PT 24 sect. 3 #19 Forum

[ltowns1]

Why can't I link the contrapostive of the conclusion to premise in this argument??? (which would be answer A) Is it because you can't infer from conclusion to premise, you have to infer from premise down to conclusion?

Is it a mistaken reversal??

[Rigo]

"Some" statements are reversible. They're not conditional logic and therefore there is no such thing as a Contrapositives with "some" statements.

[ltowns1]

"Some" statements are reversible. They're not conditional logic and therefore there is no such thing as a Contrapositives with "some" statements.

So would "A" be wrong because of the reason you cited???

[Rigo]

Sufficient assumptions are like math problems.

Premise: WS --> HL
+
(Answer Choice)
=
PTJ <--s--> /WS

Contrapose the premise to get WS in the same format as the conclusion, so now you have /HL --> /WS

PTJ is the variable that HAS to be in the answer choice because you cannot have an airtight formal logic argument that leaves out a part of the conclusion.

So you have /HL --> /WS and you need to add PTJ.
You are looking for a puzzle piece that is /HL --> PTJ in some form. /HL <--s--> PTJ also works because if some /HL are PTJ and all /HL are /WS, then it follows that some PTJ are also /WS. Note that /HL --> PTJ would also have worked so the word "some" doesn't necessarily need to be in the correct answer choice.

(A) is incorrect because it says /PTJ <--s--> HL. That would be a correct contrapositive if this weren't a some statement. However, it is a some statement so there is no such thing as a contrapositive. You're conflating two different types of logic.

(D) is correct because it is the exact puzzle piece we need to make the argument airtight. It has /HL and PTJ in the correct forms.

/HL --> /WS
+
/HL <--s--> PTJ
=
PTJ <--s--> / WS

[Rigo]

"Some" statements are reversible. They're not conditional logic and therefore there is no such thing as a Contrapositives with "some" statements.

To clarify on this point, reversing "some" statements does not mean taking the contrapositive.

/HL <--s--> PTJ
Note the double arrow. "Some" statements should be written with a double arrow because if some of A is B then some of B is also A.
So it can also be written as PTJ <--s--> /HL and be the same thing.

It would be incorrect to try and contrapose it like this:
/PTJ <--s--> HL

[ltowns1]

"Some" statements are reversible. They're not conditional logic and therefore there is no such thing as a Contrapositives with "some" statements.

To clarify on this point, reversing "some" statements does not mean taking the contrapositive.

/HL <--s--> PTJ
Note the double arrow. "Some" statements should be written with a double arrow because if some of A is B then some of B is also A.
So it can also be written as PTJ <--s--> /HL and be the same thing.

It would be incorrect to try and contrapose it like this:
/PTJ <--s--> HL

Got it

[ltowns1]

"Some" statements are reversible. They're not conditional logic and therefore there is no such thing as a Contrapositives with "some" statements.

To clarify on this point, reversing "some" statements does not mean taking the contrapositive.

/HL <--s--> PTJ
Note the double arrow. "Some" statements should be written with a double arrow because if some of A is B then some of B is also A.
So it can also be written as PTJ <--s--> /HL and be the same thing.

It would be incorrect to try and contrapose it like this:
/PTJ <--s--> HL

Hey so one more question. Based on what you said would it be fair to say that if I had a statement like most A's are B's, then i could at the very least say some B's are A's???

[Rigo]

Hey so one more question. Based on what you said would it be fair to say that if I had a statement like most A's are B's, then i could at the very least say some B's are A's???

No because "most" is not a two-way arrow.
A --m--> B

Real life example: Most presidents have graduated college.
P --m--> GC
You cannot turn around and say that most college graduates are presidents.

[ltowns1]

Hey so one more question. Based on what you said would it be fair to say that if I had a statement like most A's are B's, then i could at the very least say some B's are A's???

No because "most" is not a two-way arrow.
A --m--> B

Real life example: Most presidents have graduated college.
P --m--> GC
You cannot turn around and say that most college graduates are presidents.[/quote

Ok thanks

[msp8]

Hey so one more question. Based on what you said would it be fair to say that if I had a statement like most A's are B's, then i could at the very least say some B's are A's???

No because "most" is not a two-way arrow.
A --m--> B

Real life example: Most presidents have graduated college.
P --m--> GC
You cannot turn around and say that most college graduates are presidents.

Wait, ltowns1 wasn't asking about 'most' being two-way, but rather that 'some' can be derived from a 'most' function.

A -m--> B

So then it can be inferred that:

B -s--> A

And, in the example, some college graduates have become president.