# L.e.m.



## bigheavyq (Apr 12, 2007)

HELP!!!!
what in the world is L.E.M.? could you explain it and give me some examples?


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## Richard King (Apr 12, 2007)

They have that skinny lead singer named Michael Stipe...no wait that is R.E.M.


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## larryjf (Apr 12, 2007)

bigheavyq said:


> HELP!!!!
> what in the world is L.E.M.? could you explain it and give me some examples?



It may be "Lay Eucharistic Minister" 

It's hard to tell without context, but that might be it.


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## bigheavyq (Apr 12, 2007)

LEM has some relation to the law of non contradiction.


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## VirginiaHuguenot (Apr 12, 2007)

Law of the Excluded Middle


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## larryjf (Apr 12, 2007)

Right, Law of Excluded Middle (LEM) is: all statements are either true or false


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## bigheavyq (Apr 13, 2007)

*Lem*

okay, can I have some examples of the Law of the Excluded Middle. 
btw, I am very black and white.


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## larryjf (Apr 13, 2007)

bigheavyq said:


> okay, can I have some examples of the Law of the Excluded Middle.
> btw, I am very black and white.



The idea is that there is no relative truth, something is either true or it is false. In other words, there is no middle ground (hence the name).

Examples:
Either the color is white or it is not white.
Either I am a human being or I am not.

I don't think this law can be done in all areas properly. For instance...

Either I am brave or I am not.

I could act brave in some situations but cowardly in others.


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## Staphlobob (Apr 13, 2007)

The statement below is true.

The statement above is false.


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## Staphlobob (Apr 13, 2007)

Staphlobob said:


> The statement below is true.
> 
> The statement above is false.




Kinda stupid, but just something I read in a "new age" magazine many years ago.


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## Brian Bosse (Apr 13, 2007)

Hello Kevin,

Let A stand for the proposition "The statement below is true." 
Let B stand for the proposition "The statement above is false." 

Can we know if A and B are true or false? 
A stands for the following: B is true. Another way to say this is as follows: If A is true, then B is true. This is logically symbolized as A → B.

B stands for the following: A is false. Another way to say this is as follows: If B is true, then A is false. This is logcially symbolized as B → ¬A. 

This leads us to the very interesting statement A → ¬A, which itself leads to the conclusion ¬A. This means A is false. However, if A is false, then this leads to B being false, which leads to A being true. This goes on endlessly. This is a form of the famous _Liar Paradox_.

Sincerely,

Brian


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## Staphlobob (Apr 14, 2007)

Brian Bosse said:


> However, if A is false, then this leads to B being false, which leads to A being true. This goes on endlessly. This is a form of the famous _Liar Paradox_.



That's the aim of it. It just struck me funny when we think of the LEM and the necessity of all propositions being either true or false.


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## Brian Bosse (Apr 14, 2007)

Hello Kevin,

There is an argument that attempts to overcome these paradoxes of self-reference. Namely, that there is a distinction between referring to something and the thing itself. Another way this is said is that there is a distinction between 'use' and 'mention'. Here is an example:

Propositional logic is complete.
The word 'complete' has eight letters.

In the first sentence 'complete' is used. In the second sentence 'complete' is mentioned. In these last three sentences (including this one) 'complete' is mentioned. The point is that the use and the mentioning of a word are not one and the same, and therefore you commit a subtle equivocation when you treat them the same. Now, let's apply this to the following...

This sentence is false. 

Ok, what is the referent to 'this sentence'? Is 'this sentence' used or mentioned? Here is one way to make it more explicit...

'This sentence is false' is false. 

The phrase 'this sentence is false' has been mentioned and not used. As such, we cannot assume that the mention of this sentence means the same thing as the use of the sentence. Some have argued that this does away with the paradox. Self-reference has not been achieved. 

Brian


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## Vytautas (Apr 14, 2007)

Staphlobob said:


> The statement below is true.
> 
> The statement above is false.



Assume that both statements are true. So the statement above is false is true. So the statement above is false. So the statement above is true and false. So if both statements are true we have a contradiction. So it is false that both statements are true.

Assume both statements are false. So the statement above is false is false. So the statement above is true. So the statement above is true and false. So if both statements are false then we have a contradiction. So it is false that both statements are false. If it is false that both statements are either true or false, then one statement is true and the other is false.

Assume that the above statement is false and the below is true. So the statement below is true is false. So the statement below is false. So the statement below is true and false. So if the above statement is false and the below statement is true then we have a contradiction. So it is false that the above statement is false and the below is true. The only possibility now is that the above statement is true and the below is false.

Assume that the above statement is true and the below is false. So the statement above is false is true. So the statement above is false. So the statement above is true and false. So if the above statement is true and the below is false then we have a contradiction. So it is false that the above statement is true and the below is false. So it is false that either statement is true or false. So it is true that both statements are true and false.


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## Cheshire Cat (Apr 15, 2007)

That's interesting Brian. Thanks for posting that.


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## JohnV (Apr 15, 2007)

Sure, there are tricks that can be played like that. But that's not really getting at what the LEM is. The example about "the statement below" vs. "the statement above" is two propositions referring to two different things. The Law of the Excluded Middle refers to reference to the same thing in the same sense, but two opposing propostions about it: the opposites cannot be reconciled, for either the one or the other alone can be true, not both. The Law of the Excluded Middle asserts that there is no proposition possible which can reconcile opposing propositions concerning the same thing in the same sense. 

For example, God exists or God does not exist. These are two opposing propositions, and only one can be true. In this case the possibility that neither are true is ruled out, as is the possibility that both are true. Only one can be true, and there is no middle ground possible. 

The ontological assertion is that it is impossible to assert that God does not exist. Therefore only one possible solution presents itself, namely that God exists: no other proposition has any reference to the thing in the proposition in the sense of the original question (either God exists or he does not exist: therefore the question is, Does God exist?)

This is how the LEM has reference to the rules of thought. It is not meant to allow for paradox, but to give structure to thought in order to understand the unity of truth.


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