Logical Fallacies Explained and Debunked

[Petros Agapetos]

The Argument from Ignorance - Argumentum ad ignorantiam

The argumentum ad ignorantiam (also known as the argument from ignorance) is a logical fallacy wherein the speaker claims that a proposition is true because it has not been shown to be false, or vice versa. The argument is a form of non sequitur and a false dichotomy.

The Fallacy

Someone using the argument from ignorance will generally claim that either:

1. They don't know how an argument could be false, therefore it must be true.
2. They don't know how an argument could be true, therefore it must be false.

They are arguing for a particular default position that they prefer. If there is scientific evidence against their default position, it will frequently be dismissed or ignored.Since scientists cannot prove that global warming will occur, it probably won't.

[Petros Agapetos]

Argument from personal incredulity is a statement like "I can't see how that is possible, therefore it is impossible". It is a form of argument from ignorance. It contains an unstated premise: "if something cannot be understood to be possible, it is impossible". This overlooks the possibility that the speaker lacks knowledge or has a failure of imagination.

[Petros Agapetos]

A logical fallacy can be any one of a number of formal or informal mistakes in a deductive proof.

Note that an argument can be fallacious but still correct. For instance:
1. All fish live in the water.
2. All trout live in the water.
3. Therefore all trout are fish.

The premises are true and the conclusion is true, but the conclusion is not a valid inference from the premises. To see why, notice that we could use identical reasoning to prove that "all whales are fish" (of course, whales are mammals not fish).

Likewise, an argument can be logically valid but still wrong:
1. All bugs are insects.
2. All spiders are bugs.
3. Therefore, all spiders are insects.

One of the premises is factually incorrect (which one depends on your definition of the word bug) and the conclusion is also untrue. However, the conclusion is an accurate deduction based on these premises. Validity and soundness are also discussed in the article Validity vs. soundness.

[Petros Agapetos]

Begging the Questions (Petitio Principii)

Begging the question, which goes by the technical name petitio principii, is a logical fallacy that occurs when an argument implicitly assumes its conclusion in a premise.

Examples of Begging the Question

Consider the following argument:

"I know God exists because of all the good things He has done for me in my life."
Arranging this argument in the usual premise–conclusion sequence reveals the problem with it:

1. God has done good things for me in my life.
2. Therefore God exists.
3. The premise assumes that God exists in the first place, otherwise he couldn't "do" anything.

A more subtle example, perhaps, is the following:

I believe in the paranormal because I've actually seen a ghost.
The problem here is the assumption that what one saw was indeed "paranormal" rather than, for example a trick of the light or a hallucination. Under most people's definition, ghosts are examples of paranormal phenomena. However, one must accept that paranormal phenomena are possible to accept the premise that a "ghost" was actually seen. Since everything we can see is made of ordinary matter — i.e., emits or reflects photons according to well understood laws of physics — the underlying assumption that the "ghost" was actually outside of the ordinary laws of physics — i.e., paranormal — cannot be accepted without question. Again, reformatting the argument (and rewording the parts slightly) clarifies the problem:

1. I have seen a paranormal phenomenon (a ghost).
2. Therefore I believe in paranormal phenomena.

Note that the structure of this argument is entirely valid. We can use it for any number of real phenomena (e.g., "I have seen the moon, so I believe in the moon"). Since examples of begging the question can occur in logically valid arguments, petitio principii is considered an informal fallacy. The above example is also based on an enthymeme (a missing premise), namely that the "ghost" was a paranormal phenomenon.

[Petros Agapetos]

Equivocation is a logical fallacy that involves taking a word with more than one definition and freely substituting one definition for another. It effectively ignores the law of identity, which is fundamental to logic.

"'Reason' in language — oh, what an old deceptive female she is! I am afraid we are not rid of God because we still have faith in grammar."
— Friedrich Nietzsche

Examples

"A feather is light. Therefore, a feather cannot be dark."

There are two meanings of the word light. The first sentence assumes a meaning that is the opposite of heavy, not the opposite of dark.
This fallacy is used frequently in the service of apologetics arguments. A few relevant examples:

Atheism is based on faith.

There are multiple meanings of the word faith, for example things you trust in without critical analysis or things which people believe with good evidence.

Prayer is meditation.
Redefining prayer as only a form of mental meditation rather than petitions for things is often used to justify the efficacy of prayer in the petition context.

"No true Scotsman" fallacy.
When someone says, "That person wasn't really a Christian because he did that," they are relying on ambiguity in the word Christian and redefining it to suit their needs.

The existence of laws implies a law-giver.
This stems from a confusion between natural laws and legal laws. Even legal laws do not always require a law giver. Common law can involve customs which are Memes that evolved over time.

Evolution is only a theory.
This plays on the confusion between the scientific and colloquial definitions of the word theory.

[Petros Agapetos]

Argumentum verbosium, or proof by intimidation is a form of Argument from Intimidation - in this case, by being incredibly verbose, using a plethora of complex words to make one's self sound incredibly smart, and dazzle the opposition. The opposing side will struggle to understand what is being said, and appear to "lose" the debate.

"a fool's voice is known by multitude of words"
— Ecclesiastes 5:3

One of the things that scientists and skeptics try to do is distill discussion and arguments down to the simplest and most understandable chunks of information. The purpose is to accurately convey ideas. The author of the CTMU has the primary goal of obfuscation, not explanation. It doesn't matter how smart one is; if one cannot convey the idea in a clear and concise way, that intelligence has gone to waste.

If the person using this type of argument cannot use examples, analogies, or other methods of making it clear, then that person is more interested in dumbfounding you than having an intellectually honest debate.

Some of the most brilliant minds of history, such as Albert Einstein, Isaac Newton and Stephen Hawking, love trying to explain their brilliant ideas to common people, and frequently use analogies and examples to help educate. They didn't use high-end vocabulary to try to sound smart.

[Petros Agapetos]

Argument from fallacy

An argument from fallacy, or the fallacy fallacy is a formal fallacy which occurs when analyzing an argument and assuming that, because the argument contains a logical fallacy the conclusion of that argument must be false. It is also commonly referred to as the fallacist's fallacy.

The form of the argument from fallacy requires a meta-argument, or an argument about the claims of an argument.

There is an argument A which has a conclusion C.
That argument A contains a logical fallacy.
Therefore, C is false.

The issue here is that while the presence of a fallacy is sufficient to render argument A invalid, it does not make C false. Rather, the truth value of C is unknown, because there is no valid argument as to whether C is true or false.

Example

Bob asserts that evolution is true.
Bob says it's true because Charles Darwin said so - which is an argument from authority, and thus a fallacy.
Therefore, evolution is false.

[Petros Agapetos]

Argumentum ad verecundiam - Appeal to authority

An argument from authority is one in which a proposition is claimed to be true because an esteemed person says it is true. It is a fallacy in that it relies on the person's fame or reputation, rather than on logical arguments or empirical evidence.

Examples

"Albert Einstein believed in God. Are you saying that Einstein was wrong?"

"Robert Gentry, a world-famous astronomer, calculated that the odds of life appearing by chance are astronomically low."

"Would you charge the Declaration of Independence with error in affirming that "all men are endowed by their Creator…?"

"What do you say about the hundreds of scholarly books that carefully document the veracity and reliability of the Bible?"

"[The astronomical evidence] for God must be strong when atheistic physicists admit that “the universe exploded out of nothingness,” and agnostic astronomers claim that “supernatural forces” were so at work in the beginning that scientists are led back to “a band of theologians who have been sitting there for centuries"

[Petros Agapetos]

An Appeal to Authority is Not Always a Fallacy

It is not always a fallacy to say that "So-and-so says that X is true, therefore X is probably true." For this discussion, it is necessary to distinguish between an expert and an authority.

If a famous astronomer says that the universe is expanding, then it is very likely that the universe really is expanding. If a qualified doctor says that a patient is suffering from Parkinson's disease, that's most likely the case. In these examples, the astronomer and the doctor are experts in a field, and are addressing topics within their area of expertise. As experts, they have studied their respective fields, are familiar with the state of the art, have studied how to recognize certain events, features or conditions, know how to recognize many problems that might lead a layman astray and how to work around them, and so forth. When we take an expert's word for something, we are saying, in effect, that if we had the time to learn as much about the field as the expert has, we would be able to examine the evidence and reach the same conclusion.

Naturally, this applies only to experts speaking within their field of expertise: there is no a priori reason to take an astronomer more seriously than anyone else on the subject of foreign policy or theology.

On the other hand, if the Pope says, ex cathedra, that contraception is a sin, then that's true as well. In this case, the Pope is an authority in matters of sin: it is his job to determine what is and isn't a sin in the Catholic church. In a very real sense, contraception is a sin not because it is intrinsically bad, or even because it contradicts the Bible in some way, but merely because the Pope has declared it to be so.
Note that in science, there are experts, but (ideally) no authorities.

[Petros Agapetos]

Slippery Slope Fallacy

A Slippery Slope argument generally attempts to argue against one action "A" because of the belief that it will inevitably lead to a much worse effect "B." An example of this might be:

If you allow homosexuals to be married (A), the next thing you know they're going to have to let people marry other things like animals and trees (B)!

In this case the one presenting the argument skips over all of the intermediary steps necessary to get from "A" to "B." The conclusion in "slippery slope" arguments might be an actual concern of the arguer, but that doesn't mean we should assume "B" will follow from "A" especially if there are no obvious causes and effects linking "A" and "B" together.

In order to avoid this gap, the arguer may lay out their own string of causes and effects that lead from "A" to "B." Here's an example that might bridge the gap:

1. Allowing homosexuals to get married will destroy the traditional definition of marriage.
2. If we change the traditional definition of marriage to include homosexuals, then we'll be forced to open marriage to everything else.
3. If marriage is opened to everyone and everything, then people will be able to marry animals and trees!