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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The Law of Noncontradiction

Week 2 Lecture

The Law of Non contradiction

The law of noncontradiction says that something cannot be true and false at the same time, in the same way, at the same place.  Example. I cannot say it is 10:00 am in Los Angeles California on July 4th, 2013 and at the same exact time say it is 11:00 am in Los Angeles California on July 4th, 2013.  I am contradicting myself.  This may seem like an obvious law but think about a world where nobody recognized a contradictory statement.

Imagine driving down an unfamiliar highway only to see the following sign:

The law of noncontradiction is fundamental to countless decisions and distinction we make on a daily basis. Without the ability to understand contradiction our ability to think, communicate, and act under many circumstance would be impossible.  Imagine asking for cold water and I gave you hot water and told you it was cold. That would be a contradiction.  How could you communicate, if no one could understand or believe you because you continuously contradicted yourself?

What if I told you that everyone in this class was to receive an A at the end of this class no matter what work you did or failed to do in this online course, and then at the end of the class I gave everyone an F?  Would you be ok with my violation of the law of noncontradiction?  Why not? There is a difference (distinction) between an A and an F; and A is not an F and an F is not an A.  It is easy to see that the law of non contradiction is linked to the law of identity.

There are some state governments that would like to remove gender “labels” because some transgendered individuals may be offended at the terms male and female.  Some gender labels, such as, Mother and Father are being removed from some state government forms because of fear of offending transgender individuals.  It is commendable to desire not to offend anyone but to refuse to acknowledge important distinctions between male and female genders strikes at the very heart of critical thinking.  To refuse to acknowledge fundamental distinctions demands we deny reality itself.  The issues are not only ethical struggles within our culture but the struggle for rationality itself.

There is the danger of making the false distinction that we offend others with truth or we must put aside critical thinking in order to not offend.  True tolerance requires that we maintain our ability to make distinctions.  How should we know we must be tolerant if there ultimately is no difference between anything and anyone?  If everything is the same tolerance is an unnecessary virtue.  Truth requires tolerance because we must make important distinction that correspond to reality.

What about loans and grants?  Many of you are receiving government grants, such as, pell or acg to attend Carl Albert State College; grants you do not have to repay and loans you do have to repay.  What if  you took a $5000 loan that you were told was a government grant?  Do you think the federal government would decide to ignore the difference between your pell and loans?  A grant is not a loan and a loan is not a grant (the law of identity).  You cannot say you only took out a $5000 loan and then say you took out a $5000 grant because this would be a contradiction.  The two are not the same.

According to Paula Gottlieb Aristotle held that the law of noncontradiction is a first principle and the firmest principle (2009).  Gottlieb goes on to state: Aristotle says that it is a principle which “is necessary for anyone to have who knows any of the things that are”.  Obviously we do not need Aristotle to tell us that something is wrong when we contradict ourselves or when others make contradicting statements to us, but it is important to see the disturbing trend in our culture towards rejecting both the law of identity and the law of noncontradiction.

The importance of logic and reason to ethical theory is imperative to our ability to build a sound ethical system in which to live our lives.  There is no need to be a logician to be ethical, but everyone should understand the fundamental relationship between the laws of logic and virtue. Reason (logic) and ethics are human undertakings. 

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The Law of Identity

Week One Lecture: Truth and the Laws of Logic

Logic is a systematic process used to validate the truth or falsity of an idea or statement.  Aristotle is the philosopher who discovered and codified the laws of logic.  Aristotle was born in Stagira, North Eastern Greece in 384 B.C. and was tutor to Alexander the Great. Aristotle attempted answering the questions: how do we know that such a thing as truth really exist and are there true statements? According to Paula Gottlieb Aristotle held that the law of noncontradiction is a first principle and the firmest principle (2009).  Gottlieb goes on to state: Aristotle says that it is a principle which “is necessary for anyone to have who knows any of the things that are”.  Obviously we do not need Aristotle to tell us that something is wrong when we contradict ourselves or when others make contradicting statements to us, but it is important to see the disturbing trend in our culture marginalizing critical thinking when it conflicts with coveted ideals. However, some truths are inescapable and here are a few examples:

1. I exist:  I cannot make this statement unless I do exist.  If I said I do not exist, then who is the I making the statement.  There has to be an I to speak.
2. There is truth:   This statement must be true because to state the opposite would be self-contradicting.  Example: if I say “There is no truth” I am affirming a “truth” that there is no truth, so I would be contradicting my statement that there is no truth.Truth is inescapable.

Using logic is not always simple, but anything worthy of our limited time and energy can be difficult including the pursuit of truth.  Some truths are more difficult to uncover than others.  Scientific truth, such as, gravity, speed of light, the age of the universe have taken hundreds and thousands of years to discover. These truths took many gifted minds and failed theories and ideas to arrive at.  There is no such thing as fast food science and there should be no such thing as fast food ethics.  Moral truth can be even more complex because there are so many possible situations involving the need for sound moral judgment, so do not be discouraged at the variety of disagreement on important topics. As students of truth it is our duty to think through ethical statements and by using reason determine what ideas and statements are true and which are false.

To determine what is true or false there are three laws of logic we will need to understand.  The following is the name and brief description of each law:

1.    The Law of Identity: Simply put, something is what it is and not something else.  An apple is not an orange and a woman is not a man and a man is not a dog (although some women may disagree).

2.    The Law of Noncontradiction:  To use a previous example: “There is no truth” violates the law of noncontradiction since the statement denies truth and yet claims to be true.

3.    The Law of Excluded Middle:  Excluded middle simply means there is no middle ground.  The statement is either true or false.  Example: I exist.  There is no middle ground.  I cannot almost exist or somewhat exist, I either do or do not exist there is no middle or third option.

The Law of Identity

The law of identity simply states that A is A and not B.  According to Douglas Groothuis a thing is itself and nothing other than itself. If we say, "You're not yourself today!" we don't violate the principle of identity. We mean, rather, that you are acting out of character, acting strangely or unexpectedly, given what we know about you. The person is still identical to him- or herself even if he or she is acting strangely. Nor does this law deny the fact that things change over time. What it denies is that something cannot be what it isn't at any given time. I cannot be fifty-one years old and fifty-two years old at the same time (Groothuis, 2013). 
Some of you might be saying that this is painfully obvious but there a current social trends, ideals, as well as old and new philosophies that would challenge the concept of the law of identity. Consider Rachel Dolezal, head of the Spokane chapter of the NAACP. Genetically, Ms. Dolezal is White.  Although the head of the Spokane chapter of the NAACP is biologically white she is a self proclaimed African American. Some may say this is her own business and the NAACP, but there is more at stake here than a woman who would prefer to identify as an African American. Can we simply decide to be something we are not because we feel a certain affiliation, affection, or draw to be what we are not?  If a man can decide to be a woman or a woman can decide to be a man why cant a white woman decide to be black?  What if a person decides they do not want to be human? What does that society look like? There are scientist and futurist who are declaring the next step of human evolution is for humans to evolve into non-biological forms.  Some are talking of transferring human consciousness into complex computer systems where the body is either unnecessary or robotic. Imaging human consciousness inside a satellite in space, in a commercial jet computer system, or your cousin inhabiting a titanium robot.

Lets get a bit more philosophical.  Lets say we buy into a guy named Jean Paul Sartre that there is no essence of what we call human.  Lets say that nothing has any inherent essence.  For instance a rock should have an essence of rockiness. It should be natural, hard, solid and composed of certain minerals. What if this was just a mental construct and there was really no such thing as a rock or rockiness.  Sartre believed there was no "human Identity".  We make of ourselves whatever we choose to be.  If a man want to be a woman, a dog, or a robot his/her choices are their own.

As Professor Groothuis states above "Nor does this law deny the fact that things change over time. What it denies is that something cannot be what it isn't at any given time."  The identity of the term marriage for the first time in human history changed, it has been redefined, but can we do the same thing with gender? Is it psychologically and ethically safe to say there is no such thing as male or female, or is there is no difference between male and female? Are there essences of femaleness and maleness that are distinct?  There are currently state agencies within the U.S. that are considering doing away with gender references on state documents. Can we as individuals and society deny the identity of gender because we find this ideologically oppressive?


Hitler preached his anti-Semitic rant that Jews were not human.  Hitler appealed to evolution as his reasoning for subjecting  to work-camps, gas chambers, and medical experiments those he deemed as weak because the law of "nature" was the strong survive and the weak die.  The weak were a danger to the survival of the nation and had to be destroyed for the good of his nations future. For Hitler there was either no essence of being human or the essence of being human was his concept of strength.  His ability to distort the law of identity of millions of Jews, handicapped, Christians, and many others allowed him to sway an entire nation into committing astonishing atrocities.

This demonstrates that the law of identity has serious moral implications for humanity.

 

 

 

 

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