Download Some Principles of Logic

Business Thinking
Some Principles of Logic
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Business Thinking
APEL: 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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Business Thinking
APEL: Some principles of Logic
• Proposition
that which can be affirmed or denied
e.g. Silence is Golden
• Silence is the subject
• Golden is the predicate
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Business Thinking
APEL: Some principles of Logic
• Argument
is a series of logically related propositions
• All men are mortal
• Socrates was a man
(Major premise)
(Minor premise)
•  Socrates was mortal
(Conclusion)
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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: Some principles of Logic
• TRUTH
concerns 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 inter7
changeable)
Business Thinking
APEL: 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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Business Thinking
APEL: Some principles of Logic
•
Valid and true
All cats have four legs
My 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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Business Thinking
APEL: Some principles of Logic
•
Valid and false
All fish are cold-blooded
Whales are fish
 Whales are cold-blooded
•
Invalid and false
All cats have tails
My hamster has a tail
 My hamster is a cat
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Business Thinking
APEL: 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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Business Thinking
APEL: Some principles of Logic
• IF-THEN
• Affirming the antecedent
If (and only if) p, then q
p
q
• Denying the Consequent
If (and only if) p, then q
Not q
 not p
(VALID)
(VALID)
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Business Thinking
APEL: Some principles of Logic
• IF-THEN
• Affirming the consequent
If p, then q
q
p
• Denying the Antecedent
If p, then q
Not p
 not q
(INVALID)
(INVALID)
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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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 allpowerful
• 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: Some principles of Logic
Causal fallacies
Post hoc, ergo propter hoc
• B was caused by A because B followed A
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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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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Business Thinking
APEL: 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
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