Discernment Pt.5 	  Formal Fallacies		11-4-2001

logic: the ability to discern the implications of a given truth.

What goes wrong in our reasoning?

The reason we come up with incorrect conclusions is because of one of the following:

1.	Formal Logical Fallacies
2.	Informal Logical Fallacies
3.	Flawed Premises

Formal Logical Fallacies

This is when a conclusion doesn’t logically follow from the premises.  That is, you conclude something that is not implied in the premises as a result of an invalid reasoning process.

Examples:
Last Sunday I gave you a couple of examples of valid syllogisms.  This morning I would like to give you a couple of examples of formal fallacies.

But from there I want to show you how to intuitively pick out logical fallacies without having the memorize the names.

Last week I told you you can affirm the “if” or deny the “then.” Two formal fallacies are if you deny the “if” or affirm the “then.” 

Logicians call it “Affirming the consequent” & “Denying the Antecedent.”

Since those are hard to remember, I suggest a more intuitive name: “Failing to realize there is more than one way to skin a cat.”  

When your premise is “If A then B,” you have to keep in mind that every time you have A, you have B.  But just because you have B doesn’t necessarily mean you had A – there might be some other way to get to B besides just A.

“Affirming the consequent” (Affirming the “then”)

If A then B
B
Therefore A

If the premise is “If A then B,” you can’t prove that A is true just by showing that B is true.

Example:
If it rains, the street will get wet.
The street is wet
Therefore it rained.

There are other ways for the street to get wet.

This is the logical fallacy of Job’s friends.  They tried to prove A was true just because B was true.

Job 4:7-8  "Consider now: Who, being innocent, has ever perished?  Where were the upright ever destroyed?  8 As I have observed, those who plow evil and those who sow trouble reap it.  

Let’s reduce Eliphaz’ rhetoric down to the logical argument he is making:
Those who sow trouble reap it.  
You have reaped trouble.
Therefore, you must have sown it.

If A (you sow trouble) then B (you will reap it).
B (You reaped trouble)
Therefore A (You must have sown it)

In this argument, are the premises correct?  
Yes – Ps.7:15-16 He who digs a hole and scoops it out falls into the pit he has made. 16 The trouble he causes recoils on himself; his violence comes down on his own head

The second premise was that Job reaped trouble.  Is that true?  Yes.  Job’s life is the definition of trouble.

So the premises are true, but their conclusion was wrong, because of invalid reasoning.  

Yes, when you sow evil, you reap trouble.  But there are other ways to reap trouble as well.  You can reap a life of trouble by being such a righteous man that God decides to use you to humiliate Satan.

So if you can get trouble in life by being evil, or you can get trouble by being righteous, then it’s not valid to say, “That guy has trouble, therefore…”

Another form of the “There’s more than one way…” fallacy is called “Denying the antecedent” (denying the “if” part).

If A then B
Not A
Therefore not B

Do you see why that argument won’t work?  There might be more than one way to get to B.

This fallacy – denying the “if,” was Job’s error.

In ch.31, Job lists a whole litany of various sins, and says, “If I did any of that, then I should be punished.”

His point was that since he hadn’t done any of that, he shouldn’t have hardship.

If A (a man lives in sin) then B (He should have hardship)
Not A (I didn’t do those sins)
Therefore not B (I shouldn’t be having trouble)

That argument is not valid, because there is more than one way to get to B.  Both premises are true, but the conclusion doesn’t necessarily follow from them, because there can be another cause for trouble besides sin.

Another example:
Heb.3:14  We have come to share in Christ if we hold firmly till the end the confidence we had at first.

Some have used this as an example to prove it is impossible for a genuine believer to fall away.

If A (we hold firmly) then B (we have come to share in Christ).
Not A (someone falls away) 
Therefore Not B (He never shared in Christ).

That is not valid reasoning, because the conclusion is arrived at by affirming the “if.”  Is it possible for a believer to fall away?  Maybe, but you can’t tell from this verse.

Denying the “if” is only valid if the statement is “If and only if A then B.”

The examples of formal syllogisms I have given so far have been “if-then” propositions.  Those are called hypothetical propositions.  

There are two other kinds.  I mentioned Disjunctive propositions (Either A is true or B is true, but not both) – that’s the syllogism that hunting dogs can understand but postmodernist human beings can’t.

There is a third kind: Categorical (a statement that says something about what category something is in.

There are 4 kinds of these:
“All A's are B's”  
“No A's are B's”  
“Some A's are B's”  
“Some A's are not B's” 

Instead of memorizing the rules of syllogisms, let’s try to pick up on errors intuitively.

Some women were prophets
All prophets were leaders
All Pastors were leaders
Therefore some pastors were women

Regardless of whether you agree with the propositions, is this valid reasoning? (no)

Why not?

There is a formal name for this fallacy.  But instead of memorizing that and countless others, lets see if we can figure it out on our own intuitively.

The great thing about Categorical syllogisms is they can be drawn with circles.

(Draw circles – just because the pastors’ circle is inside the leaders’ circle, and so is the prophets’ circle, that doesn’t mean the prophets’ and pastors’ circles have to coincide.  

There is a 4th kind: The Dilemma.
If A then B
If non-A then C
Therefore either B or C

Example:
If Jesus’ claims to deity were true (A), He is God (B)
If Jesus’ claims to deity were false (A), He was a nut case (C)
Therefore Jesus was either God (B), or a nut case (C)
  
This argument can be used to defeat the very common view that Jesus was a good teacher who was not God.  A good teacher who is not God is not a logical possibility in the case of someone who claimed deity.

This is a very powerful form of argument.  Jesus used it in Lk 20:3-8
He replied, "I will also ask you a question. Tell me, 4John's baptism-was it from heaven, or from men?" 
5They discussed it among themselves and said, "If we say, `From heaven,' he will ask, `Why didn't you believe him?' 6But if we say, `From men,' all the people will stone us, because they are persuaded that John was a prophet." 

They understand Jesus’ argument.  
If A (John was from God) then B (should believe him)
If Not A (John not from God) then C (John was not a prophet)
Therefore either B or C – either John is a false prophet, or they should have obeyed him. 

Jesus uses this argument to pin them down, because they didn’t obey him, but they weren’t prepared to call him a false prophet either.

7So they answered, "We don't know where it was from." 

That doesn’t solve the problem though.  The fact remains that either B or C is true.

The fallacy here is easy to remember – a False Dilemma.  

In order for the dilemma argument to be valid, it has to cover all possibilities.  

Example: 
A salesman told us this week: “Either you will walk away and continue to spend way more than you should on vacations, or you will buy this vacation package and enjoy a lifetime of wonderful vacations.”

Obviously it’s a false dilemma, because it leaves out numerous possibilities.  
It doesn’t cover the possibility that I could walk out without buying their package and I could still not pay too much for vacations.
And it doesn’t cover the possibility that I could purchase their plan and have terrible vacations.

Another example:
Either God’s moral law is capricious & arbitrary, or there is a standard higher than God.

If God willed the moral law according to no standard (A), then He is capricious (B).
If God willed the moral law according to some higher standard (Non A), then God is not the highest standard (C).
Therefore, either B or C (Either God is capricious or He is not the highest standard).

Where is the error?

It’s a false dilemma.  If A is no standard, then Non A is some standard – but not necessarily some higher standard.     

In order for a dilemma argument it has to cover every possibility.  But that argument doesn’t cover the possibility that God willed the moral law according to the standard of His own character.    

Finding the Argument

When you are evaluating an argument, you need to check to see if there is one or more of these problems.  To do that, you must learn a very important skill: Reduce the rhetoric down to the basic argument.  

You may also have to expand an argument, when some parts are assumed.  On commercial air time generally known elements to an argument are often left unstated.  

Example: 
Our cereal is high in oat bran
Therefore you should buy our cereal.

The missing parts are:
Our cereal is better than other means of getting more oat bran
More oat bran promotes good health
You ought to pursue good health in this way
The health benefit is worth the cost of our cereal

The more questionable a premise is, the more likely it is to be the part that is not stated.

Each of the above is questionable (I don’t agree with the last three).  

The fact that most parts of most arguments are left out in our sound byte culture (I even have to leave most of the steps out of my reasoning in a letter to the editor), it makes logical fallacies that much harder to detect.

So all these formal fallacies you will generally be able to detect intuitively once you clear away the rhetoric and isolate the argument itself.

Let’s practice.  We will start with the “Pro-Falwell letters silly” letter.

His arguments:
False dilemma (9-11 must either be judgment from God or act of terrorists)

Why not both?

and

Diversity is good, because it’s our heritage.

and 

Diversity is good.
Homosexuality is part of diversity
Therefore homosexuality must be good.  
All A is B
C is A
Therefore C is B

The problem is with the first premise.  I would ask Mr. Berg if he really meant to say all forms of diversity are good – including rape, child molestation, genocide, etc.

If not, then we are left with:
Some diversity is good.
Homosexuality is a form of diversity
Therefore Homosexuality is good.

Some A is B
All C is A
Therefore all C is B

How do I demonstrate the fallacy with circles?

(Homosexuality might not be in the portion of diversity that falls in the category of good.)