Law of Excluded Middle

Week Three Lecture

The Law of Excluded Middle

The law of excluded middle (LEM) is considered the third law of logic, and it will be obvious that LEM is closely intertwined with the law of identity (LI) and  the law of noncontradiction (LNC).  First, LEM says that a statement is either true or not true, there is no third option.  Example: I exist is either true or false, there is no third option.  I cannot almost exist or somewhat exist.  This intertwines with the law of identity because the I must be I and not you or them.,  Also, LEM is intertwined with LNC because I cannot exist and and exist at the same time, in the same place, in the same way.  Think of it as claiming that there is no middle ground between being true and being false. Every statement has to be one or the other. That’s why it’s called the law of excluded middle, because it excludes a middle ground between truth and falsity. So while the law of non-contradiction tells us that no statement can be both true and false, the law of excluded middle tells us that it must be one or the other (Stanford, 2009).

Relativism would reject LEM as narrow minded because it is requiring an absolute value: true or not true.  It is easy to say I exist and affirm the truth of that statement because the person must exist to make the statement. However ethical statements can be more complicated because there are so many differing situations we might find ourselves faced with.  What about ethical declarative statements like: It is never ethical to lie. Can the law of excluded middle be used on this statement? Is it true or false that it is never ethical to lie or it is always morally acceptable to lie? Are there no third options? There are differing opinions on the ethics of truth telling, but are there only two possibilities with this statement? No.  It could be that it is always permissive to lie ( a relativist position), or it is permissible to lie in order to do no harm.  We know that lying in some instances may be the most ethical act a person might perform.  For instance, a murderer is hunting down a child to kill her and you hide her in the closet; when the killer ask where the girl is you tell him that she ran out the back.  You deceived the killer, but was your deception unethical?  If not why? This would be a good time to write your premise and conclusion (just kidding).  It appears in this circumstance there are considerations, ethical reasons to deceive, so the statement “It is never ethical to lie” is false.  This does not imply the relativist position that is is then always permissible to lie because we have a third option: it is permissible to lie in order to do no harm.

Lets take a look at another ethical declarative statement:  It is unethical to kill.  Is this statement true or not true?  Well it might depend,  Kill who or what and for what reason?  Is it unethical to kill anything including grass, spiders, or flies?  Is it unethical to kill someone who is about to kill your wife, friend, or child?  What if we change the declarative statement to be more defined:  It is unethical to murder a human being for pleasure. This statement is more specific, but a distinction should be made between murder and killing and the difference between the two terms.  Our terms must be well defined.  If our terms in our statements are ambiguous it will be difficult to reach any conclusion or possible agreement from the premises. We cannot state it is never good to kill for pleasure and then state it is sometimes good to murder for pleasure. Our interchanging of the terms murder and kill are ambiguous. When we state it is never good to murder for pleasure, this is either true or false. There are no conditions where murdering for pleasure can be conceived as permissible.  We are bound by the law of excluded middle in this instance.  It is one or the other, no third option.

The laws of logic will help us through many important distinctions we will need to make when postulating our ethical statements.  We need to determine the following:

1. who or what (law of identity), 
2. is the statement consistent (law of noncontradiction)
3. What are our options (law of excluded middle). 

It is not enough to feel, believe, or dictate a statement is true, we must think through what we feel or believe in order to live as wise and virtuous humans.   There are no easy answers.  Someone said that anyone can ask a question, but it takes thought and time to deliver the right answer.  If we want to be good persons it will take more than being nice or agreeable, true goodness  involves the whole of our human nature: what we believe, how we think, and how we act out our beliefs and thoughts.  Socrates said that the unexamined life is not worth living.  Deepak Chopra said that wisdom is judged by the things you devote your mind to.  So it is up to every human to think, and to think through the issues in life that matter, and logic and ethics are a good place to begin.  The laws of logic will not help you resolve all of your ethical dilemmas, but the tools will certainly be of great value to you when you have to make difficult ethical choices.

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