16 pm

SecondWind wrote:Consider this:

Do the following sentences have the same meaning?

1) Only people who understand quantum mechanics are good at math.

2) The only people who understand quantum mechanics are good at math.

3) Only if people understand quantum mechanics are they good at math.

Yes! "Only/The Only/Only If" are all treated the same. "Only/The Only/Only If" are all necessary condition trigger words. What follows the necessary condition trigger word is the necessary condition. All three sentences can be diagrammed as:

GM —> UQM


Statements 1 and 2 are not diagrammed the same way.

The only people who understand quantum mechanics are good at math is diagrammed:

UQM->GM

not

GM->UQM.

The only people who have accounts on TLS know how to use the Internet does not imply that knowing how to use the Internet is sufficient to ensure having an account on TLS, much like being good at math is not sufficient to ensure understanding quantum mechanics.
Last edited by neprep on Fri Nov 01, 2013 5:41 pm, edited 1 time in total.

062914123
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Re: “Only” in conditional logic

Postby 062914123 » Fri Nov 01, 2013 5:24 pm

.
Last edited by 062914123 on Thu Jul 03, 2014 2:48 pm, edited 1 time in total.

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SecondWind
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Re: “Only” in conditional logic

Postby SecondWind » Fri Nov 01, 2013 5:47 pm

neprep wrote:
SecondWind wrote:Consider this:

Do the following sentences have the same meaning?

1) Only people who understand quantum mechanics are good at math.

2) The only people who understand quantum mechanics are good at math.

3) Only if people understand quantum mechanics are they good at math.

Yes! "Only/The Only/Only If" are all treated the same. "Only/The Only/Only If" are all necessary condition trigger words. What follows the necessary condition trigger word is the necessary condition. All three sentences can be diagrammed as:

GM —> UQM


Statements 1 and 2 are not diagrammed the same way.

The only people who understand quantum mechanics are good at math is diagrammed:

UQM->GM

not

GM->UQM.

The only people who have accounts on TLS know how to use the Internet does not imply that knowing how to use the Internet is sufficient to ensure having an account on TLS, much like being good at math is not sufficient to ensure understanding quantum mechanics.



Only people who understand quantum mechanics are good at math.

Only if people understand quantum mechanics are they good at math.

Both ^ are treat the same way, correct?

GM —> UQM

blackbirdfly
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Re: “Only” in conditional logic

Postby blackbirdfly » Fri Nov 01, 2013 5:59 pm


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iamgeorgebush
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Re: “Only” in conditional logic

Postby iamgeorgebush » Fri Nov 01, 2013 9:22 pm

"Only X's understand Y" means "If a thing understands Y, then that thing is an X."

Your first example is kind of confused, because Y --> X means "If Y, then X," not "If a thing understands Y, then that thing is an X." If I were diagramming this one as part of an LR question, I would probably write "pUY --> pX."

Your second example is also confused, because "only if X understands Y" is only one half of a conditional statement and does not express any sort of conditional relationship. If that doesn't make sense, consider this:

"P only if Q" means "If P, then Q." If I were to say "only if Q," that wouldn't express anything, now would it? Your statement "only if X understands Y" similarly expresses nothing.

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jordan15
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Re: “Only” in conditional logic

Postby jordan15 » Wed Nov 06, 2013 3:11 am

OVOXO wrote:
If the statement is “…Only if X understands Y”

X —> Y

Is this correct?

Basically, the only vs only if threw me off on a question. Thanks!


That's not a conditional. That's half a sentence. It would be "diagrammed" as X.

Your first example is how I would diagram it, however you may interpret X and Y to be different from how I interpret them to be. The first rule of diagramming is to clearly establish what your variables mean. The actual diagram is easy after that.

bp shinners
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Re: “Only” in conditional logic

Postby bp shinners » Thu Nov 07, 2013 1:49 pm

Only/Only if = necessary
The only = sufficient

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SecondWind
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Re: “Only” in conditional logic

Postby SecondWind » Thu Nov 07, 2013 4:34 pm

bp shinners wrote:Only/Only if = necessary
The only = sufficient


Always? And by that do you mean what follows is the necc/suff condition?

bp shinners
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Re: “Only” in conditional logic

Postby bp shinners » Fri Nov 08, 2013 2:11 pm

SecondWind wrote:
bp shinners wrote:Only/Only if = necessary
The only = sufficient


Always? And by that do you mean what follows is the necc/suff condition?


Yep.

Whatever term comes immediately after those words is the condition indicated.

"Only the good die young." My two concepts are "good" and "die young". "Good" comes after "only", so it's necessary:
DY->G

I could rephrase it as, "The only people who die young are the good" and it would mean the same thing.




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