Archive-name: atheism/logicπAlt-atheism-archive-name: logicπLast-modified: 23 February 1993πVersion: 1.3ππ Constructing a Logical ArgumentππAlthough there is much argument on Usenet, the general quality of argumentπfound is poor. This article attempts to provide a gentle introduction toπlogic, in the hope of improving the general level of debate.ππLogic is the science of reasoning, proof, thinking, or inference [ConciseπOED]. Logic allows us to analyze a piece of reasoning and determine whetherπit is correct or not (valid or invalid). Of course, one does not need toπstudy logic in order to reason correctly; nevertheless, a little basicπknowledge of logic is often helpful when constructing or analyzing anπargument.ππNote that no claim is being made here about whether logic is universallyπapplicable. The matter is very much open for debate. This document merelyπexplains how to use logic, given that you have already decided that logic isπthe right tool for the job.ππPropositions (or statements) are the building blocks of a logical argument. Aπproposition is a statement which is either true or false; for example, "It isπraining" or "Today is Tuesday". Propositions may be either asserted (said toπbe true) or denied (said to be false). Note that this is a technical meaningπof "deny", not the everyday meaning.ππThe proposition is the meaning of the statement, not the particularπarrangement of words used to express it. So "God exists" and "There exists aπGod" both express the same proposition.ππAn argument is, to quote the Monty Python sketch, "a connected series ofπstatements to establish a definite proposition". An argument consists ofπthree stages.ππFirst of all, the propositions which are necessary for the argument toπcontinue are stated. These are called the premises of the argument. Theyπare the evidence or reasons for accepting the argument and its conclusions. ππPremises (or assertions) are often indicated by phrases such as "because",π"since", "obviously" and so on. (The phrase "obviously" is often viewed withπsuspicion, as it can be used to intimidate others into accepting suspiciousπpremises. If something doesn't seem obvious to you, don't be afraid toπquestion it. You can always say "Oh, yes, you're right, it is obvious" whenπyou've heard the explanation.)ππNext, the premises are used to derive further propositions by a process knownπas inference. In inference, one proposition is arrived at on the basis ofπone or more other propositions already accepted. There are various forms ofπvalid inference.ππThe propositions arrived at by inference may then be used in furtherπinference. Inference is often denoted by phrases such as "implies that" orπ"therefore".ππFinally, we arrive at the conclusion of the argument -- the proposition whichπis affirmed on the basis of the premises and inference. Conclusions are oftenπindicated by phrases such as "therefore", "it follows that", "we conclude"πand so on. The conclusion is often stated as the final stage of inference.ππFor example:ππEvery event has a cause (premise)πThe universe has a beginning (premise)πAll beginnings involve an event (premise)πThis implies that the beginning of the universe involved an event (inference)πTherefore the universe has a cause (inference and conclusion)ππNote that the conclusion of one argument might be a premise in anotherπargument. A proposition can only be called a premise or a conclusion withπrespect to a particular argument; the terms do not make sense in isolation.ππSometimes an argument will not follow the order given above; for example,πthe conclusions might be stated first and the premises stated πafterwards in support of the conclusion. This is perfectly valid, if πsometimes a little confusing.ππRecognizing an argument is much harder than recognizing premises orπconclusions. Many people shower their writing with assertions without everπproducing anything which one might reasonably describe as an argument. Someπstatements look like arguments, but are not. For example:ππ"If the Bible is accurate, Jesus must either have been insane, an evil liar,π or the Son of God."ππThis is not an argument, it is a conditional statement. It does not assertπthe premises which are necessary to support what appears to be its πconclusion. (It also suffers from a number of other logical flaws, but we'llπcome to those later.)ππAnother example:ππ"God created you; therefore do your duty to God."ππThe phrase "do your duty to God" is not a proposition, since it is neitherπtrue nor false. Therefore it is not a conclusion, and the sentence is not anπargument.ππFinally, causality is important. Consider a statement of the form "A becauseπB". If we're interested in establishing A and B is offered as evidence, theπstatement is an argument. If we're trying to establish the truth of B, thenπit is not an argument, it is an explanation.ππFor example:ππ"There must be something wrong with the engine of my car, because it will notπ start." -- This is an argument.ππ"My car will not start because there is something wrong with the engine."π -- This is an explanation.ππThere are two traditional types of argument, deductive and inductive. Aπdeductive argument is one which provides conclusive proof of its conclusionsπ-- that is, an argument where if the premises are true, the conclusion mustπalso be true. A deductive argument is either valid or invalid. A validπargument is defined as one where if the premises are true, then theπconclusion is true.ππAn inductive argument is one where the premises provide some evidence for theπtruth of the conclusion. Inductive arguments are not valid or invalid;πhowever, we can talk about whether they are better or worse than otherπarguments, and about how probable their premises are.ππIt is important to note that the fact that a deductive argument is valid doesπnot imply that its conclusion holds. This is because of the slightly πcounter-intuitive nature of implication, which we must now consider moreπcarefully.ππObviously a valid argument can consist of true propositions. However, anπargument may be entirely valid even if it contains only false propositions. πFor example:ππ All insects have wings (premise)π Woodlice are insects (premise)π Therefore woodlice have wings (conclusion)ππHere, the conclusion is not true because the argument's premises are false. πIf the argument's premises were true, however, the conclusion would be true. πThe argument is thus entirely valid.ππMore subtly, we can reach a true conclusion from one or more false premises,πas in:ππ All fish live in the sea (premise)π Dolphins are fish (premise)π Therefore dolphins live in the sea (conclusion)ππHowever, the one thing we cannot do is reach a false conclusion through validπinference from true premises. We can therefore draw up a "truth table" forπimplication.ππThe symbol "=>" denotes implication; "A" is the premise, "B" the conclusion. π"T" and "F" represent true and false respectively.ππPremise Conclusion Inferenceπ A B A=>Bπ----------------------------π F F T If the premises are false and the inferenceπ F T T valid, the conclusion can be true or false.ππ T F F If the premises are true and the conclusionπ false, the inference must be invalid.ππ T T T If the premises are true and the inference valid,π the conclusion must be true.ππA sound argument is a valid argument whose premises are true. A sound πargument therefore arrives at a true conclusion. Be careful not to confuseπvalid arguments with sound arguments.ππTo delve further into the structure of logical arguments would requireπlengthy discussion of linguistics and philosophy. It is simpler and probablyπmore useful to summarize the major pitfalls to be avoided when constructingπan argument. These pitfalls are known as fallacies.ππIn everyday English the term "fallacy" is used to refer to mistaken beliefsπas well as to the faulty reasoning that leads to those beliefs. This is fairπenough, but in logic the term is generally used to refer to a form ofπtechnically incorrect argument, especially if the argument appears valid orπconvincing.ππSo for the purposes of this discussion, we define a fallacy as a logicalπargument which appears to be correct, but which can be seen to be incorrectπwhen examined more closely. By studying fallacies we aim to avoid beingπmisled by them. The following list of fallacies is not intended to beπexhaustive.ππARGUMENTUM AD BACULUM (APPEAL TO FORCE)ππThe Appeal to Force is committed when the arguer resorts to force or theπthreat of force in order to try and push the acceptance of a conclusion. Itπis often used by politicians, and can be summarized as "might makes right". πThe force threatened need not be a direct threat from the arguer.ππFor example:π"... Thus there is ample proof of the truth of the Bible. All those whoπrefuse to accept that truth will burn in Hell."ππARGUMENTUM AD HOMINEMππArgumentum ad hominem is literally "argument directed at the man".ππThe Abusive variety of Argumentum ad Hominem occurs when, instead of tryingπto disprove the truth of an assertion, the arguer attacks the person orπpeople making the assertion. This is invalid because the truth of anπassertion does not depend upon the goodness of those asserting it.ππFor example:π"Atheism is an evil philosophy. It is practised by Communists and murderers."ππSometimes in a court of law doubt is cast upon the testimony of a witness by πshowing, for example, that he is a known perjurer. This is a valid way ofπreducing the credibility of the testimony given by the witness, and notπargumentum ad hominem; however, it does not demonstrate that the witness'sπtestimony is false. To conclude otherwise is to fall victim of theπArgumentum ad Ignorantiam (see elsewhere in this list).ππThe circumstantial form of Argumentum ad Hominem is committed when a personπargues that his opponent ought to accept the truth of an assertion because ofπthe opponent's particular circumstances.ππFor example:π"It is perfectly acceptable to kill animals for food. How can you argueπotherwise when you're quite happy to wear leather shoes?"ππThis is an abusive charge of inconsistency, used as an excuse for dismissingπthe opponent's argument.ππThis fallacy can also be used as a means of rejecting a conclusion. For πexample:ππ"Of course you would argue that positive discrimination is a bad thing. πYou're white."ππThis particular form of Argumentum ad Hominem, when one alleges that one'sπadversary is rationalizing a conclusion formed from selfish interests, isπalso known as "poisoning the well".ππARGUMENTUM AD IGNORANTIUMππArgumentum ad ignorantium means "argument from ignorance". This fallacyπoccurs whenever it is argued that something must be true simply because itπhas not been proved false. Or, equivalently, when it is argued thatπsomething must be false because it has not been proved true. (Note that thisπis not the same as assuming that something is false until it has been provedπtrue, a basic scientific principle.)ππExamples:π"Of course the Bible is true. Nobody can prove otherwise."ππ"Of course telepathy and other psychic phenomena do not exist. Nobody hasπshown any proof that they are real."ππNote that this fallacy does not apply in a court of law, where one isπgenerally assumed innocent until proven guilty.ππAlso, in scientific investigation if it is known that an event would produceπcertain evidence of its having occurred, the absence of such evidence can πvalidly be used to infer that the event did not occur. For example:ππ"A flood as described in the Bible would require an enormous volume of waterπto be present on the earth. The earth does not have a tenth as much water,πeven if we count that which is frozen into ice at the poles. Therefore noπsuch flood occurred."ππARGUMENTUM AD MISERICORDIAMππThis is the Appeal to Pity, also known as Special Pleading. The fallacy is πcommitted when the arguer appeals to pity for the sake of getting a πconclusion accepted. For example:ππ"I did not murder my mother and father with an axe. Please don't find meπguilty; I'm suffering enough through being an orphan."ππARGUMENTUM AD POPULUMππThis is known as Appealing to the Gallery, or Appealing to the People. Toπcommit this fallacy is to attempt to win acceptance of an assertion byπappealing to a large group of people. This form of fallacy is oftenπcharacterized by emotive language. For example:ππ"Pornography must be banned. It is violence against women."ππ"The Bible must be true. Millions of people know that it is. Are you tryingπto tell them that they are all mistaken fools?"ππARGUMENTUM AD NUMERAMππThis fallacy is closely related to the argumentum ad populum. It consists ofπasserting that the more people who support or believe a proposition, the moreπlikely it is that that proposition is correct.ππARGUMENTUM AD VERECUNDIAMππThe Appeal to Authority uses the admiration of the famous to try and winπsupport for an assertion. For example:ππ"Isaac Newton was a genius and he believed in God."ππThis line of argument is not always completely bogus; for example, referenceπto an admitted authority in a particular field may be relevant to aπdiscussion of that subject. For example, we can distinguish quite clearlyπbetween:ππ"Stephen Hawking has concluded that black holes give off radiation"πandπ"John Searle has concluded that it is impossible to build an intelligentπ computer"ππHawking is a physicist, and so we can reasonably expect his opinions on blackπhole radiation to be informed. Searle is a linguist, so it is questionable πwhether he is well-qualified to speak on the subject of machine intelligence.ππTHE FALLACY OF ACCIDENTππThe Fallacy of Accident is committed when a general rule is applied to aπparticular case whose "accidental" circumstances mean that the rule isπinapplicable. It is the error made when one goes from the general to theπspecific. For example:ππ"Christians generally dislike atheists. You are a Christian, so you mustπdislike atheists."ππThis fallacy is often committed by moralists and legalists who try to decideπevery moral and legal question by mechanically applying general rules.ππCONVERSE ACCIDENT / HASTY GENERALIZATIONππThis fallacy is the reverse of the fallacy of accident. It occurs when oneπforms a general rule by examining only a few specific cases which are notπrepresentative of all possible cases.ππFor example:π"Jim Bakker was an insincere Christian. Therefore all Christians areπinsincere."ππSWEEPING GENERALIZATION / DICTO SIMPLICITERππA sweeping generalization occurs when a general rule is applied to aπparticular situation in which the features of that particular situationπrender the rule inapplicable. A sweeping generalization is the opposite of aπhasty generalization.ππNON CAUSA PRO CAUSA / POST HOC ERGO PROPTER HOCππThese are known as False Cause fallacies.ππThe fallacy of Non Causa Pro Causa occurs when one identifies something as theπcause of an event but it has not actually been shown to be the cause. For πexample:ππ"I took an aspirin and prayed to God, and my headache disappeared. So Godπcured me of the headache."ππThe fallacy of Post Hoc Ergo Propter Hoc occurs when something is assumed toπbe the cause of an event merely because it happened before the event. For πexample:ππ"The Soviet Union collapsed after taking up atheism. Therefore we must avoidπatheism for the same reasons."ππCUM HOC ERGO PROPTER HOCππThis fallacy is similar to post hoc ergo propter hoc. It asserts thatπbecause two events occur together, they must be causally related, and leavesπno room for other factors that may be the cause(s) of the events.ππPRINCIPIO PRINCIPIIππThis is known as Begging the Question. The fallacy occurs when one assumesπas a premise the conclusion which one wishes to reach. Often, the πproposition will be rephrased so that the fallacy appears to be a validπargument. For example:ππ"Homosexuals must not be allowed to hold government office. Hence anyπgovernment official who is revealed to be a homosexual will lose his job. πTherefore homosexuals will do anything to hide their secret, and will be openπto blackmail. Therefore homosexuals cannot be allowed to hold governmentπoffice."ππNote that the argument is entirely circular; the premise is the same as the πconclusion. An argument like the above has actually been cited as the reasonπfor the British Secret Services' official ban on homosexual employees. πAnother example is the classic:ππ"We know that God exists because the Bible tells us so. And we know that theπBible is true because it is the word of God."ππCOMPLEX QUESTION / FALLACY OF INTERROGATIONππThis is the Fallacy of Presupposition. One example is the classic loaded πquestion:ππ"Have you stopped beating your wife?"ππThe question presupposes a definite answer to another question which has notπeven been asked. This trick is often used by lawyers in cross-examination,πwhen they ask questions like:ππ"Where did you hide the money you stole?"ππSimilarly, politicians often ask loaded questions such as:ππ"How long will this EC interference in our affairs be allowed to continue?"πorπ"Does the Chancellor plan two more years of ruinous privatization?"ππIGNORATIO ELENCHIππThe fallacy of Irrelevant Conclusion consists of claiming that an argument πsupports a particular conclusion when it is actually logically nothing to doπwith that conclusion.ππFor example, a Christian may begin by saying that he will argue that theπteachings of Christianity are undoubtably true. If he then argues at lengthπthat Christianity is of great help to many people, no matter how well heπargues he will not have shown that Christian teachings are true.ππSadly, such fallacious arguments are often successful because they arouseπemotions which cause others to view the supposed conclusion in a moreπfavourable light.ππEQUIVOCATIONππEquivocation occurs when a key word is used with two or more differentπmeanings in the same argument. For example:ππ"What could be more affordable than free software? But to make sure that itπremains free, that users can do what they like with it, we must place aπlicense on it to make sure that will always be freely redistributable."ππAMPHIBOLYππAmphiboly occurs when the premises used in an argument are ambiguous becauseπof careless or ungrammatical phrasing.ππACCENTππAccent is another form of fallacy through shifting meaning. In this case,πthe meaning is changed by altering which parts of a statement areπemphasized. For example, consider:ππ"We should not speak ILL of our friends"πandπ"We should not speak ill of our FRIENDS"ππFALLACIES OF COMPOSITIONππOne fallacy of composition is to conclude that a property shared by the partsπof something must apply to the whole. For example:ππ"The bicycle is made entirely of low mass components, and is therefore very πlightweight."ππThe other fallacy of composition is to conclude that a property of a numberπof individual items is shared by a collection of those items. For example:ππ"A car uses less petrol and causes less pollution than a bus. Therefore carsπare less environmentally damaging than buses."ππFALLACY OF DIVISIONππThe fallacy of division is the opposite of the fallacy of composition. Likeπits opposite, it exists in two varieties. The first is to assume that aπproperty of some thing must apply to its parts. For example:ππ"You are studying at a rich college. Therefore you must be rich."ππThe other is to assume that a property of a collection of items is shared byπeach item. For example:ππ"Ants can destroy a tree. Therefore this ant can destroy a tree."ππTHE SLIPPERY SLOPE ARGUMENTππThis argument states that should one event occur, so will other harmfulπevents. There is no proof made that the harmful events are caused by theπfirst event.ππFor example:π"If we legalize marijuana, then we would have to legalize crack and heroinπand we'll have a nation full of drug-addicts on welfare. Therefore we cannotπlegalize marijuana."ππ"A IS BASED ON B" FALLACIES / "IS A TYPE OF" FALLACIESππThese fallacies occur when one attempts to argue that things are in some wayπsimilar without actually specifying in what way they are similar.ππExamples:π"Isn't history based upon faith? If so, then isn't the Bible also a form ofπhistory?"ππ"Islam is based on faith, Christianity is based on faith, so isn't Islam aπform of Christianity?"ππ"Cats are a form of animal based on carbon chemistry, dogs are a form ofπanimal based on carbon chemistry, so aren't dogs a form of cat?"ππAFFIRMATION OF THE CONSEQUENTππThis fallacy is an argument of the form "A implies B, B is true, therefore Aπis true". To understand why it is a fallacy, examine the truth table forπimplication given earlier.ππDENIAL OF THE ANTECEDENTππThis fallacy is an argument of the form "A implies B, A is false, therefore Bπis false". Again, the truth table for implication makes it clear why this isπa fallacy.ππNote that this fallacy is different from Non Causa Pro Causa; the latter hasπthe form "A implies B, A is false, therefore B is false", where A does NOT inπfact imply B at all. Here, the problem is not that the implication isπinvalid; rather it is that the falseness of A does not allow us to deduceπanything about B.ππCONVERTING A CONDITIONALππThis fallacy is an argument of the form "If A then B, therefore if B then A".ππARGUMENTUM AD ANTIQUITAMππThis is the fallacy of asserting that something is right or good simplyπbecause it is old, or because "that's the way it's always been."ππARGUMENTUM AD NOVITAMππThis is the opposite of the argumentum ad antiquitam; it is the fallacy ofπasserting that something is more correct simply because it is new or newerπthan something else.ππARGUMENTUM AD CRUMENAMππThe fallacy of believing that money is a criterion of correctness; that thoseπwith more money are more likely to be right.ππARGUMENTUM AD LAZARUMππThe fallacy of assuming that because someone is poor he or she is sounder orπmore virtuous than one who is wealthier. This fallacy is the opposite of theπargumentum ad crumenam.ππARGUMENTUM AD NAUSEAMππThis is the incorrect belief that an assertion is more likely to be true theπmore often it is heard. An "argumentum ad nauseum" is one that employsπconstant repetition in asserting something.ππBIFURCATIONππAlso referred to as the "black and white" fallacy, bifurcation occurs whenπone presents a situation as having only two alternatives, where in fact otherπalternatives exist or can exist.ππPLURIUM INTERROGATIONUM / MANY QUESTIONSππThis fallacy occurs when a questioner demands a simple answer to a complexπquestion.ππNON SEQUITURππA non-sequitur is an argument where the conclusion is drawn from premisesπwhich are not logically connected with it.ππRED HERRINGππThis fallacy is committed when irrelevant material is introduced to the issueπbeing discussed, so that everyone's attention is diverted away from theπpoints being made, towards a different conclusion.ππREIFICATION / HYPOSTATIZATIONππReification occurs when an abstract concept is treated as a concrete thing.ππSHIFTING THE BURDEN OF PROOFππThe burden of proof is always on the person making an assertion orπproposition. Shifting the burden of proof, a special case of argumentum adπignorantium, is the fallacy of putting the burden of proof on the person whoπdenies or questions the assertion being made. The source of the fallacy isπthe assumption that something is true unless proven otherwise.ππSTRAW MANππThe straw man fallacy is to misrepresent someone else's position so that itπcan be attacked more easily, then to knock down that misrepresented position,πthen to conclude that the original position has been demolished. It is aπfallacy because it fails to deal with the actual arguments that have beenπmade.ππ π
