Archive-name: atheism/logicãAlt-atheism-archive-name: logicãLast-modified: 23 February 1993ãVersion: 1.3ãã                       Constructing a Logical ArgumentããAlthough there is much argument on Usenet, the general quality of argumentãfound is poor.  This article attempts to provide a gentle introduction toãlogic, in the hope of improving the general level of debate.ããLogic is the science of reasoning, proof, thinking, or inference [ConciseãOED].  Logic allows us to analyze a piece of reasoning and determine whetherãit is correct or not (valid or invalid).  Of course, one does not need toãstudy logic in order to reason correctly; nevertheless, a little basicãknowledge of logic is often helpful when constructing or analyzing anãargument.ããNote that no claim is being made here about whether logic is universallyãapplicable.  The matter is very much open for debate.  This document merelyãexplains how to use logic, given that you have already decided that logic isãthe right tool for the job.ããPropositions (or statements) are the building blocks of a logical argument. Aãproposition is a statement which is either true or false; for example, "It isãraining" or "Today is Tuesday".  Propositions may be either asserted (said toãbe true) or denied (said to be false).  Note that this is a technical meaningãof "deny", not the everyday meaning.ããThe proposition is the meaning of the statement, not the particularãarrangement of words used to express it.  So "God exists" and "There exists aãGod" both express the same proposition.ããAn argument is, to quote the Monty Python sketch, "a connected series ofãstatements to establish a definite proposition".  An argument consists ofãthree stages.ããFirst of all, the propositions which are necessary for the argument toãcontinue are stated.  These are called the premises of the argument.  Theyãare the evidence or reasons for accepting the argument and its conclusions. ããPremises (or assertions) are often indicated by phrases such as "because",ã"since", "obviously" and so on.  (The phrase "obviously" is often viewed withãsuspicion, as it can be used to intimidate others into accepting suspiciousãpremises.  If something doesn't seem obvious to you, don't be afraid toãquestion it.  You can always say "Oh, yes, you're right, it is obvious" whenãyou've heard the explanation.)ããNext, the premises are used to derive further propositions by a process knownãas inference.  In inference, one proposition is arrived at on the basis ofãone or more other propositions already accepted.  There are various forms ofãvalid inference.ããThe propositions arrived at by inference may then be used in furtherãinference.  Inference is often denoted by phrases such as "implies that" orã"therefore".ããFinally, we arrive at the conclusion of the argument -- the proposition whichãis affirmed on the basis of the premises and inference.  Conclusions are oftenãindicated by phrases such as "therefore", "it follows that", "we conclude"ãand so on.  The conclusion is often stated as the final stage of inference.ããFor example:ããEvery event has a cause (premise)ãThe universe has a beginning (premise)ãAll beginnings involve an event (premise)ãThis implies that the beginning of the universe involved an event (inference)ãTherefore the universe has a cause (inference and conclusion)ããNote that the conclusion of one argument might be a premise in anotherãargument.  A proposition can only be called a premise or a conclusion withãrespect to a particular argument; the terms do not make sense in isolation.ããSometimes an argument will not follow the order given above; for example,ãthe conclusions might be stated first and the premises stated ãafterwards in support of the conclusion.  This is perfectly valid, if ãsometimes a little confusing.ããRecognizing an argument is much harder than recognizing premises orãconclusions.  Many people shower their writing with assertions without everãproducing anything which one might reasonably describe as an argument.  Someãstatements look like arguments, but are not.  For example:ãã"If the Bible is accurate, Jesus must either have been insane, an evil liar,ã or the Son of God."ããThis is not an argument, it is a conditional statement.  It does not assertãthe premises which are necessary to support what appears to be its ãconclusion.  (It also suffers from a number of other logical flaws, but we'llãcome to those later.)ããAnother example:ãã"God created you; therefore do your duty to God."ããThe phrase "do your duty to God" is not a proposition, since it is neitherãtrue nor false.  Therefore it is not a conclusion, and the sentence is not anãargument.ããFinally, causality is important.  Consider a statement of the form "A becauseãB".  If we're interested in establishing A and B is offered as evidence, theãstatement is an argument.  If we're trying to establish the truth of B, thenãit is not an argument, it is an explanation.ããFor example:ãã"There must be something wrong with the engine of my car, because it will notã start." -- This is an argument.ãã"My car will not start because there is something wrong with the engine."ã -- This is an explanation.ããThere are two traditional types of argument, deductive and inductive.  Aãdeductive argument is one which provides conclusive proof of its conclusionsã-- that is, an argument where if the premises are true, the conclusion mustãalso be true.  A deductive argument is either valid or invalid.  A validãargument is defined as one where if the premises are true, then theãconclusion is true.ããAn inductive argument is one where the premises provide some evidence for theãtruth of the conclusion.  Inductive arguments are not valid or invalid;ãhowever, we can talk about whether they are better or worse than otherãarguments, and about how probable their premises are.ããIt is important to note that the fact that a deductive argument is valid doesãnot imply that its conclusion holds.  This is because of the slightly ãcounter-intuitive nature of implication, which we must now consider moreãcarefully.ããObviously a valid argument can consist of true propositions.  However, anãargument may be entirely valid even if it contains only false propositions. ãFor example:ãã   All insects have wings (premise)ã   Woodlice are insects (premise)ã   Therefore woodlice have wings (conclusion)ããHere, the conclusion is not true because the argument's premises are false. ãIf the argument's premises were true, however, the conclusion would be true. ãThe argument is thus entirely valid.ããMore subtly, we can reach a true conclusion from one or more false premises,ãas in:ãã   All fish live in the sea (premise)ã   Dolphins are fish (premise)ã   Therefore dolphins live in the sea (conclusion)ããHowever, the one thing we cannot do is reach a false conclusion through validãinference from true premises.  We can therefore draw up a "truth table" forãimplication.ããThe symbol "=>" denotes implication; "A" is the premise, "B" the conclusion. ã"T" and "F" represent true and false respectively.ããPremise Conclusion Inferenceã   A        B        A=>Bã----------------------------ã   F        F         T      If the premises are false and the inferenceã   F        T         T      valid, the conclusion can be true or false.ãã   T        F         F      If the premises are true and the conclusionã                             false, the inference must be invalid.ãã   T        T         T      If the premises are true and the inference valid,ã                             the conclusion must be true.ããA sound argument is a valid argument whose premises are true.  A sound ãargument therefore arrives at a true conclusion.  Be careful not to confuseãvalid arguments with sound arguments.ããTo delve further into the structure of logical arguments would requireãlengthy discussion of linguistics and philosophy.  It is simpler and probablyãmore useful to summarize the major pitfalls to be avoided when constructingãan argument.  These pitfalls are known as fallacies.ããIn everyday English the term "fallacy" is used to refer to mistaken beliefsãas well as to the faulty reasoning that leads to those beliefs.  This is fairãenough, but in logic the term is generally used to refer to a form ofãtechnically incorrect argument, especially if the argument appears valid orãconvincing.ããSo for the purposes of this discussion, we define a fallacy as a logicalãargument which appears to be correct, but which can be seen to be incorrectãwhen examined more closely.  By studying fallacies we aim to avoid beingãmisled by them.  The following list of fallacies is not intended to beãexhaustive.ããARGUMENTUM AD BACULUM (APPEAL TO FORCE)ããThe Appeal to Force is committed when the arguer resorts to force or theãthreat of force in order to try and push the acceptance of a conclusion.  Itãis often used by politicians, and can be summarized as "might makes right". ãThe force threatened need not be a direct threat from the arguer.ããFor example:ã"... Thus there is ample proof of the truth of the Bible.  All those whoãrefuse to accept that truth will burn in Hell."ããARGUMENTUM AD HOMINEMããArgumentum ad hominem is literally "argument directed at the man".ããThe Abusive variety of Argumentum ad Hominem occurs when, instead of tryingãto disprove the truth of an assertion, the arguer attacks the person orãpeople making the assertion.  This is invalid because the truth of anãassertion does not depend upon the goodness of those asserting it.ããFor example:ã"Atheism is an evil philosophy.  It is practised by Communists and murderers."ããSometimes in a court of law doubt is cast upon the testimony of a witness by ãshowing, for example, that he is a known perjurer.  This is a valid way ofãreducing the credibility of the testimony given by the witness, and notãargumentum ad hominem; however, it does not demonstrate that the witness'sãtestimony is false.  To conclude otherwise is to fall victim of theãArgumentum ad Ignorantiam (see elsewhere in this list).ããThe circumstantial form of Argumentum ad Hominem is committed when a personãargues that his opponent ought to accept the truth of an assertion because ofãthe opponent's particular circumstances.ããFor example:ã"It is perfectly acceptable to kill animals for food.  How can you argueãotherwise when you're quite happy to wear leather shoes?"ããThis is an abusive charge of inconsistency, used as an excuse for dismissingãthe opponent's argument.ããThis fallacy can also be used as a means of rejecting a conclusion.  For ãexample:ãã"Of course you would argue that positive discrimination is a bad thing. ãYou're white."ããThis particular form of Argumentum ad Hominem, when one alleges that one'sãadversary is rationalizing a conclusion formed from selfish interests, isãalso known as "poisoning the well".ããARGUMENTUM AD IGNORANTIUMããArgumentum ad ignorantium means "argument from ignorance".  This fallacyãoccurs whenever it is argued that something must be true simply because itãhas not been proved false.  Or, equivalently, when it is argued thatãsomething must be false because it has not been proved true.  (Note that thisãis not the same as assuming that something is false until it has been provedãtrue, a basic scientific principle.)ããExamples:ã"Of course the Bible is true.  Nobody can prove otherwise."ãã"Of course telepathy and other psychic phenomena do not exist.  Nobody hasãshown any proof that they are real."ããNote that this fallacy does not apply in a court of law, where one isãgenerally assumed innocent until proven guilty.ããAlso, in scientific investigation if it is known that an event would produceãcertain evidence of its having occurred, the absence of such evidence can ãvalidly be used to infer that the event did not occur.  For example:ãã"A flood as described in the Bible would require an enormous volume of waterãto be present on the earth.  The earth does not have a tenth as much water,ãeven if we count that which is frozen into ice at the poles.  Therefore noãsuch flood occurred."ããARGUMENTUM AD MISERICORDIAMããThis is the Appeal to Pity, also known as Special Pleading.  The fallacy is ãcommitted when the arguer appeals to pity for the sake of getting a ãconclusion accepted.  For example:ãã"I did not murder my mother and father with an axe.  Please don't find meãguilty; I'm suffering enough through being an orphan."ããARGUMENTUM AD POPULUMããThis is known as Appealing to the Gallery, or Appealing to the People.  Toãcommit this fallacy is to attempt to win acceptance of an assertion byãappealing to a large group of people.  This form of fallacy is oftenãcharacterized by emotive language.  For example:ãã"Pornography must be banned.  It is violence against women."ãã"The Bible must be true.  Millions of people know that it is.  Are you tryingãto tell them that they are all mistaken fools?"ããARGUMENTUM AD NUMERAMããThis fallacy is closely related to the argumentum ad populum.  It consists ofãasserting that the more people who support or believe a proposition, the moreãlikely it is that that proposition is correct.ããARGUMENTUM AD VERECUNDIAMããThe Appeal to Authority uses the admiration of the famous to try and winãsupport for an assertion.  For example:ãã"Isaac Newton was a genius and he believed in God."ããThis line of argument is not always completely bogus; for example, referenceãto an admitted authority in a particular field may be relevant to aãdiscussion of that subject.  For example, we can distinguish quite clearlyãbetween:ãã"Stephen Hawking has concluded that black holes give off radiation"ãandã"John Searle has concluded that it is impossible to build an intelligentã computer"ããHawking is a physicist, and so we can reasonably expect his opinions on blackãhole radiation to be informed.  Searle is a linguist, so it is questionable ãwhether he is well-qualified to speak on the subject of machine intelligence.ããTHE FALLACY OF ACCIDENTããThe Fallacy of Accident is committed when a general rule is applied to aãparticular case whose "accidental" circumstances mean that the rule isãinapplicable.  It is the error made when one goes from the general to theãspecific.  For example:ãã"Christians generally dislike atheists.  You are a Christian, so you mustãdislike atheists."ããThis fallacy is often committed by moralists and legalists who try to decideãevery moral and legal question by mechanically applying general rules.ããCONVERSE ACCIDENT / HASTY GENERALIZATIONããThis fallacy is the reverse of the fallacy of accident.  It occurs when oneãforms a general rule by examining only a few specific cases which are notãrepresentative of all possible cases.ããFor example:ã"Jim Bakker was an insincere Christian.  Therefore all Christians areãinsincere."ããSWEEPING GENERALIZATION / DICTO SIMPLICITERããA sweeping generalization occurs when a general rule is applied to aãparticular situation in which the features of that particular situationãrender the rule inapplicable.  A sweeping generalization is the opposite of aãhasty generalization.ããNON CAUSA PRO CAUSA / POST HOC ERGO PROPTER HOCããThese are known as False Cause fallacies.ããThe fallacy of Non Causa Pro Causa occurs when one identifies something as theãcause of an event but it has not actually been shown to be the cause.  For ãexample:ãã"I took an aspirin and prayed to God, and my headache disappeared.  So Godãcured me of the headache."ããThe fallacy of Post Hoc Ergo Propter Hoc occurs when something is assumed toãbe the cause of an event merely because it happened before the event.  For ãexample:ãã"The Soviet Union collapsed after taking up atheism.  Therefore we must avoidãatheism for the same reasons."ããCUM HOC ERGO PROPTER HOCããThis fallacy is similar to post hoc ergo propter hoc.  It asserts thatãbecause two events occur together, they must be causally related, and leavesãno room for other factors that may be the cause(s) of the events.ããPRINCIPIO PRINCIPIIããThis is known as Begging the Question.  The fallacy occurs when one assumesãas a premise the conclusion which one wishes to reach.  Often, the ãproposition will be rephrased so that the fallacy appears to be a validãargument.  For example:ãã"Homosexuals must not be allowed to hold government office.  Hence anyãgovernment official who is revealed to be a homosexual will lose his job. ãTherefore homosexuals will do anything to hide their secret, and will be openãto blackmail.  Therefore homosexuals cannot be allowed to hold governmentãoffice."ããNote that the argument is entirely circular; the premise is the same as the ãconclusion.  An argument like the above has actually been cited as the reasonãfor the British Secret Services' official ban on homosexual employees. ãAnother example is the classic:ãã"We know that God exists because the Bible tells us so.  And we know that theãBible is true because it is the word of God."ããCOMPLEX QUESTION / FALLACY OF INTERROGATIONããThis is the Fallacy of Presupposition.  One example is the classic loaded ãquestion:ãã"Have you stopped beating your wife?"ããThe question presupposes a definite answer to another question which has notãeven been asked.  This trick is often used by lawyers in cross-examination,ãwhen they ask questions like:ãã"Where did you hide the money you stole?"ããSimilarly, politicians often ask loaded questions such as:ãã"How long will this EC interference in our affairs be allowed to continue?"ãorã"Does the Chancellor plan two more years of ruinous privatization?"ããIGNORATIO ELENCHIããThe fallacy of Irrelevant Conclusion consists of claiming that an argument ãsupports a particular conclusion when it is actually logically nothing to doãwith that conclusion.ããFor example, a Christian may begin by saying that he will argue that theãteachings of Christianity are undoubtably true.  If he then argues at lengthãthat Christianity is of great help to many people, no matter how well heãargues he will not have shown that Christian teachings are true.ããSadly, such fallacious arguments are often successful because they arouseãemotions which cause others to view the supposed conclusion in a moreãfavourable light.ããEQUIVOCATIONããEquivocation occurs when a key word is used with two or more differentãmeanings in the same argument.  For example:ãã"What could be more affordable than free software?  But to make sure that itãremains free, that users can do what they like with it, we must place aãlicense on it to make sure that will always be freely redistributable."ããAMPHIBOLYããAmphiboly occurs when the premises used in an argument are ambiguous becauseãof careless or ungrammatical phrasing.ããACCENTããAccent is another form of fallacy through shifting meaning.  In this case,ãthe meaning is changed by altering which parts of a statement areãemphasized.  For example, consider:ãã"We should not speak ILL of our friends"ãandã"We should not speak ill of our FRIENDS"ããFALLACIES OF COMPOSITIONããOne fallacy of composition is to conclude that a property shared by the partsãof something must apply to the whole.  For example:ãã"The bicycle is made entirely of low mass components, and is therefore very ãlightweight."ããThe other fallacy of composition is to conclude that a property of a numberãof individual items is shared by a collection of those items.  For example:ãã"A car uses less petrol and causes less pollution than a bus.  Therefore carsãare less environmentally damaging than buses."ããFALLACY OF DIVISIONããThe fallacy of division is the opposite of the fallacy of composition.  Likeãits opposite, it exists in two varieties.  The first is to assume that aãproperty of some thing must apply to its parts.  For example:ãã"You are studying at a rich college.  Therefore you must be rich."ããThe other is to assume that a property of a collection of items is shared byãeach item.  For example:ãã"Ants can destroy a tree.  Therefore this ant can destroy a tree."ããTHE SLIPPERY SLOPE ARGUMENTããThis argument states that should one event occur, so will other harmfulãevents.  There is no proof made that the harmful events are caused by theãfirst event.ããFor example:ã"If we legalize marijuana, then we would have to legalize crack and heroinãand we'll have a nation full of drug-addicts on welfare.  Therefore we cannotãlegalize marijuana."ãã"A IS BASED ON B" FALLACIES / "IS A TYPE OF" FALLACIESããThese fallacies occur when one attempts to argue that things are in some wayãsimilar without actually specifying in what way they are similar.ããExamples:ã"Isn't history based upon faith?  If so, then isn't the Bible also a form ofãhistory?"ãã"Islam is based on faith, Christianity is based on faith, so isn't Islam aãform of Christianity?"ãã"Cats are a form of animal based on carbon chemistry, dogs are a form ofãanimal based on carbon chemistry, so aren't dogs a form of cat?"ããAFFIRMATION OF THE CONSEQUENTããThis fallacy is an argument of the form "A implies B, B is true, therefore Aãis true".  To understand why it is a fallacy, examine the truth table forãimplication given earlier.ããDENIAL OF THE ANTECEDENTããThis fallacy is an argument of the form "A implies B, A is false, therefore Bãis false".  Again, the truth table for implication makes it clear why this isãa fallacy.ããNote that this fallacy is different from Non Causa Pro Causa; the latter hasãthe form "A implies B, A is false, therefore B is false", where A does NOT inãfact imply B at all.  Here, the problem is not that the implication isãinvalid; rather it is that the falseness of A does not allow us to deduceãanything about B.ããCONVERTING A CONDITIONALããThis fallacy is an argument of the form "If A then B, therefore if B then A".ããARGUMENTUM AD ANTIQUITAMããThis is the fallacy of asserting that something is right or good simplyãbecause it is old, or because "that's the way it's always been."ããARGUMENTUM AD NOVITAMããThis is the opposite of the argumentum ad antiquitam; it is the fallacy ofãasserting that something is more correct simply because it is new or newerãthan something else.ããARGUMENTUM AD CRUMENAMããThe fallacy of believing that money is a criterion of correctness; that thoseãwith more money are more likely to be right.ããARGUMENTUM AD LAZARUMããThe fallacy of assuming that because someone is poor he or she is sounder orãmore virtuous than one who is wealthier.  This fallacy is the opposite of theãargumentum ad crumenam.ããARGUMENTUM AD NAUSEAMããThis is the incorrect belief that an assertion is more likely to be true theãmore often it is heard.  An "argumentum ad nauseum" is one that employsãconstant repetition in asserting something.ããBIFURCATIONããAlso referred to as the "black and white" fallacy, bifurcation occurs whenãone presents a situation as having only two alternatives, where in fact otherãalternatives exist or can exist.ããPLURIUM INTERROGATIONUM / MANY QUESTIONSããThis fallacy occurs when a questioner demands a simple answer to a complexãquestion.ããNON SEQUITURããA non-sequitur is an argument where the conclusion is drawn from premisesãwhich are not logically connected with it.ããRED HERRINGããThis fallacy is committed when irrelevant material is introduced to the issueãbeing discussed, so that everyone's attention is diverted away from theãpoints being made, towards a different conclusion.ããREIFICATION / HYPOSTATIZATIONããReification occurs when an abstract concept is treated as a concrete thing.ããSHIFTING THE BURDEN OF PROOFããThe burden of proof is always on the person making an assertion orãproposition.  Shifting the burden of proof, a special case of argumentum adãignorantium, is the fallacy of putting the burden of proof on the person whoãdenies or questions the assertion being made.  The source of the fallacy isãthe assumption that something is true unless proven otherwise.ããSTRAW MANããThe straw man fallacy is to misrepresent someone else's position so that itãcan be attacked more easily, then to knock down that misrepresented position,ãthen to conclude that the original position has been demolished.  It is aãfallacy because it fails to deal with the actual arguments that have beenãmade.ããÿã