### Introduction

The aim of this document is to explain the basics of logical reasoning, and hopefully improve the overall quality of debate.

The Concise Oxford English Dictionary defines logic as "the science of reasoning, proof, thinking, or inference." Logic will let you analyze an argument or a piece of reasoning, and work out whether it is likely to be correct or not. You don't need to know logic to argue, of course; but if you know even a little, you'll find it easier to spot invalid arguments.

There are many kinds of logic, such as fuzzy logic and constructive logic; they have different rules, and different strengths and weaknesses. This document discusses simple Boolean logic, because it's commonplace and relatively easy to understand. When people talk about something being 'logical', they usually mean the type of logic described here.

### Arguments

An argument is, to quote the Monty Python sketch, "a connected series of statements to establish a definite proposition."

Many types of argument exist; we will discuss the deductive argument. Deductive arguments are generally viewed as the most precise and the most persuasive; they provide conclusive proof of their conclusion, and are either valid or invalid.

Deductive arguments have three stages: premises, inference, and conclusion. However, before we can consider those stages in detail, we must discuss the building blocks of a deductive argument: propositions.

### Propositions

A proposition is a statement which is either true or false. The proposition is the meaning of the statement, not the precise arrangement of words used to convey that meaning.

For example, "There exists an even prime number greater than two" is a proposition. (A false one, in this case.) "An even prime number greater than two exists" is the same proposition, re-worded.

Unfortunately, it's very easy to unintentionally change the meaning of a statement by rephrasing it. It's generally safer to consider the wording of a proposition as significant.

It's possible to use formal linguistics to analyze and re-phrase a statement without changing its meaning; but how to do so is outside the scope of this document.

### Premises

A deductive argument always requires a number of core assumptions. These are called premises, and are the assumptions the argument is built on; or to look at it another way, the reasons for accepting the argument. Premises are only premises in the context of a particular argument; they might be conclusions in other arguments, for example.

You should always state the premises of the argument explicitly; this is the principle of audiatur et altera pars. Failing to state your assumptions is often viewed as suspicious, and will likely reduce the acceptance of your argument.

The premises of an argument are often introduced with words such as "Assume...", "Since...", "Obviously..." and "Because...." It's a good idea to get your opponent to agree with the premises of your argument before proceeding any further.

The word "obviously" is also often viewed with suspicion. It occasionally gets used to persuade people to accept false statements, rather than admit that they don't understand why something is 'obvious'. So don't be afraid to question statements which people tell you are 'obvious' -- when you've heard the explanation you can always say something like "You're right, now that I think about it that way, it is obvious."

### Inference

Once the premises have been agreed, the argument proceeds via a step-by-step process called inference.

In inference, you start with one or more propositions which have been accepted; you then use those propositions to arrive at a new proposition. If the inference is valid, that proposition should also be accepted. You can use the new proposition for inference later on.

So initially, you can only infer things from the premises of the argument. But as the argument proceeds, the number of statements available for inference increases.

There are various kinds of valid inference - and also some invalid kinds, which we'll look at later in this document. Inference steps are often identified by phrases like "therefore..." or "...implies that..."

### Conclusion

Hopefully you will arrive at a proposition which is the conclusion of the argument - the result you are trying to prove. The conclusion is the result of the final step of inference. It's only a conclusion in the context of a particular argument; it could be a premise or assumption in another argument.

The conclusion is said to be affirmed on the basis of the premises, and the inference from them. This is a subtle point which deserves further explanation.

### Implication in detail

Clearly you can build a valid argument from true premises, and arrive at a true conclusion. You can also build a valid argument from false premises, and arrive at a false conclusion.

The tricky part is that you can start with false premises, proceed via valid inference, and reach a true conclusion. For example:

Premise: All fish live in the ocean

Premise: Sea otters are fish

Conclusion: Therefore sea otters live in the ocean

There's one thing you can't do, though: start from true premises, proceed via valid deductive inference, and reach a false conclusion.

We can summarize these results as a "truth table" for implication. The symbol "=>" denotes implication; "A" is the premise, "B" the conclusion. "T" and "F" represent true and false respectively.

Truth Table for Implication
Premise Conclusion Inference
A B A => B
false false true
false true true
true false false
true true true

If the premises are false and the inference valid, the conclusion can be true or false. (Lines 1 and 2.)

If the premises are true and the conclusion false, the inference must be invalid. (Line 3.)

If the premises are true and the inference valid, the conclusion must be true. (Line 4.)

So the fact that an argument is valid doesn't necessarily mean that its conclusion holds -- it may have started from false premises.

If an argument is valid, and in addition it started from true premises, then it is called a sound argument. A sound argument must arrive at a true conclusion.

### Example argument

Here's an example of an argument which is valid, and which may or may not be sound:

Premise: Every event has a cause

Premise: The universe has a beginning

Premise: All beginnings involve an event

Inference: This implies that the beginning of the universe involved an event

Inference: Therefore the beginning of the universe had a cause

Conclusion: The universe had a cause

The proposition in line 4 is inferred from lines 2 and 3. Line 1 is then used, with the proposition derived in line 4, to infer a new proposition in line 5. The result of the inference in line 5 is then re-stated (in slightly simplified form) as the conclusion.

### Spotting arguments

Spotting an argument is harder than spotting premises or a conclusion. Lots of people shower their writing with assertions, without ever producing anything you might reasonably call an argument.

Sometimes arguments don't follow the pattern described above. For example, people may state their conclusions first, and then justify them afterwards. This is valid, but it can be a little confusing.

To make the situation worse, some statements look like arguments but aren't. For example:

"If the Bible is accurate, Jesus must either have been insane, an evil liar, or the Son of God."

That's not an argument; it's a conditional statement. It doesn't state the premises necessary to support its conclusion, and even if you add those assertions it suffers from a number of other flaws which are described in more detail in the "Atheist Arguments" document.

An argument is also not the same as an explanation. Suppose that you are trying to argue that Albert Einstein believed in God, and say:

"Einstein made his famous statement 'God does not play dice' because of his belief in God."

That may look like a relevant argument, but it's not; it's an explanation of Einstein's statement. To see this, remember that a statement of the form "X because Y" can be re-phrased as an equivalent statement, of the form "Y therefore X." Doing so gives us:

"Einstein believed in God, therefore he made his famous statement 'God does not play dice'.

Now it's clear that the statement, which looked like an argument, is actually assuming the result which it is supposed to be proving, in order to explain the Einstein quote.

Furthermore, Einstein did not believe in a personal God concerned with human affairs -- again, see the "Atheist Arguments" document.

#### Logical Fallacies

There are a number of common pitfalls to avoid when constructing a deductive argument; they're known as fallacies. In everyday English, we refer to many kinds of mistaken beliefs as fallacies; but in logic, the term has a more specific meaning: a fallacy is a technical flaw which makes an argument unsound or invalid.

(Note that you can criticize more than just the soundness of an argument. Arguments are almost always presented with some specific purpose in mind -- and the intent of the argument may also be worthy of criticism.)

Arguments which contain fallacies are described as fallacious. They often appear valid and convincing; sometimes only close inspection reveals the logical flaw.

Below is a list of some common fallacies, and also some rhetorical devices often used in debate. The list isn't intended to be exhaustive; the hope is that if you learn to recognize some of the more common fallacies, you'll be able to avoid being fooled by them.

##### Description of Fallacies

In order to understand what a fallacy is, one must understand what an argument is. Very briefly, an argument consists of one or more premises and one conclusion. A premise is a statement (a sentence that is either true or false) that is offered in support of the claim being made, which is the conclusion (which is also a sentence that is either true or false).

There are two main types of arguments: deductive and inductive. A deductive argument is an argument such that the premises provide (or appear to provide) complete support for the conclusion. An inductive argument is an argument such that the premises provide (or appear to provide) some degree of support (but less than complete support) for the conclusion. If the premises actually provide the required degree of support for the conclusion, then the argument is a good one. A good deductive argument is known as a valid argument and is such that if all its premises are true, then its conclusion must be true. If all the argument is valid and actually has all true premises, then it is known as a sound argument. If it is invalid or has one or more false premises, it will be unsound. A good inductive argument is known as a strong (or "cogent") inductive argument. It is such that if the premises are true, the conclusion is likely to be true.

A fallacy is, very generally, an error in reasoning. This differs from a factual error, which is simply being wrong about the facts. To be more specific, a fallacy is an "argument" in which the premises given for the conclusion do not provide the needed degree of support. A deductive fallacy is a deductive argument that is invalid (it is such that it could have all true premises and still have a false conclusion). An inductive fallacy is less formal than a deductive fallacy. They are simply "arguments" which appear to be inductive arguments, but the premises do not provided enough support for the conclusion. In such cases, even if the premises were true, the conclusion would not be more likely to be true.
##### Examples of Fallacies

Inductive Argument

Premise 1: Most American cats are domestic house cats.
Premise 2: Bill is an American cat.
Conclusion: Bill is domestic house cat.

Factual Error

Columbus is the capital of the United States.

Deductive Fallacy

Premise 1: If Portland is the capital of Maine, then it is in Maine.
Premise 2: Portland is in Maine.
Conclusion: Portland is the capital of Maine.
(Portland is in Maine, but Augusta is the capital. Portland is the largest city in Maine, though.)

Inductive Fallacy

Premise 1: Having just arrived in Ohio, I saw a white squirrel.
Conclusion: All Ohio Squirrels are white.
(While there are many, many squirrels in Ohio, the white ones are very rare).

Index Legend: blue background=includes AR examples

#### Index

·  Appeal to Belief
·  Appeal to Common Practice
·  Appeal to Emotion
·  Appeal to Flattery
·  Appeal to Novelty
·  Appeal to Ridicule
·  Appeal to Spite
·  Bandwagon
·  Begging the Question
·  Biased Sample
·  Confusing Cause and Effect
·  Division
·  Gambler's Fallacy
·  Genetic Fallacy
·  Guilt By Association
·  Personal Attack
·  Poisoning the Well
·  Questionable Cause
·  Relativist Fallacy
·  Spotlight

### Accent

#### Definition

Emphasis is used to suggest a meaning different from the actual content of the proposition.

Accent is a form of fallacy through shifting meaning. In this case, the meaning is changed by altering which parts of a statement are emphasized

Be particularly wary of this fallacy on the net, where it's easy to misread the emphasis of what's written.

#### Examples

"We should not speak ill of our friends"

It would be illegal to give away Free Beer!

The first mate, seeking revenge on the captain, wrote in his journal, "The Captain was sober today." (He suggests, by his emphasis, that the Captain is usually drunk.

#### Definition

As mentioned earlier, there is a difference between argument and explanation. If we're interested in establishing A, and B is offered as evidence, the statement "A because B" is an argument. If we're trying to establish the truth of B, then "A because B" is not an argument, it's an explanation.

The Ad Hoc fallacy is to give an after-the-fact explanation which doesn't apply to other situations. Often this ad hoc explanation will be dressed up to look like an argument. For example, if we assume that God treats all people equally, then the following is an ad hoc explanation:

#### Examples

"I was healed from cancer."
"Praise the Lord, then. He is your healer."
"So, will He heal others who have cancer?"
"Er... The ways of God are mysterious."

### Affirmation of the consequent

#### Definition

Any argument of the following form is invalid:
If A then B
B
Therefore, A

This is the converse of Denial of the Antecedent.

This fallacy is an argument of the form "A implies B, B is true, therefore A is true." To understand why it is a fallacy, examine the truth table for implication given earlier.

#### Examples

"If the universe had been created by a supernatural being, we would see order and organization everywhere. And we do see order, not randomness -- so it's clear that the universe had a creator."

If I am in Calgary, then I am in Alberta. I am in Alberta, thus, I am in Calgary. (Of course, even though the premises are true, I might be in Edmonton, Alberta.)

If the mill were polluting the river then we would see an increase in fish deaths. And fish deaths have increased. Thus, the mill is polluting the river.

#### Rebuttal

Show that even though the premises are true, the conclusion could be false. In general, show that B might be a consequence of something other than A. For example, the fish deaths might be caused by pesticide run-off, and not the mill.

### Amphiboly

#### Definition

An amphiboly occurs when the construction of a sentence allows it to have two different meanings. The fallacy occurs when the premises used in an argument are ambiguous because of careless or ungrammatical phrasing.

#### Examples

Last night I shot a burglar in my pajamas.

The Oracle of Delphi told Croseus that if he pursued the war he would destroy a mighty kingdom. (What the Oracle did not mention was that the kingdom he destroyed would be his own. Adapted from Heroditus, The Histories.)

Save soap and waste paper.

Belief in God fills a much-needed gap.

#### Rebuttal

Identify the ambiguous phrase and show the two possible interpretations.

### Anecdotal evidence

#### Definition

One of the simplest fallacies is to rely on anecdotal evidence.

It's quite valid to use personal experience to illustrate a point; but such anecdotes don't actually prove anything to anyone. Your friend may say he met Elvis in the supermarket, but those who haven't had the same experience will require more than your friend's anecdotal evidence to convince them.

Anecdotal evidence can seem very compelling, especially if the audience wants to believe it. This is part of the explanation for urban legends; stories which are verifiably false have been known to circulate as anecdotes for years.

#### Examples

"There's abundant proof that God exists and is still performing miracles today. Just last week I read about a girl who was dying of cancer. Her whole family went to church and prayed for her, and she was cured."

### Circulus in demonstrando

#### Definition

This fallacy occurs if you assume as a premise the conclusion which you wish to reach. Often, the proposition is rephrased so that the fallacy appears to be a valid argument.

#### Examples

"Homosexuals must not be allowed to hold government office. Hence any government official who is revealed to be a homosexual will lose his job. Therefore homosexuals will do anything to hide their secret, and will be open to blackmail. Therefore homosexuals cannot be allowed to hold government office."

Note that the argument is entirely circular; the premise is the same as the conclusion. An argument like the above has actually been cited as the reason for the British Secret Services' official ban on homosexual employees.

Circular arguments are surprisingly common, unfortunately. If you've already reached a particular conclusion once, it's easy to accidentally make it an assertion when explaining your reasoning to someone else.

### Converting a conditional

This fallacy is similar to the Affirmation of the Consequent, but phrased as a conditional statement.

#### Definition

This fallacy is an argument of the form "If A then B, therefore if B then A."

#### Examples

"If educational standards are lowered, the quality of argument seen on the Internet worsens. So if we see the level of debate on the net get worse over the next few years, we'll know that our educational standards are still falling."

### Denial of the antecedent

#### Definition

This fallacy is an argument of the form "A implies B, A is false, therefore B is false." The truth table for implication makes it clear why this is a fallacy.

Note that this fallacy is different from Non Causa Pro Causa. That has the form "A implies B, A is false, therefore B is false", where A does not in fact imply B at all. Here, the problem isn't that the implication is invalid; rather it's that the falseness of A doesn't allow us to deduce anything about B.

Any argument of the following form is invalid:
If A then B
Not A
Therefore, Not B

This is the converse of the fallacy of Affirmation of the Consequent.

#### Examples

If you get hit by a car when you are six then you will die young. But you were not hit by a car when you were six. Thus you will not die young. (Of course, you could be hit by a train at age seven.)

If I am in Calgary then I am in Alberta. I am not in Calgary, thus, I am not in Alberta.

"If the God of the Bible appeared to me, personally, that would certainly prove that Christianity was true. But God has never appeared to me, so the Bible must be a work of fiction."

#### Rebuttal

Show that even though the premises are true, the conclusion may be false. In particular, show that the consequence B may occur even though A does not occur.

### Equivocation / Fallacy of four terms

#### Definition

The same word is used with two different meanings.

Equivocation occurs when a key word is used with two or more different meanings in the same argument. For example:

"What could be more affordable than free software? But to make sure that it remains free, that users can do what they like with it, we must place a license on it to make sure that will always be freely redistributable."

One way to avoid this fallacy is to choose your terminology carefully before beginning the argument, and avoid words like "free" which have many meanings.

#### Examples

Criminal actions are illegal, and all murder trials are criminal actions, thus all murder trials are illegal. (Here the term "criminal actions" is used with two different meanings.

The sign said "fine for parking here", and since it was fine, I parked there.

All child-murderers are inhuman, thus, no child-murderer is human.

A plane is a carpenter's tool, and the Boeing 737 is a place, hence the Boeing 737 is a carpenter's tool.

#### Rebuttal

Identify the word which is used twice, then show that a definition which is appropriate for one use of the word would not be appropriate for the second use.

### Ignoratio elenchi / Irrelevant conclusion

#### Definition

Definition: An argument which purports to prove one thing instead proves a different conclusion.

The fallacy of Irrelevant Conclusion consists of claiming that an argument supports a particular conclusion when it is actually logically nothing to do with that conclusion.

Sadly, these kinds of irrelevant arguments are often successful, because they make people to view the supposed conclusion in a more favorable light.

#### Examples

You should support the new housing bill. We can't continue to see people living in the streets; we must have cheaper housing. (We may agree that housing s important even though we disagree with the housing bill.)

I say we should support affirmative action. White males have run the country for 500 years. They run most of government and industry today. You can't deny that this sort of discrimination is intolerable. (The author has proven that there is discrimination, but not that affirmative action will end that discrimination.)

A Christian may begin by saying that he will argue that the teachings of Christianity are undoubtedly true. If he then argues at length that Christianity is of great help to many people, no matter how well he argues he will not have shown that Christian teachings are true.

#### Rebuttal

Show that the conclusion proved by the author is not the conclusion that the author set out to prove.

### The "No True Scotsman..." fallacy

Suppose I assert that no Scotsman puts sugar on his porridge. You counter this by pointing out that your friend Angus likes sugar with his porridge. I then say "Ah, yes, but no true Scotsman puts sugar on his porridge.

This is an example of an ad hoc change being used to shore up an assertion, combined with an attempt to shift the meaning of the words used original assertion; you might call it a combination of fallacies.

Sometimes the claim is legitimate, such as "No true Christian believes killing is moral" and therefore if someone believes killing is moral they are not a true Christian. Also, no true ALF member deliberately risks lives of other sentient beings.

### Non causa pro causa

#### Definition

The fallacy of Non Causa Pro Causa occurs when something is identified as the cause of an event, but it has not actually been shown to be the cause. For example:

#### Examples

"I took an aspirin and prayed to God, and my headache disappeared. So God cured me of the headache."

This is known as a false cause fallacy. Two specific forms of non causa pro causa fallacy are the cum hoc ergo propter hoc and post hoc ergo propter hoc fallacies.

Cum hoc ergo propter hoc
This fallacy is a special case of the more general non causa pro causa.

This fallacy is similar to post hoc ergo propter hoc. The fallacy is to assert that because two events occur together, they must be causally related. It's a fallacy because it ignores other factors that may be the cause(s) of the events.

"Literacy rates have steadily declined since the advent of television. Clearly television viewing impedes learning."

### Non sequitur

#### Definition

A non sequitur is an argument where the conclusion is drawn from premises which aren't logically connected with it. For example:

#### Examples

"Since Egyptians did so much excavation to construct the pyramids, they were well versed in paleontology."

(Non sequiturs are an important ingredient in a lot of humor. They're still fallacies, though.)

### Plurium interrogationum / Many questions

#### Definition

This fallacy occurs when someone demands a simple (or simplistic) answer to a complex question.

#### Examples

"Are higher taxes an impediment to business or not? Yes or no?"

Many questions, also known as complex question, presupposition, loaded question, or plurium interrogationum (Latin, "of many questions"), is a logical fallacy. It is committed when someone asks a question that presupposes something that has not been proven or accepted by all the people involved. This fallacy is often used rhetorically, so that the question limits direct replies to those that serve the questioner's agenda.

### Reification / Hypostatization

#### Definition

Reification occurs when an abstract concept is treated as a concrete thing.

#### Examples

"I noticed you described him as 'evil'. Where does this 'evil' exist within the brain? You can't show it to me, so I claim it doesn't exist, and no man is 'evil'."

### Prejudicial Language

#### Definition

Loaded or emotive terms are used to attach value or moral goodness to believing the proposition.

#### Examples

Right thinking Canadians will agree with me that we should have another free vote on capital punishment.

A reasonable person would agree that our income statement is too low.

Senator Turner claims that the new tax rate will reduce the deficit. (Here, the use of "claims" implies that what Turner says is false.)

The proposal is likely to be resisted by the bureaucrats on Parliament Hill. (Compare this to: The proposal is likely to be rejected by officials on Parliament Hill.)

The animals were set free by animal liberation terrorists.

#### Rebuttal

Identify the prejudicial terms used (eg. "Right thinking Canadians" or "A reasonable person"). Show that disagreeing with the conclusion does not make a person "wrong thinking" or "unreasonable".

### Anonymous Authorities

#### Definition

The authority in question is not named. This is a type of appeal to authority because when an authority is not named it is impossible to confirm that the authority is an expert. However the fallacy is so common it deserves special mention. A variation on this fallacy is the appeal to rumour. Because the source of a rumour is typically not known, it is not possible to determine whether to believe the rumour. Very often false and harmful rumours are deliberately started in order to discredit an opponent.

#### Examples

A government official said today that the new gun law will be proposed tomorrow.

Experts agree that the best way to prevent nuclear war is to prepare for it.

It is held that there are more than two million needless operations conducted every year.

Rumour has it that the Prime Minster will declare another holiday in October.

The university said the lab was about to make a brilliant discovery when the ALF ruined the experiments.

#### Rebuttal

Argue that because we don't know the source of the information we have no way to evaluate the reliability of the information.

### Style Over Substance

#### Definition

The manner in which an argument (or arguer) is presented is taken to affect the likelihood that the conclusion is true.

#### Examples

Nixon lost the presidential debate because of the sweat on his forehead.

Trudeau knows how to move a crowd. He must be right.

Why don't you take the advice of that nicely dressed young man?

#### Rebuttal

While it is true that the manner in which an argument is presented will affect whether people believe that its conclusion is true, nonetheless, the truth of the conclusion does not depend on the manner in which the argument is presented. In order to show that this fallacy is being committed, show that the style in this case does not affect the truth or falsity of the conclusion.

The style over substance fallacy occurs when one emphasises the way in which the argument is presented, while marginalising (or outright ignoring) the content of the argument.

### False Analogy

#### Definition

In an analogy, two objects (or events), A and B are shown to be similar. Then it is argued that since A has property P, so also B must have property P. An analogy fails when the two objects, A and B, are different in a way which affects whether they both have property P.

#### Examples

Employees are like nails. Just as nails must be hit in the head in order to make them work, so must employees.

Government is like business, so just as business must be sensitive primarily to the bottom line, so also must government. (But the objectives of government and business are completely different, so probably they will have to meet different criteria.)

#### Rebuttal

Identify the two objects or events being compared and the property which both are said to possess. Show that the two objects are different in a way which will affect whether they both have that property.

### Slothful Induction

#### Definition

The proper conclusion of an inductive argument is denied despite the evidence to the contrary.

#### Examples

Hugo has had twelve accidents n the last six months, yet he insists that it is just a coincidence and not his fault. (Inductively, the evidence is overwhelming that it is his fault.)

Poll after poll shows that the N.D.P will win fewer than ten seats in Parliament. Yet the party leader insists that the party is doing much better than the polls suggest. (The N.D.P. in fact got nine seats.)

#### Rebuttal

About all you can do in such a case is to point to the strength of the inference.

### Fallacy of Exclusion

#### Definition

Important evidence which would undermine an inductive argument is excluded from consideration. The requirement that all relevant information be included is called the "principle of total evidence".

#### Examples

Jones is Albertan, and most Albertans vote Tory, so Jones will probably vote Tory. (The information left out is that Jones lives in Edmonton, and that most people in Edmonton vote Liberal or N.D.P.)

The Leafs will probably win this game because they've won nine out of their last ten. (Eight of the Leafs' wins came over last place teams, and today they are playing the first place team.)

#### Rebuttal

Give the missing evidence and show that it changes the outcome of the inductive argument. Note that it is not sufficient simply to show that not all of the evidence was included; it must be shown that the missing evidence will change the conclusion.

### Accident

#### Definition

A general rule is applied when circumstances suggest that an exception to the rule should apply.

#### Examples

The law says that you should not travel faster than 50 kph, thus even though your father could not breathe, you should not have travelled faster than 50 kph.

It is good to return things you have borrowed. Therefore, you should return this automatic rifle from the madman you borrowed it from. (Adapted from Plato's Republic, Book I).

#### Rebuttal

Identify the generalization in question and show that it s not a universal generalization. Then show that the circumstances of this case suggest that the generalization ought not to apply.

### Genuine but Insignificant Cause

#### Definition

The object or event identified as the cause of an effect is a genuine cause, but insignificant when compared to the other causes of that event. Note that this fallacy does not apply when all other contributing causes are equally insignificant. Thus, it is not a fallacy to say that you helped cause defeat the Tory government because you voted Reform, for your vote had as much weight as any other vote, and hence is equally a part of the cause.

#### Examples

Smoking is causing air pollution in Edmonton. (True, but the effect of smoking is insignificant compared to the effect of auto exhaust.)

By leaving your oven on overnight you are contributing to global warming.

#### Rebuttal

Identify the much more significant cause.

### Complex Cause

#### Definition

The effect is caused by a number of objects or events, of which the cause identified is only a part. A variation of this is the feedback loop where the effect is itself a part of the cause.

#### Examples

The accident was caused by the poor location of the bush. (True, but it wouldn't have occurred had the driver not been drunk and the pedestrian not been jaywalking.)

The Challenger explosion was caused by the cold weather. (True, however, it would not have occurred had the O-rings been properly constructed.)

People are in fear because of increased crime. (True, but this has lead people to break the law as a consequence of their fear, which increases crime even more.)

#### Rebuttal

Show that all of the causes, and not just the one mentioned, are required to produce the effect.

### Inconsistency

#### Definition

The author asserts more than one proposition such that the propositions cannot all be true. In such a case, the propositions may be contradictories or they may be contraries.

#### Examples

Montreal is about 200 km from Ottawa, while Toronto is 400 km from Ottawa. Toronto is closer to Ottawa than Montreal.

John is taller than Jake, and Jake is taller than Fred, while Fred is taller than John.

#### Rebuttal

Assume that one of the statements is true, and then use it as a premise to show that one of the other statements is false.

Ad Lapidem is a logical fallacy where someone dismisses a statement as absurd without giving a reason why it is supposedly absurd.

Affirming the consequent is a logical fallacy that assumes that because a hypothetical situation would bear a certain effect, that the occurrence of said effect implies that the aforementioned situation occurred.

Appeal to consequences, also known as argumentum ad consequentiam, is an argument that concludes a premise (typically a belief) to be either true or false based on whether the premise leads to desirable or undesirable consequences.

Appeal to probability is a logical fallacy, often used in conjunction with other fallacies. It assumes that because something could happen, it is inevitable that it will happen.

An argumentum ad crumenam argument, also known as an argument to the purse is a logical fallacy of concluding that a statement is correct because the speaker is rich.

Argumentum ad nauseam or argument from repetition or argumentum ad infinitum is a flawed argument, whereby some statement is made repeatedly (possibly by different people) until nobody cares to refute it anymore, at which point the statement is asserted to be true because it is no longer challenged.

Also argumentum ad logicam - assumes that if an argument is fallacious, its conclusion must be false.

This is the "fallacy fallacy" of arguing that a proposition is false because it has been presented as the conclusion of a fallacious argument. Remember always that fallacious arguments can arrive at true conclusions.

"Take the fraction 16/64. Now, cancelling a six on top and a six on the bottom, we get that 16/64 = 1/4."

"Wait a second! You can't just cancel the six!"

"Oh, so you're telling us 16/64 is not equal to 1/4, are you?"

The argument from ignorance, also known as argumentum ad ignorantiam or argument by lack of imagination, is a logical fallacy in which it is claimed that a premise is true only because it has not been proven false, or that a premise is false only because it has not been proven true.

The argument from silence (also called argumentum a silentio in Latin) is that the silence of a speaker or writer about X proves or suggests that the speaker or writer is either ignorant of X or has a motive to remain silent about X. When used as a logical proof in pure reasoning, the argument is classed among the fallacies, but it may be valid circumstantial evidence in practical reasoning.

An association fallacy is a type of logical fallacy which asserts that qualities of one are inherently qualities of another, merely by association.

A biased sample is one that is falsely taken to be typical of a population from which it is drawn.

Bulverism is a logical fallacy coined by C. S. Lewis where rather than proving that an argument is wrong, a person instead assumes it wrong, and then goes on to explain why the other person held that argument.

Chronological snobbery is the logical fallacy that the thinking, art, or science of an earlier time is inherently inferior when compared to that of the present.

Circular cause and consequence is a logical fallacy where the consequence of the phenomenon is claimed to be its root cause. This is also known as the the chicken or the egg fallacy.

"More children in town A have leukemia than in town B. Therefore, there must be something wrong with town A."

Denying the antecedent, a logical fallacy that assumes that because a hypothetical situation would bear a certain effect, that the absence of the hypothesised trigger situation means that the effect earlier described did not occur.

An etymological fallacy is a linguistical misconception based on the idea that the etymology of a word or phrase is its actual meaning.

The fallacy of the single cause, also known as joint effect or causal oversimplification, is a logical fallacy of causation that occurs when it is assumed that there is one, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes.

Ignoratio elenchi (also known as irrelevant conclusion) is the logical fallacy of presenting an argument that may in itself be valid, but which proves or supports a different proposition than the one it is purporting to prove or support.

The logical fallacy of the package deal consists of assuming that things often grouped together by tradition or culture must always be grouped that way.

The perfect solution fallacy is a logical fallacy that occurs when an argument assumes that a perfect solution exists and/or that a solution should be rejected because some part of the problem would still exist after it was implemented.

Proof by example (also known as inappropriate generalisation) is a logical fallacy whereby one or more examples are claimed as "proof" for a more general statement.

The practice of quoting out of context, sometimes referred to as contextomy, is a logical fallacy and type of false attribution in which a passage is removed from its surrounding matter in such a way as to distort its intended meaning.