A Primer on Practical Logic

Copyright (c) J. Budziszewski

"I don't know anything about logical reasoning!"  That can be remedied; here is a short lesson in applied logic.  Whenever someone makes a claim to you about politics or morals -- anything from "Morals are all relative anyway" (which you might hear at the corner convenience store) to "No one should be required to surrender his autonomy" (which you might hear at a political theory conference) -- ask these three questions.  (1) What do you mean by that?  (2) How do you know it's true?  (3) What difference does it make?

When you ask the second question -- "How do you know it's true?" -- the person to whom you are speaking should reply by giving a reason for his claim.  The reasons are the premises; the claim they are supposed to support is the conclusion.  Taken together, the premises and the conclusion make up an argument.  Here are three tests for arguments.  (1) Do the terms used in the premises have clear meanings?  (2) Is the reasoning free of fallacies?  and (3) Are the premises true?  If it passes all three tests, you can be sure that the conclusion is true.  But if it fails even one of the three tests, you know no more about whether the conclusion is true than you knew before.  Arguments that pass tests 1 and 2 are sometimes called valid whether or not they pass test 3.  Bear in mind, however, that a valid argument with false premises may still have a false conclusion.

I've been asked, "What if I just know the conclusion of an argument is false, but no matter how hard I try, I can't find anything wrong with the terms, the premises, or the reasoning?"  The answer is, "Then you change your mind."

Fallacies of Distraction

Logical fallacies come in two kinds:  Informal fallacies, sometimes called fallacies of distraction, and formal fallacies, sometimes called fallacies of form.  Following are some of the main varieties of informal fallacies.  In the section after that we will consider some of the formal kind.  I have borrowed several amusing illustrations from Douglas Wilson.

Ipse dixit ("he said it himself").  Definition:  Illegitimate appeal to authority.  Example:  "Scientific people don't believe in God, so there must not be any God."

Not all appeals to authority are illegitimate.  For instance, there is nothing wrong with consulting a geologist about the chemical composition of limestone.  Such consultation is legitimate when (a) one has reasonable assurance of the supposed authority's honesty, reliability, and qualifications, (b) the question asked concerns his own field of expertise, (c) among experts in the same field, the point about which he is asked is not a matter of serious dispute, and (d) so far as one can follow them without acquiring the same expertise, his arguments are valid.

Argumentum ad populum ("argument to the people"), short name ad populumDefinition:  Illegitimate appeal to popular opinions.  This fallacy takes many forms, three of which are so important that they have names of their own.  Argumentum ad verecundiam is illegitimate appeal to shame; argumentum ad invidiam is illegitimate appeal to envy; and argumentum ad captandum is substitution of a flattering manner for a valid argument.  Examples:  "How can you be so unpatriotic as to criticize the President's proposal?"  "You are too sensible to doubt what I say."

Not all appeals to popular opinion are illegitimate.  For instance, if there really is a “law written on the heart,” then the fact that almost all people in all times and places have called murder wrong is a strong argument that it really is.  Shame too has legitimate uses; if you are have done wrong, then those who arouse your conscience are doing you a favor.

Argumentum ad baculum ("argument to the stick"), short name ad baculumDefinition:  Illegitimate appeal to fear, especially in the form of a threat.  "If you don't agree with me about this, I'll never be your friend again."

Not all threats and appeals to fear are illegitimate.  True, the mere fact that laws are backed up with threats of punishment does not prove that they are just.  But this does not make it wrong to back up laws with threats of punishment.

Argumentum ad hominem ("argument to the man"), short name ad hominemDefinition:  Avoiding the issue by criticizing the speaker rather than his argument.  Examples:  "Why should we read Plato?  He's just a dead white European male."  "You don't believe in same-sex marriage?  How could you be such a homophobe?"  "What a hypocrite you are.  Your real reason for trying to get me to stop drinking is that you want all the liquor for yourself."  Notice that ad hominem is a fallacy even if the opponent really does have the motives or personality traits of which he is accused.

Criticizing the speaker is not always a way of avoiding the issue.  For example, if a speaker persists in statements that are already known to be false, their truth is no longer the issue; the issue now is probably why he persists in them.  A statement like "He says his products are safe only to make a sale" would be fallacious if we had no idea whether they were safe, but if we know that he knows they aren't, the statement merely answers the question "Then why does he say they are?"

Argumentum ad misericordiam ("argument to pity"), short name ad misericordiam; also known as false compassionDefinition:  Treating a person's suffering as automatically justifying his desires or opinions.  Examples:  "How could it be wrong to give the poor little fellow a fourth piece of chocolate cake?  Look how much he wants it!"

Not all compassion is false compassion.  The definition does not imply that it is wrong to practice acts of mercy; it does suggest that what the sufferer wants may be different from what he needs.

Tu quoque ("you too").  Definition:  Defending your own wrongdoing by pointing out that your opponent does the same thing you do.  Examples:  "So what if I cheated on the examination?  So did you."  "So what if Republicans buy votes?  So do Democrats."  Self-justification is not the only possible motive for pointing out that your opponent commits your sins too.  It would not be a fallacy but an act of courage to say "Yes, we both cheated, and it was wrong.  I'm going to turn myself in; will you join me?"

In one interesting variety of tu quoque, the speaker criticizes the opponent for something he is doing himself but doesn’t realize that he is doing.  Example:  “You say chastity is a virtue, but that’s just a religious opinion.”  What the speaker doesn’t realize is that he has a religious opinion too:  He thinks his opponent’s religion is wrong.

Equivocation.  Definition:  Confusing different senses of the same term.  Example:  "I know that peace is possible in the world; why, everyone in my meditation group has achieved peace already."  A common form of equivocation is accent, in which the meaning of a sentence is changed not through differing definitions but through differing emphases.  I cannot improve on Wilson's examples:  "We should not steal our neighbor's car, but it is fine if someone else does."  "We should not steal our neighbor's car, but we will anyway."  "We should not steal our neighbor's car, but it's okay to vandalize it."  “We should not steal our neighbor's car, but the folks across town are fair game."  "We should not steal our neighbor's car, but we are after the lawnmower."

Using terms in different senses is not itself fallacious; we just have to keep track of them.  For example, there is nothing faulty about the statement "Personal peace is possible, but world peace is not."

Fallacies of Form

Contradiction.  Definition:  Maintaining two contrary claims in the same sense at the same time.  Examples:  (a) At the beginning of A Tale of Two Cities, author Charles Dickens declares, "It was the best of times, it was the worst of times."  If Dickens means (as he does) that it was the best of times in one sense but the worst of times in another then this is not a contradiction, but if he means that in one and the same sense it was both best and worst then it is one.  (b) A poet declares "The sun rises, the sun sets."  If he means (as he does) that the sun rises at one time and sets at another then this is not a contradiction, but if he means that it rises and sets at the same time then it is one.  (c) A painter remarks "The house is both black and white."  If he means that the house is black in some parts and white in others then this is not a contradiction, but if he means that it is both black all over and white all over then it is one.

The principle of non-contradiction is fundamental to all valid reasoning; it must be true for truth and falsity to have any meaning at all.  Amazingly, however, it is often attacked.  A former colleague taught her students that two contradictory statements could simultaneously be true because "Convex and concave are contrary properties, yet every curve has both."  Her error lay in overlooking the fact that the statements "The curve is convex" and "The curve is concave" do not have clear meanings unless we specify from which side we are looking at the curve.  A more adequate description is that the curve is convex when viewed from an exterior point and concave when viewed from an interior point.

One also hears sometimes that Hegel's "dialectic" has made the principle of non-contradiction obsolete by showing that Thesis and Antithesis come together in Synthesis.  If Hegel did believe that he had refuted the principle of non-contradiction, he was confused.  Of course, any given "thesis" may be true in one sense or at one time even though its "antithesis" is true in another sense or at another time.  In such a case a "synthesis" may indeed sum up the senses in which or the times at which each is true.  This is exactly what we have achieved by analyzing such examples as "It was the best of times, it was the worst of times."  But that is not real contradiction.

Contradiction is not the only kind of incoherency.  Consider the exhortation “Remember, the meaning of the speaker can never be recovered from what he says.”  It is incoherent, even though it is not contradictory.

Petitio principii ("little principles"); also known as circularity or begging the questionDefinition:  Assuming what must be proven; including the conclusion among the premises, usually in camouflage.  Another example from Wilson:  "Of course George Washington crossed the Delaware!  How else could he have made it to the other side?"  A common form of petitio principii is tendentious definition.  A good example may be found in a textbook on "racism and sexism" which defines racism not as racial prejudice, but as racial prejudice plus power.  Adding that all black people are powerless, she concludes that no black person can be a racist.  The fallacy is obvious:  Rather than carry the burden of justifying black racism while condemning white racism, she simply defines black racism out of existence.

Complex question.  Definition:  Wording a yes-or-no question in such a way as to exclude a legitimate response.  The classical example:  "Have you stopped beating your wife?"

False alternative.  Definition:  Oversimplifying the alternatives; forcing a choice when the alternatives are either non-exhaustive or non-exclusive.  When oversimplification has reduced the apparent options to just two false alternative is often called false dichotomy, bifurcation, or the either-or fallacy.  Examples:  "Are you a liberal or a moderate?"  "Do you go to school or work?"  The problem with the first example is that the alternatives are non-exhaustive, for one might be neither liberal nor moderate.  The problem with the second is that the alternatives are non-exclusive, for one may go to school and work at the same time.  Notice that false dichotomy is often used in a way that resembles complex question.  For instance the query "Are you liberal or do you have a brain?" excludes a legitimate response by intelligent conservatives, and the query "Are you conservative or do you have a heart?" excludes a legitimate response by compassionate conservatives.  These questions would escape fallacy only if it were literally impossible for a liberal to be intelligent or a conservative to be compassionate.

Not all alternatives are false alternatives.  For example, "Are you a liberal or a moderate?" proposes a false alternative, but "Are you a liberal or something else?” does not.

Appeal to the excluded middle, also known as neutralism.  Definition:  Reasoning as though a meaningful statement could be some third thing besides true or false.  Example:  "I don't have a position on the morality of abortion; I'm pro-choice."  Obviously, between the two mutually exclusive alternatives "Permitting abortion is ethical" and "Permitting abortion is unethical," the speaker does have a position:  he is committed to the former.  Unfortunately, entire political and ethical philosophies are based on the illusion that one never really has to take sides.

Like the principle of non-contradiction, the principle of excluded middle is sometimes attacked.  The objection runs, "Don't we speak of 'half-truths'?  Aren't truth and falsehood just the endpoints of a continuum?"  Although the expression "half-truth" is useful, it is not to be taken literally; its meaning has nothing to do with fractions.  For instance, if a painter calls the statement "The house is black" a half-truth, what he probably means is either that the house is gray, or that parts of the house are black but other parts aren’t.  Sometimes when people speak of half-truths they are trying to express probability statements:  “There is a fifty-fifty chance that the house is black.”

Post hoc ergo propter hoc ("after this, therefore because of this").  Definition:  Establishing causation solely by chronological sequence.  Examples:  "When I crow, the sun comes up; therefore, I am the cause of the sunrise."  One paradise for post hoc ergo propter hoc reasoning is politics.  For example, if the economy improves immediately after a new president takes office, most people give him the credit.  Actually, (a) it takes time for the government to make changes in policy, and (b) even after the government has made them, their economic effects generally do not kick in for at least eighteen months.

Don't think that chronological sequence has nothing to do with causation; the problem is that chronological sequence by itself is no argument for causation.

Composition.  Definition:  Attributing to the whole the properties of the parts.  Examples:  "Chlorine and sodium are both poisons, so salt must also be poisonous."  "All of the floor tiles are square, so the floor itself must be square."

The converse of composition is division, attributing to the parts the properties of the whole, as in the statement "Salt is wholesome, so chlorine and sodium must be wholesome" or the statement "The floor itself is square, so all of the floor tiles must be square."  The hazard of these two fallacies is great in political theory, where properties of individuals and of communities are often thoughtlessly interchanged.  For example the utilitarian John Stuart Mill incorrectly reasoned that if individual happiness is the good for an individual, then aggregate happiness is the good for the aggregate of individuals.  In the same way, some writers on diplomacy incorrectly reason that since every individual in the nation has a will, the nation as a whole has a will.

Apriorism; also known as sweeping generalizationDefinition:  Leaping to conclusions from limited or selected instances.  Example:  "Every Baptist I know is uneducated, so I guess all Baptists are uneducated."

Affirming the consequent; also known as substituting the converse for the propositionDefinition:  Reasoning that if P implies Q, then Q implies P.  Example:  "If there were no heaven, people would believe in it anyway; they do believe in it, so there must be no heaven."

Substituting the inverse for the proposition.  Definition:  Reasoning that if P implies Q, then not-P implies not-Q.  Example:  "The instructor said that if I didn't write the essay, I wouldn't get an A.  Well, I wrote the essay, but I still didn't get an A.  He lied."

Failing to distribute the middle term, also known as faking the connectionDefinition:  Reasoning that if all A are X and all B are X, then all A are B.  Example:  "All religious people go to church, and all religious phonies go to church, so all religious people must be phonies."

Special pleading.  Definition:  Claiming for someone an exemption from a rule even though the person exempted falls within the category to whom the rule rightly applies.  Examples:  "I know I told you not to exceed the speed limit, but when I do it, that's different."  "I know I said that censorship is wrong, but that guy just has to be shut up."

Not every exemption from a rule is special pleading.  We must ask "To whom is the rule meant to apply?"  Speed limits are not meant to apply to policemen in pursuit of speeders, and laws against the use of drugs are not meant to apply to persons taking them by prescription because of medical conditions.  We must also distinguish between rules which have no exceptions, and rules which do.  The speed limit may be written without exceptions, not because there are no exceptions but because it would be impossible to list all of them.  No traffic cop would ticket a driver for going 40 in a 30 mile an hour zone in order to get away from someone who was shooting at him.

Compound Fallacies

Compound fallacy is combining several different fallacies in the same statement.  The combination may be complicated, as the following examples show.

A quadruple compound fallacy.  After sympathetically describing the efforts of guidance counselors in a public high school to set up "support groups" for homosexual teenagers, a television reporter in my town concluded, "This isn't about right and wrong; it's about saving the lives of these students."  The statement combined the following fallacies:  Contradiction, because although the reporter implied that the guidance policy was right, she also insisted that right and wrong were not at issue; appeal to the excluded middle, because to say that right and wrong were not at issue was to suggest that the statement "The guidance policy is right" may have been some third thing other than true or false; false alternative, because although she presented listeners with a choice between saving lives and considering right and wrong, one can save lives at the same time as considering right and wrong; and ad misericordiam, because the fact that one should have compassion for teenagers who practice deadly behaviors does not demonstrate that encouraging them in the same behaviors would do them good.

Another quadruple compound fallacy.  A student reports to me that in a graduate seminar on public policy, the professor asked, "All of you here are too intelligent to be pro-life, right?"  The statement combined four fallacies:  Ad hominem, because it attacked the intelligence rather than the arguments of the defenders of unborn children; ad invidiam, because it appealed to a widespread attitude of contempt without justifying that contempt; ad captandum, because it used flattery rather than reasoning to persuade; and ad baculum, because it appealed to the personal anxieties of students who did not want their teacher or classmates to consider them stupid.

So-Called Fallacies That Aren't Fallacies

Sometimes people incorrectly label views they don’t like as fallacies just to avoid having to deal with them.  For example, the natural moral law tradition is sometimes dismissed on grounds that it is based on something called the “naturalistic fallacy” -- trying to derive an ought from an is, or supposing that evaluative conclusions can be drawn from descriptive premises.  Actually, though, deriving an ought from an is is not a fallacy.

As the philosopher Peter Geach pointed out, if the function of a soccer ball is to be used in playing soccer (descriptive premise), and if a given ball is unsuitable for playing soccer (another descriptive premise), then it is a bad soccer ball (validly drawn evaluative conclusion).  Here is another example.  If the purpose of eyes is that they see, then eyes that see well are good eyes, and eyes that see poorly are poor ones; given their purpose, this is what it means for eyes to be “good.”  Moreover, good is to be pursued; the appropriateness of pursuing it is what it means for anything to be good.  Therefore, the appropriate thing to do with poor eyes is try to turn them into good ones.  If it really were impossible to derive an ought from the is of the human design, then the practice of medicine would make no sense.

-- Adapted from this book.