Wednesday, May 02, 2012

Analyzing an Argument

In the previous post, I suggested that consistency was a key to analyzing an argument.

From studies in formal logic (the form determines the correctness), one form stands out: Modus Ponens.

When I studied it many years ago, the classical form was given like this:

All men are mortal.
Socrates is a man.
Therefore, Socrates is mortal.

The first statement is called the Major Premise, and the second is called the Minor Premise.  The last statement is the Conclusion.

The full version of the logical statement is as follows:

If the major premise, "All men are mortal," is true and the minor premise, "Socrates is a man," is true, then the conclusion, "Socrates is mortal," is necessarily true.

This form is the heart of deductive reasoning.

Now, let us examine the details of the form.  Is it true that "all men are mortal?"  Perhaps we can claim it is true by definition.  Being a man is being mortal.  On the other hand, it does not follow that being mortal is being a man, because we have seen that other things, from dogs to grass, also die.

It may be possible for there to be a man somewhere who is now alive and will never die.  The only way I could demonstrate to everybody that all men are mortal is to kill all men.  And then, my argument would be proved, but A) there would be no one left alive to be interested in my proof, or B) one of them might spring back to life and my argument would fall on deaf ears, anyway, though it was disproved.

Major premises of this sort fall in the category of statements which are generally accepted by "all men everywhere."  By "accepted," we mean "believed to be true."  In mathematics, we call these things "axioms," the starting principles that we assume to be true (and don't try to prove), and in theological circles, we call them "faith principles."

Major premises are generally things that are asserted. Minor premises are generally things that can be observed.  In Apologetics, we call Major Premises "Presuppositions."

In analyzing a deductive argument, we generally accept the truth of the major premise, because then, we can see where it leads the argument.  If a consequence of accepting the truth the major premise leads us to a contradiction, then we challenge the major premise.

In yesterday's blog about consistency, we looked at three different major premises, i.e., three different assumptions made about the Old Testament, the New Testament, and their relationship to each other.

We saw that different denominations start with different major premises; they look at the same Biblical evidence (minor premises), and get different conclusions.  They were all logical, i.e., they followed the rules of deductive reasoning.  Yet they came to different conclusions, precisely because they started with different major premises, not because one group was more rational than the other.

This is an important point, not only in courses in logic, but also, in any argument that occurs between two people.  These arguments frequently occur in family situations, where a husband and wife reach different conclusions about an incident (minor premise) and fail to understand that their difference is in what they are assuming (the major premise) to be true, not in the actual facts they see.

A man comes home with lipstick on his collar.  He may not even know it is there.  The wife observes the lipstick and concludes the husband has been fooling around with another woman.  In this case, the major premise of the wife might be, "I cannot trust my husband."  The husband's might be, "I am a trustworthy husband."  The minor premise is clear:  There is lipstick on the collar.  The wife's major premise requires her to conclude her husband was unfaithful.

Note that the husband now thinks the wife is not being logical, because he assumes she has adopted the same major premise he holds, and her conclusion does not logically follow.  But she is being logical.  She is just holding to a different major premise than he believes.

Let's say, for argument's sake, that the husband had run into Aunt Sally (you know, the huggy one who always has her face painted to perfection) at a business luncheon with his male colleagues.  He had forgotten all about it.

Here's the issue:  The conclusion of a deductive argument is influenced just as much by the major premise as by the minor premise.  Anyone familiar with John Gray's "Men are from Mars, Women are from Venus" series of books will understand why men and women frequently have different major premises that lead them to different conclusions using the same evidence (minor premises).

It is because our presuppositions (what we believe and accept to be true, but can't prove) determine our conclusions.  Obviously, if two people are looking at the same facts and using the same rules of logic, then the only thing that can lead them to different conclusions is their presuppositions.

I have used several words for our relationship to our major premises, assumptions, presuppositions, beliefs, and faith principles.  You cannot separate conclusions in deductive arguments from belief.  This is not only true for people of faith; it is universally true.  Major premises are normally assumed, accepted, believed, etc., to be true, i.e., they are accepted by faith.  It doesn't have to be a religious faith.  Even an atheist believes there is no God.  That is an act of faith.

As  I look at all the evidence for belief in God, I conclude that an atheist has a greater amount of blind faith than I do, but that is another lesson.

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