3 Logic.pptx

THE THIRD ACT OF THE MIND
REASONING AND SYLLOGISM
 What we get from a judgment, or a proposition.
 In a judgment what we do we connect one idea
with another idea. The connecting entity is called
copula.
 when we say Royston is rational being. (...)
 I affirm one idea (Royston) with another idea
(rational being).
 What is that statement or proposition. I affirm a
truth.

THE THIRD ACT OF THE MIND
REASONING AND SYLLOGISM
 The human mind (we) cannot be satisfied in its
quest for truth.
 It cannot be content (satisfied) with the truths,
which we have already attained. We cannot
satisfy with truth we have already discovered.
 We try to discover new truths.
 We learn many truths by the direct perception of
reality.
 But the truths, which we attain through direct
perception, are commonplace truths.

SEARCHING FOR TRUTH
 Our mind wants to go beyond the boards of
limited truths that are known by the direct
perception of reality.
 The immediate inference is just a small step in
the advancement of knowledge.
 Immediate inference is the method of
concluding from the truth or falsity of one
statement to the truth or falsity of another
statement without the aid of another judgment.

WE ARE IN SEARCH OF TRUTH
 We have seen that in the immediate inference
we can derive some new meaning implied in a
given proposition.
 But we do not have such advancement of
knowledge in the immediate inference.
 The new meaning is just an immediate derivation
of the meaning contained in one single
statement.

WE ARE GOING TO INTRODUCE THE NEW
THING
 It is the third act of the mind, namely, reasoning,
which gives us insights into new truths.
 This process of reasoning is also known as
mediate inference.
 In the immediate inference, we have seen opposites
of propositions: eg. in contradictory If A is true then
O is false.
 But in mediate inference, there is always a
possibility of new truth.

1. NATURE OF REASONING
Reasoning or mediate inference is a
process by which from certain truths already
known, the mind passes to another truth distinct
from these but necessarily following from them.
 When we say that the mind by means of the
reasoning process comes to know truths, it does
not mean that those new truths are entirely
new.
 We know the basic thing by which we arrive at
new known truth.

NEW IS ALWAYS CONNECTED TO THE
PREVIOUS ONE
 The new element in our knowledge is related to
what was known previously.
 The new truth is virtually contained in the known
truths.
 In a reasoning, What becomes actually known in
a conclusion was potentially known in the
statements that produced it.

IN REASONING WE COMPARE TWO
JUDGEMENTS TO ARRIVE A NEW TRUTH
 In the process of Judgment, we compare two ideas
among themselves. We make connection b/w 2 ideas.
 But in reasoning, we compare two judgments in
order to arrive at a new truth.
 We cannot, however, arrive at new truth by the mere
juxtaposition of two disparate truths.
 Juxtaposition = act of placing side by side
(especially in order to compare)
 The judgments must have some logical connection
between them.

NO LOGICAL CONNECTION
 Example
 Water is hot.
 Oxygen is an element.
 From the above two judgments, we cannot arrive at
some new truth because they do not have any logical
connection between them.
 Table has 4 legs
 Cow has 4 legs
 A cow is a table

WE NEED TO HAVE A LOGICL CONNECTION
 Example
 All inorganic substances are minerals.
 Metals are inorganic substances
 Therefore metals are minerals.
 In this example, the first two propositions have a
logical connection between them because the
idea, ‘inorganic substances’ establishes an
identity between minerals and metals. Hence we
can draw a valid conclusion.

CONSISTENCY OF INFERENCE
 From what has been said so far we can understand
what constitutes matter and form of reasoning.
 The MATTER consists of the various ideas and
judgments of the inference.
 The FORM consists of that special arrangement
of ideas and judgments in virtue of which the
conclusion follows with necessary force from the
given ideas and judgments.
 This logical connection between ideas and judgments
is called consequence or consistency of
inference.

4.2. DEDUCTIVE AND INDUCTIVE REASONING
 There are two main types of reasoning:
deduction and induction.
 A deduction is a process of reasoning in which we
conclude from a general law or principle to
particular instances falling under the general law
or principle.
 All men are mortal.
 Peter is a man.
 Therefore Peter is mortal.

INDUCTION
 In induction the reverse process takes place.
 Induction is a process of reasoning in which we
conclude from the individual cases to the
existence of general laws or principles.
 Water, anywhere on land or sea, when at sea
level, freezes in every instance at 0° C.
 Therefore, all water freezes at sea level at 0° C.

WE ANALYSE
 Of course, no attempt has ever been made to
freeze water at every spot on the globe, which is
at sea level;
 but since, whenever and wherever done, water
always froze, it is rightly concluded that freezing
is a property necessarily connected with the
essence of water and has, therefore, the value of a
universal law applicable to all water.

FROM UNIVERSAL TO PARTICULAR
FROM PARTICULAR TO UNIVERSAL
 Thus, in deduction, the mind concludes from the
truth of the universal to the truth of the particulars
whereas in induction from the truth of the
particulars to the truth of the universal.
 We shall treat deductive reasoning in this section
and induction reasoning in the next.

3. TRUTH AND VALIDITY
 We have already made this distinction in the
Introduction.
 By the validity or consistency of reasoning we mean
whether the conclusion necessarily follows from the
given propositions.
 If It follows, the reasoning is valid; otherwise
invalid.
 Logic as such concentrates on the validity of
reasoning.
 It is not directly concerned with the truth of the
propositions that are contained in the reasoning
process.
 But in practice, both the validity of reasoning and the
truth of its contents go hand in hand.

EXAMPLE
 The distinction between validity and truth will be
clear from the following examples:
 No fishes are mammals.
 The whale is a fish.
 Therefore, the whale is not a mammal.
 In this example, the conclusion is not true,
because the statement: “Whale is a fish” is false.
 But the reasoning is consistent because the
conclusion follows strictly from the preceding
propositions.

EXAMPLE
 All fishes are mammals.
 The whale is a fish.
 Therefore, the whale is a mammal.
 Here the conclusion is true.
 But the propositions from which it is derived are false.
 Hence we can state the following rules of mediate
inference regarding the relation between validity and
truth.:
 1. The conclusion, if drawn with consistency from true
judgments must always be true.
 2. The conclusion, if drawn with consistency from false
judgments may be true or false.
ERROR IN THE SYLLOGISM

4. SYLLOGISM
 Syllogism is a valid deductive argumentation
having two premises and a conclusion.
 There are two main types of syllogisms:
Categorical
 and Hypothetical.

4.1. CATEGORICAL SYLLOGISM
A categorical syllogism is a form of
deductive argumentation in which
from two categorical proposition a
third proposition follows with
necessity.
 This is the simpler definition.

ANOTHER DEFINITION
 There is another definition, which gives an
insight into the nature of syllogism more clearly.
A categorical syllogism is an
argumentation, in which two terms,
by virtue of their identity of non-
identity with a common third are
declared to be identical or non-
identical with each other.

LET US CLARIFY WHAT HAPPENS INA
SYLLOGISM
 The propositions from which the conclusion is
deduced are called premises or antecedents.
 The subject of the conclusion is called the
Minor Term (S).
 The predicate of the conclusion is called the
Major Term (P).
 The subject and predicate of the conclusion are
also called extremes.

FURTHER CLARIFICATION
 The third term or the idea with which they are
compared in the premises is called the Middle
Term (M).
 The premise, which contains the major term, is
called the Major premise.
 The premise, which contains the minor term, is
called the minor premise.

IN A SYLLOGISM
 M P
 Major Premise: All men are mortal.
 S M
 Minor Premise: Socrates is a man.
----------------------------------------------------
S P
 Conclusion: Socrates is mortal.
 Extremes

NOTE:
 Although there are only three distinct terms,
each of them appears twice within the syllogism.
 The middle term (M) appears in each of the
premises but never in the conclusion.
 The minor term (S) appears once in the premise
and once in the conclusion.
 The major term (P) likewise appears once in the
premise and once in the conclusion.

4.1.1. FUNDAMENTAL PRINCIPLES OF
SYLLOGISM
 The fundamental principle of syllogistic reasoning
can be stated in two parts as follows:
 FIRST PART
 Two things that are identical with a common third
are identical with each other; and two things of
which one is identical with a common third and the
other non-identical, differ from each other.
 Every organism is endowed with life.
 A cat is an organism.
 Therefore, a cat is endowed with life.

WE ANALYSIS
 In this example the middle term is ‘organism.’
 The term organism is identified in the major
premise with “endowed with life”; in the minor,
it is identified with ‘cat.’
 Having separately identified ‘cat’ and “endowed
with life” with a common third ‘organism,’ we
may now identify them with each other in the
conclusion: “A cat is endowed with life.”

THE SECOND PART OF THE PRINCIPLE MAY BE
ILLUSTRATED AS FOLLOWS:
 No purely material substance is an organism.
 A rock is a purely material substance.
 No rock is an organism.
 Here in the major premise, we state the non-identity
of the major term ‘organism’ with the middle term
“purely material substance.”
 In the minor, we declare the major term ‘rock’ to be
identical with the middle term ‘material substance.’
 Accordingly, in the conclusion, we declare the two
extremes (S and P) ‘rock’ and ‘organism’ to be non-
identical with each other.

4.1.2. SYLLOGISTIC AXIOMS
 The fundamental principle of a syllogism is
expressed in that is called the Dictum de omni et
nullo - the law of All and None.
 Dictum de omni dicitur de singulis.
 Dicturm de nullo negatur de singulis.
 This may be rendered as follows:
 1. Whatever can be affirmed of a logical whole
can be affirmed of its logical parts.
 2. Whatever can be denied of a logical whole
can be denied of its logical parts.

WITH AN EXAMPLE LET US ILLUSTRATE
AXIOM 1:
 Every science is a systematic body of knowledge.
 Physics is science,
 Therefore, Physics is a systematic body of
knowledge.
 In this example the logical whole is ‘science’ and the
logical part is ‘physics.’
 “Systematic body knowledge” is affirmed of the
logical whole ‘science.’
 So it can also be affirmed of its logical part of
‘physics.’

AXIOM 2:
 No man is infallible.
 Peter is a man.
 Therefore, Peter is not infallible.
 Here the logical whole is ‘man’ and the logical
part is ‘Peter.’
 ‘Infallible’ is denied of the logical whole ‘man.’
So it is also denied of its logical part ‘Peter.’

4.1.3. GENERAL RULES OF SYLLOGISM:
 There are eight general rules of syllogism
 1. The syllogism should consist of no more than
three terms.
 2. The middle term must be distributed in at
least one of the premises.
 3. No term, which is not distributed in a premise,
may be distributed in the conclusion (tell the
meaning of it)
 4. No conclusion can be drawn from two negative
premises.

RULES
 5. Two affirmative premises require an
affirmative conclusion.
 6. A negative premise requires a negative
conclusion.
 7. No conclusion can be drawn from two
particular premises.
 8. If one premise is particular, the conclusion
must be particular.

NOTE:
 Rule 1 pertains to the very structure of the
syllogism.
 Rules 2 and 3 pertain to the quantity of the
terms.
 Rules 4, 5 and 6 pertain to the quality of its
propositions.
 Rules 7 and 8 are corollaries or specific
applications of the previous rules as it will be
shown later.

4.1.4. EXPLANATION OF THE RULES
 Rule 1: The syllogism should consist of no more
than three terms.
 This rule is a requirement of the very structure of
the syllogism and hardly requires to be justified.
 To err is human.
 To forgive is divine.
 These two propositions have clearly four terms and
it is easy to find them out.
 But we may have an arrangement of premises in
which there are apparently three terms but actually
four.

ANOTHER SYLLOGISM
 Every egg comes from a hen.
 Every hen comes from an egg.
 Therefore, every egg comes from an egg.
 The conclusion does not follow because there are
actually four terms:
 1. egg,
 2. that which comes from a hen,
 3. hen
 and 4. that which comes from an egg.

THE FALLACY OF RULE I
 The fallacy that violates Rule l is called the
fallacy of four terms.
 It is usually committed in the ambiguous use of
the major term or minor term or the middle term.
 Accordingly, we have the fallacies of the
ambiguous major, ambiguous minor and
ambiguous middle.
 Ambiguous = open to dispute, having many
possible interpretations; obscure, vague

AMBIGUOUS MAJOR
 Light is essential to guide our steps
 Lead is not essential to guide our steps.
 Therefore, lead is not light.
 This involves the fallacy of ambiguous major
because the word ‘light’ in the major premise is
opposed to ‘darkness’ while in the conclusion it is
opposed to ‘heavy.’
 We find an equivocal meaning in it

AMBIGUOUS MINOR
 No man is made of paper
 All pages are men.
 No pages are made of paper
 In this syllogism, the word ‘page’ is used in the
minor premise to mean ‘boy servant’ while in the
conclusion it means ‘pages of a book.’
 So, it involves the fallacy of ambiguous minor.
 We again find an equivocal meaning in it.
‘boy servant’
‘pages of a book.’

AMBIGUOUS MIDDLE
 All cold is dispelled by heat.
 His ailment is cold.
 His ailment is dispelled by heat.
 In this example, there is confusion between a cold
that is an ailment and a cold which is the absence
of heat.
 Hence, there is the fallacy of ambiguous middle.
 We again find an equivocal meaning in it

RULE 2: THE MIDDLE TERM MUST BE
DISTRIBUTED (UNIVERSAL) IN AT LEAST ONE OF
THE PREMISES
 The function of the middle term is to serve as a
common point of reference for uniting or
disuniting S and P in the conclusion.
 If the middle term is undistributed in both the
premises, there is no guarantee that S and P are
referred to the same part of the extension of M.

 Everyone who has pneumonia is sick.
 Everyone who has measles is sick.
 Therefore, whoever has measles has pneumonia.
 In this example, we can see people who are afflicted
with pneumonia and people who are afflicted with
measles, they belong to two different parts of the
extension of those who are sick.
 In order to unite or disunite the two terms of the
conclusion, the middle term must be taken
universally in at least one of the premises.
 The violation of Rule 2 results in the fallacy of the
undistributed middle.

LET US GO BACK TO THE PREVIOUS
SECTION
 Keeping in mind what has been said in the
previous section about the distribution of terms in
each of the four types of propositions (A, E, I and
O) it is useful to gain practice in marking off the
quantity of each term as indicated below.
 The letter ‘u’ signifies universal
 and the letter ‘p’ signifies particular.


REMEMBER THE RULE IN QUANTITY OF
THE PREDICATE TERM
 1. The predicate term of an affirmative
proposition. (A or I) is always to be taken as
particular (undistributed).
 2. The predicate term of a negative proposition (E
or O) is always to be taken as universal
(distributed).

THERE IS A FALLACY IN THIS SYLLOGISM
 Pu Mp
 All men are mortal.
 Su Mp
 All animals are mortal.
 Su Pp
 Therefore, all animals are men.

WE ANALYSE
 The reason why M is marked ‘p’ in both the
premises is simply that it appears in both
premises as the predicate of an affirmative
proposition.
 Therefore, the middle term is not distributed in
any of the premises, the above syllogism commits
the fallacy of undistributed middle.

RULE 3: NO TERM, WHICH IS NOT DISTRIBUTED
IN A PREMISE, MAY BE DISTRIBUTED IN THE
CONCLUSION
 The justification of this rule is quite simple.
 Syllogism being a form of deductive reasoning
(i.e. concluding from the truth of the universal to
the truth of the particulars), the conclusion
cannot be more general than what is given in the
premises.
 What is true of a term in respect of part only of its
extension need not be true of the rest.
 Thus, if either of the terms S or P is particular in a
premise, it must remain particular in the
conclusion.

RULE 3 CONTINUES
 To make such a term universal in the conclusion
would be equivalent to inserting more in a
conclusion than the premises themselves warrant.
 The violation takes the form of the overextension
of S or P in the conclusion.
 These forms are respectively designated as the
fallacy of the illicit minor
 and the fallacy of the illicit major.

THE FALLACY OF ILLICIT MINOR
 Mu Pp
 All metals conduct heat and electricity.
 Mu Sp
 All metals are elements.
 Su Pp
 Therefore, all elements conduct heat and
electricity.
Overextension
of Suject term
in the
conclusion

ANOTHER EXAMPLE
 Mu Pp
 All Germans are industrious.
 Mu Sp
 Some Germans are Jews.
 Su Pp
 Therefore, all Jews are industrious.
Overextension
of subjet term in
the conclusion

THE FALLACY OF ILLICIT MAJOR:
 Mu Pp
 All fishes are cold-blooded.
 Su Mu
 No whales are fishes.
 Su Pu
 Therefore, no whales are cold-blooded.
Overextension
of Mejor term in
the conclusion

EXAMPLE
 Mu Pp
 All men are animals.
 Su Mu
 No brutes are men.
 Su Pu
 Therefore, No brutes are animals.
Overextension of
the predicate term
in the conclusion

RULE 4: NO CONCLUSION CAN BE DRAWN
FROM TWO NEGATIVE PREMISES
 When both premises are negative, it means that
the major term and the minor term are both
excluded from the extension of the intended
middle term.
 So no comparison between the minor and major
terms is possible.
 We cannot say whether they are related or not.

EXAMPLE
 Horses have no horns.
 Camels have no horns.
 Nothing follows from these two negative
premises.

ANOTHER EXAMPLE
 Sometimes there are apparently negative
premises, which give a valid conclusion.
 Actually one or both are affirmative.
 “Whatever is not compound” is an element.
 Gold is “not compound.”
 Therefore, gold is an element.

EXAMPLE
 The negative particle ‘not’ belongs to the middle
term and not to the copula.
 The syllogism may be rewritten as follows:
 All non-compounds are elements.
 Gold is a non-compound.
 Therefore, gold is an element.

RULE 5: TWO AFFIRMATIVE PREMISES
REQUIRE AN AFFIRMATIVE CONCLUSION.
 When both premises are affirmative, both the
major and the minor terms arc identified with the
middle term.
 That can give no ground for asserting that the
minor term is non-identical with the major
term.
 In other words, the conclusion cannot be
negative, but affirmative.

EXAMPLE
Milk is healthful for children.
Some dairy product is milk.
Therefore, some dairy product is
healthful for children.

RULE 6: A NEGATIVE PREMISE REQUIRES A
NEGATIVE CONCLUSION.
 When one of the premises is affirmative and the
other negative, then one of the extremes major or
minor terms, (S and P) agrees with the middle
term (M) and the other disagrees with the middle
term (M).
 But this implies that the major and minor terms
(S and P) disagree among themselves.

EXAMPLE
 Hence, the conclusion must also state that the
major and minor terms disagree and thus the
conclusion must be negative.
 No good soldiers are good statesmen.
 The Germans are good soldiers.
 Therefore, the Germans are not good
statesmen.
 Rules 7 and 8 are not strictly rules, but corollaries
of the rules stated already. a direct consequence
or result

RULE 7: NO CONCLUSION CAN BE DRAWN
FROM TWO PARTICULAR PREMISES
 Any combination of two particular premises
automatically involves a violation of either Rule
2 or Rule 3. Let us examine why this is so.
A combination of two I propositions:
 Suppose we were to employ two I propositions as
our major and minor premises, we would have a
premise arrangement in which all the terms
would be particular (undistributed).

E.G. SOME FLOWERS ARE WHITE.
 In this proposition, a part of the extension of the
predicate (white things) is affirmed of the subject.
Hence the predicate is undistributed.
 Regardless, then, of where the M term appears in
either of these premises, it would be particular in
both of them. Hence we have the fallacy of the
undistributed middle.
 This means a violation of rule 2.

A COMBINATION OF AN I AND AN O
PROPOSITION
 With this combination of premises, we would have
only one universal term, namely, the predicate of
the O proposition.
 In order to avoid an undistributed middle, it is
necessary to reserve the predicate of the O
proposition for the placement of the M term.
 Next, the conclusion must be negative because one
of the premises (the O proposition) is negative
(Rule 6) and the predicate of the conclusion would
be universal.

IF WE TRY TO MAKE A COMBINATION, IT WILL
END IN FALLACY
 Yet the only universal term we had in our premises
has already been used for the placement of M.
 This means that the P term, whether it appears as
subject or predicate of the major premise, will be
particular.
 Hence it results in the fallacy of illicit major.
 Any attempt, then, to conclude from an I and an O
combination would result in the fallacy of either the
undistributed middle or the illicit major.

RULE 8: IF ONE OF THE PREMISES IS PARTICULAR,
THE CONCLUSION MUST BE PARTICULAR
A combination of two affirmative
premises
 With this combination, if one premise is universal
(an A proposition) and the other particular (an I
proposition), we have only one universal term,
namely, the subject of the universal premise (the
A proposition).
 To avoid the undistributed middle we must use
the subject of the A proposition for the placement
of M.

8TH RULE
 Since the remaining terms are particular, the S
term too is particular (in the minor premise).
 In order to avoid an illicit minor, we must keep it
particular as a subject of the conclusion.
 The conclusion itself, therefore, will be a
particular proposition (I).

A COMBINATION IN WHICH ONE PREMISE
IS AFFIRMATIVE AND THE OTHER
NEGATIVE
 If one premise of this combination is universal
and the other is particular (both cannot be
particular), these possibilities arise an E and an I
combination, and an A and an O combination.
 In either of these combinations, we have two
universal terms: the subject of the universal
premise and the predicate of the one that is
negative.
 One of these terms must be used for the
placement of M to avoid an undistributed middle.

8TH RULE
 Moreover, since one of the premises is negative,
the conclusion will be negative, and the predicate of
the conclusion universal.
 To avoid an illicit major the remaining universal
term must distribute the P term in the major premise.
 The S term, then, as one of the remaining particulars,
must be kept particular in the conclusion; otherwise,
we would have an illicit minor.
 To avoid an illicit minor the conclusion itself must
be particular (an O proposition).

4.1.5. FIGURES OF SYLLOGISM
 Depending on the varying position of the middle
term, a syllogism may assume different forms
within its structure, which are called figures.
 Hence by the figure of a syllogism we mean the
form of a syllogism as determined by the
position of the middle term in the premises.
 The middle term can be the subject of both
premises, predicate of both premises, subject of
the major and predicate of the minor, or
predicate of the major and subject of the
minor.

FIGURES OF SYLLOGISM
 When the General Rules of syllogism are applied
to the peculiarities of each Figure, we get a new
set of rules, which are called the Special Rules.

4.1.5.1. SPECIAL RULES OF THE FIRST
FIGURE
 1. The minor premise must be affirmative.
 2. The major premise must be universal.
 Proofs: Suppose (if) the minor premise to be
affirmative; then the major premise would be
affirmative (G.R. 5) and its predicate undistributed
and the conclusion would be negative (G.R. 6).
 But in the first figure, the predicate of the conclusion
is the predicate of the major premise.
 The supposition of a negative minor premise thus
results in the fallacy of illicit major. (over extension
of major term)
 Therefore the minor premise must be affirmative.

NOTE:
 The second rule is proved from the first, because the
minor premise must be affirmative.
 If in minor premise its predicate, the middle term is
undistributed, then the middle term must be
distributed in the major premise (G.R. 2).
 It is the subject of the major premise, which is
therefore universal.
 Note: In the first figure both extremes occupy the
same position, respectively, in the premise and the
conclusion. This accounts for the special clearness
of the first figure syllogisms.

4.1.5.2. SPECIAL RULES OF THE SECOND
FIGURE
 1. One of the premises must be negative.
 Proofs: The middle term is the predicate of both
premises, and if both were affirmative, the middle
term would be undistributed in both, which
violates G.R. 2.
 The second rule is proved from the first. Since
one of the premises is negative, the conclusion
must be negative (G.R. 6) and its predicate
distributed.

SPECIAL RULES 2 FIGURE
 The predicate of the conclusion is the subject
of the major premise, which is therefore
universal.
 Note: In the second figure the minor term
occupies the same position in premise and
conclusion, and the major term occupies a
different position in premise and conclusion.

4.1.5.3. SPECIAL RULES OF THE THIRD
FIGURE
 2. The conclusion must be particular.
 Proofs: The proof of the first rule is the same as the proof
of the first rule of the first figure.
 The second rule follows from the first. Since the minor
premise is affirmative, its predicate is undistributed; its
predicate is subject of the conclusion, which is therefore
particular.
 Note: In the third figure the major term occupies the same
position in premise and conclusion; the minor term
occupies a different position in premise and conclusion.

4.1.5.4. SPECIAL RULES OF THE FOURTH
FIGURE
 1. If the major premise is affirmative, the
minor premise is universal.
 2. If the minor premise is affirmative, the
conclusion is particular.
 3. If a premise is negative, the major premise is
universal.

SPECIAL RULE 4 FIGURE
 Proofs: 1. If the major premise is affirmative, its
predicate, the middle term, is undistributed.
 The middle term is the minor premise must therefore
be distributed (G.R. 2).
 It is the subject of the minor premise, which must
therefore be universal.
 Proofs: 2. If the minor premise is affirmative, its
predicate, the minor term, is undistributed and is
therefore undistributed in the conclusion (G.R.3),
which is therefore particular.

SPECIAL RULE 4 FIGURE
 Proofs: 3. If one premise is negative, the
conclusion is negative (G.R.6) and its predicate
distributed.
 The major term must therefore be distributed in
its premise (G.R. 3), where it is subject. The
major premise must therefore be universal.
 Note: In the fourth figure both extremes occupy
different positions, respectively, in premise and
conclusion.

ALL FIGURES
 1. Special Rules of the First figure
 2. Special Rules of the Second Figure
 1. One of the premises must be negative.
 3. Special Rules of the Third Figure
 2. The conclusion must be particular.
 4. Special Rules of the Fourth Figure
 1. If the major premise is affirmative, the minor premise is
universal.
 2. If the minor premise is affirmative, the conclusion is partic
 3. If a premise is negative, the major premise is universal.

4.1.6. MOODS OF THE SYLLOGISM
 The mood of a syllogism is the respective
designation of the premises and conclusion as A,
E, I or O propositions.
 for instance, If we use the letters AEI, it indicates
that the first proposition is A, the second E and the
conclusion I.
 If we simply use AI, we indicate the major and minor
premises without considering the conclusion.
 Theoretically, with respect to only the major and
minor premises, there are sixteen 16 possible
moods.

16 MOODS
 AA
 AE
 AI
 AO
 EA
 EE*
 EI*
 EO*
 IA
 IE*
 II*
 IO*
 OA
 OE
 OE*
 OO*

POSSIBLE PAIRS
 The Moods that are marked by an asterisk (*) are
invalid because they stand for either two negative
premises (G.R. 4) or two particular premises
(G.R. 7).
* = invalid
 In addition, IE is excluded by G.R. 3; for the major
term is distributed in the negative conclusion, but is
undistributed in the I premise.
 The remaining eight possible pairs, namely, AA, AE,
AI, AO, EA, EI, IA, OA must now be tried in each
figure.

VALID MOODS OF THE FIRST FIGURE
 AE and AO are excluded by the first Special
Rule and IA and OA by the second special rule.
 It leaves AA, AI, EA, and EI as possible pairs of
premises in the First figure.
 Now, AA and AI require an affirmative
conclusion,
 EA and EI require a negative conclusion
 and AI and EI require a particular conclusions.

VALID MOODS
 The possible moods thus are AAA, (AAI), AII, EAE
(EAO) and EIO.
 Where it is legitimate to draw the conclusions A and
E, it is also legitimate to draw the conclusions I and
O, respectively; and therefore the moods AAA and
EAE in an ordinary way render the moods AAI and
EAO unnecessary; the latter pair are as ‘weakened
moods’ or ‘subaltern moods’; and are not included
in the list.
 The valid moods left then are AAA, EAE, AII and
EIO.

VALID MOODS OF THE SECOND FIGURE
 AA, AI and IA are excluded by the first Special
Rule and IA and OA excluded by the second
Special Rule.
 That leaves EA, AE, EI and AO, as possible
pairs of premises, these could yield six moods;
but as before, disregarding the ‘weakened
moods,’
 we are left with four valid moods, EAE, AEE,
EIO, and AOO.

VALID MOODS OF THE THIRD FIGURE
 AE and AO are excluded by the first Special
Rule.
 That leaves AA, IA, AI, EA, OA and EI as
possible pairs of premises;
 these yield six valid moods, viz (i.e.).
 AAI, IAI, AII, EAO, OAO, and EIO.

VALID MOODS OF THE FOURTH FIGURE
 AI and AO are excluded by the first Special
Rule, and OA by the third Special Rule.
 That leaves AA. AE, EA, EI, IA as possible
pairs of premises; these could yield six valid
moods, but disregarding the ‘weakened mood’
AEO,
 we are left with five, viz. AAI, AEE, IAI, EAO,
and EIO.

MNEMONIC VERSES
 The medieval philosophers invented some
Mnemonic verses as a key to the valid moods of
different figures.
 Mnemonic = designed to assist the memory
 Each word indicates the figure and mood of the
syllogism and its vowels indicate the quantity
and quality of the component propositions.

FIGURE I - BARBARA, CELARENT,
DARII, FERIO
FIGURE I
 Barbara - AAA
 Celarent - EAE
 Darii - AII
 Ferio - EIO

FIGURE II CESARE, CAMESTRES,
FESTINO, BAROCO
FIGURE II
Cesare - EAE
Camestres - AEE
Festino - EIO
Baroco - AOO

FIGURE III DARAPTI, DISAMIS, DATISI,
FELAPTON, BOCARDO, FERISON
FIGURE III
Darapti - AAI
Disamis - IAI
Datisi - AII
Felapton - EAO
Bocardo - OAO
Ferison -EIO

FIGURE IV BRAMANTIP, CAMENENS,
DIMARIS, FESAPO, FRESISON
FIGURE IV
Bramantip - AAI
Camenens - AEE
Dimaris - IAI
Fesapo - EAO
Fresison-EIO

MNEMONIC VERSES OF ALL FIGURES
 Figure I - Barbara, Celarent, Darii, Ferio
 Figure II Cesare, Camestres, Festino,
Baroco
 Figure III Darapti, Disamis, Datisi,
Felapton, Bocardo, Ferison
 Figure IV Bramantip, Camenens, Dimaris,
Fesapo, Fresison

FIGURE I
 M P
 S M
 S P
1. Barbara AAA
A All M is P All men are mortal.
A All S is M All kings are men.
A All S is P All kings are mortal.
2. Celarent EAE
E No M is P No man is perfect.
A All S is M All politicians are men.
E No S is P No politician is perfect.

FIGURE I
 M P
 S M
 S P
3. Darii AII
A All M is P All educated men are tolerant opposition.
I Some S is M Some impulsive men are educated.
I Some S is P Some impulsive men are tolerant
opposition.
4. Ferio EIO
E No M is P No wise man is imprudent.
I Some S is M Some Indians are wise men.
O Some S is not P Some Indians are not imprudent.

FIGURE II
 P M
 S M
 S P
1. Cesare EAE
E No P is M No fish have lungs.
A All S is M All whales have lungs.
E No S is P No whale is fish.
2. Camestres AEE
A All P is M All honest persons are trustworthy.
E No S is M No liars are trustworthy.
E No S is P No liars are honest.

FIGURE II
P M
S M
S P
3. Festino EIO
E No P is M No good Christian hates his neighbour.
I Some S is M Some men hate their neighbour.
O Some S is not P Some men are not good Christians.
4. Baroco AOO
A All P is M All scientists are learned.
O Some S is not M Some men are not learned.
O Some S is not P Some men are not scientists.

FIGURE III
M P
M S
S P
1. Darapti AAI
A All M is P All brutes are animals.
A All M is S All brutes are mortal.
I Some S is P Some mortal beings are
animals.
2. Disamis IAI
I Some M is P Some flowers are roses.
A All M is S All flowers are beautiful.
I Some S is P Some beautiful things are roses.

FIGURE III
M P
M S
S P
3. Datisi AII
A All M is P All evildoers will be punished.
I Some M is S Some evildoers are robbers.
I Some S is P Some robbers will be punished.
4. Felapton EAO
E No M is P No misers are spendthrifts.
A All M is S All misers abuse wealth.
O Some S is not P Some who abuse wealth are not
spendthrifts.

FIGURE III
M P
M S
S P
5. Bocardo OAO
O Some M is not P Some men are not philosophers.
A All M is S All men are rational.
O Some S is not P Some rational beings are not
philosophers.
6. Ferison EIO
E No M is P No aggressive war is justifiable.
I Some M is S Some aggressive wars are successful.
O Some S is not P Some successful things are not
justifiable.

FIGURE IV
P M
M S
S P
1. Bramantip AAI
A All P is M All murders are crimes.
A All M is S All crimes are detestable.
I Some S is P Something detestable is murder.
2. Camenes AEE
A All P is M All animals are sentient beings.
E No M is S No sentient beings are lifeless.
E No S is P No lifeless beings are animals.

FIGURE IV
3. Dimaris IAI
I Some P is M Some organisms are animals.
A All M is S All animals are living beings.
I Some S is P Some living beings are organisms.
4. Fesapo EAO
E No P is M No plants are sentient beings.
A All M is S All sentient beings are living beings.
O Some S is not P Some living beings are not plants.
5. Fresison EIO
E No P is M No inorganic bodies are living beings.
I Some M is S Some living beings are sentient beings.
O Some S is not P Some sentient beings are not inorganic
bodies.

EASY TO REMEMBER
 Not the positions of Middle term in each figure
 Figure I
 Figure II
 Figure III
 Figure IV

4.1.7. REDUCTION
 Many syllogisms can be transposed from one
figure into another.
 This process is known as reduction.
 Taken in a wide sense, it means the transposition
of the moods or any figure into the moods of any
other figure.
 But it is used in a restricted sense to mean the
transposition of the moods from other figures
into the first.

DEFINITION
The reduction is the process of
expressing the reasoning of a
syllogism in the second, third
and fourth figures into moods
of the FIRST FIGURE.

SECOND, THIRD AND FOURTH FIGURES
INTO MOODS OF THE FIRST FIGURE
 .

ARISTOTLE
 He assigned a privileged position to the first figure.
 He called the first figure as the perfect syllogism.
 Why? Because it is dictum de omni et nullo or the
law of All and None.
 The basic formula of the syllogism is directly
applicable to the first figure.
 In the first figure, the mind passes spontaneously
from one idea to another and its arguments are clear
to follow and easy to accept.

REDUCTION FROM IMPERFECT FIGURES TO
PERFECT FIGURE
 The dictum de omni et nullo is not directly
applicable to the moods of the other figures,
which accordingly are called ‘imperfect’ figures.
 If the moods of the imperfect figures can be
reduced to the moods of the perfect figure, the
fundamental principle can be directly applied to
them.
 That is why Aristotle gave great importance to
reduction.
 Modern Logicians say that Aristotle claimed too
much for reduction.

REDUCEND AND REDUCT
 Though reduction to the first figure remains
important, we cannot admit any positive
imperfection in other figures, because they have
their own independent movement of thought.
 The given figure in the second, third and fourth
is called the Reducend.
 The syllogism in the first figure to which it is
reduced is called the Reduct.

TWO KINDS
 Reduction is of two kinds: Direct and Indirect.
 In Direct Reduction the reducends of most
moods are transposed into their reducts by means
of conversion and interchanging of the
premises.
 Indirect reduction consists in proving, with the
help of the first figure, which the
contradictories of the conclusion of the
reducends are false and hence the conclusions are
true.

EXCEPTION FOR BAROCO AND BOCARDO
 All reducends except Baroco and Bocardo are
reduced directly.
 BAROCO and BOCARDO are customarily
reduced indirectly, though they can be reduced
directly as shown below.
 With the help of the Mnemonic verses, a direct
reduction can be effected with mechanical ease.
 But it will arrive in an invalid conclusion

INITIAL CONSONANT
 We have already seen that each word indicates the
mood and figure of the syllogism and the vowels
indicate the quality and quantity of the
propositions.
 Besides this, most consonants also have meaning.
 The initial consonant of the reducend and reduct is
the same.
 Thus Festino reduce to Ferio and Darapti to Darii.
 Excluding the consonants like l, n, r and t, which
have no significance,

THE FOLLOWING IS THE MEANING OF
OTHERS
c - indirect reduction per contradictionem
m - methathesis, i.e., interchange of premises.
p - per accidens conversion of the preceding
proposition.
s - simple conversion of the preceding
proposition.
 preceding = go before, come before.

NOTE THE RELATIONS
F2 Cesare
F2 Camestres Celarent F1
F4 Camenens
Direct relation

NOTE THE RELATIONS
F3 Darapti
F3 Disamis Darii F1
F3 Datisi
F4 Dimaris
Direct relation

NOTE THE RELATIONS
F2 Festino
F3 Felapton
F3 Ferison Ferio F1
F4 Fesapo
F4 Fresison
Direct relation

NOTE THE RELATIONS
Direct relation
F4 Bramantip Barbara F1
Indirect relation
F2 Baroco Barbara F1
F3 Bocardo

INDIRECT REDUCTION OF BOCARDO AND
BAROCO
 The indirect reduction of Bocardo and Baroco is
quite complicated.
 It is effected as follows:
 Substitute for the O premise the contradictory of the
conclusion.
 That yields a valid Barbara syllogism with a
conclusion that contradicts an original premise given
true and which is therefore false.
 The new Barbara syllogism is valid, but has a false
conclusion; that can only be because one of its
premises is false.

REDUCTIO AD ABSURUDUM
 One of its premises is given true; the other must be
false, namely, the contradictory of the original
conclusion.
 Thus by a syllogism in the first figure the
contradictory of the original conclusion has been
proved false, that is, the original conclusion has
been proved true.
 This method is called Reductio ad absurudum
(reduction to absurdity) because it begins with the
supposition that the contradictory of the given
conclusion is true but ultimately such a supposition
is found to be absurd and false.

REDUCTIO PER IMPOSSIBLE
 It is also called Reductio per impossible
(Reduction to impossibility).
 Keeping in mind what has been said about the
method of direct and indirect reduction, we can
now apply it to the moods of the second, third
and fourth figures and reduce them to the first.

WHAT FIGURE IS IT? WHAT MOOD IS IT?
No fish have lungs.
All whales have lungs.
No whale is fish.
EAE
Figure II Cesare, Camestres,
Festino, Baroco;

MOODS OF THE SECOND FIGURE
Cesare
No P is M
All S is M
No S is P
s
Celarent
No M is P
All S is M
No S is P

All honest persons are
trustworthy.
No liars are trustworthy.
No liars are honest.
 AEE
Baroco;

CAMESTRES CELARENT
Camestres
 All P is M
 No S is M
 No S is P
m
 No S is M
 All P is M
s
 Celarent
 No M is S
 All P is M
 No P is S
s
 No S is P

No good Christian hates his neighbour.
Some men hate their neighbour.
Some men are not good Christians.
 E No P is M
 I Some S is M
 O Some S is not P
Baroco;

FESTINO FERIO
 Festino
 No P is M
 Some S is M
 Some S is not P
s
 Ferio
 No M is P
 Some S is M
 Some S is not P

All scientists are learned.
Some men are not learned.
Some men are not scientists.
 A All P is M
 O Some S is not M

BAROCO BARBARA
 Baroco
 All P is M
 Some S is not M
 Some S is not P
 Suppose, some S is not P is false. Then All S is P, its
contradictory is true.
 Substituting it (contradictory of conclusion) for the
O premise, we reach the syllogism in Barbara
(with P as a middle term)

BARBARA
 All P is M
 All S is P
 All S is M
 This conclusion, All S is M contradicts the O
premise, which is given true.
 Therefore All S is M is false.
 It has been reached however by a valid syllogism.

? HOW CAN IT BE FALSE?
 Because one premise, All P is M is given true, the
other premise, All S is P is supposed true.
 This premise must therefore be false.
 Since it is false that All S is P, its contradictory,
Some S is not P must be true.

 Darapti
 All M is P
 All M is S
 Some S is P
p
 Darii
 All M is P
 Some S is M
 Some S is P
Moods of the Third Figure

DISAMIS DARII
 Disamis
 Some M is P
 All M is S
 Some S is P
s

 Darii
 Some P is M
 All M is S
m
 All M is S
 Some P is M
 Some P is S
s
 Some S is P

DATISI DARII
 Datisi
 All M is P
 Some M is S
 Some S is P
s
 Darii
 All M is P
 Some S is M
 Some S is P

FELAPTON FERIO
 Felapton
 No M is P
 All M is S
 Some S is not P
p
 Ferio
 No M is P
 Some S is M
 Some S is not P

BOCARDO BARBARA
 Some men are not philosophers.
 All men are rational.
 Some rational beings are not philosophers.
 O Some M is not P
 A All M is S

BOCARDO BARBARA
 Bocardo
 Some M is not P
 All M is S
 Some S is not P
 Suppose the conclusion is false, then its
contradictory: All S is P, must be true.
 Substituting it for the O premise, we reach the
syllogism in Barbara with S as the middle term.

BARBARA
 All S is P
 All M is S
 All M is P
 This conclusion, All M is P, contradicts the O
premise, which is given true.
 It is therefore false. It has been reached, however,
by a valid syllogism.

HOW CAN IT BE FALSE?
 Because, while one premise, All M is S, is given
true, the other premise, All S is P, is only
supposed true.
 It must, therefore, be false.
 Since it is false that All S is P, its contradictory.
Some S is not P, is true.

FERISON FERIO
 Ferison
 No M is P
 Some M is S
 Some S is not P
s
 Ferio
 No M is P
 Some S is M
 Some S is not P

All murders are crimes.
All crimes are detestable.
Some thing detestable is murder.

Mood of the Fourth Figure
 Bramantip
 All P is M
 All M is S
 Some S is P
m
 Barbara
 All M is S
 All P is M
 All P is S
p
 Some S is P

All animals are sentient beings.
No sentient beings are lifeless.
No lifeless beings are animals.

CAMENES CELARENT
 Camenes
 All P is M
 No M is S
 No S is P
m
 Celarent
 No M is S
 All P is M
 No P is S
s
 No S is P

DIMARIS DARII
Dimaris
 Some P is M
 All M is S
 Some S is P
m
Darii
 All M is S
 Some P is M
 Some P is S
s
 Some S is P

FESAPO FERIO
 Fesapo
 No P is M
 All M is S
 Some S is not P
s
p
 Ferio
 No M is P
 Some S is M
 Some S is not P

FRESISON FERIO
 Fresison
 No P is M
 Some M is S
 Some S is not P
s
s
 Ferio
 No M is P
 Some S is M
 Some S is not P

NOTE:
 Though Baroco and Bocardo are usually reduced
indirectly, it is possible, however, to reduce them
directly to Ferio and Darii, respectively, as
follows:
 But rules are not strict
 They are flexible
 If we reduce into Barbara we will not get a valid
conclusion.

BAROCO FERIO
 Baroco
 All P is M
 Some S is not M
 Some S is not P
 Contrapose
 Obvert
 Ferio
 No not-M is P
 Some S is not-M
 Some S is not P

BOCARDO DARII
 Bocardo
 Some M is not P
 All M is S
 Some S is not P
Contrapose  Some not-P is M
 All M is S m
 Darii
 All M is S
 Some not-P is M
 Some not-P is S
Contrapose
 Some S is notP

4.2. HYPOTHETICAL SYLLOGISM
 Hypothetical propositions express the dependence
of one judgment on another.
 The truth of a hypothetical statement consists in
the truth of the dependence of one judgment on
the other.
 In the hypothetical syllogism one premise, usually
called the major, is a hypothetical proposition and
the other premise usually called the minor and the
conclusion are categorical propositions.
 Accordingly, there are three types of hypothetical
syllogisms: CONDITIONAL,
DISJUNCTIVE and CONJUNCTIVE.

4.2.1. CONDITIONAL SYLLOGISM
 Conditional propositions are if statements.
 Such propositions consist of two parts: the antecedent,
which expresses the condition that is introduced by the
particle ‘if’ and the consequent, which expresses the
result of the fulfilment of the condition.
 When both premises and the conclusion are ‘if’ statements,
the syllogism is called a pure conditional syllogism.
 If a man is of regular habits, he will be happy.
 If a man is happy, he will live long.
 If a man is of regular habits, he will live long.

MIXED CONDITIONAL SYLLOGISM
 A syllogism, in which the major premise is
conditional and the minor and conclusion are
categorical propositions, is called a mixed
conditional syllogism.
 If a man has free will, he is responsible for his
actions
 Man has free will.
 Therefore, he is responsible for his actions.
 Since the pure conditional syllogisms are rare, by a
conditional syllogism we usually mean a syllogism
in which the major premise is a conditional
proposition and the minor and conclusion are
categorical propositions

4.2.1.1. VALID MOODS OF CONDITIONAL
SYLLOGISM
 A conditional syllogism has two valid moods or
two possible ways of drawing a valid
conclusion.
 They are known as
 the modus ponens or constructive mood
 and modus tollens or destructive mood.

MODUS PONENS AND MODUS TOLLENS
 In the modus ponens, the minor premise posits or
affirms the antecedent and the conclusion posits
or affirms the consequent.
 It is called modus ponens because it lays down a
truth.
 In the modus tollens, the minor premise sublates
or denies the consequent and the conclusion
sublates or denies the antecedent.
 It is called modus tollens because it removes
(tollere) an error.

MODUS PONENS
 1. Minor posits antecedent
 2 Conclusion posits consequent
 If he has cancer of the stomach, he is seriously ill.
 He has cancer of the stomach.
 Therefore, he is seriously ill.
 It should be noted that the quality of the
enunciations of the conditional major has no
reference to the mood of the syllogism. i.e.
 To posit an antecedent means to take it over as it is
given: if the antecedent is affirmative, it is kept
affirmative; if it is negative, it is kept negative.
 Hence, the syllogism in the modus ponens takes one
of the four following forms.

FIRST TWO FORMS
1. Both antecedent and consequent affirmative
If A is B, then A is C. If a man takes poison, he will die.
A is B. This man has taken poison.
Therefore, A is C. Therefore he will die.
2. Negative antecedent, affirmative consequent
If A is not B, A is C. If the child is not sick, it will play.
A is not B. It is not sick.
Therefore, A is C. Therefore, it will play.

SECOND TWO FORMS
3. Affirmative antecedent, negative consequent
If A is B, then C is not D. If it rains, he will not come.
A is B. It rains.
Therefore, C is not D. Therefore, he will not come.
4. Both antecedent and consequent negative
 If A is not B, C is not D. If it does not rain, the corn
will not grow.
 A is not B. It does not rain.
 Therefore, C is not D. Therefore, the corn will not
grow.

FALLACY OF AFFIRMNG THE CONSEQUENT.
 If we affirm the consequent in the minor premise
instead of the antecedent, we commit the fallacy
of affirming the consequent.
 If he has cancer of the stomach, he is seriously ill.
 He is seriously ill. affirming the consequent
 Therefore, he has cancer of the stomach.
 This syllogism is invalid because it commits the
fallacy of affirming the consequent.
 We may ask why our reasoning is inconsistent if
we affirm the consequent.

THE REASON WILL BE CLEAR IF WE
EXAMINE THE FOLLOWING EXAMPLE
 Let us take the enunciation, “He is seriously ill.”
 We can suppose a number of conditions that may
guarantee its fulfilment:
 If he has typhoid fever,
 If he has acute appendicitis,
 If he has advanced tuberculosis He is seriously ill.
 If he has cholera,
 If he has a fractured skull,
 If he has cancer of the stomach,

EXPLANATION
 If we posit any one of the above antecedents, we
are correct in positing also the consequent, “He is
seriously ill.”
 In this case, we cannot infer conversely the
fulfilment of any of the specific antecedents
above, for the simple reason that the mere
positing of the consequent leaves indefinite the
question as to which of the antecedents has been
fulfilled.

MODUS TOLLENS
 1. Minor sublates or denies consequent
 2. Conclusion sublates or denies antecedent
 If you work hard, you will be tired.
 You are not tired.
 Therefore, you did not work hard.
 The consequent “you will be tired” is sublated in
the minor premise, and the antecedent “you work
hard” is sublated in the conclusion.

EXPLANATION
 To sublate means to establish the contradictory of an
enunciation.
 To sublate an affirmative is to make it negative; to
sublate a negative enunciation is to make it
affirmative.
 In sublating an enunciation, care must be taken not to
establish the contrary.
 If no men were mad, lunatic asylums would be
superfluous (excessive).
 Lunatic asylums are not superfluous.
 Therefore, some men are mad.
 We cannot say in conclusion that “all men are
mad,” because it is not contradictory but the
contrary of the enunciation “no men are mad.”

FIRST TWO FORMS
 Just as the syllogisms in the modus ponens, the
syllogisms in the modus tollens may assume one of the
following 4 forms:
1. Both antecedent and consequent affirmative
 If A is B, then A is C. If I oversleep, I shall be late for
class.
 A is not C. I am not late for class.
 A is not B. Therefore, I did not
oversleep.
2. Negative antecedent, affirmative consequent
 If A is not B, then C is D. If the cat is not at home,
the mice will play.
 C is not D. The mice do not play.
 Therefore A is B. Therefore, the cat is at

SECOND TWO FORMS
3. Affirmative antecedent, negative consequent
 If A is B, then A is not C. If you are virtuous, you
will not unhappy.
 A is C. You are unhappy.
 Therefore, A is not B. Therefore, you are not virtuous.
4. Both antecedent and consequent negative
 If A is not B, A is not C. If you do not study, you
will not pass.
 A is C. You have passed.
 Therefore, A is B. Therefore, you studied.

FALLACY OF DENYING THE ANTECEDENT
 No valid conclusion can be drawn by sublating the
antecedent.
 It results in the fallacy of denying the antecedent.
 If he has cancer of the stomach, he is seriously ill.
 He has not cancer of the stomach.
 Therefore, he is not seriously ill.
 The argument is inconsistent because it commits the
fallacy of denying the antecedent.
 The reason for the inconsistency is obvious.
 If “he has no cancer of the stomach,” there are still
other dangerous diseases, which can make him
seriously ill.

NOTE
 Summing up, we may state the law of the conditional
syllogism as follows:
 From the truth of the antecedent follows the truth
of the consequent, but from the falsity of the
antecedent, the falsity of the consequent does not
follow.
 From the falsity of the consequent follows the
falsity of antecedent, but from the truth of
consequent, the truth of antecedent does not follow.

4.2.2. DISJUNCTIVE SYLLOGISM
 Disjunctive syllogism is one, which employs a disjunctive
proposition as major premise and categorical propositions
as minor premise and conclusion.
 Dealing with the disjunctive propositions we have seen that
there are two types of disjunctives: proper and improper.
 In a proper disjunctive the alternatives given are mutually
exclusive.
 E.g. The accused is either sane or insane
 Here ‘sane’ and ‘insane’ are mutually exclusive.
 In an improper disjunctive, the alternatives are not mutually
exclusive.
 E.g. This student is either intelligent or industrious.
 In this proposition, the alternatives ‘intelligent’ and
‘industrious’ are not mutually exclusive.
 A student can be both intelligent and industrious.

4.2.2.1. PROPER DISJUNCTIVE
 Proper disjunctive has two valid moods: modus
ponendo tollens and modus tollendo ponens.
 If the conclusion denies, the mood is ponendo
tollens, so-called because by establishing (ponendo)
the minor premise, it destroys (tollens) the other
alternative.
 If the conclusion affirms, the mood is tollendo
ponens, so-called because by destroying (tollendo)
the minor premise, the syllogism establishes
(ponens) the other alternatives.

Modus Ponendo Tollens
 1. Posit one alternative in the minor
 2. Sublate the other in the conclusion
1. A is either B or C. One is either a born or
naturalized citizen.
 A is B. John was born in this country.
 Therefore, A is not C. Therefore, John is not a
naturalized citizen.
2. Either A or B is C. Either India or England won the
cricket match.
 A is C. India won.
 Therefore, B is not C. Therefore, England did not win.

Modus Tollendo Ponens
 I. Sublate one alternative in the minor
 2 Posit the other in the conclusion
1. A is either B or C. The accused is either
guilty or innocent.
 A is not B. He is not guilty.
 Therefore, A is C. Therefore, he is innocent.
2. Either A or B is C. Either the world or God is
self-sufficient.
 A is not C. The world is not self-sufficient.
 Therefore, B is C. Therefore, God is self-sufficient.

GENERAL RULE OF THE STRICT DISJUNCTIVE
As in the conditional syllogism, if one part is posited,
it must be posited just as it stands, whether
affirmative or negative; the part that is sublated must
be turned into the contradictory of the original.
To fail to follow this essential rule would make us
guilty of a fallacy.
The general rule of the strict disjunctive may be stated
as follows:
 The alternatives of the strict disjunctive cannot
both be true together or false together. If one
alternative of the strict disjunctive is true, the other
must be false; and if one is false, the other must be
true.

4.2.2. IMPROPER DISJUNCTIVE
 Improper disjunctive syllogism is not valid in the
modus ponendo tollens.
 If one member is posited in the minor premise, we
cannot sublate the other or others in the conclusion,
because they are not mutually exclusive and hence
may be true.
 The rose is liked either for its beauty or its sweet
smell.
 It is liked for its beauty.
 Therefore, it is not liked for its sweet smell.
 The alternatives are mutually exclusive.
 The rose may be liked both for its beauty and sweet
smell. Therefore, the argument is invalid.

LET US TAKE ONE MORE EXAMPLE:
 The car stopped running either because of a
bad fuel pump, or because of a defect in the
ignition, or because it ran out of petrol.
 But the fuel pump was bad and there was a
defect in the ignition.
 Therefore, the car did not run out of petrol.
 Here again, the conclusion is invalid, because the
truth of one or more of the parts in the minor does
not imply the falsity of the remainder in the
conclusion.

EXAMPLE
 Improper disjunctive, however, is valid in the
modus tollendo ponens.
 The following example illustrates the point:
 Your sickness was caused either by overwork
or too little sleep or an improper diet.
 You have not been overworking, and you have
been getting enough sleep.
 Therefore, your sickness must have been
caused by improper diet.

NOTE
 Assuming the original proposition to be true, the
conclusion of the above argument necessarily
follows from its premises.
 The rule of improper disjunctive may be stated as
follows:
 All the alternatives may be true together, but cannot
be false together. If one alternative is true, the other
or others are not necessarily false; if one or more
alternatives are false, at least one must be true.

4.2.3. CONJUNCTIVE SYLLOGISM
 Conjunctive syllogism is one, which employs a
conjunctive proposition as the major premise and
a categorical proposition as minor and conclusion.
 A conjunctive proposition involves two alternatives,
which cannot both be true at the same time.
 If one part is true, then the other must be false.
 The conjunctive syllogism is valid only in the modus
ponendo tollens.
 You cannot love God and hate your neighbour.
 You love God.
 Therefore, you do not hate your neighbour.

EXPLANATION
 Because of the nature of a conjunctive proposition, it
would be invalid to place a syllogism in the modus
tollendo ponens.
 You cannot be both an American and European.
 You are not a European.
 Therefore, you are not an American.
 As a matter of fact, you may be an Asiatic.
 The above syllogism is invalid for the simple reason
that the non-truth of one alternative does not
necessarily imply the truth of the other.

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