GeneralLogic for the millions

Logic forthe mi l l ions

Mander,A.E. (Alfred Ernest),b. 1892Producer's Note

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'The trouble with most folks is not so much their ignorance,as their'knowingso manythings whichain't so."

—Josh Bi l l ings

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'He who cannot reason is a fool ; he who wi l l not is a bigot; he who dare not is aslave."

—W.Drummond

'Ever)'argument that has been used to justifythe teaching of grammar maybeappl ied with greatercogencyto the teaching of logic. If it is desirable that aperson shal l speak correctly, it is much more desirable that he shal l thinkco rrectl y."

Bal lard

Digitized bythe InternetArchive in2010http://www.archive.org/detai ls/logicformi l l ionsOOma nd

F o rewo rd

Thinking is ski l led work. It is not true that we are natural lyendowed with theabi l ityto think clearlyand logical ly—without learning how,or withoutgracftttfngjt is ridiculous to suppose that any less ski l l is required for thinkingthan for carpentering,or for playing tennis,golf,or bridge,or for playing somemusical instrument.People with untrained minds should no more expect tothinkclearlyand logical lythan people who have never learnt and neverpractised can expect to find themselves good carpenters,golfers,bridge-players,orpianists.Yet ourworld is ful l of people who apparentlydosuppose that thinking is entirely unski l led work; that thinking clearly andaccurately is so easyand so"natural" that nobody need trouble to learn how todo it; that "anybodycan think";and that anyone person's thinking is quite asrel iable as any other person's.This accounts for the fact that,as a people,weare so much less efficient in this respect than we are in our sports.For nobodyassumes that anygame isso easythatwe are al l first-class players"natural ly,"without having to learn how to play orwithout practice.

Those who are in earnest in wishing to think more clearly,more accurately,and more rational ly should face their task in the spirit in which theywould setthemselves to learn the rules, to learn the technique,and to practise some new

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game.Theyshould be prepared to devote as much time and attention to thisas theywould to learning golf,bridge,or music.

SECTION PACE

Rel iabi l ityof Observation

Testimony(Evidence)of Observation

Third-hand(or Thirtieth-hand)Evidence

VGENERALIZATION97

What is General ization?

Testi ng a General ization

False General ization

General i zation: "Empirical"a nd"Explained"

Scientific General izations and Natural Laws

VI EXPLANATION 1 15

How we"Explain"a Fact

Explanation—by Parts and Factors

Explanation—by Circumstances and Conditions

Explanation—byCause and Effect

"Post hoc,propter hoc"

Explanation—by F unction

Testi ng an Explanation

VI ITHEORIES 137

What is a Theory?Testing a Theory Problem-solving Theories Evolution

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VI I I DEDUCTIVE REASONING 155

Deduction

Deductions:Val id and Inval id

"Certain"and"Probable"Deductions

/Xt Fal lacies in Deduction

SECTION PAGE

IXTESTING OUR'GROUNDS'FORBELIEF 175

Bare Assertion;Dogma;Tradition

Classification: the First Necessity

Testing a Judgment of Others

Testing an Observed Fact (or Evidence thereof)

Testi ng a General ization

Testing whether a fact is"Explained"

Testi ng a Theory

Testi ng a Deduction

Testing an Axiom or a Definition

Probabi l ity

XPRACTICE 193

APPENDIX197

Some Notes on Causation and Determinacy

LOGIC FORTHE MILLIONS

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Section I Checks and Safeguards

STICKING TO THE POINT

The firstessential to clear thinking(and speaking) is the abi l ityto"see" thepoint—to recognize what exactly is the point in question—and then to stick tothatpoint unti l it has been dealtwith.

It is the markof a vague,muddled,and feeble thinker (or speaker) that he driftsalways from one point to another;wandering hither and thither; neversettl inganything;quitting each question in turn as soon as anotherattracts hisattention; leaving every"hare" immediately another is started,and fol lowi ngthatone only unti l yet anotherappears; "mind wandering"; not thinking.A clear thinker "sees" the pointat issue; recognizes exactlywhat it is he wantsto know,or wants to decide;sets to work to sort out al l the relevant

4facts and arguments from others which are irrelevant;considers only thosewhich are relevant to the question before him; thinks always with purpose,keeping steadi lyin mind the question that is to be answered, the problem thatis to be solved.

Al l real ,constructive thinking is aimed atanswering some question,solvingsome problem,making some decision.Muchof what is commonlycal ledthinking(and much talking) is indeed nothing more than"mind wandering."Let us cultivate the habit of considering one point at a time,and sticking to thatpoint unti l we have made up our minds about it.Let us not drift about from onequestion to another, in the end leaving everything"in the air," unsettled,unsolved.The bestwayto develop as clear thinkers is to thinkalways bythemethod of asking ourselves questions and then striving to answerthem;andalways answering each question before passing on to the next. It is useful tostate the question definitely—if possible, to put it down in writing—and thenrefer to it,and come back to itagain and again and again.

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SPEAKING THE SAME LANGUAGE

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To saythat two persons speak the same language is to say that they use thesame words with the same meanings.When we say that we are al l

Engl ish-speaking people, thatsignifies onlythat the majority of everydaywords mean more or less the same thing to al l of us.But there are many wordswhich have different meanings to different persons.Probably no two personsspeak exactlythe same language.

We should note that a language is not merely a col lection of words: it is therelation of words to meanings.To speak or write the same words does not ofitself show that we are using the same language.The word"genial"occurs inboth German and Engl ish;but if a German were to use the word in the Germansense and we were to accept it in the Engl ish sense,we should completelymisunderstand him.The word"lovely" is commonly used in sl ightly differentsenses in England and New Zealand.The word"Sol icitor"means somethingquite different inAmerica from what it means in England: in America it meansone who sol icits orders,a salesman or commercial travel ler;

6in Engl ish it means a lawyer. "Dumb," l ikewise, has a meaning in Americadifferentfrom the meaning it has in England.

Again, there is a word, "conscience," in both French and Engl ish.But if aFrenchman were to use the word in the French sense,and we were to accept itin the Engl ish sense,we should entirely misunderstand his meaning.Wespeak different languages.Yet because German and French and Engl ish areso widelydifferent,we are not l ikelyto be misled when a German oraFrenchman,speaking his language, happens to use a word which occurs inour language too.We recognize that we speak different languages;and so weare on ourguard against confusing his use of the word with ourown.

The word"homely"occurs in both Engl ish and American-Engl ish.To mostEngl ishmen"a homelygirl" is an expression with quite anagreeable flavour: itmeans a pleasant, natural sort of girl who possesses the domestic qual itieswhich would make her a good wife and mother.But it would be unwise todescribe such a girl as"homely" to anAmerican.For to him the word has adifferent meaning: to him it means plain and unattractive,

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coarse and ugly.So, in regard to this word atany rate, the Engl ish and theAmericans are speaking different languages.

There is probably less dangerof misunderstanding when we are deal ing withGermans than when we are deal ing with Americans.For in the former case werecognize that we are speaking different languages.We are therefore on ourguard;and in translating from one language to the other we exercise greatcare to get the exact meaning intended—what the word real ly means to theperson who uses it.But in deal ing with Americans we maysuppose that weare speaking the same language;and so we are apt to take it forgranted that agiven word must mean the same thing to them that it means to us.The word''homely" is but one of hundreds of cases in whicha completemisunderstanding may result.

But what of ourselves?Of us,apart from the Americans,who cal l ourselvesEngl ish-speaking people?Dowe al l speakexactlythe same language? Irepeat:we do not.We al l speak languages which are more or less simi lar;andfor the

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8sake of rough-and-ready convenience we lump them al l together as theEngl ish language.But when we come to look into the matter more closely,wefind that our respective languages are not entirelyand exactly the samelanguage.

I repeat: to say that two persons use the same language, is to say that theyuse the same words with the same meaning.No doubt there are many Engl ishwords which do have approximatelythe same meaning to al l of us. If therewere not,we could not understand one another at al l .But consider how manywords there are—how many everydayEngl ish words—which mean differentthings to different people.And can you saythat two persons are real lyspeaking the same language if—even though they use the same words—theymeandifferent things bythem?Can you?Think itover.

Suppose that when I use the word"Elephant," I mean the same thing that youmean when you use the word"Camel ."Obviously, in thatcase,you and I wi l l

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be"al l atsea" if we try to talk to one another aboutelephants or camels.Youwi l l be

9meaning one thing,and I another. In that respect,at any rate,we shal l bespeaking different languages.We shal l be in the position of a Frenchman anda Chinese(neitherof whom understands the other's language) trying to carryon a conversation. Indeed,we shal l be in a worse position.Forwe maytake itforgranted that we are speaking the same language,whereas they wi l l real izethattheyare not. I assume that the word"Elephant"means the same to you asto me.You assume that it means the same to me as to you.And if it does not,then ourargument (as to whetheranelephant has a trunk) is l iable to becomesomewhat heated.You wi l l think that I am a fool : I shal l think that you are one.We shal l perhaps growangry orcontemptuous.The argument wi l l becomemore and more involved, incoherent,absurd.And this is the usual result whentwo persons are talking to each other in different languages and yet mistakethem for the same language.

Obviously, it is not l ikelythat you and I speak different languages in regard tothe word"Elephant."For, if we have the sl ightestdoubtabout it, I can take youto the Zoo and point to an

10animal ,or show you a picture,or describe the creature in words,and say:"There!See!That is what the word'Elephant'means to me."

It is with abstract terms that we chieflyexperience difficulty.Considera wordl ike"Social ism."SirWi l l iam Harcourt is reported once to have said: "We are al lSocial ists nowadays."The leader of the Labour Partyalso described himselfas a"Social ist." Is it l ikelythat they both meant the same thing?Or is it morel ikelythat, in this connection, theywere in factspeaking different languages?Do Prohibitionists and Anti-Prohibitionists mean preciselythe same thing whenthey use the word"Liberty*?

Are we sure that we al l mean the same thing when we speak of an"educatedman"?Orof"God"?Orof a"democrat"?Orof"capital"?Orof"instinct"?Or ofan action being"right"?

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There are hundreds of words l ike these—words in everyday use—in regard towhich we cannot be sure(unless we have made sure) that we ourselves arespeaking the same language.

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The great majorityof arguments and discussions in everyday l ife are utterlyfuti le—sheer waste of time and temper—hopeless from the start . . .simplybecause the parties are using the same words,but using them in differentsenses.They are speaking different languages,and they do not recognize thefact.They would have a better chance of convincing each other if one werespeaking Russian and the other Portuguese—for then at least theywouldrecognize the necessity of cal l ing i n an interpreter.

Therefore I urge you neverto take part inanyargument at al l—on anysubject—with anyone—unless you have first made quite sure that both partiesare using the words in the same sense.

Try it during the coming week.You wi l l find the practice so i l luminating and souseful that you wi l l probablycarryon with it al l the restof your l ife! Just test itwhen you are in conversation with anybody:ask him what he means bysometerm that you find yourselves using.Find out whether you and the other manare real ly using thatterm in the same sense: i .e.speaking the same language.

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Exercise in Definition.

Setout in otherwords—as clearly and conciselyas you can—what you meanbyeach of the fol lowing terms.Then take opportunities of asking your friendswhat theymean by these same terms.

(a)Social ism. (f)Democracy.

(6) Instinct. (g)Moral Courage.

(c)Ed ucation. (h)Conscience.

(d)God. (f) International ism.

(e)Progress(social). (/)A"right to l ive."

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