LESSONS IN LOGIC: The Contradiction

This is one of the fundamental principles of logic which everyone should know and understand, yet it is one of the principles that seem to be least known and understood.  In this short lesson, we will try to explain the basic principle of contradiction and what it means in relation to logic, reason and critical thinking (i.e. ‘right reasoning’).

By the way: a contradiction is also a fallacy: and a big one, at that.

As always, we start with the definition:

Definition of contradiction

1 : act or an instance of contradicting the defendant’s contradiction of the plaintiff’s accusations

2a : a proposition, statement, or phrase that asserts or implies both the truth and falsity of something… both parts of a contradiction cannot possibly be true …”— Thomas Hobbes

b : a statement or phrase whose parts contradict each other a round square is a contradiction in terms

3a : logical incongruity

b : a situation in which inherent factors, actions, or propositions are inconsistent or contrary to one another

OK, for the purposes at hand — understanding the basic rules of formal logic — we are going to use 2a as the meaning of ‘contradiction:’ when two or more statements are asserted as fact where it is impossible for both or all of them to be true at the same time.  The simplest example would be:

I exist at this exact place and in this exact point in time.

I do not exist at this exact place and at this exact point in time.

It is impossible for me to both exist and not exist at the same exact place and the same exact point in time, therefore, these two statements ‘contradict’ each other. (my apologies to the folks in quantum mechanics, but this is true and you need to rethink your theories based on the idea that a thing can exist and not exist at the same time.)

In formal logic, a contradiction is known as an ‘absurdity.’  In short, this means that a contradiction has no relation to objective reality.  It is a ‘make believe,’ or an ‘impossibility.’  One might say it is the stuff of childish thinking and reasoning.  While it may be amusing, it is laughable because it has no real substance or existence.  Hence the term, ‘absurd.’

In formal logic, absurdities are important because they destroy the argument in which they are found.  There is a saying in logic: ‘From an absurdity, all things follow.’  Meaning, once one accepts something that is absurd as factual, then any claim of truth based on that claim must be accepted.  So, if we accept that something can and cannot exist at the same place and time, then we can claim that there is a unicorn sliding down a rainbow to a pot of gold guarded by a leprechaun.  If we accept that something exists and does not exists at the same time, we must accept that we are — in fact — dealing with a unicorn sliding on a rainbow toward a pot of gold guarded by a leprechaun.  None of us would believe the story about the unicorn because we know these things do not exist in the real or objective world.   But, if we had caught the contradiction, we could have stopped there and we could have avoided having to deal with the whole story about the imaginary unicorn.

OK,  let’s go over this again — just to make sure we understand it:

A contradiction is when two or more statements are asserted as fact where it is impossible for both or all of them to be true at the same time.

Contradictions are known as ‘absurdities.’

From an absurdity, all things follow.

Now, here is why it is important to understand contradictions.  When a formal or informal argument is being made and a contradiction is encountered, it renders that argument ‘unsound.’  This means the argument cannot exist in the real world, therefore, the conclusions are unlikely to exist in the real world.  In short, it destroys the logic supporting the argument.  A rational person has little to no reason to accept an unsound argument.  Therefore, a rational person has little to no reason to accept an argument containing a contradiction.  Or, to put it another way, logic allows you to dismiss any argument that contains a contradiction.  You can just ignore it and you are perfectly justified in doing so.*

This is why we should all know and understand what contradictions are and what they mean to us when we are trying to think our way through whatever issue or argument we may encounter in our lives.  This is especially true where matters such as money and politics are concerned.  You will often catch salesmen in contradictions.  Well, guess what?  If they contradict themselves, that means you cannot and should not trust a single thing they have said to you.  The same applies to politicians.  Now, I am not saying they are lying to you.  They may be, or they may actually believe what they are saying.  Either way, it does not matter.  Once you know that you cannot have two contradicting things at the same time, you know that you cannot trust any conclusion that depends upon those two things.  Therefore, when you catch someone trying to make you believe something that is based on a contradiction, you can and probably should reject it — no matter who it is or what they want you to believe.  Just ask them to come back when they resolve the contradiction in their argument and walk away.

 

*NOTE: it is possible for the conclusion of an unsound argument to be factually true, but that still does not mean we have to accept that conclusion as true because it rests on a foundation that does not support it.  It would be like saying:

The moon is made totally out of green cheese. 

The moon is made totally out of moon rock. 

The astronauts brought back rocks from the moon.

While it is true, the astronauts did bring back rocks from the moon, it is a contradiction to state that the moon is made totally out of green cheese and moon rock.  Therefore, we can reject the conclusion that the astronauts brought back rocks.  They may have actually brought back green cheese.  We cannot be sure from the information given in this argument.

 

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