How to Convert Categorical Statements to Standard Form?

[mousesgr]

how to convert the below statement to standard form?
is it valid?

premises :
1. only John is not aware of the problem of HK
2. some people who are aware of the problems of HK are not empowered by the PRC

conclusion : John is ewpowered by the PRC

 

[honestrosewater]

premises :
1. only John is not aware of the problem of HK
2. some people who are aware of the problems of HK are not empowered by the PRC

conclusion : John is ewpowered by the PRC

You know you'll have two terms per proposition, a subject term and a predicate term, right? Can you identify the two terms in each proposition?

 

[mousesgr]

You know you'll have two terms per proposition, a subject term and a predicate term, right? Can you identify the two terms in each proposition?

1. only John (subject) is not aware of the problem of HK (middle term)
2. some people who are aware of the problems of HK (middle term)are not empowered by the PRC(predicate)

conclusion : John(subject) is ewpowered by the PRC(predicate)

i don't know how to convert them to A, E, I, O form
for no. 1 , if can i convert it to
"all people who do not aware of the problem of HK are people who identify to John"
it cannot be convert to A, E, I, O form

 

[honestrosewater]

It's much easier if you clean up the argument and put it in standard form. Let
J: John
H: People who are aware of the problems of HK
P: People who are empowered by the PRC
So
1. only John is not aware of the problem of HK.
becomes
1) Only J is not H.

2. some people who are aware of the problems of HK are not empowered by the PRC.
becomes
2) Some H are not P.

C. John is ewpowered by the PRC.
becomes
C) J is P.

(Doesn't the following look easier to deal with?)
1) Only J is not H.
2) Some H are not P.
C) J is P.

Now to translate them. (1) is tricky. I actually had to PM someone to get the correct translation. I can't improve on their explanation so here it is.

Statements of the form:

Only P are Q.

are referred to as exclusive statements. The proper way to handle them is to reverse subject and predicate and write as an A-statement:

All Q are P.

So in your case, "Only J are not H" translates to "All (not H) are J."

Example:

Only Fred is not invited to my party.
All persons not invited to my party are Fred.

Of course, you can translate "All not H" to "No H", to read:

No persons invited to my party are Fred

(2) is already in standard form. (C) will become an A statement because the subject class has only one member, John. So you now have

1) No H are J.
2) Some H are not P.
C) All J are P.

Is that a valid argument?

 

[mousesgr]

1) No H are J.
2) Some H are not P.
C) All J are P.

Is that a valid argument?

it is invalid...

but i still can't understand why is "All not H" equivalent to "No H" ?

 

[honestrosewater]

it is invalid...

but i still can't understand why is "All not H" equivalent to "No H" ?

I wish I could help, but I'm not the best one to explain it to you as I didn't spend much time on syllogistic logic. I hope you still try to find out, but, just so you know, in this case, you don't actually need to know what (1) is since (C) is an A statement; The only valid syllogism form with an A statement as its conclusion is AAA-1, and (2) is not an A statement, so the argument is invalid regardless of what (1) happens to be.

 

[quantumdude]

but i still can't understand why is "All not H" equivalent to "No H" ?

That's because they aren't equivalent. Sorry, I was the mystery author of that PM that Rachel quoted. It turns out that this requires more care than I was able to exercise at 1:30 in the morning, which is about when I received the message.

It is true that statements of the form "Only P are Q" are exclusive. But the fact that we are negating the predicate in "Only J are not H" makes this a little more complicated. The statement is actually a compound statement. In other words, it expresses 2 propositions.

First, it says that "All J are not H". For if any members of the class J are in the class H, then the statement cannot be true. That means that in the Venn diagram, the overlap of the circles for J and H must be empty.

Second, it says that "All not H are J", as I said. This is what the "only" gets us. That means that there cannot be any members outside of H that are not also in J. In other words, in a Venn diagram you can't have any members in the space outside the overlapping circles for J and H. This Venn diagram does not correspond to a standard form A, E, I or O statement.

 

[quantumdude]

This Venn diagram does not correspond to a standard form A, E, I or O statement.

I probably should say another word about this, too. The statement "All (not H) are J" is an A-statement, if you call the subject class "not H". If the subject class is simply H, then it is not an A-statement.