Please explain to me this mistake in my logic [Archive]

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Arnold Winkelried

11-23-2010, 07:36 PM

This question comes from a GD thread discussing the Pope Benedict XVI's recent pronouncement on health care. But the logic question is not really related to that topic.

Here are four quotes from the GD thread:

Quote 1
No, I support the Pope's agenda in total: if we reversed our stance on abortion, I'd favor UHC.

Quote 2 (me responding to Bricker)
So, in countries without UHC, you think abortion should be legal?

Quote 3 (John Mace responding to me)
If A then B. Not B, therefore not A.
You think that's a logically true statement? Really?

Quote 4 (Bricker responding to me)
No. You have given the inverse (http://www.jimloy.com/logic/converse.htm) of my statement.

Let
p = "abortion should be / is illegal"
q = "UHC should be government policy"

In (quote 1) in this thread, Bricker is saying
If p, then q. (if abortion is illegal, I agree that UHC should be government policy)

Bricker's link (quote 4) says:
"If a statement is true, the contrapositive is also logically true." and defines
"statment: if p then q"
"contrapositive: if not q then not p"

The contrapositive "If not q then not p" would be
"If UHC is not government policy, then abortion should be legal."
which is what I said in Quote 2 above. What I said in Quote 2 was the contrapositive, not the inverse, and Bricker is mistaken in Quote 4 in calling it the inverse.

My assertion:
My statement in quote 2 (the contrapositive of quote 1) is logically derived from Bricker's statement in quote 1.

Where am I wrong? I am assuming, based on the responses from John Mace and Bricker, that I am making some basic mistake in logic?!?!

John Mace

11-23-2010, 07:59 PM

Well, I totally flubbed that one. :smack:

What you can surmise is:

Bricker has not reversed his stance on UHC, therefore we have not changed our policy on abortion.

You and I both assigned the "not' statements incorrectly.

Chronos

11-23-2010, 08:28 PM

You switched from "should be government policy" to "is government policy".

Blake

11-23-2010, 09:09 PM

Where am I wrong?

You are constructing a strawman by switching term associations.

Bricker's statement was "if abortion is illegal, UHC should be government policy".

The contrapositive of that is "If UHC should not be government policy, then abortion is legal".

According to Bricker, UHC should not be government policy, therefore we can conclude that abortion is legal. Which is perfectly correct.

Note that the term "should" must remain with the term "UHC", and the term "is" must remain with the term "abortion". You however switched that association. you went from

"if abortion is illegal, then UHC should be government policy"

to

"If UHC is not government policy, then abortion should be legal."

Notice how in Bricker's statement the green words are both together, whereas in your conclusion red is now paired with green?

You can't logically do that.

Blake

11-23-2010, 09:39 PM

Arnold Winkelried

11-24-2010, 02:26 PM

I understand now where I went wrong. Thanks guys!

Reno Nevada

11-24-2010, 03:19 PM

To give an analogy.

"If Marijuana is considered safe by the medical community, you believe it should be legal."

I assume you agree with that? Therefore can we conclude that since

"Marijuana is illegal, you believe it has been proven unsafe by the medical community."

Right?

.

Actually, this analogy is flawed. The correct contrapositive would be:

if you believe Marijuana should not be legal, then it is not considered safe by the medical community.

I believe that Bricker's syllogism could be restated as:

If abortion is illegal, I believe that UHC should be provided

The correct contrapositive is:

If I do not believe that UHC should be provided, then abortion is legal.

Note: my restatement seems like it implies an "if and only if" relationship, so I might well be wrong there.