## help understanding Negation Introduction

What is the basis for reason? And mathematics?

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ProfAlexHartdegen
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### help understanding Negation Introduction

Okay, as I wrote in another thread I am reading a book called the Logic Book by Bergmann.

There are a few concepts which again I don't understand the point about which include the use of subderivations.

First, does the forum offer some way to type the symbols used in symbolic logic? Okay here is the problem.
Sorry for the crude representation but as you know the forum isn't conducive to writing symbolic logic. The subderivation is offset a bit to clarify what it is:

For :

Negation Introduction (~I)
|............| P____
|............|
|............| Q
|............|
|............| ~Q
|
|....... ~P

They give an English example:

premise (or statement?) 1: If the union votes for the contract and the management agrees to the terms of the contract, then the contract will be signed.
premise (or statement?) 2: The management agrees to the terms of the contract, but the contract will not be signed.
Conclusion?: The union does not vote for the contract.

They give a symbolized version of the argument but I'm experiencing trouble understanding how the argument works. I can't understand the use of each individual rule. I mean I know you could apply that rule but I don't see why you use the rule. The 'plan' or the 'forest from the trees' if you will.

Derive: ~U
1| (U & M) ⊃ S.................Assumption
2| M & ~S_____..............Assumption
..|
3|......|U_________..............Assumption
4|......| M.....................2 &E
5|......| U & M................3,4 &I
6|......|S.......................1,5 ⊃E
7|......|~S......................2 &E
8| ~U............................3-7 ~I

I'm sorry but I just don't see how these arguments; especially lines lines 4,5,6 and 7 lead to line 8! Can someone help me to understand? thank you so much!
Last edited by ProfAlexHartdegen on Sat Aug 12, 2017 6:58 pm, edited 1 time in total.

Harbal
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### Re: help understanding Negative Introduction

Have you allowed for the possibility of no one having a pen?

ProfAlexHartdegen
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### Re: help understanding Negation Introduction

I understood the joke but I'm sure it will be more humorous after I understand the Logic .

Let's try rephrasing the argument into standard English.

The management agrees to the terms of the contract.
The union votes for the contract and the management agrees to the terms of the contract.
The contract will be signed.
The contract will not be signed.

The union does not vote for the contract.

I'm sorry I just don't understand how the argument proceeds from one line to the next or how they're linked and why.
Last edited by ProfAlexHartdegen on Sat Aug 12, 2017 6:59 pm, edited 1 time in total.

ProfAlexHartdegen
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Joined: Mon Jul 31, 2017 5:43 pm

### Re: help understanding Negation Introduction

Okay, I watched a video about Negation Introduction (and Negation Elimination). Here: https://www.youtube.com/watch?v=fqows_3Dwac

Is the point to take any lines derived from the Assumption that contradict to show that the negative of the assumption can be derived? That seems comprehensible to me because you do that with the Truth-Trees, which close when there is a contradiction in an atomic sentence.

Dubious
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### Re: help understanding Negation Introduction

ProfAlexHartdegen wrote:
Fri Aug 11, 2017 6:44 am
I understood the joke but I'm sure it will be more humorous after I understand the Logic .

Let's try rephrasing the argument into standard English.

The management agrees to the terms of the contract.
The union votes for the contract and the management agrees to the terms of the contract.
The contract will be signed.
The contract will not be signed.

The union does not vote for the contract.

I'm sorry I just don't understand how the argument proceeds from one line to the next or how they're linked and why.
Being miserably poor in the art of logic...as was recently pointed out, take the following for what it's worth though I hesitate to ask what that would amount to.

I think your rephrasing would make more sense if more formally given:

IF management agrees to the terms of the contract....and
IF the union votes for the contract
The contract will be signed
The contract will not be signed

I think it's misleading, confusing and redundant to again repeat in the second clause what was already given in the first.

Anyways, as IF statements we don't know whether either premise is true or not. If ONE is negative the contract will not be signed. In that sense the argument is valid since both conclusions are valid.

Harbal
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### Re: help understanding Negation Introduction

I'd be interested to know why the union won't sign the contract.

Dubious
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### Re: help understanding Negation Introduction

Harbal wrote:
Sat Aug 12, 2017 10:02 pm
I'd be interested to know why the union won't sign the contract.
I'm not a member! You have to ask them. Sound logical?? Maybe its because management want's to screw them!

Harbal
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### Re: help understanding Negation Introduction

Dubious wrote:
Sat Aug 12, 2017 10:05 pm
Maybe its because management want's to screw them!
In that case, I don't blame them for not signing, I wouldn't put up with my manager screwing me, not even if he offered me a pay increase.

Dubious
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### Re: help understanding Negation Introduction

Harbal wrote:
Sat Aug 12, 2017 10:12 pm
Dubious wrote:
Sat Aug 12, 2017 10:05 pm
Maybe its because management want's to screw them!
In that case, I don't blame them for not signing, I wouldn't put up with my manager screwing me, not even if he offered me a pay increase.
Logically what's TRUE for you can be an either/or situation for someone else. Logic confirms it!

Harbal
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### Re: help understanding Negation Introduction

Dubious wrote:
Sat Aug 12, 2017 10:17 pm
Harbal wrote:
Sat Aug 12, 2017 10:12 pm

In that case, I don't blame them for not signing, I wouldn't put up with my manager screwing me, not even if he offered me a pay increase.
Logically what's TRUE for you can be an either/or situation for someone else. Logic confirms it!
The only thing that logic confirms is that you aren't employing any.

Dubious
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### Re: help understanding Negation Introduction

Harbal wrote:
Sat Aug 12, 2017 10:23 pm
Dubious wrote:
Sat Aug 12, 2017 10:17 pm
Harbal wrote:
Sat Aug 12, 2017 10:12 pm

In that case, I don't blame them for not signing, I wouldn't put up with my manager screwing me, not even if he offered me a pay increase.
Logically what's TRUE for you can be an either/or situation for someone else. Logic confirms it!
The only thing that logic confirms is that you aren't employing any.
Prove it! Show me where I went wrong...unless you're just trying to be mean and nasty.

Dubious
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Joined: Tue May 19, 2015 7:40 am

### Re: help understanding Negation Introduction

Dubious wrote:
Sat Aug 12, 2017 10:41 pm
Harbal wrote:
Sat Aug 12, 2017 10:23 pm
Dubious wrote:
Sat Aug 12, 2017 10:17 pm

Logically what's TRUE for you can be an either/or situation for someone else. Logic confirms it!
The only thing that logic confirms is that you aren't employing any.
Prove it! Show me where I went wrong...unless you're just trying to be mean and nasty.
I'm still waiting!

You're the one who made the assertion. Maybe you're right. So when you make a gratuitous statement that wasn't asked for categorically denying the validity of someone's argument it's up to that person to come up with one which effectively counters it. I wouldn't in the least mind if you or anyone else could show what logic errors there may have been in what I wrote.

So again, what's your reason for saying The only thing that logic confirms is that you aren't employing any.?

wtf
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### Re: help understanding Negation Introduction

ProfAlexHartdegen wrote:
Thu Aug 10, 2017 10:59 pm
First, does the forum offer some way to type the symbols used in symbolic logic?

Code: Select all

``````Negation Introduction
|............|    P____
|............|
|............|    Q
|............|
|............|  ~Q
|
|....... ~P
``````
You can line these up with the code tag. It's the </> button on the formatting palette above the Edit window.

I'm not even sure if I formatted your intent correctly. I know logic from using it in math but I never really learned to do these formal logic proofs and this notation always confuses me.

I don't remember if this site supports math markup or not, but you can always copy/paste symbols from http://math.typeit.org/.

ProfAlexHartdegen
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Joined: Mon Jul 31, 2017 5:43 pm

### Re: help understanding Negation Introduction

thanks for the serious reply and the tip. As for the others, I don't appreciate them hijacking my thread. I am trying to learn an academic subject and the notation and discussion is rather challenging for me too. Although I have a decent aptitude for math, advanced mathematics has been difficult for me always.

However, I've been told by several random people that I have a logical mind so I thought this book (the Logic Book) might help me to strengthen my skills in this subject of Logic as well as help to facilitate my understanding of advanced math. Logic is the underlying basis for many forms of persuasion too. As a teenager, I read the Sherlock Holmes stories and so I've been curious always about real Logic. I know there are several variants and this is one of the more modern though traditional types.

I've learned a lot more from this book than I ever would learn from your average professor who was teaching a course about it.

Still there are many points that need clarifying and restating for me to comprehend fully.

Harbal
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### Re: help understanding Negation Introduction

ProfAlexHartdegen wrote:
Sun Aug 13, 2017 6:32 am
As for the others, I don't appreciate them hijacking my thread.
This place is not exclusively for you, other people are allowed to take part.

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