Argument Analysis

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It is amazing how readily people can be distracted from the salient points of an argument—granting that they are able to identify them in the first place.  That’s one reason more attention is paid to rhetoric, the art of persuasion, than to logic, the science of knowing what can reasonably be said.  And this is complicated by the fact that some fallacious arguments sound so reasonable that they are offered ingenuously and accepted readily.  George Orwell’s essay, “Politics and the English Language,” provides a clear example.  It was a staple of college reading texts for years, but it is based on a fallacy that goes something like this:  if politics can corrupt language use, then language use can corrupt politics.  The essay goes on to plead for clarity in writing.  It was no doubt accepted so readily because both of these messages were attractive to English teachers.  (Actually, it lacks unity and is not, itself, a good example of essay writing.)

In fact, to say “if politics can . . . etc.” is like saying “If a man can eat a hamburger, then a hamburger can eat a man,” or “if a man can ride a horse, then a horse can ride a man.”  These statements are patently ridiculous, but in the “politics” case both parts of the if/then construction sound as if they might be true.  Nonetheless, to show that they are, we have to prove each of them independently.  We can’t use one as the warrant for the other, any more than we can in the parallel “hamburger, and “horse” cases.

 

To deal with any complicated set of claims we must be able to identify the various factors that might influence us.  To do this, we need to define two terms, credibility and plausibility.  For our purposes, credibility includes the substance of the argument, the series of reasoned, logical connections that make the argument worth supporting.  Plausibility lies outside of credibility and includes all of the aspects of the argument that have a vague, confidence-building character such as the reputation of the speaker, the appearance of fairness, and even the fact that she is saying things that affirm views that we already hold.  (The logos of Classical Rhetoric is the same as credibility.  Both ethos and pathos are a part of plausibility.)  We will call an argument that offers no more than plausibility a plausibility argument.  The usual newspaper editorial is likely to be a plausibility argument for it is too short to offer much more.  Do we generally trust the editorial positions taken by the paper?  Does the editorial sound fair and balanced?  Does the point being argued confirm our own prejudices?  Do we have some other reason for wanting to believe what is being said?  Unfortunately, the answers to these questions do not show that the position being taken is clearly worth holding, although they might tell us something about the newspaper, and even about ourselves.

 

Credibility has two dimensions.  Some arguments merely display a truth contained in the conjunction of the premises, and we can call them certainty arguments.  The syllogism is a good example:  “Socrates must be mortal, granted that he is a man and all men are mortal.”  There is no new information contained in the conclusion that Socrates is mortal, and if the premises are true we can be certain of the truth of the claim.  The propositional calculus gives us arguments of the same type:  “Of course I didn’t tighten the bolt too much—if over-tightening would break it and it isn’t broken!”  Many mathematical arguments belong here as well, though they are less obvious and may require us to draw a diagram:  “Of course the angles of a triangle sum to a straight-angle if it is true that alternate interior angles are equal.”

The other type of argument that contributes to credibility is the probability argument.  This kind of argument leads to a determined likelihood and includes both probability and statistics.  For example, one has a greater chance of dying while driving 20 miles to buy a Powerball ticket than one does of winning the jackpot.  We know this because it is the kind of thing that can be calculated (if we have the necessary statistics at hand), just as we know that the odds of getting heads when flipping a coin is one in two.  Even though the Powerball/mortality calculation may seem esoteric, it is sounder than any advice that our parents or a priest might give us to help with some problem in our lives.  Although plausibility is powerfully on their side, there may not be much credibility to their arguments.

 

Since arguments involving plausibility and credibility have such different degrees of reliability, the first step in analyzing an argument is to separate out the various strands.  Although arguments are frequently represented as chains, they are more likely to be nets or webs.  Information may be drawn from many sources and these will feed into sub-arguments which form strands in the net.  Some strands may be connected in various ways to others.  Some may be used only to increase the plausibility of the position being taken, and others may be necessary to reach a conclusion.  There may also be many conclusions of varying degrees of importance in a complicated argument.

Now, since we are looking at a net, we need to ask ourselves two related questions:  does a bad argument tarnish a good one, and are two arguments leading to the same conclusion better than one?  Let’s begin with the first.  Suppose that I have a completely convincing certainty argument.  Does it become progressively less compelling as I add bad arguments to it?  Of course not.  To take this even further, is any argument affected by the infinity of bad arguments that we haven’t even considered?  (This may sound absurd, but it must be a reasonable conjecture if a conclusion can be tarnished by bad arguments.)  We should note that I may lose plausibility as I continue to add bad arguments to my case, but that shouldn’t affect anyone’s judgment.  The same sort of thing can be said about probability arguments.  The results of a well-constructed experiment are not thrown into questions by badly designed experiments that draw the same conclusion.

 

If a bad argument cannot tarnish a good one, can additional good arguments help it?  In answering the first question we have already answered this one, but it might be worthwhile to spell it out.  To think that this is true is to think that the availability of arguments is somehow connected to the certainty of the conclusion.  If other arguments were generated by the validity of the first, we would be entitled to feel that many arguments are better than one, but the fecundity of a situation in spawning arguments may stem from matters quite unrelated to their validity.  Before the Michelson-Morley experiment it may have been easier to argue for the existence of the ether than against it.  And before the development of plate-tectonics it may have been easier to argue against continental drift.  Nonetheless, for claims that might be true, but which lack certainty, additional arguments may increase their plausibility.

 

This means that every strand of an argument net is independent and the argument is, in the final analysis, only as good as the strongest strand that leads from the available facts to the conclusion.  The popular notion that convergent arguments are additive suggests that we could creep up on certainty (or recede from it) by adding weak or even bad arguments to our position—that mere numbers, in the long run, will turn the trick one way or the other.  That, of course, is nonsense.  Many certainty arguments prove the Pythagorean Theorem, but any one of them is sufficient to make a case for it, and no bad argument can damage the certainty of that conclusion.

 

We need to bear one other thing in mind.  A strand consisting of probability arguments is weaker than any one of them looked at separately.  If there is an 80% chance of A being true, and if there is a 60% chance of B being true (if A is true), then there is only a 48% chance of B being true if we don’t know whether A is true.  In effect, we are taking a slice of the pie, and then we are taking a slice of the slice.  The resulting piece is the smallest by far.

 

To analyze an argument net, then, we should do three things:

  • We should insulate ourselves from the appeal of plausibility arguments.
  • We should search out the credibility arguments and rate the strength of the net at the strength we perceive in the single argument we find most certain, and then . .
  • We should ignore, for the moment, all the other strands of the argument.

Now, what should we do if we have only plausibility arguments in favor of some conclusion?  If we need not act we should wait for greater certainty . . . and if we must act, we should be very, very careful.

 

Note

This article is based upon a paper, “Plausibility and Argument Analysis,” that I gave at Conference 87 at Christopher Newport College in Newport News, Virginia in 1987.