# Please explain to me this mistake in my logic **URL:** \ **Category:** Factual Questions\ **Created:** [November 24, 2010, 1:36am UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730 "2010-11-24T01:36:50Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [November 24, 2010, 1:36am UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730/1 "2010-11-24T01:36:50Z")
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 > [@Pope calls health care an "Inalienable Right". What's the right-wing spin?](https://boards.straightdope.com/t/pope-calls-health-care-an-inalienable-right-whats-the-right-wing-spin/561262/91): > > 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) > [@Pope calls health care an "Inalienable Right". What's the right-wing spin?](https://boards.straightdope.com/t/pope-calls-health-care-an-inalienable-right-whats-the-right-wing-spin/561262/92): > > So, in countries without UHC, you think abortion should be legal? Quote 3 (John Mace responding to me) > [@Pope calls health care an "Inalienable Right". What's the right-wing spin?](https://boards.straightdope.com/t/pope-calls-health-care-an-inalienable-right-whats-the-right-wing-spin/561262/94): > > If A then B. Not B, therefore not A. > You think that’s a logically true statement? Really? Quote 4 (Bricker responding to me) > [@Pope calls health care an "Inalienable Right". What's the right-wing spin?](https://boards.straightdope.com/t/pope-calls-health-care-an-inalienable-right-whats-the-right-wing-spin/561262/95): > > 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?!?! ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [November 24, 2010, 1:59am UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730/2 "2010-11-24T01:59:32Z")
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. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [November 24, 2010, 2:28am UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730/3 "2010-11-24T02:28:41Z")
You switched from “should be government policy” to “is government policy”. ---
**Author:** ![Blake](https://avatars.discourse-cdn.com/v4/letter/b/a9a28c/32.png) [@Blake](https://boards.straightdope.com/u/Blake)\ **Post date:** [November 24, 2010, 3:09am UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730/4 "2010-11-24T03:09:10Z")
> [@Arnold\_Winkelried](#): > > 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. ---
**Author:** ![Blake](https://avatars.discourse-cdn.com/v4/letter/b/a9a28c/32.png) [@Blake](https://boards.straightdope.com/u/Blake)\ **Post date:** [November 24, 2010, 3:39am UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730/5 "2010-11-24T03:39:28Z")
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? “If Negroes are as smart as Caucasians, you believe they should be allowed to attend the same colleges.” You agree with that? So you must also agree that “Negroes are not allowed to attend the same colleges as Caucasians, therefore you believe they are not be as smart”. ---
**Author:** ![Arnold\_Winkelried](https://avatars.discourse-cdn.com/v4/letter/a/3d9bf3/32.png) [@Arnold\_Winkelried](https://boards.straightdope.com/u/Arnold_Winkelried)\ **Post date:** [November 24, 2010, 8:26pm UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730/6 "2010-11-24T20:26:51Z")
I understand now where I went wrong. Thanks guys! ---
**Author:** ![Reno\_Nevada](https://avatars.discourse-cdn.com/v4/letter/r/6f9a4e/32.png) [@Reno\_Nevada](https://boards.straightdope.com/u/Reno_Nevada)\ **Post date:** [November 24, 2010, 9:19pm UTC](https://boards.straightdope.com/t/please-explain-to-me-this-mistake-in-my-logic/561730/7 "2010-11-24T21:19:19Z")
> [@Blake](#): > > 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.