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BS3916 Thinking about Management

2. Some Principles of Logic

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BS3916 Thinking about Management2: Some principles of Logic

• Terms

a word or combination of words that can stand by itself as the subject or predicate of a proposition

• Silence is Golden (Both are terms)

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BS3916 Thinking about Management 2: Some principles of Logic

• Proposition

that which can be affirmed or deniede.g. Silence is Golden

• Silence is the subject

• Golden is the predicate

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BS3916 Thinking about Management 2: Some principles of Logic

• Argument

is a series of logically related propositions

• All men are mortal (Major premise)

• Socrates was a man (Minor premise)

Socrates was mortal (Conclusion)

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BS3916 Thinking about Management 2: Some principles of Logic

• DEDUCTION (from the general to the particular)

• If the premises are true and the argument is valid then the argument must be true

• All of the information is contained (at least implicitly) in the premises

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BS3916 Thinking about Management 2: Some principles of Logic

• INDUCTION (inference of a general condition from a set of observed instances)

• If the premises are true then the conclusion is probably but not necessarily true

• The conclusion contains information not present, even implicitly, in the premises

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BS3916 Thinking about Management 2: Some principles of Logic

• TRUTHconcerns the factual correctness or otherwise of the premises

• VALIDITY refers to whether the conclusion is correctly drawn

(according to the rules of logic) from the premises

• Propositions are true or false; arguments are valid or invalid (these terms are not inter-changeable)

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BS3916 Thinking about Management 2: Some principles of Logic

• Deductive logic is concerned with the construction of rules for the production of valid arguments (and the exposure of invalid ones)

• NB an invalid argument might have a true conclusion (making it harder to spot) and a valid argument might have a false conclusion

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BS3916 Thinking about Management 2: Some principles of Logic

• Valid and trueAll cats have four legsMy pet is a cat

my pet has four legs

• Invalid and true The industrious are prudent

Ants are prudent Ants are industrious

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BS3916 Thinking about Management 2: Some principles of Logic

• Valid and falseAll fish are cold-bloodedWhales are fish

Whales are cold-blooded

• Invalid and false All cats have tails

My hamster has tail My hamster is a cat

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BS3916 Thinking about Management 2: Some principles of Logic

• Construct two arguments….

• One which is valid but has a false conclusion

• One which is invalid but in which all of the prepositions are true

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BS3916 Thinking about Management 2: Some principles of Logic

• IF-THEN• Affirming the antecedent (VALID)

If (and only if) p, then qp

q• Denying the Consequent (VALID)

If (and only if) p, then qNot q

not p

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BS3916 Thinking about Management 2: Some principles of Logic

• IF-THEN• Affirming the consequent (INVALID)

If p, then qq

p

• Denying the Antecedent (INVALID)If p, then qNot p

not q

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BS3916 Thinking about Management 2: Some principles of Logic

IF and IFF• IF is an ambiguous word…. (a) If I pass my exams, I will be a graduate (b) If I win the pools, I will become rich

• In (a) IF means if and only if (sometimes Iogicians call this IFF)

• In (b), there are are other ways of becoming rich (e.g. by inheritance)

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BS3916 Thinking about Management 2: Some principles of Logic

SOME and ALL

• English is imprecise .. When we say All cats are mammals we are really saying…

• All cats are (some of the entire category) of mammals

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BS3916 Thinking about Management 2: Some principles of Logic

Contradictions…

• To deny that All cats are mammals we do not go to the opposite extreme and say No cats are mammals

• The existence of one, egg-laying cat is sufficient for us to argue that Not all cats are mammals without going to the opposite extreme of saying No cats are mammals

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BS3916 Thinking about Management 2: Some principles of Logic

SYLLOGISMS

• Are a triad of connected propositions that have to follow the rules of logic.

• When these rules are broken, we have examples of fallacies

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BS3916 Thinking about Management 2: Some principles of Logic

Fallacy of the undistributed middle

• All followers of Tony Blair love opera

• I am a lover of opera

• Therefore I am a follower of Tony Blair

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BS3916 Thinking about Management 2: Some principles of Logic

Fallacy of the illicit process

• Some clever men are eccentric

• Smith is not eccentric

• Therefore Smith is not a clever man

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BS3916 Thinking about Management 2: Some principles of Logic

Fallacy of the Two Middle Terms

• Chalk is different from cheese

• Cheese is different from butter

• Therefore butter is different from chalk

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BS3916 Thinking about Management 2: Some principles of Logic

Valid argument form: Reductio ad absurdum

• To prove: p

• Assume not-p

• Deduce a false statement

• Conclude that if not-p is false, then

p must be true

• Used extensively in mathematics where it is known as indirect proof

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BS3916 Thinking about Management 2: Some principles of Logic

Valid argument form: The dilemma

• Either p or q

• If p, then r

• If q, then s

• Either r or s

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BS3916 Thinking about Management 2: Some principles of Logic

Theological example• There is evil in the world• Either God cannot prevent evil or he does not

wish to• If God can’t prevent evil, he is not all-powerful• If God does not want to prevent evil, he is not

benevolent• Therefore God is not all powerful or he is not

benevolent

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BS3916 Thinking about Management 2: Some principles of Logic

Fallacies of Deduction

Affirming the Consequent

• If p then q; q; p

• If we play good football, we will win

• We have won

• Therefore we played good football

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BS3916 Thinking about Management 2: Some principles of Logic

Fallacies of Deduction

Denying the antecedent

• If p then q; not p; not q

• If Jeffrey Archer testifies, he is innocent

• Jeffrey Archer is not willing to testify Jeffrey Archer is not innocent

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BS3916 Thinking about Management 2: Some principles of Logic

Fallacies of Induction

Insufficient statistics

• Every cat I have seen has a tail all cats have tails

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BS3916 Thinking about Management 2: Some principles of Logic

Fallacies of Induction

Biased statistics

• Every time, I wait for a bus there are always buses going in the opposite direction

• Therefore there are always more buses going in the opposite direction

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BS3916 Thinking about Management 2: Some principles of Logic

Causal fallacies

Post hoc, ergo propter hoc

• B was caused by A because B followed A

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BS3916 Thinking about Management 2: Some principles of Logic

Causal fallacies

Confusion of cause and effect

• Sober students have money

• Drunk students have no money give drunk students money to make them

sober

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BS3916 Thinking about Management 2: Some principles of Logic

Causal fallacies

Common cause

• When it’s cold, I put on warm clothes

• When it’s cold, I catch a cold Warm clothes give me a cold

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BS3916 Thinking about Management 2: Some principles of Logic

Equivocation

• Only man has a sense of humour

• No man is a woman

• No women have a sense of humour

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BS3916 Thinking about Management 2: Some principles of Logic

Petitio Principii (lit. Asking for the Principle

Or ‘Begging the Question’)

Assuming what we should be trying to prove but is this true in this case ?

•All true pleasures lead to happiness

•All unselfish acts are true pleasures all unselfish acts lead to happiness

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BS3916 Thinking about Management 2: Some principles of Logic

Exercises (1 of 6)

• If the Tories win the next by-election, they will win the general Election

• If they lose the by-election, it follows they will not win the General Election

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BS3916 Thinking about Management 2: Some principles of Logic

Exercises (2 of 6)

• Since no monetarists were Keynesians and Margaret Thatcher was not a Keynesian, then Margaret Thatcher was a monetarist

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BS3916 Thinking about Management 2: Some principles of Logic

Exercises (3 of 6)

• An increase in the money supply leads to inflation

• So the way to cure inflation is to curb the money supply

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BS3916 Thinking about Management 2: Some principles of Logic

Exercises (4 of 6)

• All BAMBA students work hard

• All students who work hard pass their examinations

All BAMBA students will pass their examinations

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BS3916 Thinking about Management 2: Some principles of Logic

Exercises (5 of 6)

• BAMBA students who hate logic are intelligent

• BAMBA students who hate logic will not fail their exams

• As those who are not intelligent fail their exams

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BS3916 Thinking about Management 2: Some principles of Logic

Exercises (6 of 6)

• Marx’s theories cannot be taken seriously since his prediction that there would be an increasing degree of polarisation and concentration into opposing classes is ridiculous