Archive-name: atheism/logic
Alt-atheism-archive-name: logic
Last-modified: Tue Sep 10 10:07:20 1996
Version: 3.2

                                      
Constructing a Logical Argument

  Introduction
  
   There is a lot of argument on Usenet; unfortunately, most of it is of
   very low quality. This document attempts to provide you with a gentle
   introduction to logic. Hopefully it will help you to spot bogus
   arguments and improve the level of debate.
   
   Logic is the science of reasoning, proof, thinking, or inference
   [Concise OED]. Logic will let you analyze an argument or a piece of
   reasoning, and work out whether it is correct or not. To use the
   technical terms, logic lets you work out whether the reasoning is
   valid or invalid.
   
   Of course, you don't need to study logic to reason correctly. However,
   a little basic knowledge of logic is often helpful when constructing
   or analyzing an argument.
   
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  Caveats
  
   Note that I am not claiming that logic is the only way of conducting
   discussion and debate. Whether logic is universally applicable is
   itself an issue which is very much open to debate. This document only
   explains how to use logic; you must decide whether logic is the right
   tool for the job.
   
   Note also that this document deals only with simple boolean logic.
   Other sorts of mathematical logic, such as fuzzy logic, obey different
   rules. When people talk about logical arguments, though, they usually
   mean the type being described here.
   
   One problem with boolean logic is that people don't have to be
   consistent in their goals and desires. People use fuzzy logic and
   non-logical reasoning to handle their conflicting goals; boolean logic
   isn't good enough. For example:
   
     "John wishes to speak to the person in charge. The person in charge
     is Steve. Therefore John wishes to speak to Steve."
     
   Logically, that's a totally valid argument. However, John may have a
   conflicting goal of avoiding Steve, meaning that the answer obtained
   by logical reasoning may be inapplicable to real life. Garlic tastes
   good, strawberry ice cream tastes good, but strawberry garlic ice
   cream is only logically a good idea.
   
   Sometimes, principles of valid reasoning which were thought to be
   universal have turned out to be false. For example, for a long time
   the principles of Euclidean geometry were thought to be universal
   laws.
   
   However, keeping those caveats and limitations in mind, let's go on to
   consider the basics of boolean logic.
   
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  Basic concepts
  
   The building blocks of a logical argument are propositions, also
   called statements. A proposition is a statement which is either true
   or false. For example:
   
     "The first programmable computer was built in Cambridge."
     
     "Dogs cannot see colour."
     
     "Berlin is the capital of Germany."
     
   Propositions may be either asserted (said to be true) or denied (said
   to be false).
   
   Note: This is a technical meaning of the word "deny", not the everyday
   meaning.
   
   When a proposition has been asserted based on some argument, we
   usually say that it has been affirmed.
   
   The proposition is generally viewed as the meaning of the statement,
   and not the particular arrangement of words used. So "An even prime
   number greater than two exists" and "There exists an even prime number
   greater than two" both express the same (false) proposition.
   
   Sometimes, however, it is better to consider the wording of the
   proposition as significant, and use linguistic rules to derive
   equivalent statements if necessary.
   
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  What is an argument?
  
   An argument is, to quote the Monty Python sketch, "a connected series
   of statements to establish a definite proposition". There are three
   stages to an argument: premises, inference, and conclusion.
   
    Stage one: Premises
    
   For the argument to get anywhere, you need one or more initial
   propositions. These initial statements are called the premises of the
   argument, and must be stated explicitly.
   
   You can think of the premises as the reasons for accepting the
   argument, or the evidence it's built on. Premises are often indicated
   by phrases such as "because", "since", "obviously", "let's assume",
   and so on.
   
   (The phrase "obviously" is often viewed with suspicion, as it gets
   used to intimidate people into accepting things which aren't true at
   all. If something doesn't seem obvious to you, don't be afraid to
   question it. You can always say "Oh, yes, you're right, it is obvious"
   when you've heard the explanation.)
   
    Stage two: Inference
    
   Next the argument continues step by step, in a 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. The new proposition can, of course, be used in later
   stages of inference.
   
   There are various kinds of valid inference -- and also some invalid
   kinds, but we'll get to those later. Inference is often denoted by
   phrases such as "implies that" or "therefore".
   
    Stage three: Conclusion
    
   Finally, you arrive at the conclusion of the argument, another
   proposition. The conclusion is often stated as the final stage of
   inference.
   
   The conclusion is affirmed on the basis the original premises, and the
   inference from them. Conclusions are often indicated by phrases such
   as "therefore", "it follows that", "we conclude" and so on.
   
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  Types of argument
  
   There are two traditional types of logical argument: deductive and
   inductive.
   
    1. A deductive argument is one which provides conclusive proof of its
       conclusions. It is either valid or invalid.
       A valid deductive argument is defined as one where if the premises
       are true, then the conclusion must also be true.
    2. An inductive argument is one where the premises provide some
       evidence for the truth of the conclusion.
       Inductive arguments are not valid or invalid, but we can talk
       about whether they are better or worse than other arguments. We
       can also discuss how likely their premises are.
       
   There are forms of argument in ordinary language which are neither
   deductive nor inductive. However, we'll concentrate on deductive
   arguments, as they are often viewed as the most rigorous and
   convincing.
   
   Here is an example of a deductive argument:
   
     * 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
       
   Note that the conclusion of one argument might be a premise in another
   argument. A proposition can only be a premise or a conclusion of a
   particular argument; the terms don't make sense in isolation.
   
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  Recognizing an argument
  
   Sometimes arguments won't follow the order described above. For
   instance, the conclusions might be stated first, and the premises
   stated afterwards in support of the conclusion. This is perfectly
   valid, if sometimes a little confusing.
   
   Arguments are harder to recognize than premises or conclusions. Lots
   of people shower their writing with assertions, without ever producing
   anything you might reasonably call an argument.
   
   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."
     
   The statement above isn't an argument; it's a conditional statement.
   It doesn't assert the premises which are needed to support what looks
   like its conclusion. (Even if you add those assertions, it still
   suffers from a number of other logical flaws -- see the section on
   this argument in the "Atheist Arguments" document.)
   
   Here's another example:
   
     "God created you; therefore obey and worship God."
     
   The phrase "obey and worship God" is neither true nor false. Therefore
   it isn't a proposition, and the sentence isn't an argument.
   
   Causality is important as well. Suppose we're trying to argue that
   there's something wrong with the engine of a car. Let's look at two
   statements of the form "A because B". Here's the first:
   
     "The car won't start because there's something wrong with the
     engine."
     
   That's not an argument for there being something wrong with the
   engine; it's an explanation of why the car won't start. We're
   explaining A, using B as the explanation.
   
   Now consider a second statement:
   
     "There must be something wrong with the engine of the car, because
     it won't start."
     
   Here we're arguing for A, giving B as evidence. The statement "A
   because B" is an argument.
   
   The difference between the two cases might not be completely clear.
   So, remember that "A because B" is equivalent to "B therefore A". The
   two statements then become:
   
     "There's something wrong with the engine, therefore the car won't
     start."
     
   And:
   
     "The car won't start, therefore there's something wrong with the
     engine."
     
   We're supposed to be arguing that there's something wrong with the
   engine, but now it's plain that the first statement doesn't do that at
   all. Only the second statement is arguing that there's something wrong
   with the engine.
   
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  Implication in detail
  
   There's one very important thing to remember:
   
     The fact that a deductive argument is valid doesn't necessarily
     mean that its conclusion holds.
     
   That may seem confusing, but it's because of the slightly
   counter-intuitive nature of how implication works.
   
   Obviously you can build a valid argument out of true propositions. But
   you can also build a completely valid argument using only false
   propositions. For example:
   
     * All insects have wings (premise)
     * Woodlice are insects (premise)
     * Therefore woodlice have wings (conclusion)
       
   The conclusion isn't true because the argument's premises are false.
   If the argument's premises were true, however, the conclusion would be
   true. So the argument is entirely valid.
   
   More subtly, you can reach a true conclusion from false premises --
   even ludicrously false ones:
   
     * All fish live in the ocean (premise)
     * Sea otters are fish (premise)
     * Therefore sea otters live in the ocean (conclusion)
       
   However, there's one thing you can't do: start with true premises, go
   through a valid deductive argument, and arrive at a false conclusion.
   (Remember the definition of a valid deductive argument.)
   
   So, here's a "truth table" for implication. The symbol "=>" denotes
   implication; "A" is the premise, "B" the conclusion. "T" and "F"
   represent true and false respectively.
   
   CAPTION: 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.)
       
   A sound argument is a valid argument whose premises are true. A sound
   argument therefore arrives at a true conclusion. Be careful not to
   confuse sound arguments with valid arguments.
   
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  Real life, and other things not considered
  
   This document has considered logical argument as a process in
   isolation from the real world. Nothing has been said about how
   premises are arrived at, or how they are themselves checked to see if
   they accord with the way things actually are.
   
   Ultimately, the conclusion of a valid logical argument is only as
   compelling as the basic premises it is derived from. Logic in itself
   does not solve the problem of verifying the basic assertions which
   support arguments; for that, we need some other tool.
   
   In real life, the dominant means of verifying basic assertions is
   scientific enquiry. The philosophy of science and the means of
   scientific enquiry are both huge topics, and quite beyond the scope of
   The Atheism Web.
   
   You can criticize more than just the soundness of an argument. In
   everyday life, arguments are almost always presented with some
   specific purpose in mind. As well as criticizing the argument itself,
   you might criticize the apparent intent of the argument. That sort of
   criticism is outside the scope of this document, however.
   
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  Further reading
  
   For a readable introduction to logic, try Flew's "Thinking Straight",
   listed in the Atheist Media document. The Electronic Resources
   document also lists LOGIC-L, a LISTSERV mailing list devoted to
   discussing the teaching of elementary logic.
     _________________________________________________________________
                                      
  Fallacies
  
   To delve further into the structure of logical arguments would need
   lengthy discussion of linguistics and philosophy. It's simpler -- and
   probably more useful -- to summarize some major pitfalls you should
   avoid when constructing an argument. These pitfalls are known as
   fallacies.
   
   In everyday English the word "fallacy" is used to refer to mistaken
   beliefs, as well as to the faulty reasoning that leads to those
   beliefs. In logic, the term is generally used for a form of
   technically incorrect argument -- especially if the argument appears
   valid or convincing.
   
   So for the purposes of this discussion, a fallacy is a logical
   argument which looks correct, but which can be seen to be incorrect
   when examined more carefully. If you learn to recognize fallacies,
   hopefully you'll be able to avoid being misled by them.
   
   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 Niktor Project at <http://www.almanac.bc.ca/> has
   another excellent list of logical fallacies.
   
   Sadly, many of the examples below have been taken directly from
   Usenet, though some have been rephrased for the sake of clarity.
   
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  List of fallacies
  
     * Anecdotal evidence
     * Argumentum ad baculum / Appeal to force
     * Argumentum ad hominem
     * Argumentum ad ignorantiam
     * Argumentum ad misericordiam
     * Argumentum ad populum
     * Argumentum ad numerum
     * Argumentum ad verecundiam
     * Argumentum ad antiquitatem
     * Argumentum ad novitatem
     * Argumentum ad crumenam
     * Argumentum ad lazarum
     * Argumentum ad nauseam
     * The fallacy of accident / Sweeping generalization / Dicto
       simpliciter
     * Converse accident / Hasty generalization
     * Non causa pro causa
     * Post hoc ergo propter hoc
     * Cum hoc ergo propter hoc
     * Petitio principii / Begging the question
     * Circulus in demonstrando
     * Complex question / Fallacy of interrogation / Fallacy of
       presupposition
     * Ignoratio elenchi / Irrelevant conclusion
     * Equivocation / Fallacy of four terms
     * Amphiboly
     * Accent
     * Fallacies of composition
     * Fallacy of division
     * The slippery slope argument
     * "A is based on B" fallacies / "...is a type of..." fallacies /
       Fallacy of the Undistributed Middle
     * Affirmation of the consequent
     * Denial of the antecedent
     * Converting a conditional
     * Bifurcation
     * Plurium interrogationum / Many questions
     * Non sequitur
     * Red herring
     * Reification / Hypostatization
     * Shifting the burden of proof
     * Straw man
     * The extended analogy
     * Tu quoque
     * Audiatur et altera pars
     * Ad hoc
     * Argumentum ad logicam
     * The "No True Scotsman..." fallacy
       
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    Anecdotal evidence
    
   One of the simplest fallacies is to rely on anecdotal evidence. For
   example:
   
     "Violent crime is on the increase because you hear a lot more about
     it on the news these days."
     
   It's quite valid to use personal experience to illustrate a point; but
   such anecdotes don't really 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.
   
    Argumentum ad baculum / Appeal to force
    
   An Appeal to Force happens when someone resorts to force (or the
   threat of force) to try and push others to accept a conclusion. This
   fallacy is often used by politicians, and can be summarized as "might
   makes right". The threat doesn't have to come directly from the person
   arguing. For example:
   
     "... Thus there is ample proof of the truth of the Bible. All those
     who refuse to accept that truth will burn in Hell."
     
     "... In any case, I know your phone number and I know where you
     live. Have I mentioned I am licensed to carry concealed weapons?"
     
    Argumentum ad hominem
    
   Argumentum ad Hominem literally means "argument directed at the man".
   There are two types, abusive and circumstantial.
   
   If you argue against some assertion by attacking the person who made
   the assertion, then you have committed the abusive form of argumentum
   ad hominem. A personal attack isn't a valid argument, because the
   truth of an assertion doesn't depend on the virtues of the person
   asserting it. For example:
   
     "Atheism is an evil philosophy. It is practised by Communists and
     murderers."
     
   Sometimes in a court of law doubt is cast on the testimony of a
   witness. For example, the prosecution might show that the witness is a
   known perjurer. This is a valid way of reducing the credibility of the
   testimony given by the witness, and not Argumentum ad Hominem.
   However, it doesn't demonstrate that the witness's testimony is false.
   
   If you argue that someone should accept the truth of an assertion
   because of that person's particular circumstances, then you have
   committed the circumstantial form of argumentum ad hominem. For
   example:
   
     "It is perfectly acceptable to kill animals for food. How can you
     argue otherwise when you're quite happy to wear leather shoes?"
     
   This is an abusive charge of inconsistency, used as an excuse for
   dismissing the opponent's argument. The fallacy can also be used as a
   means of rejecting a particular conclusion. For example:
   
     "Of course you would argue that positive discrimination is a bad
     thing. You're white."
     
   This particular form of Argumentum ad Hominem, when you allege that
   someone is rationalizing a conclusion for selfish reasons, is also
   known as "poisoning the well".
   
    Argumentum ad ignorantiam
    
   Argumentum ad ignorantiam means "argument from ignorance". The fallacy
   occurs when it's argued that something must be true, simply because it
   hasn't been proved false. Or, equivalently, when it is argued that
   something must be false because it hasn't been proved true.
   
   (Note that this isn't the same as assuming that something is false
   until it has been proved true; that's a basic scientific principle.)
   
   Here are a couple of examples:
   
     "Of course the Bible is true. Nobody can prove otherwise."
     
     "Of course telepathy and other psychic phenomena do not exist.
     Nobody has shown any proof that they are real."
     
   Note that this fallacy doesn't apply in a court of law, where you're
   generally assumed innocent until proven guilty.
   
   Also, in scientific investigation if it is known that an event would
   produce certain evidence of its having occurred, the absence of such
   evidence can validly be used to infer that the event didn't occur.
   
   For example:
   
     "A flood as described in the Bible would require an enormous volume
     of water to be present on the earth. The earth does not have a
     tenth as much water, even if we count that which is frozen into ice
     at the poles. Therefore no such flood occurred."
     
   In science, we can validly assume from lack of evidence that something
   hasn't occurred. We cannot conclude with certainty that it hasn't
   occurred, though.
   
   Of course, the history of science is full of logically valid bad
   predictions. In 1893, the Royal Academy of Science were convinced by
   Sir Robert Ball that communication with the planet Mars was a physical
   impossibility, because it would require a flag as large as Ireland,
   which it would be impossible to wave. (Source: Fortean Times Number
   82.)
   
   See also Shifting the Burden of Proof.
   
    Argumentum ad misericordiam
    
   This is the Appeal to Pity, also known as Special Pleading. The
   fallacy is committed when someone appeals to pity for the sake of
   getting a conclusion accepted. For example:
   
     "I did not murder my mother and father with an axe! Please don't
     find me guilty; I'm suffering enough through being an orphan."
     
    Argumentum ad populum
    
   This is known as Appealing to the Gallery, or Appealing to the People.
   You commit this fallacy if you attempt to win acceptance of an
   assertion by appealing to a large group of people. This form of
   fallacy is often characterized by emotive language. For example:
   
     "Pornography must be banned. It is violence against women."
     
     "For thousands of years people have believed in Jesus and the
     Bible. This belief has had a great impact on their lives. What more
     evidence do you need that Jesus was the Son of God? Are you trying
     to tell those people that they are all mistaken fools?"
     
    Argumentum ad numerum
    
   This fallacy is closely related to the argumentum ad populum. It
   consists of asserting that the more people who support or believe a
   proposition, the more likely it is that that proposition is correct.
   For example:
   
     "The vast majority of people in this country believe that capital
     punishment has a noticable deterrent effect. To suggest that it
     doesn't in the face of so much evidence is ridiculous.
     
     "All I'm saying is that thousands of people believe in pyramid
     power, so there must be something to it."
     
    Argumentum ad verecundiam
    
   The Appeal to Authority uses admiration of a famous person to try and
   win support for an assertion. For example:
   
     "Isaac Newton was a genius and he believed in God."
     
   This line of argument isn't always completely bogus; for example, it
   may be relevant to refer to a widely-regarded authority in a
   particular field, if you're discussing that subject. For example, we
   can distinguish quite clearly between:
   
     "Hawking has concluded that black holes give off radiation"
     
   and
   
     "Penrose has concluded that it is impossible to build an
     intelligent computer"
     
   Hawking is a physicist, and so we can reasonably expect his opinions
   on black hole radiation to be informed. Penrose is a mathematician, so
   it is questionable whether he is well-qualified to speak on the
   subject of machine intelligence.
   
    Argumentum ad antiquitatem
    
   This is the fallacy of asserting that something is right or good
   simply because it's old, or because "that's the way it's always been."
   The opposite of Argumentum ad Novitatem.
   
     "For thousands of years Christians have believed in Jesus Christ.
     It must therefore be a good thing, for it to have persisted all
     that time even in the face of persecution."
     
    Argumentum ad novitatem
    
   This is the opposite of the Argumentum ad Antiquitatem; it's the
   fallacy of asserting that something is more correct simply because it
   is new, or newer than something else.
   
    Argumentum ad crumenam
    
   The fallacy of believing that money is a criterion of correctness;
   that those with more money are more likely to be right. The opposite
   of Argumentum ad Lazarum.
   
    Argumentum ad lazarum
    
   The fallacy of assuming that someone poor is sounder or more virtuous
   than someone who's wealthier. This fallacy is the opposite of the
   Argumentum ad Crumenam.
   
    Argumentum ad nauseam
    
   This is the incorrect belief that an assertion is more likely to be
   true, or is more likely to be accepted as true, the more often it is
   heard. So an Argumentum ad Nauseam is one that employs constant
   repetition in asserting something; saying the same thing over and over
   again until you're sick of hearing it.
   
   (On Usenet, your argument is often less likely to be heard if you
   repeat it over and over again, as people will tend to put you in their
   kill files.)
   
    The fallacy of accident / Sweeping generalization / Dicto simpliciter
    
   A sweeping generalization occurs when a general rule is applied to a
   particular situation, but the features of that particular situation
   mean the rule is inapplicable. It's the error made when you go from
   the general to the specific. For example:
   
     "Christians generally dislike atheists. You are a Christian, so you
     must dislike atheists."
     
   This fallacy is often committed by people who try to decide moral and
   legal questions by mechanically applying general rules.
   
    Converse accident / Hasty generalization
    
   This fallacy is the reverse of the Fallacy of Accident. It occurs when
   you form a general rule by examining only a few specific cases which
   aren't representative of all possible cases. For example:
   
     "Jim Bakker was an insincere Christian. Therefore all Christians
     are insincere."
     
    Non causa pro causa
    
   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:
   
     "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.
   
    Post hoc ergo propter hoc
    
   The fallacy of Post Hoc Ergo Propter Hoc occurs when something is
   assumed to be the cause of an event merely because it happened before
   that event. For example:
   
     "The Soviet Union collapsed after instituting state atheism.
     Therefore we must avoid atheism for the same reasons."
     
   This is another type of false cause fallacy.
   
    Cum hoc ergo propter hoc
    
   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.
   
    Petitio principii / Begging the question
    
   This fallacy occurs when the premises are at least as questionable as
   the conclusion reached. For example:
   
     "Aliens are abducting innocent victims every week. The government
     must know what is going on. Therefore the government is in league
     with the aliens."
     
    Circulus in demonstrando
    
   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. For example:
   
     "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. Another example is the classic:
   
     "We know that God exists because the Bible tells us so. And we know
     that the Bible is true because it is the word of God."
     
   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.
   
    Complex question / Fallacy of interrogation / Fallacy of presupposition
    
   This is the interrogative form of Begging the Question. One example is
   the classic loaded question:
   
     "Have you stopped beating your wife?"
     
   The question presupposes a definite answer to another question which
   has not even been asked. This trick is often used by lawyers in
   cross-examination, when they ask questions like:
   
     "Where did you hide the money you stole?"
     
   Similarly, politicians often ask loaded questions such as:
   
     "How long will this EU interference in our affairs be allowed to
     continue?"
     
   or
   
     "Does the Chancellor plan two more years of ruinous privatization?"
     
   Another form of this fallacy is to ask for an explanation of something
   which is untrue or not yet established.
   
    Ignoratio elenchi / Irrelevant 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.
   
   For example, a Christian may begin by saying that he will argue that
   the teachings of Christianity are undoubtably 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.
   
   Sadly, such fallacious arguments are often successful because they
   arouse emotions which cause others to view the supposed conclusion in
   a more favourable light.
   
    Equivocation / Fallacy of four terms
    
   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.
   
    Amphiboly
    
   Amphiboly occurs when the premises used in an argument are ambiguous
   because of careless or ungrammatical phrasing.
   
    Accent
    
   Accent is another form of fallacy through shifting meaning. In this
   case, the meaning is changed by altering which parts of a statement
   are emphasized. For example, consider:
   
     "We should not speak *ill* of our friends"
     
   and
   
     "We should not speak ill of our *friends*"
     
   Be particularly wary of this fallacy on the net, where it's easy to
   mis-read the emphasis of what's written.
   
    Fallacies of composition
    
   One Fallacy of Composition is to conclude that a property shared by
   the parts of something must apply to the whole. For example:
   
     "The bicycle is made entirely of low mass components, and is
     therefore very lightweight."
     
   The other Fallacy of Composition is to conclude that a property of a
   number of individual items is shared by a collection of those items.
   For example:
   
     "A car uses less petrol and causes less pollution than a bus.
     Therefore cars are less environmentally damaging than buses."
     
    Fallacy of division
    
   The fallacy of division is the opposite of the Fallacy of Composition.
   Like its opposite, it exists in two varieties. The first is to assume
   that a property of some thing must apply to its parts. For example:
   
     "You are studying at a rich college. Therefore you must be rich."
     
   The other is to assume that a property of a collection of items is
   shared by each item. For example:
   
     "Ants can destroy a tree. Therefore this ant can destroy a tree."
     
    The slippery slope argument
    
   This argument states that should one event occur, so will other
   harmful events. There is no proof made that the harmful events are
   caused by the first event. For example:
   
     "If we legalize marijuana, then more people would start to take
     crack and heroin, and we'd have to legalize those too. Before long
     we'd have a nation full of drug-addicts on welfare. Therefore we
     cannot legalize marijuana."
     
    "A is based on B" fallacies / "...is a type of..." fallacies / Fallacy of
    the Undistributed Middle
    
   These fallacies occur if you attempt to argue that things are in some
   way similar, but you don't actually specify in what way they are
   similar. Examples:
   
     "Isn't history based upon faith? If so, then isn't the Bible also a
     form of history?"
     
     "Islam is based on faith, Christianity is based on faith, so isn't
     Islam a form of Christianity?"
     
     "Cats are a form of animal based on carbon chemistry, dogs are a
     form of animal based on carbon chemistry, so aren't dogs a form of
     cat?"
     
    Affirmation of the consequent
    
   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. Here's an example:
   
     "If I fall into the swimming pool, I get wet. I am wet, so I must
     have fallen into the swimming pool."
     
   This is the converse of Denial of the Antecedent.
   
    Denial of the antecedent
    
   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.
   
     "If I fall into the swimming pool, I get wet. I did not fall into
     the swimming pool, therefore I am not wet."
     
   This is the converse of the fallacy of Affirmation of the Consequent.
   
    Converting a conditional
    
   This fallacy is an argument of the form "If A then B, therefore if B
   then A".
   
     "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."
     
     "If it's raining outside and I don't have an umbrella I get wet. So
     if I get wet, then it's raining outside and I don't have an
     umbrella."
     
   This fallacy is similar to the Affirmation of the Consequent, but
   phrased as a conditional statement.
   
    Bifurcation
    
   Also referred to as the "black and white" fallacy, bifurcation occurs
   if you present a situation as having only two alternatives, where in
   fact other alternatives exist or can exist.
   
    Plurium interrogationum / Many questions
    
   This fallacy occurs when someone demands a simple (or simplistic)
   answer to a complex question.
   
    Non sequitur
    
   A non sequitur is an argument where the conclusion is drawn from
   premises which aren't logically connected with it. For example:
   
     "Since Egyptians did so much excavation to construct the pyramids,
     they were well versed in paleontology."
     
   (Personally, I rather enjoy reading examples of this fallacy. A really
   good non sequitur can cause the 'boggle' response, or even make me
   burst out laughing. Indeed, non sequiturs are an important ingredient
   in a lot of humour. They're still fallacies, though.)
   
    Red herring
    
   This fallacy is committed when someone introduces irrelevant material
   to the issue being discussed, so that everyone else's attention is
   diverted away from the points made, towards a different conclusion.
   
    Reification / Hypostatization
    
   Reification occurs when an abstract concept is treated as a concrete
   thing.
   
    Shifting the burden of proof
    
   The burden of proof is always on the person asserting something.
   Shifting the burden of proof, a special case of Argumentum ad
   Ignorantiam, is the fallacy of putting the burden of proof on the
   person who denies or questions the assertion. The source of the
   fallacy is the assumption that something is true unless proven
   otherwise.
   
   For further discussion of this idea, see the "Introduction to Atheism"
   document.
   
     "OK, so if you don't think the grey aliens have gained control of
     the US government, can you prove it?"
     
    Straw man
    
   The straw man fallacy is when you misrepresent someone else's position
   so that it can be attacked more easily, then knock down that
   misrepresented position, then conclude that the original position has
   been demolished. It's a fallacy because it fails to deal with the
   actual arguments that have been made.
   
     "To be an atheist, you have to believe with absolute certainty that
     there is no God. In order to convince yourself with absolute
     certainty, you must examine all the Universe and all the places
     where God could possibly be. Since you obviously haven't, your
     position is indefensible."
     
   The above straw man argument appears at about once a week on the net.
   If you can't see what's wrong with it, read the "Introduction to
   Atheism" document.
   
    The extended analogy
    
   The fallacy of the Extended Analogy often occurs when some suggested
   general rule is being argued over. The fallacy is to assume that
   mentioning two different situations, in an argument about a general
   rule, constitutes a claim that those situations are analogous to each
   other.
   
   This fallacy is best explained using a real example from a debate
   about anti-cryptography legislation:
   
     "I believe it is always wrong to oppose the law by breaking it."
     
     "Such a position is odious: it implies that you would not have
     supported Martin Luther King."
     
     "Are you saying that cryptography legislation is as important as
     the struggle for Black liberation? How dare you!"
     
    Tu quoque
    
   This is the famous "you too" fallacy. It occurs if you argue that an
   action is acceptable because your opponent has performed it. For
   instance:
   
     "You're just being randomly abusive."
     
     "So? You've been abusive too."
     
   This is a personal attack, and is therefore a special case of
   Argumentum ad Hominem.
   
    Audiatur et altera pars
    
   Often, people will argue from assumptions which they don't bother to
   state. The principle of Audiatur et Altera Pars is that all of the
   premises of an argument should be stated explicitly. It's not strictly
   a fallacy to fail to state all of your assumptions; however, it's
   often viewed with suspicion.
   
    Ad hoc
    
   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:
   
     "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."
     
    Argumentum ad logicam
    
   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 6 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 "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.