# The Law of Identity



## Davidius (Apr 28, 2007)

> The law of identity states that if any statement is true, then it is true; or, every proposition implies itself: *A implies A.*
> 
> ...Without the first [law], identity or sameness is lost...



I am just now starting to get interested in Christian Philosophy as well as Logic. Could someone explain the Law of Identity to me? I get the Law of Contradiction and the Law of Excluded Middle, but I'm having trouble with this.


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## Brian Bosse (Apr 28, 2007)

Hello CC,

As you stated, the law of indetity could be represented by:

*LOI:* If A, then A.

The other two laws commonly refered to as the laws of thought are the law of non-contradiction and the law of excluded middle. These could be represented as...

*LNC:* ~(A and ~A). ('~' represents "it is not the case that".) 

*LEM:* (A or ~A).


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## Davidius (Apr 28, 2007)

Brian Bosse said:


> Hello CC,
> 
> As you stated, the law of indetity could be represented by:
> 
> ...



Perhaps I am making this too hard on myself, lol. I do understand that the LOI is correctly expressed as *If A, then A* as in the quote, but I am not quite sure that I understand what that means. Is it just "If the car is red, then the car is red"? I think I'm having trouble understanding why this would even be necessary to point out and use as a necessary law. What does it mean that "without this law, identity or sameness is lost"?


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## Brian Bosse (Apr 28, 2007)

Hello CC,



> Is it just "If the car is red, then the car is red"? I think I'm having trouble understanding why this would even be necessary to point out and use as a necessary law. What does it mean that "without this law, identity or sameness is lost"?



"If the car is red, then the car is red" is precisely what it means. It is not unlike saying that everything is what it is. I know it is rude to answer a question with a question, but please indulge me. Why is it important to acknoweldge the law of non-contradiction or excluded middle? 

Brian


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## Herald (Apr 28, 2007)

Mmmm...then one of my favorite sayings, "It is what it is" is faithful to the Law of Identity. Cool!


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## Davidius (Apr 28, 2007)

Brian Bosse said:


> Hello CC,
> "If the car is red, then the car is red" is precisely what it means. It is not unlike saying that everything is what it is.



But wouldn't it just be a violation of the NLC to say that something is what it is and also is what it is not? 



> I know it is rude to answer a question with a question, but please indulge me.


Ask away! Questions will make me think and help me learn the material better.



> Why is it important to acknoweldge the law of non-contradiction or excluded middle?



Is this question meant to show that those things are just as "given" as the LOI? Would the answer be that we must acknowledge these three foundational laws so that we have something from which to derive other principles?


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## Brian Bosse (Apr 28, 2007)

Hello CC,



> But wouldn't it just be a violation of the NLC to say that something is what it is and also is what it is not?



Yes. But what you just said is ~((A-->A)^(A-->~A)). This is the law of non-contradiction and not the law of identity. The law of identity is simply A-->A. 



> Is this question meant to show that those things are just as "given" as the LOI? Would the answer be that we must acknowledge these three foundational laws so that we have something from which to derive other principles?



My main point in asking the question was to point out that your question equally applies to the law of non-contradiction and excluded middle. Yes, these three laws are considered the axiomatic basis for rationality. It is interesting that there are some schools of thought that deny the law of excluded middle, and some to a small degree deny the law of non-contradiction. However, no one has said much about the law of identity. 

Brian


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## Davidius (Apr 28, 2007)

Brian Bosse said:


> Hello CC,
> 
> 
> 
> Yes. But what you just said is ~((A-->A)^(A-->~A)). This is the law of non-contradiction and not the law of identity. The law of identity is simply A-->A.



So, whereas the NLC would be "The car is red and green," the LOI would be "The car is a slice of pizza"?




> My main point in asking the question was to point out that your question equally applies to the law of non-contradiction and excluded middle. Yes, these three laws are considered the axiomatic basis for rationality.



okay


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## JohnV (Apr 28, 2007)

David:

What the LoI says is that you can't talk about two things contradicting or about two things being exclusive of each other until you have affirmed what that thing is that you're talking about. It is what it is, and you have to deal with it as it is, and then it also becomes clear that it is not something else, or cannot be warped or morphed into something else just by talking about it. It either is or it isn't what it is. 

This is the layman's version of it. Brian's version is more definitive. Once you get the hang of it, then you can hardly say it any other way anymore.


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## Davidius (Apr 28, 2007)

JohnV said:


> David:
> 
> What the LoI says is that you can't talk about two things contradicting or about two things being exclusive of each other until you have affirmed what that thing is that you're talking about. It is what it is, and you have to deal with it as it is, and then it also becomes clear that it is not something else, or cannot be warped or morphed into something else just by talking about it. It either is or it isn't what it is.
> 
> This is the layman's version of it. Brian's version is more definitive. Once you get the hang of it, then you can hardly say it any other way anymore.



Thanks, John! I was going to ask what all the symbols meant.


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## Brian Bosse (Apr 28, 2007)

Hello CC,



> So, whereas the NLC would be "The car is red and green," the LOI would be "The car is a slice of pizza"?



Technically, an example of a violation of LNC would be "the car is red and it is not the case that the car is red."

Technically, an example violation of LOI would be "the car is not the car."

Brian


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## Davidius (Apr 28, 2007)

Brian Bosse said:


> Hello CC,
> 
> 
> 
> ...



Ok, that makes sense. Thanks for bearing with me.


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## yeutter (Apr 28, 2007)

A does not equal not A. Something can not both be itself and not itself.


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## Philbeck (May 2, 2007)

David are you 21 yet, because I think we need to have another weekend adventure!


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## Civbert (May 2, 2007)

yeutter said:


> A does not equal not A. Something can not both be itself and not itself.


 You forgot to add the winking smiley.


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## Davidius (May 2, 2007)

Philbeck said:


> David are you 21 yet, because I think we need to have another weekend adventure!



Nope. July 13th!


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## JohnV (May 2, 2007)

The law of identity is strictly related to the law of age. You can't say you are who you are unless you've been born. And in the case of a Christian, you cannot say you are who you are unless you are born again.


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