INTERPRETATION | EVALUATION | CONSIDERATIONS | TERMS | SUMMARY

Interpretation and Evaluation

INTERPRETATION AND ANALYSIS

Reasoning, and the language through which it's expressed, are sometimes complex and frequently imprecise.  Thus, they're often open to various interpretations, and different interpretations lead to different analyses.  If our assessment of an argument is to be of any value, it must make an earnest attempt to address the actual intent of the arguer, rather than either an innocent misunderstanding or a deliberate misrepresentation of it.

 Interpretation  When formulating an argument of our own, we should take care to keep opportunities for misinterpretation to a minimum.  We must strive to make the meaning as clear as necessary for the argument to be correctly understood, primarily by the target audience, but also by others who might likely come across it, whether they're inclined to agree or disagree with it.  We must ensure that our argument is both coherent (that it holds together logically) and consistent (that it contains no conflicting claims, except for any we intend to refute).  We should clarify any potentially ambiguous statements, and explain any ideas that might not be obvious to everyone.

In assessing the arguments of others, we should employ the same criteria by which we judge our own.  In addition, we must ensure that those arguments are interpreted with fidelity to the probable intent of the arguer.  (Otherwise, we'll end up critiquing a viewpoint we ourselves have made up, not the actual views of the arguer.)  To ensure such fidelity, we must apply what are called the principles of fairness and charity.  The principle of fairness instructs us to represent the reasoning of others faithfully, without distortion, exaggeration, omission of key ideas, or insertion of ideas not contained in the original.  The principle of charity enters the picture if there is some ambiguity in another person's reasoning—meaning that it could legitimately be interpreted in more than one way; charity requires us to interpret the other person's argument in its most favorable light.  In other words, in representing someone else's argument, we should apply the same rules that we'd prefer the other person apply to his or her interpretation of our own reasoning.  Only when we've interpreted an argument fairly and charitably can we then critique it honestly and forthrightly.

 Analysis  As we apply our fairest and most charitable interpretation to each statement, we should identify the argument's conclusion, the overall claim which the other statements are intended to support in one way or another.  The conclusion is typically given some prominent status, such as being positioned near the end or the beginning of the argument, or in some cases being repeated, either verbatim or with variations.  Occasionally, a conclusion is not explicitly stated, but is forcefully implied by the supporting statements.  (This paragraph is an example of a discussion whose claim is positioned at the beginning.)

Once the conclusion or central claim has been identified, we may then organize the rest of the material in the argument so that the linkage of ideas leading to that central claim is clear.  Some premises furnish direct support of the conclusion; these are called grounds for the claim (reasons to believe that the claim is true).  Other premises may offer support, not directly for the conclusion's claim, but for other supporting statements; such premises are classified as grounds for grounds.

Still other statements, whose function is to provide justification for trusting certain assumptions, are called warrants.

For the most part, bicyclists have the same legal rights and responsibilities as operators of other vehicles.
Bicycles are treated as vehicles in the Uniform Vehicle Code.

In the foregoing example, the second statement serves as a warrant to justify the assumption put forth in the first statement (since the Uniform Vehicle Code serves as a national guide for the formulation of state traffic laws).

Some statements in an argument might have no logical relationship to the issue at hand, but serve instead to clarify, define, describe, emphasize, explain, illustrate, or limit various points that arise as the argument progresses.

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INTERPRETATION | EVALUATION | CONSIDERATIONS | TERMS | SUMMARY

 

Evaluations: Validity and Soundness, Strength and Cogency

With the preceding basics under our belts, we're now ready to consider some specific measures of how logically convincing an argument is.

 Validity  An argument is said to be valid if its conclusion must be true whenever all of its premises are true.

Before 1969, no human had set foot on the moon.
It's before 1969.
So, no human has set foot on the moon.

The foregoing is a valid argument.  Although it's not actually true that it's before 1969, if that premise were true, then the conclusion would also have to be true in light of the first premise, whose truth in any case is a matter of historical record.

An argument whose conclusion does not necessarily follow when all of its premises are true is said to be invalid (pronounced ĭn-`vă-lĭd).

George Washington was the first U.S. president.
John Adams was the second U.S. president.
So, Thomas Jefferson was the third U.S. president.

Although all of the three previous statements happen to be true according to the historical record, the conclusion does not logically follow from the two premises.  Washington's and Adams's being the first and second U.S. presidents does not logically lead to Jefferson's being the third.  (Notice that neither Jefferson nor the third presidency is mentioned in either of the two premises.)  Thus, this argument is invalid.

A third premise, such as...

Thomas Jefferson was one of the first three U.S. presidents.

...or...

In alphabetical order by last name, the first three U.S. presidents were John Adams, Thomas Jefferson, and George Washington.

...would be needed to introduce these other two terms into the argument, and thus provide the information and logical linkages to make it valid and lead inescapably to the conclusion.

 Soundness  An argument is said to be sound if both of the following conditions apply: (1) it is valid (i.e., its conclusion must be true if all of its premises are true); and (2) all of its premises are indeed true.  An argument that does not meet both of these conditions is classified as unsound.

Andrew Carnegie is a philanthropist.
Andrew Carnegie is an atheist.
So, it's possible for an atheist to be a philanthropist.

The conclusion of this argument logically follows when both premises are true, so the argument is valid; and indeed it happens that both premises are true.  Thus, this argument is sound.

Heifetz plays the Brahms violin concerto masterfully.
The Brahms violin concerto is being played masterfully.
So, the Brahms violin concerto is being played by Heifetz.

Although the two premises of this argument are judgments, let's assume that most classical music authorities would agree that they're both true.  Even so, it doesn't follow that Heifetz must be playing, because there are other violinists besides Heifetz who also play the Brahms concerto masterfully.  Thus, even though it's still possible that Heifetz might be the performer in this case, the argument is unsound because it's invalid.

Now let's consider this one:

The inventor of the automobile was German.
Henry Ford was the inventor of the automobile.
So, Henry Ford was German.

The logic in this argument leads fluidly to the conclusion.  However, one of the premises—the second—is false.  Henry Ford (an American) built an automobile in 1893, and in 1908 was first to put auto manufacturing on a production-line basis.  But the automobile had already been invented in the 1880s by two Germans, Gottlieb Daimler and Karl Benz.  So, although the argument is valid, the fact that one of its premises is false renders the argument unsound and casts its conclusion into doubt.

That an argument is unsound or invalid is not to say that it's worthless.  Although an argument might not be able to prove an idea true with absolute certainty, it might well show that an idea has a high probability of being true, and this is often an acceptable objective.  Whereas an argument is either valid or invalid, relative strength and cogency fill in the the broad, gray areas of probability.

 Strength  An argument is said to be strong when its conclusion would more probably be true than false if all of its premises were true.  An argument whose conclusion is not very probable when its premises are true is said to be weak.  Probability is statistically expressed as a percentage between 0 and 100, with 0 percent being certainly false and 100 percent being certainly true.  With respect to logic, fifty percent is the break-even point, at or below which an argument is considered weak; i.e., its conclusion is more likely to be false than to be true, even when all of its premises are true.  At exactly fifty percent probability, the likelihood of being false and being true are equal, which is no more convincing than a random coin toss.  Above fifty percent, the odds shift in favor of the conclusion's being true when all the argument's premises are true, and the argument becomes strong—but only relatively so, never certainly.  The odds and strength increase as the probability approaches one hundred percent.

What degree of cogency we ought to demand depends on the situation.  A strength of fifty-plus is adequate for many purposes, but most people would prefer a probability greater than ninety percent when it comes to gambling something important, such as their jobs or their lives, on the outcome.  Following is an example of an argument whose strength we might guess at somewhere around eighty percent:

The stock market has always gained in aggregate value over any continuous period of twenty years.
So, a long-term investor will make money in the stock market.

This is a strong argument, even though its conclusion is far from certain for any individual investor.  Investors often make poor decisions, and particular investments can go belly-up, even in a bull market.  But a long-term investor who makes informed choices, diversifies his portfolio, and keeps a cool head through both boom and bust alternations will nearly always average a far higher rate of return than the slot-machine gambler or lottery player.  Compare this argument to another:

Last week Chris won $50 on a one-dollar lottery ticket.
So, the lottery is a great investment.

The fact remains that the aggregate payout of a competently run lottery is never greater than its aggregate intake.  The argument ignores all the losing one-dollar tickets that Chris had bought over the preceding fifty or more weeks, which, after his recent win, still leave him a dollar or more in the hole overall.  Nor does it take into account the thousands of other current players, most of whom won nothing in last week's lottery.

Note that, in this case, the supporting premise is founded on the single odd instance of a random win, rather than on a well established statistical record as in the stock-market example.  The chances of coming out ahead in the lottery, while greater than zero, are significantly less than fifty percent.  That is, the odds are always that the lottery player will lose more than he wins.  Even if he wins occasionally, it's very unlikely that his overall losses in a pure-chance game of more-than-two-to-one odds will ever be completely recouped.  Thus, the lottery argument is weak.

 Cogency  An argument is said to be cogent when both of the following conditions apply: (1) it is strong (i.e., its conclusion is probably true if all of its premises are true); and (2) all of its premises are indeed true.  An argument that does not meet both of these conditions is classified as uncogent.  As with strength and weakness, cogency and uncogency are relative terms, not absolute.

All life forms we've observed are carbon-based.
So, all life forms are carbon-based.

This is a very strong and (so far) cogent argument, since we've observed millions of life forms, and  all without exception fit the carbon-based pattern.  However, we're fairly sure we haven't yet observed all life forms on earth, and there might well be life forms elsewhere in the universe, perhaps some of which might have very different chemistries.  For this reason, we can't be absolutely certain of the argument's conclusion; nonetheless, we can be very confident that the next terrestrial life form we discover—and fairly confident that the next hundred or the next thousand—will be carbon-based.

As we can see, there are parallel relationships between validity and soundness, and between strength and cogency.  Indeed, there's a degree of conceptual overlap, since validity and soundness are absolute extensions of strength and cogency, respectively.  However, there is this difference: A valid argument could also be said to be strong, and a sound argument could also be said to be cogent.  But a strong or cogent argument cannot be claimed to be valid or sound, unless the probability that its conclusion is true is fully 100 percent (i.e., absolutely certain).  Any statistical value less than 100 percent reflects only a probability, never a certainty.  Whereas a sound argument's conclusion must be true if all of its premises are true, there is always some chance that a cogent argument's conclusion could be false despite that all of its premises are true.

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OTHER CONSIDERATIONS: Relevance, Sufficiency, and Acceptability

If the objective of an argument is not just to persuade emotionally, but to formulate a solidly coherent line of reasoning that leads systematically to a conclusion, then the evidence and reasoning provided must be relevant to the point being made, sufficient to establish and defend that point, and acceptable to the target audience.  And to evaluate all of these, the argument must be understood with faithful regard to the arguer's true intent.

 Relevance  Evidence and argumentation in support of an idea must have some logical connection to that idea.  Material that lacks such a connection is irrelevant.  For example, in a war-crimes trial, the defendant's patriotism and obedience to orders may be considerations as to why he might have committed the crimes, but they do not in the least counter the charge that he did in fact commit them.  Thus, claims of patriotism and obedience may indicate shared responsibility with superiors, but are irrelevant to the simple issue of whether the defendant did or did not commit the crimes.

See if you can identify the conclusion in the following argument, and then pick out any premises that are irrelevant to that conclusion.

J. Robert Oppenheimer was the scientific director of the Manhattan Project.
The Manhattan Project was the U.S. government program to develop an atomic bomb.
Oppenheimer was suspected of having communist ties.
Oppenheimer was scientific director of the government program to develop an atomic bomb.

If you identified the fourth statement as the conclusion, you're right on target.  Next we examine each of the premises to see what (if any) support they give to the conclusion.
The first statement identifies Oppenheimer as scientific director of something called the Manhattan Project.
The second statement identifies the Manhattan Project as the government program to develop an atomic bomb.
Taken together, the first and second statements lead directly to the inescapable conclusion.
The third statement mentions Oppenheimer, but plays no part in connecting him to either the Manhattan Project or the atomic bomb, and thus is irrelevant to the conclusion.  (The statement might be relevant in an argument about why Oppenheimer's security clearance was subsequently revoked; but that's an altogether different argument.)

Sometimes an idea having little or no direct connection to the conclusion may be advanced to help explain a concept, by showing a parallel relationship to the unfamiliar idea under discussion from a familiar one that's used to illustrate the point.  Use of parallel ideas for illustration is called analogy.  The closer in concept that an analogy is to the subject in question, the better.  "Learning logic is like learning to play the piano" is a very weak analogy, for the one is almost exclusively intellectual, whereas the other is also physical and emotional.  The two processes are similar only in that both require practice to acquire proficiency.  "Learning logic is like learning geometry" is a stronger analogy, because the numerical and spatial relationships dealt with in geometry are in many ways similar to the rational relationships that govern logic (as we'll graphically see later).  An analogy is relevant only to the extent that its own qualities and relationships run closely parallel to those of the subject in question, and for much the same reasons.

 Sufficiency  In addition to being relevant to the conclusion, an argument's premises should, when taken together, be sufficient to lead methodically from the evidence to the conclusion, without leaving it to the audience to fill in logical gaps with their own assorted assumptions.  The single premise, "All men are mortal," is not by itself sufficient to conclude that "Socrates is mortal."  It needs an additional premise, "Socrates is a man," which explicitly ties the individual Socrates to a category of things (men) which are all mortal.

We humans are diverse.  We live in different cultures and by different traditions, have different tastes, study different subjects, practice different trades.  Our experiences being different, it's not surprising that many of our assumptions are, too, in some cases even to the point of mutual contradiction.  Often we can get by discussing issues within our own social, vocational, or religious group using a host of unspoken common assumptions.  But we need to make those assumptions explicit when engaging outsiders, in whose experience, traditions, assumptions, and knowledge base such assumptions might seem less than obvious, or perhaps even antithetical—just as some of the assumptions others favor might seem antithetical to ours.

Consider the problem of trying to argue (as some have) a supposedly scientific point against biological evolution, using the second law of thermodynamics (that entropy can never decrease in a closed system) as evidence.  Such an argument might well persuade an uncritical and scientifically illiterate audience, that higher orders of complexity cannot naturally evolve from lower orders.  But it would be insufficient to convince a scientist, or even a moderately knowledgeable non-scientist, who not only does not assume that the earth's biosphere is a closed system, but knows full well that it isn't.  (Relatively slight local decreases in entropy on earth, in terms of photosynthesis, growth, reproduction, mutation, and natural selection, are enabled and driven by solar radiation, the product of enormous increases in entropy, in terms of five million tons of the sun's mass converted into energy every second.)

A sufficient logical argument takes for granted as few pertinent assumptions as possible.  Otherwise, gaps appear in the line of thought.  The argument becomes incoherent, the reasoning is disrupted, and it ceases to be convincing to any knowledgeable critical thinker—which is to say, to any person in a reasonable position to be somewhat in touch with reality.

 Acceptability  In formulating an argument, an arguer should be attentive to the prevailing expectations, beliefs, attitudes, demographics, and education level of the target audience—especially if that audience is diverse.  An argument ought to take advantage of whatever relevant innate agreement there might be.  But it must also anticipate and address questions and challenges.  The arguer's assumptions must either be in accord with those of the audience, or else be supported by persuasive evidence, which at the very least presents the argument's assumptions as credible, if not compelling, alternatives to existing opinion.  If such matters are adequately addressed, the argument and its premises are said to be acceptable.  If not, the argument will likely fail to convince, even if it's flawless in all other respects.

Considering, for example, the often emphatically conflicting views of different religions, we can well imagine that a Christian argument supporting the concept of the Holy Trinity might be entirely acceptable to a Christian audience, but considered wholly unacceptable (if not downright blasphemous) by a Jewish or Muslim audience, in the absence of (and perhaps even in the face of) thoroughly compelling and unambiguous supporting evidence.

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TERMS

Click a term to review its definition or explanation in the text.

• interpretation

• coherent / incoherent

• consistent / inconsistent

• principle of fairness

• principle of charity

• ground

• warrant

• valid / invalid

• sound / unsound

• strong / weak

• cogent / uncogent

• relevance / relevant / irrelevant

• analogy

• sufficiency / sufficient / insufficient

• acceptability / acceptable / unacceptable

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Summary

The various topics we've studied in this section apply to all logical arguments—those with which we agree and those with which we disagree, and those we formulate ourselves in either support for or challenge to some viewpoint.  We've seen how statements are built around two grammatical subassemblies—subject and predicate—and we've begun to grasp some of the ways in which subject and predicate phrases link statements conceptually.  Finally, we've become acquainted with various general ways of evaluating arguments.

This concludes the Basic Concepts section, which has focused on fundamental concepts and methods for reasoning logically.  In the next section (which we might think of as the "comics page" of this website), we turn to things that all too often go wrong with reasoning—things we ought to avoid in our own reasoning, and things that should trigger a "sucker alert" when we hear them from others.

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