APPLICATIONS OF
LOGICAL REASONING
VI SEMESTER
ADDITIONAL COURSE
(In lieu of Project)
BA PHILOSOPHY
(2011 Admission)
UNIVERSITY OF CALICUT
SCHOOL OF DISTANCE EDUCATION
Calicut university P.O, Malappuram Kerala, India 673 635.
School of Distance Education
UNIVERSITY OF CALICUT
SCHOOL OF DISTANCE EDUCATION
STUDY MATERIAL
Additional Course (In lieu of Project)
BA PHILOSOPHY
VI Semester
APPLICATIONS OF LOGICAL REASINING
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CONTENTS
PAGE No
MODULE I
4
MODULE II
11
MODULE III
14
MODULE IV
17
MODULE V
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Aims and objectives:
1. To develop the student’s critical thinking and intellectual problem-solving
capability.
2. To test the ability of the student to apply the theory and solve problems
involving tests of reasoning.
3. To develop skill for linguistic analysis and the ability to detect errors in
reasoning.
MODULE I
REDUCTION OF ORDINARY LANGUAGE SENTENCES INTO
STANDARD FORM SENTENCES.
The traditional logic recognized four forms of propositions(A, E , I , O). A
proposition which is not expressed in one of these forms is to be reduced to
one of these according to the meaning of the proposition.
Categorical propositions are classified with regard to quality and
quantity: From the point of view of quality categorical propositions are either
affirmative or negative.
An Affirmative proposition is one in which an agreement is affirmed
between the Subject and Predicate, or in which the Predicate is asserted of the
Subject , e.g. snow is white. A Negative proposition is one which the Predicate
is denied of the Subject. It indicates a lack of agreement between the Subject
and Predicate. E.g. The room is not cold.
The quantity of a proposition is determined by the extension of the
Subject . on the basis of quantity categorical propositions are either universal
or particular.
A universal proposition is one in which the Predicate refers to all the
individual objects denoted by the Subject . (the subjects is taken in its full
extension) E.g. All men
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are rational. A particular propositions is one in which the Predicate belongs
only to a part of the denotation of the subject. E.g. some metals are white.
Particular propositions usually begin with some word or phrase showing
that the subject is limited in extent. The logical sign of particular proposition is
“some”, but other qualifying words or phrases, such as “the greatest
part”, ‘nearly all’, ‘several’, ‘a small number’, ‘a few’, etc. also indicate
particularity.
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A.E.I.O. Combining quantity and quality we get four types of categorical
propositions, Universal Affirmative,Universal Negative,Particular
Affirmative,Particular Negative.. A.E.I.O. are used to symbolise them
A and I from affirmo stand for ‘affirmative’ propositions; E and O, the
vowels from ‘Nego’ for negative propositions.
The four types of propositions are:
Universal affirmative: It is a categorical proposition in which the
predicate agrees with the whole subject, e.g. All men are rational.
All S is P
Universal negative proposition: It is a categorical proposition in
which the predicate does not at all agree with any part of the subject.
E.g. No men are perfect.
No S is P
particular affirmative proposition: is a categorical proposition in
which the predicate agrees only with a part of the subject. E.g. some
flowers are red.
Some S is P
particular negative proposition is a categorical proposition in
which the P does not agree with a part of the S. e.g. some Indians are
not religious.
Some S is not P
S = Subject; P = Predicate
The purpose of reducing sentences to logical form is to make the meaning of
the sentence clear in logical reasoning. If propositions are stated in their logical
form, testing of inferences becomes easier.
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The points to be remembered in changing sentences to logical form are:
1.The meaning of the original proposition is to be preserve in the standard
form proposition.
2.The proposition must contain all the three parts in he proper order, subject,
copula and predicate.
3. A suitable copula must be used between the subject and the predicate.
4. The sign of negation must go with the copula, and not with the predicate.
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5. Compound sentences must be split up into simple propositions.
6. The quantity and quality of the proposition must be decided and stated
clearly.
The following procedure is to be followed while reducing propositions to
their logical form:
Subject and predicate of the given proposition are to be identified. Subject is
that about which the assertion is made. Predicate is that which is asserted of
the subject.
Having identified the subject and predicate , the quality of the proposition is
to be known, affirmative or negative whether the predicate is affirmed or
denied of the subject.
Next, the quantity of the proposition is to be known. If the predicate is affirmed
or denied of the entire denotation of the subject, the proposition is Universal. If
the predicate is affirmed or denied of a part of the denotation of the subject,
the proposition is Particular.
Certain general rules are to be followed :
*Sentences which have words like ‘all’, ‘every’ , each ,any, whoever, with the
subject and words like always, necessarily with the predicate are to be
reduced into A form.
Every ticket-holder must be admitted.
L.F: All ticket-holders are persons who must be admitted.
Any man can do that
L.F: All men are persons who can do that.
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Any criminal is punishable
L.F: All criminals are punishable.
Poets always love nature.
L.F: All poets are lovers of nature.
Virtues are absolutely desirable.
L.F: All virtues are desirable.
*Sentences with all, every, any etc containing the signof negation , not are to
be reduced to O form.
All that glitters is not gold
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L.F: Some things that glitters are not gold.
Every disease is not fatal
L.F: Some diseases are not fatal
Any fruit is not sweet
L.F: Some fruits are not sweet
Not every good bowler is a good batsman.
L.F: Some good bowlers are not good batsmen
Every cloud does not bring rain
L.F: Some clouds are not those which bring rain
*Sentences with no, none, never, nothing, nobody, not one, not a single, are to
be reduced to E proposition.
Not a single student has passed
L.F: No student is one who has passed.
Nothing done in hurry is well done.
L.F: No acts done ina hurry are acts which are well done.
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Not one was saved in the shipwreck
L.F: No sailors are those who were saved in wreck
Misers are never happy
L.F: No misers are happy.
No lazy man succeeds in life.
No lazy men are successful.
None can live for ever
L.F: No persons are those who can live for ever
*Sentences containing words as some, most, a few, mostly, generally, all but
one, almost all, frequently, often, many, certain, nearly all, a small number,
the majority, sometimes, nearly always are to be reduced to the particular( I
or O).
Girls are generally shy
L.F: Some girls are shy
Many a flower is born to blush unseen
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L.F: Some flowers are things born to blush unseen
Most Hindus are vegetarians
L.F; Some Hindus are vegetarians
Many rules are easy
L.F: Some rules are easy
A few students do not work hard
L.F: Some students are not those who work hard
Most of the students are not hostellers
L.F: Some students not hostellers
*Sentences containing words as few, seldom, hardly.
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, scarcely, are to be reduced to O if there is no sign of negation and to I if
there is a sign of negation.
Few men are reliable
L.F: Some men are reliable
Few men have not suffered disappointments in life
L.F: Some men are those who have suffered disappointments in life
Students seldom pass this examination in the first attempt
L.F: Some students are not those who pass this examination in the first
attempt
*Singular proposition is reduced to a Universal proposition when the singular
subject is a definite individual or a collection of individuals. If the subject is an
indefinite singular term,the singular proposition should be taken as a
Particular proposition.
Gandhiji is the Father of Indian Nation.- A
The sky is blue.-A
One minister is not rich
L.F: Some ministers are not rich
*Indefinite or indesignate propositions are treated as Universal when the
predicate is an invariable and common attribute of the subject.
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*Indefinite propositionsare treated as Particular when predicate is only an
accidental quality.
Glass is breakable
L.F: All glasses are breakable.
Material bodies gravitate
L.F: All material bodies are things which gravitate.
Lemons are not apples.
L.F: No lemons are apples
Catholics are Christians
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All Catholics are Christians
Indians are poor
L.F: Some Indians are poor
Trains are not punctual
L.F: Some trains are not punctual
*Sentences containing words as except, all but, save, called exceptive
propositions are to be reduced to Universal if the exceptions are definitely
specified. If the exceptions are indefinite, the exceptive sentences are reduced
to Particular propositions.
All students except Shyam have passed
L.F: All students except Shyam are those who have passed
No students except Shyam have failed
L.F: No students except Shyamare those who have failed
All students except two have passed
L.F: Some students are those who have passed
No students except two have passed
L.F: Some students are not those who have passed
All but James passed
L.F: All persons other than James are persons who passed
All but a few were saved
L.F: Some persons are those who were saved
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All metals except one are solid
L.F: Some metals are solid.
*Exclusive sentences containing words as alone, only, none but, none except
no one else but, nothing but are reduced to E proposition. By contradicting the
original subject and used as the
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subject of the logical proposition. Exclusive sentences may also be changed
into Universal propositions by inter-changing the original subject and
predicate.
None but citizens can hold property.
L.F: No non-citizens are persons who cn hold property.
Or
All those who can hold property are citizens
Only the wise are fit to rule
L.F: No non-wise persons are fit to rule
Or
All persons fit to rule are wise
Graduates alone can vote
L.F: No non-graduates are voters
Or
All voters are graduates
*Where the quantity of the proposition is not explicit, it is the meaning of the
sentence that must be taken into account in reducing to the logical form .
To be wise is to be happy
L.F: All wise people are happy
To err is human
L.F: All cases of erring are human
Blessed are the pure
L.F: All pure persons are blessed
There are bright colours
L.F: Some colours are bright
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MODULE II
Conversion of
A, E ,I, O
propositions according to relations of
opposition between categorical propositions as shown in the traditional
square of opposition.
IMMEDIATE INFERENCE
Inference is a mental process of drawing something new from something
known.
Mediate inference consists in drawing a new proposition from two known
propositions. The mediate inference asserts the agreement or disagreement of a
subject and predicate after having compared each with a common element or
middle term. The conclusion is thus reached mediately or indirectly. There are
two kinds of immediate inferences: Opposition and Eduction.
Traditional logic considers opposition of propositions as a system of inferences.
Traditionally opposition deals with inferences within the four-fold scheme of
propositions. Opposition of propositions is a scheme of inferences between two
propositions which have the same subject and the same predicate , but differ
either in quantity or in quality or both in quantity and quality.
There are four kinds of logical opposition, contrary opposition, contradictory
opposition, sub-contrary opposition, and sub-altern opposition.
1. Contrary Opposition or contrariety: is the relation between two
universal propositions having the same S and P but differing in quality only.
A and E
E.g. All A is B--. No A is B.
All misers are unhappy.----No miser is unhappy.
2. Contradictory opposition is the relation between two propositions
having the same S and P but differing both in quality and quantity. I
and O; I and E
A and O
E.g. All boys are clever-some boys are not clever.
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I and E
Some boys are clever- No boys are clever.
3. Subcontrary opposition or subcontrariety: is the relation between
two particular propositions having the same S and P but differing in
quality only. I and O
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E.g. Some able men are honest.
Some able men are not honest.
4. Subaltern opposition or subalternation: is the relation between
two
propositions having the same S and P but differing in quantity only. In
subalternation the universal is called subalternant and
corresponding particular is called subalternate. A and I : E and O
the
All men are mortal - Some men are mortal.
No men are mortal- Some men are not mortal.
As an immediate inference opposition consists in drawing out from the
truth or falsity of a given proposition the truth or falsity of its logical opposite
having the same subject and predicate but differing in quality only or in
quantity only or in both.
Laws of Oppositional Inference
1. Law of Contrary Opposition
Between contraries if one is true the other s false, and if one is false the
other is doubtful. Contrary propositions cannot both be true, but both may be
false.
All men are rational T
No men are rational F
No students are industrious F
All students are industrious-undetermined
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2. Law of Contradictory Opposition
If one of the contradictories is rue the other must be false; if one is false
the other must be true. Both can neither be true or false at the same time.
No men are perfect T/F
Some men are perfect T/F
3. Law of Subcontrary Opposition
Between subcontraries if one is false the other is necessarily true; but if
one is true the other is doubtful. Both may be true; both cannot be false.
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Some men are angels F
Some men are not angles T
Some students are honest T
Some students are not…undetermined
Some fruits are sweet T
Some fruits are not sweet T
4. Law of Subalternation
Between subalterns if the universal is true the corresponding particular
is also true; but if the universal is false the particular is doubtful.
E.g. No gamblers are honest T
Some gamblers are not honest T
All students are clever F
Some students are clever--undetermined
If the particular proposition is true its corresponding universal is
doubtful; but if the particular is false the universal must be false.
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Some politicians are not honest T
No politicians are honest--undetermined
Some men are not rational F
No men are rational F
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MODULE III
Changing categorical propositions into converse, obverse, and
contrapositive according to rules of eduction/immediate inference.
Conversion, Obversion, Contraposition and Inversion are immediate
inferences.
Conversion
Conversion is an immediate inference in which from a given proposition
another proposition having the original predicat as the new subject , and the
original subject as the new predicat but expressing the same meaning as that
of the given proposition. The proposition to be converted is called the
convertend and the converted proposition is called the converse. It is a process
by which from a proposition of the form S-P a proposition of the form P-S is
inferred. Conversion expresses the same idea by interchanging the subject
and predicate.
Rules of conversion:
Term undistributed in the convertend not be distributed in the converse.
Keep the same quality
Interchange subject and predicate
Two types of conversion, simple conversion and conversion by limitation
Simple conversion---quantity and quality not changed
Conversion of E and I
No Hindus are Muslms- convertend
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No Muslims are Hindus-- Converse
Conversion by limitation—quantity changed
Conversion of A:
All tigers are animals(convertend)
Some animals are tigers(converse)
O proposition has no converse. The subject undistributed in the convertend
become distributed in the converse. This would go against the rule of
distribution.
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Obversion
Obversion is an immediate inference in which from a given proposition a new
proposition is inferred which has the original subject as subject and the
contradictory of the original predicate as it’s predicate. The quality of the
proposition is also changed. The original proposition is called obvertand and
the inferred proposition is called the obverse.
Obvertend
obverse
A--All tigers are animals
E—No tigers are non-animals
E—No liers are honest
A—All liers are non-honest
I—Some students are sportsmen
sportsmen
O—Some students are not non-
O—Some men are not lazy
I—Some men are non-lazy
Contraposition
Contraposition is an immediate inference in which from a given proposition
another proposition having the contradictory of the given predicate as it’s
subject is inferred.
There are two forms of contraposition, partial and full. When the predicate of
the contrapositive is the same as the original subject, it is partial
contraposition. When the predicate of the inferred proposition is also the
contradictory of the original subject, it is full contraposition.
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To get the contrapositive, first obvert and then convert the obverse.
Contraposition of A:
All tigers are animals
No tigers are non-animals (obverse)
No non-animals are tigers (partial contrapositive)
All non-animals are non-tigers (full contrapositive)
Contraposition of E:
No liers are reliable
All liers are non-reliable(obverse)
Some non-reliable persons are liers (partial contrapositive)
Some non-reliable persons are not non-liers (full contrapositive)
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Contraposition of I:
Some metals are heavy
Some metals are not non-heavy (obverse)
Some non-heavy things are not metals (no converse, hence no contrapositive)
I
proposition has no contrapositive
Contraposition of O:
Some politicians are not honest
Some politicians are non-honest (obverse)
Some non-honest persons are politicians (partial contrapositive)
Some non-honest persons are not non-politicians (full contrapositive).
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MODULE IV
Detecting fallacies according to the rules of categorical syllogism.
CATEGORICAL SYLLOGISM
Definition of Syllogism
A Syllogism is a form of mediate deductive inference, in which the conclusion
is drawn from two premises, taken jointly. It is a form of deductive inference
and therefore the conclusion cannot be more general than the premises. It is a
mediate form of inference because the conclusion is drawn from two premises,
and not from one premise only as in the case of immediate inference.
Eg : All men are mortal
All kings are men
.` . All kings are mortal.
Structure of Syllogism
A syllogism consists of three terms. The predicate of the conclusion is
called the Major Term; subject of the conclusion is called the Minor Term; and
that term which occurs in both the premises, but does not occur in the
conclusion, is called the Middle Term. The Major and Minor terms are called
Extremes, to distinguish them from the Middle term.
The Middle Term occurs in both the premises, and is the common
element between them. The conclusion seeks to establish a relation between
the Extremes—the major term and the minor term. The middle term performs
the function of an intermediary. The middle term is thus “middle” in the sense
that it is a mediating term, or a common standard of reference, with which two
other terms are compared and is thus means by which we pass from premises
to conclusion. The middle term having performed its function of bringing the
extremes together drops out from the conclusion. Thus, we reach the
conclusion in a Syllogism, not directly or immediately, but by means the
Middle term.
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The premise in which the major term occurs is called the Major Premise and
the premise in which the minor term occurs is called the Minor Premise, For
example, in the following Syllogism:
All men are mortal
All kings are men
.`. All kings are mortal.
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The term ‘mortal’ is the major term, being the predicate of the
conclusion; the term `kings` is minor term, because it is the subject of the
conclusion; the term `men` which occurs in both the premises but is absent
from the conclusion, is the middle term. The first premise `All men are mortal`
is the major premise, because the major term `mortal` occurs in it; the second
premise `All kings are men` is the minor premise, because the minor term
`kings’ occurs in it .
It may be pointed out that when a syllogism is given in strict logical form,
the major premise is given first, and the minor premise comes next, and last of
all comes the conclusion. The symbol M stands for the Middle term, S stands
for the Minor term and P stands for the Major term. The above syllogism can
be represented as,\
All M is P
All S is M
.`. All S is P
General Rules of Categorical Syllogism and the Fallacies.
I. Every syllogism must contain three, and only three terms
and these terms must be used in the same sense throughout.
There are two ways in which this rule is violated. If a syllogism consists of 4
terms instead of three, we commit the fallacy of 4 terms quartenioterminorum e.g.
The book is on the table
The table is on the floor
.`.The book is on the floor
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Here there are four terms, viz., “The book”, “on the table,” “The table” and “on
the floor.” Hence no conclusion can follow.
There is another way in which the above rule can be violated. If any term in a
syllogism is used ambiguously in the two different premises, we commit a
fallacy. If a term is use in two different meanings, it is practically equivalent to
two terms and the syllogism commits the fallacy of equivocation. There are
three forms of equivocation. They are:
1.Fallacy of ambiguous major
2.Fallacy of ambiguous minor
3.Fallacy of ambiguous middle
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1.Fallacy of ambiguous major is a fallacy which occurs when a syllogism
uses its major terms in one sense in the premise and in a different
sense in the conclusion.
e.g., Light is required for taking a photograph.
Feather is not required for taking a photograph
.`. Feather is not light.
‘Light’ in the major premise is used in the sense of ‘physical phenomenon’ ; in
the conclusion it is used in the sense of ‘not heavy’
2.The fallacy of ambiguous minor occurs when in a syllogism the minor
term means one thing in the minor premise and quite another in the
conclusion.
e.g., No boys are part of a book.
All pages are boys.
.`.No pages are part of a book.
In this syllogism, minor term ‘pages’ mean ‘boy servant’ in its premise
and the ‘side of a paper’ in the conclusion. Hence the fallacy of ambiguous
minor.
3.The fallacy of ambiguous middle will be committed by a syllogism if it
uses the middle term in one sense in the major premise and in another
sense in the major premise and in another sense in the minor premise.
e.g.,All criminal actions ought to be punished by law
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prosecutions for theft are criminal actions
.`.. prosecutions for theft ought to be punished by law
The middle term ‘criminal actions’ means ‘crimes’ in the major premise
and an ‘action against a criminal’ in the minor premise. Hence the
syllogism commits the fallacy of ambiguous middle.
II. Every syllogism must contain 3 and only 3 propositions.
Syllogism is a process of reasoning in which a conclusion is drawn from
two given premises. Two propositions are given ad a third one is inferred.
III.The middle term must be distributed at least once in the premises.
The function of a middle term in a syllogism is to serve as the connecting
link between the minor and major terms. In the major premise P is
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compared with M and in the minor premise S is compared with the same
M. thus the relation between S and P is established through the
mediation of M.
The violation of this rule leads to the fallacy of undistributed middle.
e.g., All donkeys are mortal.
All monkeys are mortal.
.`.All monkeys are donkeys.
In this argument the middle term ‘mortal’ is undistributed in both the
premises as the predicate of an affirmative proposition. Hence the fallacy of
undistributed middle occurs.
IV. No term which is undistributed in the premises can be distributed
in the conclusion.
This rule guards us against inferring more in the conclusion than what
is contained in the premises. In any syllogism, the conclusion cannot be more
general than the premises.
The violation of this rule would result in two fallacies illicit major and
illicit minor. The fallacy of illicit major occurs when the major term which is
not disturbed in the major premise is distributed in the conclusion.
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e.g. All men are selfish MAP
No apes are men SEM
.`.No apes are selfish SEP
The major term ‘selfish’ is undistributed in the major premise but
distributed in the conclusion. Hence the fallacy of illicit major.
The fallacy of illicit minor is one which occurs when the minor term is
distributed in the conclusion without being distributed in the minor premise.
e.g.
All thugs are murderers
MAP
All thugs are Indians
MAS
.`.All Indians are murderers
SAP
Here the minor term ‘Indians’ is distributed in the conclusion without
being distributed in the minor premise. So it commits the fallacy of illicit
minor.
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V. From two negative premises, no conclusion is possible.
We cannot draw any conclusion from two negative premises. For, the
major premise being negative, the major term does not agree with M. in the
minor premise also, the minor term has no relation with M. Thus there is no
mediating link between S and P. In the absence of a common link between S
and P, no relation can be established between them.
The violation of this rule commits the fallacy of two negative premises.
e.g. No monkeys are rational
No men are monkeys.
No conclusion is possible
VI. If one premise is negative, the conclusion must be negative and
if the conclusion is negative one premise must be negative.
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If one premise is negative the other premise must be negative. In the
negative premise ‘M’ does not agree with the other term. In the affirmative
premise ‘M’ agrees with the other term. Hence in mediating between the two
terms, ‘M’ can establish only a relation of disagreement between S and P in the
conclusion. In other words the conclusion must be negative.
VII. Two particular premises yield no valid conclusion.
This is proved by examining the four possible combinations of two
particular premises.
I
O
I
O
I
I
O
O
X
X
X
X
VIII. If any one premise is particular the conclusion must be particular.
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MODULE V
Deriving the logical conclusion from two given premises.
Logic deals with the question of validity of arguments. Logic is the science of
the valid forms of reasoning. The study of logic contributes towards forming a
critical habit of mind which has it’s own value. The task of logic is to clarify the
nature of the relationship which holds between premises and conclusion in a
valid argument. To infer means to recognize what is implied in the premises. If
we recognize that the conclusion is implied in the premises , then we can say
that the inference is valid. Every scientist aims to arrive at correct conclusions
on the basis of certain evidence. He has to see that his reasoning is in
accordance with valid argument patterns. Such knowledge is provided by logic.
Logic provides us the tools for the analysis of arguments. Knowledge of logic is
helpful for the formation of critical habit of mind and for detecting fallacies in
thinking.
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By practicing various logical exercises our intellect become sharpened. Logic
cultivates and develops our reasoning power. It trains and disciplines the mind
. Intellectual discipline is of great importance to man.
Deriving valid conclusions from the premises: Examples
1.All systematic knowledge of a particular subject is Science
Logic is a systematic knowledge of a particular subject
.`. ……………………………………….
Answer- Logic is a Science
2All logicians are those who know how to reason well
Some not-good reasoners are logicians
.`. ……………………………………….
Answer-Some not-good reasoners are those who know how to reason well
3.All repeaters are women students
All who have passed are repeaters
.`. ……………………………………….
Answer-All who have passed are women students
4. ,All youths are inexperienced
All students are youths
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.`. ……………………………………….
Answer-All students are inexperienced
5. No lazy men are great
Gopal is lazy
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.`. ……………………………………….
Answer- Gopal is not lazy
6. All successful students are clever
Some mischievous students are successful
.`. ……………………………………….
Answer—Some mischievous students are clever
7. No tale –bearers are reliable
Some men are tale-bearers
.`. ……………………………………….
Answer—Some men are not reliable.
8. All misers are unhappy
X is a miser
.`. ……………………………………….
Answer— X is unhappy
9. All men are mortal
X is a man
.`. ……………………………………….
Answer—X is mortal
10. All wicked people are unhappy
Some people are wicked
.`. ……………………………………….
Answer—Some people are unhappy
11. All statesmen are far-sighted
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All politicians are statesmen
.`. ……………………………………….
Answer –All politicians are far-sighted
12. All statesmen are far-sighted
Some politicians are not far-sighted
.`. ………………………………………
Answer—Some politicians are not statesmen
13. All clever people are enterprising
All publishers are clever
.`. ………………………………………
Answer—All publishers are enterprising
14. No men are angels
Some rational beings are men
.`. ………………………………………
Answer—Some rational beings are not angels
15. All greedy men are discontented
All misers are greedy
.`. ………………………………………
Answer—All misers are discontented
16. All discontented persons are unhappy
All misers are discontented
.`. ………………………………………
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Answer— All misers are unhappy
17. All unhappy men are selfish
All misers are unhappy
.`. ………………………………………
Applications of Logical Reasoning
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School of Distance Education
Answer—All misers are selfish
18. No mortals are perfect
All men are mortal
.`. ………………………………………
Answer —No men are perfect
19. No men are perfect
All politicians are men
.`. ………………………………………
Answer---No politicians are perfect
20. No politicians are perfect
All ministers are politicians
.`. ………………………………………
Answer —No ministers are perfect
21. All men are mortal
Socrates is a man
.`. ………………………………………
Answer —Socrates is mortal
22. All organisms are mortal
All men are organisms
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.`. ………………………………………
Answer —All men are mortal
23.All composite things are mortal
All organisms are composite
.`. ………………………………………
Answer —All organisms are mortal
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Applications of Logical Reasoning
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