Quick Conditional Inference Question

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Captain Rodeo
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Quick Conditional Inference Question

Postby Captain Rodeo » Sat Aug 18, 2012 7:43 pm

A-->B
A--->C

B some C--- is that a valid inference? I think it was mentioned in LRB, or I read it somewhere touching on this. I just forgot what and where it was...

Thanks!

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 7:52 pm

austinyo wrote:A-->B
A--->C

B some C--- is that a valid inference? I think it was mentioned in LRB, or I read it somewhere touching on this. I just forgot what and where it was...

Thanks!


Refer below for better responses.
Last edited by dowu on Sat Aug 18, 2012 10:28 pm, edited 1 time in total.

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Captain Rodeo
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Re: Quick Conditional Inference Question

Postby Captain Rodeo » Sat Aug 18, 2012 8:01 pm

Ya, that's what I thought... I just thought I read something weird somewhere that stated that- but I think it had to do with "some" being used in the arrow- where in that case part of the statement is reversible... I guess you could call it a pseudo-biconditional, because it is reversible. I dunno- it's on LRB pgs. 306 & 311-312

And maybe it's a formal logic question then? I guess I was inserting the "If...then" in my head, my bad.

Anyway, thank you for your response nmop_apisdn

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 8:23 pm

Lol no problem. Sorry for coming off rudely. I just re read my post.


But yeah, the only way you would be able to infer "some" from "all" is if the two "all/most" statements have something in common.

A few examples:

All horses that live here are white.
All horses that live here are female.

Valid inference: most (i think some works too) horses that live here are white females.
-------------------------------
All of his cards are green.
Some cards have flowers with them.

Valid inference: some of his cards are green with flowers in them.
-------------------------------
All of my dads rings are gold.
Most gold rings have diamonds in them.

Valid inference: some of my dads gold rings have diamonds in them.
-------------------------------
Most roads in my neighborhood are one-way streets.
Most roads in my neighborhood travel west.

Valid inference: some roads in my neighborhood are one-way streets that travel west.
--------------------------------
Some cars at this dealership are white.
Some cars at this dealership are Hondas.

Valid inference: you cannot make a valid inference with two "some" statements.
-------------------------------

Let me know if you have any more questions! I typed this on
my cell phone, so it's possible that I've confused you.

hopper123
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Re: Quick Conditional Inference Question

Postby hopper123 » Sat Aug 18, 2012 9:41 pm

Is there a possibility to venn diagram this?

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 9:45 pm

hopper123 wrote:Is there a possibility to venn diagram this?


Yes, absolutely. You should be thinking of these types of statements AS a venn diagram. The logic behind them is basically the same.

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 9:50 pm

Now that I look back at my Manhattan book, the way I learned this was through the use of venn diagrams.

Take a look.

(Sorry, this one is sideways.)

Image



This one actually addresses the OP's question lol. I'm glad I was correct!


Image

hopper123
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Re: Quick Conditional Inference Question

Postby hopper123 » Sat Aug 18, 2012 9:56 pm

Wait didn't the OP say that All A's are B's and all A's are C's would make some B's are C's, which is what your book says?

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:00 pm

hopper123 wrote:Wait didn't the OP say that All A's are B's and all A's are C's would make some B's are C's, which is what your book says?



You can logically infer:

All As are Bs.

Inference: some Bs are As.
------------------------
All As are Cs.

Inference: some Cs are As.
-----------------------

Yes, given these two statements, when combined, you can logically infer that some Bs are Cs.
Last edited by dowu on Sat Aug 18, 2012 10:34 pm, edited 5 times in total.

hopper123
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Re: Quick Conditional Inference Question

Postby hopper123 » Sat Aug 18, 2012 10:01 pm

nmop_apisdn wrote:
hopper123 wrote:Wait didn't the OP say that All A's are B's and all A's are C's would make some B's are C's, which is what your book says?


No your book says most + most, but that is a weaker form of all + all....

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:06 pm

hopper123 wrote:
nmop_apisdn wrote:
hopper123 wrote:Wait didn't the OP say that All A's are B's and all A's are C's would make some B's are C's, which is what your book says?


No your book says most + most, but that is a weaker form of all + all....


Lol, most and most are entirely different from all and all.

hopper123
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Re: Quick Conditional Inference Question

Postby hopper123 » Sat Aug 18, 2012 10:08 pm

nmop_apisdn wrote:
hopper123 wrote:Wait didn't the OP say that All A's are B's and all A's are C's would make some B's are C's, which is what your book says?


I don't think the book is saying that. I'm not sure he it's possible to infer that, given those statements.

The only things you can logically infer is:

All As are Bs.

Inference: some Bs are As.

All As are Cs.

Inference: some Cs are As.

I think. Someone correct me if I'm wrong.



Tell me: how is most + most result in a some but all + all not result in a some. That seems a bit bizarre.

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:10 pm

Fail.
Last edited by dowu on Sat Aug 18, 2012 10:30 pm, edited 1 time in total.

hopper123
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Re: Quick Conditional Inference Question

Postby hopper123 » Sat Aug 18, 2012 10:12 pm

nmop_apisdn wrote:
hopper123 wrote:
nmop_apisdn wrote:
hopper123 wrote:Wait didn't the OP say that All A's are B's and all A's are C's would make some B's are C's, which is what your book says?


No your book says most + most, but that is a weaker form of all + all....


Lol, most and most are entirely different from all and all.


I didn't say they are the same...I just said most + most is a weaker form of all + all. I could be wrong but I was always under the impression that all > most > some.

kaiser
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Re: Quick Conditional Inference Question

Postby kaiser » Sat Aug 18, 2012 10:13 pm

If most A's are B's and most A's are also C's, then yes, it must inherently follow that there is at least some overlap between B and C. It could be incredibly small, perhaps just a single occurrence, but it could also be a perfect 100% overlap. However, the principle remains that, if most A's are B's and most A's are also C's, then some B's must be C's (and vice versa, as is always the case when you are using "some"). The math of course supports this, since "most" is defined as anything greater than 50%.

Now lets change it up to the "all" formulation. If all A's are B's, and all A's are also C's, then of course it also follows that some B's are C's (and vice versa), assuming there is at least one A in the world.
Last edited by kaiser on Sat Aug 18, 2012 10:14 pm, edited 1 time in total.

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:14 pm

hopper123 wrote:
Tell me: how is most + most result in a some but all + all not result in a some. That seems a bit bizarre.


The problem, I believe, is that B and C don't share something with each other, the way A and B/ A and C do.

For example:

All apples are red. (All A -> B)

All apples have stems. (All A -> C)

(from what you're saying) Some red have stems. (Some B -> C)

IDK, I'm getting confused now.

kaiser
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Re: Quick Conditional Inference Question

Postby kaiser » Sat Aug 18, 2012 10:16 pm

nmop_apisdn wrote:
hopper123 wrote:
Tell me: how is most + most result in a some but all + all not result in a some. That seems a bit bizarre.


The problem, I believe, is that B and C don't share something with each other, the way A and B/ A and C do.

For example:

All apples are red. (All A -> B)

All apples have stems. (All A -> C)

(from what you're saying) Some red have stems. (Some B -> C)

IDK, I'm getting confused now.


That is correct. There is overlap between things that are red, and things with stems.

P.S. You are overthinking this, as the "most/most --> some" is the only pertinent thing in this thread

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:17 pm

Fuck, nevermind. I think that's right. I think that if:

All A -> B
All A -> C

Some B -> C.

The book doesn't address two "all" statements, so it's weird.

I was thinking that it had to say:

All A -> B

All C -> A

Therefore, some B -> A.


BLAHHHH, now I am confused.

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:19 pm

kaiser wrote:That is correct. There is overlap between things that are red, and things with stems.

P.S. You are overthinking this, as the "most/most --> some" is the only pertinent thing in this thread


Yeah, so for some reason I was thinking that we were trying to make a statement about apples. It didn't make sense to me, semantically, so I was like WTF. But yeah, that makes sense that some B's are C's.

Okay, so:

All apples are red(apples).

All apples have stems.

It follows that some red (apples) have stems. So yes, some B have C follows from All A have B and all A have C. IDK why I was so thrown off. :(

VasaVasori
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.

Postby VasaVasori » Sat Aug 18, 2012 10:25 pm

.
Last edited by VasaVasori on Sat May 02, 2015 10:56 pm, edited 1 time in total.

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:26 pm

VasaVasori wrote:I would agree that given:

1. A -> B
2. A -> C
3. at least one A exists

you can conclude that some B's are C's.

Consider this, for example:

All clouds are white.
All clouds are in the sky.

And, so, we can conclude:

Some white things are in the sky.
Some things that are in the sky are white.


Makes sense. Like I said, I was getting tripped up on the semantics (lack thereof) in the statements. I should probably stop studying.

Its funny how I contradicted myself in this thread. I feel dumb.

kaiser
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Re: Quick Conditional Inference Question

Postby kaiser » Sat Aug 18, 2012 10:29 pm

nmop_apisdn wrote:
kaiser wrote:That is correct. There is overlap between things that are red, and things with stems.

P.S. You are overthinking this, as the "most/most --> some" is the only pertinent thing in this thread


Yeah, so for some reason I was thinking that we were trying to make a statement about apples. It didn't make sense to me, semantically, so I was like WTF. But yeah, that makes sense that some B's are C's.

Okay, so:

All apples are red(apples).

All apples have stems.

It follows that some red (apples) have stems. So yes, some B have C follows from All A have B and all A have C. IDK why I was so thrown off. :(


No worries. Here is another example to help clarify a bit more:

All Americans like Baseball
All Americans like Cars

Just imagine it as a Venn Diagram. "Americans" has to be entirely within the intersection between "Baseball" and "Cars". Perhaps that intersection solely consists of Americans (in other words, we are the only country that likes both at the same time. Or perhaps that overlap includes more than just Americans. But it doesn't matter since we already have enough to say that some people who like baseball also like cars (and some people who like cars like baseball, since "some" works both ways).

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:32 pm

kaiser wrote:
nmop_apisdn wrote:
kaiser wrote:That is correct. There is overlap between things that are red, and things with stems.

P.S. You are overthinking this, as the "most/most --> some" is the only pertinent thing in this thread


Yeah, so for some reason I was thinking that we were trying to make a statement about apples. It didn't make sense to me, semantically, so I was like WTF. But yeah, that makes sense that some B's are C's.

Okay, so:

All apples are red(apples).

All apples have stems.

It follows that some red (apples) have stems. So yes, some B have C follows from All A have B and all A have C. IDK why I was so thrown off. :(


No worries. Here is another example to help clarify a bit more:

All Americans like Baseball
All Americans like Cars

Just imagine it as a Venn Diagram. "Americans" has to be entirely within the intersection between "Baseball" and "Cars". Perhaps that intersection solely consists of Americans (in other words, we are the only country that likes both at the same time. Or perhaps that overlap includes more than just Americans. But it doesn't matter since we already have enough to say that some people who like baseball also like cars (and some people who like cars like baseball, since "some" works both ways).


Word. Thanks for your help dude!


Conversely,

All A -> B

All C -> D

You cannot logically infer anything given these two "all" statements. I guess this is what I was really thinking about haha. FML.

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dowu
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Re: Quick Conditional Inference Question

Postby dowu » Sat Aug 18, 2012 10:36 pm

That wasn't so "quick", was it, OP? lol

TERS
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Re: Quick Conditional Inference Question

Postby TERS » Sat Aug 18, 2012 11:18 pm

Well, this is embarrassing.




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