Chapter 1 : TERMS

Chapter 1 : TERMS

1 UNIVOCAL – things which have same sense.

Ex. The book is a reading material.

The book is a source of knowledge.

EQUIVOCAL – things which are entirely in different senses.

Ex. fan : device causing flow of air

fan : enthusiastic supporter

ANALOGOUS – things which are the same and somewhat different in sense

Ex. hand of the clock

hand of the body

MATERIAL – a reference made to a term simply as a word which is not related to its meaning

Ex. A Christian without Christ means “I Am Nothing”.

LOGICAL – referring to a term which only exists on the mind

Ex. Angels have feathers.

REAL – refers to actual and real things

Ex. The drivers are ought to follow traffic rules.

UNCONNECTED - term which either connotes or denote the other

Ex. brown - - hot

CONNECTED – terms are related wherein one either connote or denote the other.

CONVERTIBLE – have the same comprehension and extension

Ex. idiot - - dumb

NON – CONVERTIBLE – terms which are related wherein one includes the other in its comprehension but the other is excluded in its comprehension.

Ex. plant - - tree

RELATIVE – term wherein one should refer to the preceding

Ex. mother – children

STRICTLY OPPOSED

CONTRADICTORIES – two terms wherein one is the simple negation of the other

Ex. alien - - non-alien

CONTRARIES – refers to terms which are opposite in nature

Ex. wrong - - right 2

PRIVATIVE – two terms wherein one expresses the perfection while the other expresses the absence of the perfection that should be possessed

Ex. beautiful - - ugly

DISPARATE – terms which are incompatible

Ex. egg plant - - tomato

SUBSTANCE – refers to the subject wherein its nature demands to be what it is

QUANTITY – accident that categorizes substance into sub-parts

QUALITY – accident which determines the substance

DISPOSITIONS – easily changed perfections disposing the subject well or badly in its operation

Ex. studious, industrious

CAPACITIES or INCAPACITIES – potentials for their operation with its corresponding deficiency excluding its lack

Ex. able to hike, genius

EFFECTIVE QUALITIES - qualities affecting the senses

Ex. spicy, sour

FIGURE – qualitative ending of a quantity

FORM – quality added to the beauty of the quantity being terminated

RELATION – accident in a subject resulted from the reference to some things

Ex. stout, identical

ACTION – accident resulting from the action of the subject towards something else

Ex. crying, sliding

PASSION – accident resulting from the subject’s being acted

Ex. being punched, being dragged

TIME – when the accident happened

Ex. previously, now

PLACE – where the accident happened

Ex. in school, there

POSTURE – accident arising by the subject from the order of parts in a given space

Ex. sitting, lying

HABIT – accident wherein the subject’s belongings are tackled 3

Chapter 2: PROPOSITIONS

Proposition - is that which a judgment is expressed. it is always expressed in a declarative sentence and it is answerable by a yes or no

Judgment- a mental operation wherein two ideas are affirmed or negated

Basic Elements of a Proposition Subject term Predicate term Copula- acts as a linker between the subject and the predicate

-indicates whether the term is denied or affirmed -must be a linking verb and in a present form

Ex. Velez College students are beautiful.S C P

Subject and Predicate Are material elements (matter) which are united by affirmation or separated by negation.

May be a single term (one word)

Example: Man is rational.

May be complex term 9combination of two or more words)

Example: human beings are given the power of choice where one can decide for his/her own granting he/she will be always ready to face all the consequences for every decision that has been made.

Copula Links subject and predicate.

Constitutes the formal element of the proposition.

Indicates whether one term is denied or affirmed of another.

Example: Velez College is the best school for students taking up medical courses.

“is” is used as the copula and it expresses affirmation.

Example: some politicians are not honest.

“are not” is used as the copula and it expresses denial or negation.

The Types of Proposition1.) Categorical Proposition-the predicate either affirms or denies the subject directly

2.) Hypothetical Proposition-has “If..then” antecedentEx: If it rains, the ground is wet.

3.) Single proposition- Has S, C and P whether negated or notEx: Benzelle is not happy.

4.) Multiple Proposition- has more than one subject and predicateEx: Kuya Kim will teach and the students will listen. 4

Categorical Propositions

Basic Aspects

Quality: affirmative propositionEx: His cat is fat.

Quality: negative propositionEx: Boys are not allowed to talk.

Quantity: universal proposition- universal subject term.Ex: Every woman is cherished.

Quantity: particular proposition– particular subject termEx: Some students are studying.

Quantity: singular proposition – singular subject termEx: Naomi is my pet.

Quantity: collective proposition – collective subject termEx: The class is energetic.

QUANTITY OF PROPOSITION

1.) Universal Proposition- has a universal subject term.

Example: All Pasay city residents are responsible.

No man is capable of doing everything he wishes to do.

2.) Particular Proposition- has a particular subject term.

Example: Some students are not responsible.

Not all children are intelligent.

3.) Singular- has a singular subject term.

Example: Saint Paul’s College is a Catholic school.

That woman is beautiful.

4.) Collective Proposition- has a collective term for its subject.

Example: The crowd is going wild.

THE DISTRIBUTION OF THE PREDICATE TERM

1.) The ordinary A, E, I and O Proposition

a.) Universal Affirmative (A) proposition has a universal subject term and an positive copula.

Example: Every X is Y.

Every animal is a living thing. 5

b.) Universal Negative (E) proposition has a universal subject term and a negative copula.

Example: No X is Y.

No black is yellow.

c.) Particular Affirmative (I) proposition has a particular subject term and an positive copula.

Example: Some X is Y.

Some schools are progressive.

d.) Particular Negative (O) proposition has a particular subject term and a negative copula.

Example: Some X is not Y.

Some priests are not good.

Special Types of Proposition

1.) Single Categorical – has one subject and one predicate or complex.Ex: (simple) Pearls are precious.

(complex) Fear of the Lord is the beginning of faith.

2.) Multiple Categorical

A. Openly or overtly multiple proposition

a) Copulative proposition- uses coordinate and correlative conjunction like and, not only, bothEx: Clint and Xian are meant together.

b) Adversative proposition- uses subordinate clause like but, despite, whereas.Ex: Donna is still working, although she is already tired.

c) Relative proposition- uses time relation like before, during, when.Ex: The guests will arrive before lunchtime.

d) Causal proposition- introduces reason or cause in a given statement like because, for, sinceEx: She left because she doesn’t belong to their group.

e) Comparative proposition- compares relation of termsEx: Stephanie is not as tall as kuya Ben.

B. Hidden or covertly multiple proposition -expresses 2 or more judgments-judgments are called exponents

a.)Exclusive proposition- uses expression like only, none, but, aloneExample: Infirmary is only for Alyssa.Exponents: Infirmary is for Alyssa.

There is no other room.

6b.)Exceptive proposition- uses expression like except save

Example: All students, except three, have passed the project.Exponents: Three students have not passed the project.

The other students have passed the project.

c.) Reduplicative proposition- calls specific attentionExample: As a teacher, Mr. Luther must be a role model to others.Exponents: Mr. Luther is a teacher.

He must be a role model to others. The reason for doing so is because he is a teacher.

3.) Hypothetical Proposition

a.) Conditional proposition- usually in the form of if… thenExample: If I were you, then I would go after him.Antecedent: if I were youConsequent: then I would go after him.

b.) Disjunctive proposition

1.) Proper disjunctive- terms that can’t be true and false at the same timeEx: John is either straight or gay.

2.) Improper disjunctive- terms that cannot be all false but can be true at the same timeEx. His sadness was due either to his accusations or to his failed project.

c.) Conjunctive proposition- terms that cannot be all trueEx: We cannot listen and study our lessons at the same time.

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Chapter 3: INFERENCE

Inference in general

There are a lot of propositions which are ought to be true on the basis of the evidence of the sense. Statements which are verified or falsified by direct seeing, hearing, feeling or by direct perceiving like “It is valentines day,” “She is not feeling well” are some examples. Some accept only by the basis of authority. Example, if we believe in the preaching of the priest, we accept his teachings as true. It is the process where by from the truth-value of one or more propositions called inference. Possible truths are obtained by inference.

Types of Inferences

Immediate Inferences Mediate Inferences

In the first kind of inference, this proceed from one proposition directly to another proposition. On the other hand, the mediate inferences proceed from two or more propositions to another which is implied in the given propositions.

Example of Immediate Inference: No fish is a human. Therefore, no human is a fish.

Example of Mediate Inference: Boys are not allowed to enter the gate. My cousin is a boy.

So, he is not allowed to enter the gate.

Forms and matter of Inferences

Examples: No soft is a pillow. So, no pillow is a soft.

Following: No X is Y. So, no Y is X.

Plastic is a non- conductor of electricity. Tupperware is a plastic.Therefore, plastic is a non-conductor of electricity.

Following: M is P S is M So, S is P.

The First Principle or the Basic Laws of Thought

5.) The Principle of Identity

6.) The Principle of Contradiction7.) The Principle of Excluded Middle

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Chapter 4: OPPOSITIONAL INFERENCE

The Modes of Opposition

>> It involves a relation between one statement and its opposites. In terms of opposition of proposition, we have the relation between two proposition having the same subject and predicate, but they’re differ in quality, quantity or both quality and quantity.

FOUR MODES OF OPPOSITION:

1. Contradiction – differ both in quantity and quality.

Examples: No S is P -- Some S is P Not all S is P -- Every S is P

2. Contrariety – universal proposition that differ in quality

Examples: No S is P -- Every S is P 3. Subcontrariety – two particular proposition that differ in quality

Examples: Some S is P -- Not all S is P4. Subalternation – universal and particular proposition having the same quality of the copula. Examples: Some S is P -- Every S is P Some S is not P -- No S is P

THE LAWS OF OPPOSITION

1. law of contradiction A. if one is true, the other is false

Examples: No cheater is honest is true Some cheater are honest is false

B. if one is false, the other is true Examples:

It is false that some rabbits are able to think It is true that no rabbits is able to think

2. law of subalternation A. if the universal statement is true, the subaltern is also true

Examples: It is true that no benign tumors is incurable It is false that some benign tumors are not incurable

B. if the particular statement is true, the subaltern is doubtful Examples: It is true that some artists are creative Every artist is creative is doubtful

9C. if the particular statement is false, the subaltern is likewise false.

Examples: That some radicals are reactionary is false. It is likewise false that every radical is reactionary.

D. If the universal is false, the subaltern is doubtful Examples: It is false that no TV show is good for the children It is doubtful whether some TV shows are not good for the children

3. law of contrariety A. Cannot be true at the same time.

Examples: If it is true that no hero is a coward It is false that every hero is a coward

B. Cannot be false at the same time Examples: It is false that no child is egocentric We cannot be certain that every child is egocentric

4. law of subcontrarietyA. subcontraries cannot be false at the same time

Examples: It is false that some obstacles are insurmountable It is true that not all obstacles are insurmountable

B. subcontraries cannot be true at the same time Examples: It is true that some movies are purely for entertainment It is false that some movies are not purely for entertainment

SUMMARY:

IF A is true, O is false IF A is false, O is true I is true I is doubtful E is false E is doubtful

IF E is true, I is false IF E is false, I is true O is true O is doubtful A is false A is doubtful

IF I is true, E is false IF I is false, E is true A is doubtful A is false O is doubtful O is true

IF O is true, A is false IF A is false, A is true E is doubtful E is false I is doubtful I is true

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Chapter 5: EDUCTION

TYPES OF EDUCTION

A. Obversion – whose subject is the same as the original subject but whose predicate is the contradictory of the given predicate.

Examples: No fish is unable to swim (obvert) Every fish is able to swim (obverse)

Obversion of A, E, I and O

1. E obverts to A No S is P Every S is P2. A obverts to E Every S is P No S is P3. I obverts to O Some S is P Some S is not P4. O obverts to I Some S is not P Some S is P

B. Conversion – whose subject is the original predicate and whose predicate is the original subject. Examples: No sinner is a saint (obvert) No saint is a sinner (obverse)

C. Contraposition – “partial” whose subject is the contradictory of the original predicate but whose predicate is the same as the original subject; “full” whose subject is the contradictory of the given predicate and whose predicate is the contradictory of the given subject.

Contraposition of A, E and O

A. Given: every S is P Obverse: No S is P Converse: No P is S Obverse: Every P is S E. Given: No S is P Obverse: Every S is P Converse: Some P is S

Obverse: Some P is not S

11O.

Given: Some S is not P Obverse: Some S is P Converse: Some P is S Obverse: Some P is not S

D. Inversion – “partial” whose subject is the contradictory of the given subject but whose predicate is the same as the given predicate; “full” whose subject and predicate are the contradictories of the given subject and predicate.

Inversion of A

Given: Every S is P Obverse: No S is P Converse: No P is S Obverse: Every P is S Converse: Some S is P (partial inverse) Obverse: Some S is not P (full inverse)

Inversion of A

Given: No S is P Converse: No S is P Obverse: Every P is S Converse: Some Sis P (partial inverse) Obverse: Some S is not P (full inverse)

E. Methods of Material implication

1. The method of added determinants Examples: A child is a person A naughty child is a naughty person2. The method of omitted determinants Examples: An actress is a woman A good actress is a good woman3. The method of complex conception Examples: A five-peso bill is money A fake five-peso bill is fake money4. The method of converse relation Examples: Jorge is the son-in-law of stella Stella is the mother-in-law of jorge

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Chapter 6: MEDIATE INFERENCE: REASONING

INFERENCE – path to the truth

MEDIATE INFERENCE – logical thinking

CONCLUSION – latest truth attained

PREMISES – it is the reference of the conclusion

ARGUMENT – expression of logical thinking

MATERIAL CORRECTNESS – propositions of the truth

FORMAL CORRECTNESS – coherent connection among propositions wherein the conclusion must follow the premises

MATERIALLY CORRECT BUT FORMALLY INCORRECT ARGUMENT

Ex. Monkeys eat.

Mammals eat

So, mammals are monkey.

MATERIALLY INCORRECT BUT FORMALLY CORRECT ARGUMENT

Ex. All politicians are honest.

Arroyo is a politician.

Ergo, she is honest.

TYPES of ARGUMENT

INDUCTIVE – from a particular situation to a universal truth

Ex. Mother KA of the Augustinian Parish is modest.

Mother TOR is also modest.

Mother SE is likewise modest.

Therefore, all the ten nuns in the Augustinian Parish are modest.

DEDUCTIVE – from a more universal truth to a less universal truth

Ex. No man without food can live.

Arman is a man.

Ergo, he can’t live without food.

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Chapter 7: THE CATEGORICAL SYLLOGISM

The categorical syllogism is an argument proceeds from statements concerning the relationship of two terms to a third term, to conclusion concerning the relationship of two terms to each other.

The Basic Elements1. Minor Term ( S ) – subject of the conclusion2. Major Term ( P ) – predicate of the conclusion,either the subject or predicate of the major premise3. Middle Term ( M ) – occurs in each of the premises but not in the conclusion4. Major Premise – the proposition containing the major and middle terms5. Minor Premise – the proposition containing the minor and middle terms6. Conclusion – the statement being proved.

The Figures of Categorical Syllogism

Figure I MP All voters are at least 18. SM He is a voter. SP Ergo, he is at least 18.

Figure II PM Some who are honest are not educated. SM But all professionals are educated. SP Ergo, some professionals are not honest.

Figure III MP Some philosophers are not realistic. MS Every philosopher is a thinker. SP Some thinkers are not realistic.

Figure IV PM Some socialists are revolutionary. MS All revolutionaries advocate reforms. SP Ergo, some who advocate reforms are socialists

The Underlying Principles of the Categorical Syllogism

1. Principle of Reciprocal Identity: two terms that are identical with a third term are identical with each other.

2. Principle of Reciprocal Non-Identity: two terms, one of which is identical with a third, but the other of which is not, are not identical with each other.

3. Principle of All (Dictum de Omme ) : What is affirmed universally of a term is affirmed of anything that comes under that term.

4. Principle of None (Dictum de Nullo): Whatever is denied universally of any term is denied of anything that comes under that term.

14The Rules for a Valid Categorical Syllogism

Rule No.1 There must be three and only three terms – the major, minor & middle terms. There is a violation of this rule when there are four terms in the syllogism giving rise to what is

known as the “fallacy of four term construction” or “logical quadruped”. The following are examples of arguments with four terms: A diligent man works hard. A lazy man hardly works. Therefore, a lazy man is diligent.

Rule No. 2 The middle term does not occur in the conclusion. This so because the function of the middle term is to compare the minor and major terms and this

comparison happens only in the premises.

The following arguments violate the 2nd rule and are therefore invalid. Men have a spiritual nature. Men have biological needs. Therefore, men are spiritual beings with biological needs.

Rule No. 3 The major or minor term may not be universal in the conclusion if it is only particular in the premises.

This rule implies that if the major or minor term is particular in the premises, it must be taken as a particular term in the conclusion, not as a universal term.

If the major term is overextended in the conclusion, then there is a “fallacy of illicit major”. If the minor term is overextended in the conclusion, then there is a “fallacy of illicit minor”.

The following arguments are invalid due to an illicit process:

Fallacy of Illicit Minor: All philosophers are wise people. Mu + Pp But all philosophers are men. Mu + Sp Therefore, all men are wise people. Su + Pp

Fallacy of Illicit Major: Plants are organisms. Mu + Pp But animals are not plants. Su - Mu Therefore, animals are not organisms. Su- Pu

Rule No. 4 The middle term must be used as a universal term at least once. This rule implies the role of the middle term in the reasoning process, which is to mediate

between the major and minor terms. If the middle term is used twice as a particular term, then there is a “fallacy of undistributed

middle term”. A violation of the above rule is illustrated in the following syllogism:A Lutheran is a Christian.A Seventh - day Adventist is a Christian.Ergo, a Seventh - day Adventist is a Lutheran.

15 Rule No. 5 Two negative premises yield no valid conclusion.

If both premises are negative, then the middle term is not identified with or does not agree with the major and minor terms. In that case, the middle term does not really function as a mediating term. As a result, no conclusion can be made. Thus, we cannot validly say—

A scholar does not have failing grades. Mercy does not have failing grades. Ergo, she’s a scholar. Some syllogisms have propositions which are only apparently negative and yield valid

conclusions. This is the case with the following syllogism:No one who is uninspired is in love.You are not inspired.Therefore, you are not in love. The above syllogism does not violate the rule because the second premise is not really negative.

Rule No. 6 If both premises are affirmative, the conclusion must be affirmative. This rule follows from the fact that when both premises are affirmative, the major and minor

terms agree or are identified with the middle term. It is closely related to the reciprocal identity. This is expressed by the affirmative copula.

Therefore, the conclusion which expresses this identity must be an affirmative proposition. It would be wrong to argue that: Anyone with an IQ of 141 is genius. Alex has an IQ of 141. Ergo, he is not a moron. Aside from violating rule no. 6, the first syllogism also violates rule no. 1 and the 2nd also

violates rule no. 4.

Rule No. 7 If one premise is negative, the conclusion must be negative. This rule is justified by the principle of non-reciprocal identity. If one premise is affirmative, and

the other is negative, that mean s one of the two terms is identical with the middle term while the other is not.

The following argument is invalid due to the violation of this rule; An astronaut possesses inalienable rights. No child is an astronaut. Ergo, a child possesses inalienable rights.

Rule No. 8 If one premise is particular, the conclusion must be particular. To justify this rule, we need to show that of the possible combinations of premises of which one

is particular and the other is universal, the only valid conclusion that can be drawn is a particular proposition.

The 4 possible combinations of premises wherein one is particular and the other is universal are: A and I E and I A and O E and O* If the premises are A and I, the only universal term is the subject of A: all the others are particular terms. Thus, A Mu + Pp Mu + Sp Mu + Pp or or I Sp + Mp Pp + Mp Mp + Sp Sp + Pp Sp + Pp Sp + Pp

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The 2nd pair of premises is that of E and I. E has a universal subject and predicate. I has a particular subject and predicate. In this combination, there are 2 universal terms and 2 particular terms. This is shown below:

E Mu – Pu E Pu – Mu Or I Sp + Mp I Mp + Sp Sp – Pu Sp – Pu

The 3rd set of premise is that of A and O. Here, there are again 2 universal terms and 2 particular terms.

The 4th combination is that of E and O. Because both premises are negative, no valid conclusion can be drawn from them.

Whenever rule no. 8 is violated, there is a violation either of rule no. 3, 4, or 5. This is seen in the following examples:

Some rich men oppress the poor. Mr. Katibayan is a rich man. Ergo, Mr. Katibayan oppresses the poor.

Some Christians are Catholics. No pagan is a Christian. Ergo, no pagan is a Christian.

Rule No. 9 From two particular premises, no valid conclusion can be drawn. To prove this rule, one need only show that of the possible combinations of premises both of

which are particular, not one will yield a valid conclusion. When this rule is violated, there is also a violation of rule no. 3, 4, or 5. Consider the following

examples: Some fruits are rich in Vitamin A. Some fruits are lemons. Ergo, some lemons are rich in Vitamin A.

The Figures and Moods of SyllogismIt is useful because it gives us a better understanding of the form or structure of this type of argument and also provides us with another means of testing the validity of the categorical syllogism.

Every syllogism has 3 propositions and each proposition is either A, E I or O. By the mood of the categorical syllogism, we understand the specific combination of the propositions that make up the syllogism.The following are the 64 possible moods of syllogism. However, not all of them are valid syllogisms.

AAA AEA AIA AOA AAE AEE AIE AOE AAI AEI AII AOI AAO AEO AIO AOO

EAA EEA EIA EOA EAE EEE EIE EOE EAI EEI EII EOI EAO EEO EIO EOO

IAA IEA IIA IOA 17

IAE IEE IIE IOE IAI IEI III IOI IAO IEO IIO IOO

OAA OEA OIA OOA OAE OEE OIE OOE OAI OEI OII OOI OAO OEO OIO OOO

Most of the above combinations are immediately seen as invalid once we apply the general rules.A careful inspection will yield the following tentatively valid moods:

AAA EAE IAI OAO AAI EAO IEO AEE EIO AEO AII AOO

The above moods, however, are not valid in each of the four figures. For example, mood AAA is only valid in the first figure as shown in the analysis below:

I II III IV

A Mu + Pp Pu + Mp Mu + Pp Pu + Mp A Su + Mp Su + Mp Mu + Sp Mu + SpA Su + Pp Su + Pp Su + Pp Su + Pp

24 valid resulting syllogisms when 12 moods are constructed in 4 figures

Fig. I AAA Fig. II EAE Fig. III ((AAI)) Fig. IV EIOAEA AEE AII ((AAI))AII EIO IAI AEEEIO AOO EIO ((EAO))

((EAO)) IAI

(AAI) (EAO) OAO(EAO) (AEO) (AEO)

5 moods in parenthesis [( )] = arguments with weakened conclusions

Example: E No immortal is dead individual.A Every fairy is a an immortal.O Ergo, not all fairies are dead individual.

4 moods in enclosed in double parenthesis [(( ))] = syllogisms with strengthened premises

Example: A All cats have furs.A All cats are four-legged animals.I Ergo, some four-legged animals have furs. 18

Syllogistic Reduction

- code names are used in traditional logic of each syllogism figures that one valueReduction - transformation of a syllogism

- first figure is considered as the perfect figurefigures:

I II III IVbArbArA cEsArE dArApTI frEsIsOncEIArEnt cAmEstrEs dAtIsI brAmAntIpdArII fEstInO dIsAmIs cAmEnEsfErIo bArOcO fErIsOn fEsApO

fEIAptOn dImArIsbOcArdO

- first letter of the code names signify the mood of the first figure into which it may be reducedExample: cEsArE is reducible to mood cEIArEnt

Direct Reduction

Example:dIsAmIs to dArII

dIs Some toys are educational. (to be converted)Am All toys provide enjoyment.Is Some toys that provide enjoyment are useful things. (to be converted)

(then premises are transposed)dA All toys provide enjoyment.rI Some useful things are toys.I Ergo, some useful things provides enjoyment.

The Indirect Reduction of BOCARDO and BAROCO

- cannot be reduced directly bOcArdO and bArOcO so we use the first figure, bArbAra, making it valid and also it implies an indirect reduction.

Example:

bO Some flowers are not fertilized plants.cAr All flowers are watered plants.dO Ergo, some watered are not fertilized plants.

dIs Some flowers are unfertilized plants.Am All flowers are watered plants.Is Ergo, some watered plants are unfertilized plants.

dA All flowers are watered plants.rI Some unfertilized plants are flowers.I Ergo, some unfertilized plants are watered plants.

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Testing the Validity by the Venn diagram Method

-represented by 3 intersecting Venn circles: major, minor, & middle terms

Example: All birds are swift.Some birds are penguins.Ergo, some penguins are swift.

In diagramming the syllogism- we must first diagram the universal premise (i.e. major premise)- major premise asserts that “ there are no birds who are not swift (MS = O).”- so the B is shaded outside of S- minor premise asserts that “there is at least one bird which are penguins (MR ≠ O)- so X is placed in the appropriate area

B – Birds P – Penguins S – Swift

Conclusion: “Some penguins are swift” meaning there is at least one penguin that can be swiftshown by the X in the area common to the circles representing “birds” and “swift”

Testing the Validity by the Antilogism Method

- is a syllogism whose conclusion has been replaced by its contradictory- developed by Christian Ladd-Franklin

meets the following conditions:- it has 2 universal propositions and 1 particular propostion or 2 equations ‘=’ and 1 inequation ‘≠’- 2 equations have common term which occurs once affirmatively and once negatively- inequations will contain the other terms, identically as they occur in the equations

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Example:

All animals are friendly. CS = O

All bunnies are cuddly. MC = O

Ergo, all bunnies are friendly. MS = O

Antilogism:All C are S. CS = O

All M are C. MC = O

Some M are not S MS ≠ O

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Chapter 8: THE HYPOTHETICAL SYLLOGISM The hypothetical syllogism is another form of deductive argument and is governed by a set of rules different from those of the categorical syllogisms. In hypothetical syllogism, at least the first premise must be a hypothetical or sequential position.

The hypothetical argument is an argument whose 1st premise is a sequential or hypothetical proposition, one member of which is affirmed or denied in the second premise, and the other member of which is consequently affirmed or denied in the conclusion.

The Conditional SyllogismIn all its types, it always has a conditional proposition for its major premise.

1.) Simple conditional argument – has a conditional proposition for major premise and categorical propositions for minor premise and conclusion.

Examples:a) If man were God, then he would be all-knowing. But man is not all- knowing. Ergo, he is not God.

The rules for a valid simple conditional syllogism are based on the very nature of the conditional proposition which asserts that there is a necessary sequence between its elements – the antecedent A and the consequent C.

The rules may be stated as follows:I. .The truth of the antecedent necessarily implies the truth of the consequent. So, if we posit,

affirm, or accept the antecedent in the minor premise, the we necessarily posit, affirm or accept the consequent in the conclusion.

II. The falsity of the consequent implies the falsity of the antecedent. So, if we sublate, deny or reject the consequent in the minor premise, then we necessarily sublate, deny or reject the antecedent in the conclusion.

III. The falsity of the antecedent does not necessarily imply the falsity of the consequent. Thus, it would not be correct to proceed from the negation of the antecedent in the minor premise to the negation of the consequent in conclusion.

IV. The truth of the consequent does not necessarily imply the truth of the antecedent. So, it would not be valid to argue from the affirmation of the consequent in the minor premise to the affirmation of the antecedent in the conclusion.

In the light of the above rules, there can only be 2 valid forms of the simple conditional syllogism and these are:

(1) Positing Mood (2) The Sublating Mood If A, then C. If A, then C. But A. But not C. Ergo, C. Ergo, not A.

The two forms below are invalid:1) If A, then C. 2) If A, then C. But not A. But C. Ergo, not C. Ergo, A

22The following arguments illustrate the valid forms:

a) If a person is nearsighted, then he needs glasses. Bernard is nearsighted.. + A Ergo, he needs glasses. + Cb) If a person is nearsighted, then he needs glasses. Abelard does not need glasses. - C Ergo, he’s not nearsighted. – A

The following arguments illustrate invalid forms:

a) If a person is nearsighted, then he needs glasses. Alice is not nearsighted. – A Ergo, she does not need glasses. – Cb) If a person is nearsighted, then he needs glasses Agnes needs glasses. Ergo, she is nearsighted.

A simple conditional argument may have a valid form but its major premise may be a false conditional statement. Such a syllogism is formally correct but materially incorrect.

Example: If a man is wealthy, then he is happy. Mr. Roces is wealthy. Ergo, he is happy.

2.) The reciprocal conditional syllogism has for its major premise an “only if…then…” proposition. Example: Only if a student has a general average of at least 1.2 would he graduate summa cum laude. This student has a general average of 1.2. Therefore, he would graduate summa cum laude.

3.) The biconditional syllogism has for its major premise a statement containing the expression “if and only if”. Example: If and only if one gets a perfect score in all quizzes will I exempt him from the final exam. Mario got a perfect score in all quizzes. Ergo, he’ll be exempted from the final exam.

4.) The pure conditional statement has a conditional proposition for premises and conclusion. Example: If A is B, then C is D. If X is Y, then A is B. Ergo, If X is Y, then C is D.

To be a valid argument, the common element in the argument must be taken once as antecedent and once as consequent

The following examples illustrate invalid forms of this syllogism:

a) If a being is material, then it has a beginning. If a being is created, then it has a beginning. Ergo, if being is created, then it is material.

235.) The conditional sorites is a syllogism with 3 or more simple conditional propositions for premises. In testing the validity of this argument, we apply the rules of pure conditional syllogism.

Example : If you don’t pay your accounts, you won’t be given an admission slip. If you don’t have your admission slip, then you can’t take the exam. If you don’t take the exam, then you’ll get IE. Ergo, if you don’t pay your accounts, you’ll get an IE.

The Disjunctive Syllogism- It is an argument in which the major premise is a disjunctive proposition and the minor premise and conclusion are categorical propositions.

The Types of Disjunctive Syllogism

1. The Perfect (Proper or Strict) Disjunctive Syllogism: The alternatives presented in the major premise are such that they cannot be both affirmed or

denied. There are two valid forms of the argument.

a) Positing Mood – minor premise posits or accepts one member of the Disjunction and the conclusion sublates or rejects the other.

b) Example: This argument is either valid or invalid. This argument is valid. Ergo, it is not valid.

c) Sublating Mood – minor sublates or rejects one of the members of the disjunction and the conclusion affirms or posits the other.

Example: You are either a Catholic or not.You are not a Catholic.

Ergo, you are a non- Catholic.

2. The Imperfect ( Improper or Broad ) Disjunctive SyllogismThe major premise presents alternatives that cannot be denied but can be affirmed of one and the same subject at the same time. For this reason, there is only one valid mood for an argument in this type, and this is the sublating mood wherein the minor premise negates one alternative and the conclusion accepts or affirms the other.

Example: Either you try or you won’t succeed. You won’t try. – Ergo, you won’t succeed. + Valid

Either you try or you won’t succeed. You will try. + Ergo, you will succeed. – Invalid

24The Conjunctive Syllogism

The major premise expresses alternatives that cannot be true at the same time; its major premise affirms or denies one of the alternatives and the conclusion consequently affirms or denies the other.The rule of this syllogism is simply to affirm one alternative in the minor and to deny the other in the conclusion.

Example: You cannot study properly and watch a TV show at the same time. You are watching a TV show. + Ergo, you are not studying properly. – Valid

You cannot study properly and watch a TV show at the same time. You are not watching a TV show. – Ergo, you are studying properly. + Invalid

25

Chapter 9: VARIATIONS OF THE SYLLOGISM

The Enthymeme

- is a syllogism with one part of the argument missing

3 forms:

1. First Order: Major premise is omitted.Example: A murderer is guilty at court.

Therefore, he should be imprisoned.2. Second Order: Minor premise is omitted.

Example: What is guilty at court should be imprisoned.Therefore, a murderer should be imprisoned.

3. Third Order: Conclusion omitted.Example: What is guilty at court should be imprisoned; and a murderer is guilty at court.

- not necessarily an abbreviated categorical syllogism. It may also be an abridged hypothetical syllogism.

Example: Since the paper was torn, the students threw the paper away.

The Exclusive Syllogism

- at least one of the propostions is an exclusive statement; it contains the expressions “only,” “solely,” “alone,” or “none but.”

Example: The excellent in the field of fables is the father of fables. Only Aesop is excellent in the field of fables.Therefore, only Aesop is the father of fables.

2 ways of testing the validity of this argument:

1. Consists in drawing the components of the given syllogism and testing the validity of each.If both are valid, the whole argument is valid; otherwise, it is invalid.

Example:

IThe excellent in the field of fables is the father of fables. Mu + PpAesop is excellent in the field of fables. Su + MpErgo, Aesop is the father of fables. Su + Pp

IIThe excellent in the field of fables is the father of fables. Mu + PpWho is not Aesop is not excellent in the field of fables. Su - MuErgo, who is not Aesop is not the father of fables. Su - Pu

26Given: The excellent in the field of fables is the father of fables.

Only Aesop is excellent in the field of fables.

So, only Aesop is the father of fables.

Equivalent: The excellent in the field of fables is the father of fables. Mu + SpThe excellent in the field of fables is Aesop. Mu + PpSo, who is the father of fables is Aesop. Su + Pp

The Epichireme

- is a syllogism in which a proof or reason is attached to one or both of the premises.

Examples:

1. A being that is not rational is essentially different from man.Cats are not rational (because they are incapable of forming ideas).Ergo, cats are essentially different from man.

The Polysyllogism

- an argument consisting of two or more complete arguments linked; a chain argument

The Sorites

- an abbreviated polysyllogism.

2 forms:

1. Aristotelian sorites - subject of the preceding premise is used as predicate of the following premise- conclusion which is composed of the subject of the last premise and the predicate of the first premise

2. Goclenian sorites - subject of the preceding premise is used as the predicate of the following premise- conclusion which is composed of the subject of the last premise and the predicate of the first premise

Aristotelian S A Goclenian A PSorites A B Sorites: B A

B C C BC P S CS P S P

27The Dilemma

- presents alternatives in which ever he chooses leads to the disadvantage

4 forms:

1. Simple Constructive Dilemma

Premises: If A, then CIf B, then C

either ABut

or BConclusion: Ergo, C

2. Complex Constructive Dilemma

Premises: If A, then CIf B, then D

either ABut

or BConclusion: Ergo, C or D.

3. Simple Destructive Dilemma

Premises: If A, then C and Deither not C

Butor not D

Conclusion: Ergo, not A

4. Complex Destructive Dilemma

Premises: If A, then CIf B, then D

either not CBut

or not DConclusion: Ergo, either not A or not B

28

Summary

Chapter 1 Terms 1 – 3

Chapter 2 Propositions 4 – 7

Chapter 3 Inference 8

Chapter 4 Oppositional Inference 9 – 10

Chapter 5 Eduction 11 – 12

Chapter 6 Mediate Inference 13

Chapter 7 Categorical Syllogism 14 – 21

Chapter 8 Hypothetical Syllogism 22 -25

Chapter 9 Variations of Syllogism 26 – 28

Allocation of Topics

Bantilan, Sheina Mae Chapters 7 & 8

Barte, Anne Bernadette Chapters 7 & 9

Campado, Vincent Mae Chapters 2 & 3

Kaindoy, Chaelle Chapters 1 & 6

Lagulao, Jermyn Mae Chapters 4 & 5

Bachelor in Science of Occupational Therapy – 1A. All Rights Reserved © 2010.