Inverse Obverse

[j_p]

Can anyone refresh my memory on the math definitions of these terms?

And what the third terms is?

[Dave]

Say what now? Math definition of what, precisely?

[ydoaPs]

inverse, converse, contrapositive, ect.?

[Asimov Pupil]

inverse as in putting it under one as a fraction?

[j_p]

Contrapositive? What's that?

It sounds like the mood of a verb in Latin; when the action is contrary to the intention of the speaker.

 

I digress.

 

I am referring logical statements of contradiction that I was taught in middle school math, I think when we were being introduced to algebraic proofs:

 

Statement:

If A then B

 

Contradictions:

If A then not B.

If not A then B.

 

And then there is:

If not A then not B;

 

which is not a contradiction; I believe the last is the obverse of the statement.

 

I believe one of the first is the inverse of the statement; but I can not remember what the other one is called.

 

Thank you for your efforts.

[Dave]

Actually, the thing you call "obverse" is the contrapositive of a logical statement. I've never heard the word inverse used in these terms though.

[j_p]

Sigh. I really thought someone here would know this; now I have to actually work to find out what I want to know.

 

If I ever find out what I'm talking about, I'll let you know.

[ydoaPs]

The Converse of p=>q is q=>p

 

The Inverse of p=>q is ~p=>~q

 

The Contrapositive of p=>q is ~q=>~p

[Tom Mattson]

The obverse is NOT the contrapositive. It is equivalent to the converse of a statement.

 

Sigh. I really thought someone here would know this; now I have to actually work to find out what I want to know.

 

It shouldn't take that much work if you are taking a course. Looking up the definitions in a book should be sufficient. You should be looking under immediate inferences of categorical statements.

 

Try this: http://sask.usask.ca/~wiebeb/Immediate.html

 

Incidentlly, this is traditionally regarded as philosophy, not math.

[j_p]

Oh, I'm not taking a course; I just keep noticing logical errors in discussions [if all cats are grey, then, if you are grey, you're a cat], and those algebraic proofs keep popping into my head.

 

I thought it was logic, rather than philosophy.

 

Let me check out that link ...

 

ah, yes, that is what I was looking for.

My grey cat example is the non-legitimate assertion of the converse of a universal positive statement.

 

And the link's link ...

Oh, yes, they're both going into Tools and Reference.

 

Wait a minute, now I am confused about your initial statement; "The obverse ... is equivalent to the converse ...".

The link has "obverse", "converse", and "contrapositive" [which I apparently remembered incorrectly as "inverse"].

Am I missing something?

 

Thank you so much; it was like a song stuck in my head. How could I have neglected to search under the term "inference"?

[Tom Mattson]

Oh' date=' I'm not taking a course; I just keep noticing logical errors in discussions [if all cats are grey, then, if you are grey, you're a cat'], and those algebraic proofs keep popping into my head.

 

Ah, in that case you might want to invest in a book on the logic of categorical statements.

 

I thought it was logic, rather than philosophy.

 

Logic is a branch of philosophy. It's also a branch of mathematics, but the math people don't usually deal with categorical statements. They usually deal with symbolic logic. That's probably why no one here knew the answer!

 

Wait a minute, now I am confused about your initial statement; "The obverse ... is equivalent to the converse ...".

The link has "obverse", "converse", and "contrapositive" [which I apparently remembered incorrectly as "inverse"].

Am I missing something?

 

Sorry, I had two parts of my post and I hit "send" without finishing one of them. The obverse is equivalent to the converse when looking at conditional statements. For categorical statements, use the chart in the link to see what is equivalent to what.

 

Thank you so much; it was like a song stuck in my head. How could I have neglected to search under the term "inference"?

 

Hey, no problemo.

[Johnny5]

Contrapositive? What's that?

It sounds like the mood of a verb in Latin; when the action is contrary to the intention of the speaker.

 

I digress.

 

I am referring logical statements of contradiction that I was taught in middle school math' date=' I think when we were being introduced to algebraic proofs:

 

Statement:

If A then B

 

Contradictions:

If A then [i']not[/i] B.

If not A then B.

 

And then there is:

If not A then not B;

 

which is not a contradiction; I believe the last is the obverse of the statement.

 

I believe one of the first is the inverse of the statement; but I can not remember what the other one is called.

 

Thank you for your efforts.

 

You are confused for no reason at all, because it is not necessary to have a name for these things, as Tom Mattson said.

 

Mathematicians deal with symbolic logic, and there are just so many ways of vary (if x then y), using 'not', all of which can be understood using a truth table.

 

But I understand why you want a name to refer to the variations. The ones I am familiar with are: inverse, converse, contrapositive.

 

Original statement: If A then B

Converse: If B then A

Contrapositive: If not B then not A

Inverse: If not A then not B

 

The contrapositive is redundant, because it can be proven to be logically equivalent to the original statement. But this happens often in logic, that is no reason not to know how to manipulate logical expressions.

 

Regards

[j_p]

And there is every reason to know how to manipulate them, lest others manipulate you.

 

It is much better to recognize the non-legitimate assertion of a converse of a universal positive statement than to think, "Wait a minute, that doesn't sound right ...".

 

One may not need words to have ideas, but it makes it easier. I think Huxley addresses that in the preface to BNW; or maybe it was Orwell. I haven't read either book in years.

 

I never associate logic with philosophy; in my only straight philosophy class, we started out with logical arguments for and against the existence of an omniscient and omnipotent God. I could never get past the essential illogical of proving a belief. I worried about fulfilling that requirement for years.

 

But that one week in algebra taught me more than Cicero and Socrates combined about dissecting an argument.

[Johnny5]

It is much better to recognize the non-legitimate assertion of a converse of a universal positive statement than to think' date=' "Wait a minute, that doesn't sound right ...".

[/quote']

 

This is exactly right.

 

Regards