DOUBTLESS ... Chapter 2

 

CHAPTER 2.  Comments on logic; the syllogism; begging the question.

Now that we know that doubts are inevitably numerous--that is the lay of our land--we may take our first steps out of doubt.  

Before we do so, we need to clear up an unavoidable question--what is the role of logic in discussions about the faith?

The short answer is that logic makes sure that our statements are coherent.  Logic cannot tell us what to think about something; it can only tell us how to think about it.

For example, if I tell you that a red car is parked in front of my house and that a red car is not parked in front of my house, I have violated the the law of contradiction.  The law of contradiction says that a thing cannot both be and not be something in the same respect.  In this case, the violation is easy to spot; in reality, it is not normally so simple.

In order to talk about logic, we need some basic vocabulary: premise, conclusion and syllogism.__1  

A premise is a statement about something.  E.g., All men are mortal and Peter is a man are both premises.

A conclusion is a statement which is true if certain, specified premises are true.  If All men are mortal and Peter is a man are both true, then the conclusion follows, Peter is mortal.  

A syllogism is the combination of premises and a conclusion which follows from them.  We may now say that All men are mortal, Peter is a man and Peter is mortal forms a syllogism.  

Let's put this syllogism together.

PREMISE-1.  All men are mortal.
PREMISE-2.  Peter is a man.
CONCLUSION.  Peter is mortal.

When we construct a syllogism, we need to make sure that both premises are true and that the conclusion is properly drawn.  In the example above, if the all men are not mortal, the truth of PREMISE-2 is useless and does not let me draw the conclusion.  If PREMISE-2 is false and PREMISE-1 is true, the conclusion again cannot be drawn.  Both premises have to be true for the conclusion to be accepted.

We may now examine an important error in reasoning that will come up shortly:  begging the question.  Begging the question means that we assume what we are supposed to prove is true.  Let's see how it happens.

You ask Paul how he knows that the pope is infallible.  He replies that he is sure of this since the pope said so at Vatican I, and since the pope is infallible, he must be right.  

You ask Peter how he knows that the Bible is the word of God.  He replies that "All scripture is given by inspiration of God" (2 Timothy 3:16).

In either case, Peter and Paul beg the question.  Paul is supposed to provide evidence for papal infallibility, but he cites the pope himself in such a fashion as to assume papal infallibility.  Peter cites the Bible to argue that the Bible is divinely inspired, which assumes that the Bible is divinely inspired. 

Let's put Paul's argument into syllogistic form.

PREMISE.  At Vatican I, the pope declared that he is infallible.
CONCLUSION.  The pope is infallible.

This structure makes Jimmy's circularity visible.  We do not have two premises from which the conclusion follows.  The conclusion is really just a brief restatement of the conclusion.

The wise tell us that most people do not beg the question as transparently as Peter and Paul.  For instance, Paul might have more plausibly argued, "At Vatican I, the dogma that the pope cannot err in matters of faith and morals was promulgated."  At least then he could hope that the unwary would not realize up front that he had simply reworded his conclusion and used it as a premise.  

The wise admit that many of the best minds beg the question unconsciously in this way.  It is recommended to the dishonest that in order to pull off such a deception, to use a long, rambling argument to distract the audience from noticing the circle.__2

Question-begging comes in many disguises.__3  "Truth may have its norms," says H. W. R. Joseph, "but error is infinite in its aberrations."__4  

The moral of the story is to be on the look-out for an argument in which the conclusion is found hiding among the premises.  

ENDNOTES
1.  Our definitions of premise, conclusion and syllogism depend on Aristotle's Prior Analytics.
2.  We will explore how we can save Peter's argument in a future chapter.  It is not clear how to save Paul's argument.  The decrees of Vatican I make it pretty clear that the pope is declaring himself to be infallible.  
3.  See Aristotle's Topics, VIII for a brief survey.  William T. Parry and Edward A. Hacker, Aristotelian Logic (State University of New York, 1991), pp. 444-448 for details.
4.  H. W. R. Joseph, An Introduction to Logic, 2nd ed. (repr. 1966; Oxford, 1916), p. 569.