All Thought Is Not Valid: Logic 101 Day 1

I thought I was going to die ...

I forget the exact words of the discussion, but it went something like this:

She: "Those people have good jobs just because they know somebody.  It's not fair." 

He:  "Yeah, you know what they say, 'It's not what you know.  It's who you know.'" 

Me:  "Well, just because you know someone at the company doesn't mean you can get a job at that company.  If that was so, then I'd be working at some great companies because I have some friends that work at great companies." 

She:  "Yeah, if you know someone working at the company, your chances of working there are much better. I tried to get a job there, but was turned down.  It's because I didn't know anybody there.  That other dude got a job there, so it's just because he knows someone working there already.  It's not fair." 

He:  "Yeah, she makes a valid point." 

Me:  "Well, no.  Actually her point is not valid." 

She:  "What?!  How dare you say my point is not valid!" 

It was about this time her eyes about popped out of her skull and the veins in her neck started bulging.  She looked like one of those mad women at a protest.

He:  "Watch out, man."

I tried to explain what validity meant and how her point was not valid, but it was too late.  I was already labeled as insensitive and other horrible things.  Further intellectual discussion was hopeless.  I then turned my attention from teaching a miniature lesson in logic to getting ready to block punches, kicks, and wild cat scratches.

What is an Argument?

The word argument, as used in logic, means a series of statements arranged in a certain order to arrive at a conclusion.  One may think of an argument as a conclusion and the reasons for believing the conclusion.   A student studies many such arrangements of statements in a introductory logic course.

As soon as someone asks me for the reasons why I think such-and-such is true, they are asking to hear my argument.  An argument does not necessarily mean yelling and shouting.   To many, this is exactly what it means.  However, to someone who studies mathematics, logic, or philosophy, an argument is simply the manner in which the reasons support a conclusion.

What is a Valid Argument?

Many people I have met use the word "valid" to mean whatever is being discuss is worth hearing or should be considered or respected.  They may say, "I have a valid opinion" or "he has a valid point."  (The logic students snicker).  A person's point of view may or may not be valid.  Not all thought is valid.

By definition, an argument is valid when the conclusion necessarily follows from the premises.  That is, if the reasons are true, then, by the structure of the argument, the conclusion must also be true.  Students of logic and advanced mathematics students study these forms of arguments to justify their conclusions and statements.  An argument is said to be invalid if you cannot necessarily come to the stated conclusion based only on the reasons given.  It is not saying that the conclusion is false; it is saying you cannot logically arrive at this conclusion based on the reasons given.

I will not try to summarize a semester's worth of study in one blog entry.   Go to college and take rigorous courses.   Get yourself some books on introductory logic and study them on your own.

An example of a Valid Argument:

(Premise 1)  All acts that intentionally harm an innocent human being are immoral and should be illegal.

(Premise 2)  Abortion is an act that intentionally harms an innocent human being.

(Conclusion)  Therefore, abortion is immoral and should be illegal.

Whether you agree with my premises or conclusion does not matter.  This is a valid argument.  That is, if the premises are true, then the conclusion is necessarily true also.  So, if the premises can be shown to be true, then rejecting the conclusion would be an irrational way of thinking.

An example of an Invalid Argument:

(Premise 1)  If macroevolution is true, then we would expect to see similarities between species.

(Premise 2)  We do see similarities between different species.

(Conclusion)  Therefore, macroevolution is true.

This is an invalid argument.  You cannot logically arrive at this conclusion based on this reasoning.  The argument is invalid by what is called the fallacy of affirming the consequent.  This is also the fallacy used in my opening example.  This and many other fallacies are discussed in a first semester course in logic.  This being an invalid argument is not denying that macroevolution is true; it is stating that you cannot arrive at the truth of the conclusion based on the reasons given.  Sadly, so many people (including educators) use this argument to try to justify that macroevolution (single-celled animals evolving into humans) is true.

Validity vs. Truth:

"Valid" does not mean "true."  "Invalid" does not mean "false."  You can have a valid argument full of false statements.  You can also have an invalid argument full of true statements.  You can have a true conclusion from an invalid argument and you can have a false statement as a conclusion in a valid argument.  Validity deals with the structure and positioning of these statements; that's it.

Here's an example of a valid argument with false statements:

(Premise 1)  All men are honey badgers.
(Premise 2)  All honey badgers are chihuahuas.
(Conclusion)  Therefore, all men are chihuahuas.

I know this is a silly example, but, believe it or not, this is a valid argument.  That is, IF the premises were true, then the conclusion MUST also be true.   However, as is in this case, since at least one of the premises is false (in fact, both are false), we say that this is not a sound argument.  It is a valid argument, but since at least one of the premises can be shown to be false, then the conclusion is not necessarily true.  It would not be reasonable to accept this conclusion.

Here's an example of an invalid argument with true statements:

(Premise 1)  Some fathers are accountants.
(Premise 2)  Some accountants are over 50 years old.
(Conclusion)  Therefore, some fathers are over 50 years old.

Each of these premises are true and the conclusion is true.  Almost everyone can provide evidence of each of these statements.  However, this argument is invalid because you cannot arrive at the conclusion (even though it is true) simply by using these premises.   That is, the reasons (premises) do not necessarily lead to this conclusion.

What is a Sound Argument?

An argument is considered to be sound if: (1) it is valid in its structure, and (2) the premises are shown (or known) to be true.  If an argument is sound, then only an irrational person would deny the conclusion.  There are two methods for refuting someone's argument: (1) show their argument to be invalid, or (2) show at least one of their premises to be false.

Why Does It Matter?

Logic is used in all forms of thinking.  Poor logic leads to poor thinking.  Good logic leads to good thinking.  Invalid arguments are the result of sloppy thinking (or an insufficient education).  By using invalid arguments we fool ourselves and possibly mislead others.  All rational thought depends on sound reasoning.  We need to think, speak, and act using sound reason.

Bad ideas can have bad consequences.   Bad reasoning can have bad consequences.

Good ideas and sound reasoning often has good consequences.