LRB pg 327 et.al - Mistaken Reversal and Mistaken Neg Contra

[hunterama1]

Greetings and Happy New Year.

So far the LRB has pretty airtight.

However, this statement on page 376 which I've seen mentioned prior is not holding up to me: "Remember, a Mistaken Negation and a Mistaken Reversal are contrapositives to eachother..."

Let's take a look at this diagramatically:

Conditional:

A B this equals it's contrapositive B A which equals of course A <----- B

To be sure as per LGB 29:

"A contra positive denies the necessary condition thereby making it impossible for the sufficient condition to occur"

and

"Because the contrapositive both reverses and negates it is a combination of a Mistaken Reversal and Mistaken Negation. Since the contrapositive is valid, it as if two wrongs do make a right."

This is not entirely clear (or correct!?! (brass I know)) to say because the Mistaken Negation "plus" the Mistaken Reversal don't equal the same, valid conditional of a negated NC contrapositive which forces the SC into negation.


My position elucidated: Let's take look at the Mistaken Negation of the above original conditional A B

If A B this MN would then as a next step force A B

but

the contrapositive A B is in fact B A

Now again, you say as per above "Remember, a Mistaken Negation and a Mistaken Reversal are contrapositives to eachother..." (LR 376)

Well the Mistaken Reversal of A B is B A (A <---- B) and the contrapositive of B A is of course A B

Now "clearly" this Mistaken Reversal is not the contrapositive of the Mistaken Negation above (A B ).

The Mistaken Reversal can never be the "contrapositive" of Mistaken Negation - as an MR is never negated by simply being reversed - no matter which way you point the arrow. And of course if you take the "contrapositive" of the Mistaken Reversal - both conditions are negated resulting in A B not just one as in the MN A B.

So I find this LRB 'sidebar' concept flawed.

Ironically it was placed in the Flaw in the Reasoning Section.

To make this an interrogatory- how exactly can you convince me that the MN and the MR are contrapositives "of eachother".

I don't really see them as "contrapositives" in any context of a properly inferred conditional statement short of what they are - Mistakes - Mistaken Reversals and Mistaken Negations in of themselves and conditionally dis-related to one another.

Over to you, boss.

[Dave Killoran]

Hey Hunter,

Happy new year, and thanks for the question! I don't find it brass at all--you have a right to ask questions, and it is my job to try to answer them

I want to take a look at two different sections of your question and see if we can explain this so it is clearer.

First point: "a Mistaken Negation and a Mistaken Reversal are contrapositives of each other."

What I mean here is that the MN of a statement, and then the MR of that same statement, are in fact contrapositives of each other. Let's look at an example:

Original statement: A B

MR of that statement: B A
MN of that statement: A B

Now, when you look at that MR and MN, I think you will see that they are contrapositives of each other. This is one reason conditional reasoning can be so vicious--if you draw an erroneous conclusion, other erroneous conclusions begin to appear logical.

Second point: "Because the contrapositive both reverses and negates it is a combination of a Mistaken Reversal and Mistaken Negation. Since the contrapositive is valid, it as if two wrongs do make a right."

Let's again use an example to make this clear:

Original statement: A B

MR of that statement: B A
MN of that statement: A B

Now, when you take that MN and MR and combine them, the terms reverse ( B A) and then you add in the negations (which were A and B), resulting in:

Combination of two flaws: B A

vs

Original statement contrapositive: B A

As you can see, they are identical, and thus, adding the two flaws together does produce the contrapositive.

From one standpoint, the "mistakes" in a MR and MN are that they only go half of the way. A contrapositive both reverses and negates. A Mistaken Reversal just reverses, and does not negate; a Mistaken Negation just negates, and does not reverse.

Don't worry about offending me in asking these questions--I'm pretty hard to offend! And conditional reasoning is one of the slickest concepts around, and it can get extremely tricky at times. I love explaining stuff like this, so thanks for the question!

Please let me know if convinced you on both those points. Thanks!

[hunterama1]

I got the first half of what you explained and that was imminently helpful, however, I did get stuck on the second part a little when you talked of 'combining' the MR and MN.

Can you mechanically explain how you 'combine' these two?

[Dave Killoran]

Let's split this topic into two separate posts, if you don't mind, since we're adding in new questions. I feel like the main part of our discussion is informative enough for others that we should keep that part separate I'll answer the first part, and if you can separate the second part and re-post that in a new thread, I'll then answer that. sorry for the inconvenience!

Second point revisited: "Because the contrapositive both reverses and negates it is a combination of a Mistaken Reversal and Mistaken Negation. Since the contrapositive is valid, it as if two wrongs do make a right."

First, let's consider what the physical action is of creating a contrapositive: you both reverse and negate the terms.

Let's use the same example to make this clear:

Original statement: A B

So, to create the contrapositive, you take two physical steps:

1. You reverse the terms: B A

2. You negate the terms: B A.

That second diagram is the contrapositive of the original statement. Remember--the idea is that it is the combination of the two flaws:

• Note that the reversing part is similar to a Mistaken Reversal; the negation part is similar to a Mistaken Negation. One step (negation) takes the A and B and turns them into A and B; the other step takes those variables and reverses them.

Please let me know if that helps. Thanks!

[hunterama1]

Thank you - yes this helps!

Also, I noticed this concept of the MR and MN applying to the statement is mentioned specifically in the LRB.

So - airtight as usual.

I have edited my prior post to remove what may appeared to have been a separate topic. However, the topics related to LRB page 470 question 2 are also this subject of MR and MN's the explanations of which are still 'suspect' in my book.

There is another explanation asserting an MR relationship just prior to this which also parallels my concerns so in my next post I will put these forward together in the context of this post with the hopes of further fleshing out and clarifying this topic.

I am finishing up LRB today and I just want to say also that I can't tell you how much I appreciate the work you've done to put these outstanding texts together.

A 21 gun salute to you and the outstanding group of folks you've put together there at Hilton Head!

[Dave Killoran]

Thanks Hunter--we appreciate it!

Wait, I thought I had addressed your uncertainty about page 470. Is something still unclear? Let me know and I'll tackle it for you

And we're actually in Charleston now, but HHI is a great place too

Thanks!

[hunterama1]

Your welcome.

Regarding page 470 I have added it to the subject line so the subject of MR and MN are seen to be on both of these pages.

The wordings of these answer choices are a little tricky.

In the interest of clarity and for confirmation of diagrams for these MR's, negated MR's, and MN's would you be so kind as to arrow diagram that which is explained in the answer choices. I do understand the explanations (finally) but arrow diagrams corresponding exactly will show these particular acrobatic conditionals in a little better light.

For example in answer choice D the answer explanation states: "...This outcome is possible under any single-arrow conditional scenario..." - showing this scenario's would help me nail it down even though I think I've got it.

Also, these answers choices and answer choice E of problem 2 on page 466 - again address the Mistaken Reversal--- all of these answer choices introduce with the quantity indicator "Some..." however none of the answer choice explanations for answer choices using or introduced by "some" going forward after the Formal Logic chapter introducing " " as an arrow are diagrammed in the explanations again. The same criticism could be said for answer choices employing "most" and "many" these are not diagrammed but rather explained.

It appears that the use of as an arrow choice (or for that matter) is not always used and that " " would be used just to show the arrow direction to determine MR, NMR, or MN. But in any event, no diagrams are heard from again in this regard (most/ some answer choices) after the Formal Logic chapter and I am thus technically in the dark because I'm left to fend for myself diagrammatically for these answer choices.

I think the superior method in attacking answer choices is to a large degree to disregard the content and focus on the the form as you foster. And the best way to disregard the content and focus on the form is to use a diagram. So maybe you were concerned that you might be beating us over the head with diagrams and so opted to verbally explain the answer scenario's more so than diagramming all of them but from a visual perspective I think the diagrams are always king.

Thus if you could for good measure, kindly diagram the Mistaken Reversal discussed in answer choice E of 466 as well in addition to addressing those of 470 #2- I think this would fall as reinforcement under the overall topic mastering MR, NMR's and MN's!

Thanks so much for your generosity of time. It has not gone unnoticed or unappreciated.


GT UN or UA

[hunterama1]

On second thought I will post my diagrams for these for a spot check.

Be back soon...

[Dave Killoran]

Ok, sounds good. Thanks!