logical fallacies

Logical fallacies are errors that occur in arguments. In logic, an argument is the giving of reasons (called premises) to support some claim (called the conclusion).

There are many ways to classify logical fallacies. I prefer listing the conditions for a good or cogent argument and then classifying logical fallacies according to the failure to meet these conditions

fallacies of assumption

Every argument makes some assumptions. A cogent argument makes only warranted assumptions, i.e., its assumptions are not questionable or false. Fallacies of assumption make up one type of logical fallacy.

One of the most common fallacies of assumption is begging the question. Here the arguer assumes what he should be proving. Most arguments for psi (ESP and psychokinesis) commit this fallacy. For example, many believers in psi point to the ganzfeld experiments as proof of paranormal activity. They note that in many experiments a .25 success rate was predicted by chance but a meta-analysis found a success rate of .34. One defender of psi claims that the odds of getting 34% correct in these experiments was a million billion to one. That may be true, but one is begging the question to ascribe the amazing success rate to paranormal powers. It could be evidence of psychic activity, but there might be some other explanation as well. The amazing statistic doesn't prove what caused it. The fact that the experiment is trying to find proof of psi isn't relevant. If someone else did the same experiment but claimed to be trying to find proof that angels, dark matter, or aliens were communicating directly to some minds, that would not be relevant to what was actually the cause of the amazing statistic. The experimenters are simply assuming that any amazing stat they get is due to something paranormal. I call this assumption the psi assumption.

Another common--and fatal--fallacy of assumption is the false dilemma. Here one assumes that the only reasonable alternatives are the ones you present, when in fact there are others that should not be ignored.This tactic can be persuasive if one of the alternatives is clearly unacceptable.

Not all fallacies of assumption are fatal. Some cogent arguments might make one or two questionable or false assumptions, but still have enough good evidence to support their conclusions. Some, like the gambler's fallacy, are fatal, however. Odds for something with a fixed probability will never increase or decrease depending upon recent occurrences. If the odds were 50/50 before you flipped the coin, they'll still be 50/50 on the next flip--regardless of what side came up on the first flip or the last five or ten flips. (If the coin is loaded, the odds weren't 50/50 to begin with.)

fallacies of relevance

Another quality of a cogent argument is that the premises are relevant to supporting its conclusion. Giving irrelevant reasons for your conclusion need not be fatal, provided you have sufficient relevant evidence to support your conclusion. However, if all the reasons you give to support your conclusion are irrelevant, then your reasoning is said to be a non sequitur.

The divine fallacy (aka the argument from incredulity) is a type of non sequitur. Just because you can't figure out something doesn't imply that some god, alien, or paranormal force is at work.

One of the more common fallacies of relevance is the ad hominem, an attack on the one making the argument rather than an attack on the argument. This fallacy was discussed in detail in a previous post on this blog. One of the most frequent types of ad hominem attack is to attack the person's motives rather than his evidence. For example, a recent conspiracy crank who didn't like my 9/11 conspiracies article wondered how long I've been a member of the New World Order and the Nazi party, but he had no substantive criticisms to offer.

Other examples of irrelevant reasoning are the ad populum fallacy, the irrelevant appeal to tradition, the sunk-cost fallacy, and the argument to ignorance, also discussed in detail in a previous blog post.

fallacies of incompleteness or omission

A third quality of a cogent argument is sometimes called the completeness requirement: A cogent argument should include all the relevant evidence. Cherry picking, or selecting only the evidence that favors one's position, is called selective thinking and it is the basis for most beliefs in the psychic powers of so-called mind readers and mediums. It is also the basis for many, if not most, occult and pseudoscientific beliefs. Selective thinking is essential to the arguments of defenders of untested and unproven remedies. Suppressing or omitting relevant evidence is obviously not fatal to the persuasiveness of an argument, but it is fatal to its cogency. The regressive fallacy is an example of a fallacy of omission. The false dilemma is also a fallacy of omission.

fallacies of unfairness

 

A fourth quality of a cogent argument is fairness. A cogent argument doesn't distort evidence nor does it exaggerate or undervalue the strength of specific data. Giving improper weight to evidence is, perhaps, the most common flaw in argumentation. Another violation of the fairness principle is called the straw man fallacy, discussed in detail in a previous post to this blog.

fallacies of ambiguity

A fifth quality of cogent reasoning is clarity. Some fallacies are due to ambiguity, such as the fallacy of equivocation: shifting the meaning of a key expression in an argument. For example, the following argument uses 'accident' first in the sense of 'not created' and then in the sense of 'chance event.'

Since you don't believe you were created by a god then you must believe you are just an accident. Therefore, all your thoughts and actions are accidents, including your disbelief in any god.

fallacies of insufficient evidence

Finally, a cogent argument provides a sufficient quantity of evidence to support its conclusion. Failure to provide sufficient evidence is to commit the fallacy of hasty conclusion. One type of hasty conclusion that occurs quite frequently in the production of superstitious beliefs and beliefs in the paranormal is the post hoc fallacy.

Some fallacies may be classified in more than one way, e.g., the pragmatic fallacy, which at times seems to be due to vagueness and at times due to insufficient evidence.

The logical fallacies mentioned above are due to some lack regarding the content of the arguments. Some logical fallacies are due to the form of the argument; these are known as formal fallacies.

formal fallacies

Affirming the consequent (AC) is a formal fallacy. AC has the form:

If p then q.
q.
So, p.

p and q represent different statements. A statement with the form "if p then q" is called a conditional statement. p is called the antecedent and q is called the consequent of the conditional statement.

Arguments with the form AC are fallacious because they are invalid. Being invalid means that their conclusions do not follow from their premises, i.e., it is possible for their premises to be true and their conclusions false. A valid argument is one in which the conclusion follows from its premises, i.e., it is impossible for its premises to be true and its conclusion false.

Below are some examples of the fallacy of affirming the consequent:

If my astrologer is psychic, then she predicted the forest fires in Russia.
She predicted the forest fires in Russia.
So, my astrologer is psychic.

If a god created the universe, we should observe order and design in Nature.
We do observe order and design in Nature.
So, a god created the universe.

If telepathy is present, we will get greater than chance results from our card-guessing experiment.
We got greater than chance results from our card-guessing experiment.
So, telepathy is present.

If he's lying, he will sweat.
He's sweating.
So, he's lying.

If the suspect is lying, then he will evoke a galvanic skin response (from sweating).
The suspect evoked a galvanic skin response.
So, the suspect is lying.

In each of the above examples of the fallacy of affirming the consequent, the premises of the argument may be true but the conclusion does not follow from the premises. The invalidity of these arguments has nothing to do with their content and is due entirely to their fallacious form. A statement p never follows from the statements if p then q and q. Even if the premises of an AC argument are true, the conclusion doesn't follow from them. Being fallacious, however, does not mean that the conclusion is false. For example, the following examples of AC have true conclusions:

If President Obama is a Christian, then he is not a Muslim.
He is not a Muslim.
So, President Obama is a Christian.

If President Obama was born in Hawaii, then he is an American citizen.
He is an American citizen.
So, President Obama was born in Hawaii.

Some might wonder: are not all conclusions from experimentation invalid on this ground from the point of view of formal logic? Don't scientists commit this fallacy when they reason that if my hypothesis is correct then we will observe x, y, and z when we do experiment E; we observed x, y, and z when we did experiment E; so our hypothesis is correct? Yes, they would, but that is not how competent scientists reason. They reason by the valid form of modus ponens:

If x, y, and z occur in experiment E as predicted by our hypothesis, then our hypothesis is confirmed. X, y, and z occurred in experiment E as predicted by our hypothesis. So, our hypothesis is confirmed

Competent scientists also reason by the valid form of modus tollens:

If our hypothesis is confirmed, then x, y, and z will occur in experiment E as predicted by our hypothesis. X, y, and z did not occur in experiment E as predicted by our hypothesis. So, our hypothesis is not confirmed.

Valid reasoning, however, is not enough to establish the truth of the conclusion. All premises must also be true in the above example for the reasoning to be cogent. The key to solid, cogent reasoning about a scientific experiment is the justification of the first premise: is it really true that your hypothesis will be confirmed if what you predict occurs? Many researchers unjustifiably assume that if what they predict will occur does in fact occur, then they have confirmed their hypothesis. All of the examples above of affirming the consequent could be rewritten as valid arguments. For example, the following would be valid:

If we get greater than chance results from our card-guessing experiment, then telepathy occurred.
We got greater than chance results from our card-guessing experiment.
So, telepathy occurred.

(The problem with this last argument, as some of you may have noticed, is with the questionableness of the first premise.)

_____

Denying the antecedent (DA) is a formal fallacy. DA has the form:

If p then q.
Not p.
So, not q.

Arguments with the form DA are fallacious because they are invalid, i.e., it is possible for their premises to be true and their conclusions false.

Below are some examples of the fallacy of denying the antecedent:

If atheism is true, then I'm wasting my time praying for rain.
Atheism is not true.
So, I am not wasting my time praying for rain.

If acupuncture is quack medicine, then sticking people with needles to relieve pain is absurd.
Acupuncture is not quack medicine.
So, sticking people with needles to relieve pain is not absurd.

If we get greater than chance results from our card-guessing experiment, then telepathy is present.
We did not get greater than chance results from our card-guessing experiment.
So, telepathy is not present.

If he's not sweating, then he's telling the truth.
He sweating.
So, he's not telling the truth.

If the suspect evokes a change in galvanic skin response (from sweating), then he is lying.
The suspect did not evoke a change in galvanic skin response.
Therefore, the suspect is not lying.

In each of the above examples of the fallacy of denying the antecedent the premises of the argument may be true but the conclusion does not follow from the premises. The invalidity of these arguments has nothing to do with their content and is due entirely to their fallacious form. A statement not q never follows from the statements if p then q and not p. Even if the premises of a DA argument are true, the conclusion doesn't follow from them. Being fallacious, however, does not mean that the conclusion is false. For example, the following examples of DC have true conclusions:

If President Obama is Muslim, then he is not a Christian.
He is not a Muslim.
So, President Obama is a Christian (i.e., he is not not a Christian).

If President Obama was born in Nigeria, then he is not an American citizen.
He was not born in Nigeria.
So, President Obama is an American citizen.

For more on the concepts of validity, induction, and deduction, click here.