Chapter 1

Terms

Term – A term is a group of words which connotes a thought.Example: school, country, ball

Co-significant Word – A co-significant is a word which doesn’t represent any thought.Example: in, the a, an, of, or

Significant Word – a significant word is a word which defines a certain thought.Example: mother, church, people, town, message

Properties of a term

Comprehension - comprehension is the sum of the total notes implying the elements making a thing to be what it is.

- It refers to the superiority of a term

Extension - Extension possesses the characteristics represented by the notes in the comprehension.- It refers to the inferiority of a term

COMPREHENSION EXTENSIONsport softball

dessert mango floatsoap Safeguard

Classification of terms

Singular term – a singular term stands for only one certain subject.Example: Peter, this paper, the roadway

Universal term – a universal term can be applied to every member of a class.Example: all, every, any, anything, whatsoever, no, none, nothing

Collective term – a collective term is a term wherein the extension is only limited to a portion of the total absolute extension.

Example: a number of, practically all, not all, not everyone

Univocal Term – a Univocal Term refers to things which have same sense.Example: The book is a reading material.

The book is a source of knowledge.

Equivocal Term –an equivocal term refers to things which are entirely in different senses.Example: fan: device causing flow of air

fan: enthusiastic supporterAnalogous Term – an analogous term refers to things which are the same and somewhat different

in sense.Example: hand of the clock

hand of the body

Material Supposition – a material supposition is a reference made to a term simply as a wordwhich is not related to its meaning.

Example: A Christian without Christ means “I Am Nothing.”

Logical Supposition – a logical supposition refers to a term which only exists on the mind.Example: Angels have feathers.

Real Supposition – a real supposition refers to actual and real things.Example: The drivers are ought to follow traffic rules.

Unconnected Term - an unconnected term refers to a term which either connotes or denotes the other.

Example: brown – hot

Connected Term – a connected term is a related term wherein one either connotes or denotes the other.

* Convertible Term – a convertible term have the same comprehension and extension.Example: idiot - dumb

* Non- Convertible Term – a non- convertible term is a related term wherein one includes the other in its comprehension but the other is excluded in itscomprehension.

Example: plant – tree

* Relative Term – a relative term is a term wherein one term should refer to the preceding term.

Example: mother – children

Strictly Opposed Term

* Contradictories – contradictories refer to two terms wherein one is the simple negation of the other.

Example: alien - non-alien

* Contraries – contraries refer to terms which are opposite in nature.Example: wrong – right

* Privative Term – a privative term refers to two terms wherein one expresses the perfection while the other expresses the absence of the perfection that should be possessed.

Example: beautiful – ugly* Disparate Term – a disparate term is a term which is incompatible.

Example: egg plant – tomato

Substance – a substance is a subject wherein its nature demands to be what it is.

Quantity – a quantity is an accident that categorizes substance into sub-parts.

Quality – a quality is an accident which determines the substance.

Dispositions – dispositions are easily changed perfections disposing the subject well or badly in its operation.

Example: studious, industrious

Capacities or Incapacities – capacities or incapacities refers to the potentials for their operation with its corresponding deficiency excluding its lack.

Example: able to hike, genius

Effective qualities – effective qualities affects the senses.Example: spicy, sour

Figure – a figure is qualitative ending of a quantity.

Form – a form is a quality added to the beauty of the quantity being terminated.

Relation – a relation is an accident in a subject resulted from the reference to some things.Example: stout, identical

Action – an action is an accident resulting from the action of the subject towards something else.Example: crying, sliding

Passion – a passion is an accident resulting from the subject’s being acted.Example: being punched, being dragged

Time – time refers to when the accident happened.Example: previously, now

Place – place refers to where the accident happened.Example: in school, there

Posture – posture is an accident arising by the subject from the order of parts in a given space.Example: sitting, lying

Habit – habit is an accident wherein the subject’s belongings are tackled.

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” antecedent

Example: If it rains, the ground is wet.

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

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

Categorical PropositionsBasic Aspects

Quality: affirmative propositionExample: His cat is fat.

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

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

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

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

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

Quantity of Propositions

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.

Particular Proposition - has a particular subject term.Example: Some students are not responsible.

Not all children are intelligent.

Singular- has a singular subject term.Example: Saint Paul’s College is a Catholic school.

That woman is beautiful.Collective Proposition- has a collective term for its subject.

Example: The crowd is going wild.

The distribution of the predicate term

The ordinary A, E, I and O Proposition1. Universal Affirmative (A) proposition has a universal subject term and an positive copula.

Example: Every X is Y.Every animal is a living thing.

2. Universal Negative (E) proposition has a universal subject term and a negative copula.Example: No X is Y.

No black is yellow.

3. Particular Affirmative (I) proposition has a particular subject term and an positive copula.Example: Some X is Y.

Some schools are progressive.

4. 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.Example: (simple) Pearls are precious.

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

2. Multiple Categorical

2. a. Openly or overtly multiple proposition2. a. 1. Copulative proposition- uses coordinate & correlative conjunction like not only,

both, andExample: Clint and Xian are meant together.

2. a. 2. Adversative proposition- uses subordinate clause like but, despite, whereas.Example: Donna is still working, although she is already tired.

2. a. 3. Relative proposition- uses time relation like before, during, when.Example: The guests will arrive before lunchtime.

2. a. 4. Causal proposition - introduces reason or cause in a given statement like because, for, since

Example: She left because she doesn’t belong to their group.

2. a. 5. Comparative proposition- compares relation of termsEx: Stephanie is not as tall as kuya Ben.

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

2. b. 1. Exclusive proposition- uses expression like only, none, but, aloneExample: Infirmary is only for Alyssa.Exponents: Infirmary is for Alyssa.

There is no other room.

2. b. 2. Exceptive proposition- uses expression like except saveExample: All students, except three, have passed the project.Exponents: Three students have not passed the project.

The other students have passed the project.

2. b. 3. 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

3. 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.

3. b. Disjunctive proposition3. b. 1. Proper disjunctive- terms that can’t be true and false at the same time

Example: John is either straight or gay.

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

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

Chapter 3

Inference

Inference in generalThere 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 Inferences1. Immediate Inferences - proceed from one proposition directly to another proposition

Example: No fish is a human. Therefore, no human is a fish.

2. Mediate Inferences - proceed from two or more propositions to another which is implied in the given propositions

Example: 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

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

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

* Following:M is PS is M

So, S is P.

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

The First Principle or the Basic Laws of Thought

1.) The Principle of Identity2.) The Principle of Contradiction3.) The Principle of Excluded Middle

Chapter 4

Oppositional Inference

The Modes of OppositionIt 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 P

4. 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 1. a. if one is true, the other is false

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

1. 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

2. 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

2. 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

2. c. 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.

2. 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 contrariety3. 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

3. 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 subcontrariety4. a. 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

4. 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

Chapter 5

Eduction

Types of EductionA. 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

O.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

Chapter 6

Mediate Inference: Reasoning

Inference – an inference is a path to the truth.

Mediate Inference – a mediate inference means a logical thinking.

Conclusion – conclusion is the latest truth attained.

Premises – premises are the references of the conclusion.

Argument – an argument is an expression of logical thinking.

Material Correctness – material correctness refers to propositions of the truth.Formal Correctness – formal correctness refers to the coherent connection among propositions

wherein the conclusion must follow the premises.

Materially Correct but Formally Incorrect ArgumentEx. Monkeys eat. Mammals eat So, mammals are monkeys.

Materialy Incorrect but Formally Correct ArgumentEx. All politicians are honest. Arroyo is a politician. Ergo, she is honest.

Types of Argument

1. Inductive Argument – An Inductive Argument is an argument wherein a universal truth is formed from a particular situation.

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.

2. Deductive Argument– A Deductive Argument is an argument wherein a more universal truth is transformed to a less universal truth.

Ex. No man without food can live. Arman is a man. Ergo, he can’t live without food.

Chapter 7

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.

The Rules for a Valid Categorical Syllogism

Rule No.1 There must be three and only three terms – the major, minor & middle terms.4 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”.5 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.

A smart girl studies. A dull girl seldom studies. Therefore, a dull girl is smart.

Rule No. 2 The middle term does not occur in the conclusion.6 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.

Men are rational animals. But men are mortals. Therefore, men are mortal rational animals.

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

premises.

7 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.

8 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”.

9 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.

10 This rule implies the role of the middle term in the reasoning process, which is to mediate between the major and minor terms.

11 If the middle term is used twice as a particular term, then there is a “fallacy of undistributed middle term”.

12 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.

Some scientists are atheists.But physicists are atheists.Therefore, physicists are scientisits.

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

13 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.

14 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.15 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.16 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.17 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.

18 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.

Imported fruits are expensive.

But grapes are impoted fruits. Therefore, grapes are not cheap.

19 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.20 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.

21 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.

All good athletes are not tall. But all good athletes are physically fit. Ergo, everyone who is physically fit is tall.

Rule No. 8 If one premise is particular, the conclusion must be particular.22 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.

23 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

24 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 – Pu25 The 3rd set of premise is that of A and O. Here, there are again 2 universal terms and 2

particular terms.26 The 4th combination is that of E and O. Because both premises are negative, no valid

conclusion can be drawn from them.

27 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.28 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.29 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.

Some beautiful girls are smart. Some girls are ugly. Ergo,some ugly girls are smart.

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

There are only 24 valid resulting syllogisms when 12 moods are constructed in 4 figures, these are:

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)

The 5 moods in parenthesis [( )] represents 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.

The 4 moods in enclosed in double parenthesis [(( ))] represents 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.

Syllogistic Reduction

- A kind of logical argument in which one propositions (the conclusion) is inferred from two others (the premises) of a certain form.- code names are used in traditional logic of each syllogism figures that one value

Reduction - transformation of a syllogism- the first figure of the mood is considered as the perfect figure

Figures:

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

fEIAptOn dImArIsbOcArdO

- the first letter of the code names signify the mood of the first figure into which it may be reduced

Example: cEsArE to cEIArEntPu - Mu Mu - PuSu + Mp Su + MpSu - Pu Su - Pu

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.

Testing the Validity by the Venn diagram Method

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

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 is 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”

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

Testing the Validity by the Antilogism Method- It 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 propostions or 2 equations ‘=’ and 1 inequation ‘≠’- 2 equations have common term which occurs once affirmatively and once negatively- Inequation will contain the other terms, identically as they occur in the equations

Example:All animals are friendly. CS = O

All bunnies are cuddly. MC = O

Ergo, all bunnies are friendly. MS = O

Antilogism:All cars are swift. CS = O

All BMW are cars. MC = O

Some BMW are not swift. MS ≠ O

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

The 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.

5. 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. A snake is an amphibian or not. A snake is not an amphibian. Ergo, a snake is a non- amphibian.

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

The 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

Chapter 9

Variations of the Syllogism

The Enthymeme - it is a syllogism with one part of the argument missing

it has 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.

- It is 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

- It means 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

Given: 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

- It 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

- It is a string of any number of propositions forming together a sequence of syllogisms such that the conclusion of each syllogism, together with the next proposition, is a premise for the next, and so on. Each constituent syllogism except the very last, because the conclusion of the last syllogism is not a premise for another syllogism; a chain argument

Example:

It is hot.If we touch it while it is still hot we will get burned.Therefore, if we touch it we will get burned.

If we touch it we will get burned.If we get burned, we will go to the hospital.Therefore, if we touch it we will go to the hospital.

The Sorites

- It is a specific kind of polysyllogism in which the predicate of each proposition is the subject of the next premise; 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 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

Example:

S A Books are mind-stimulator equipment.A B Mind-stimulator equipment is not an energy-giver device.B P What is not an energy-giver device is not advisable.S P Ergo, books are not advisable.

The Dilemma

- It 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, CExample:

If yoga is healthy then it should be executed everyday.If eating is nourishing, then it should be executed everyday.But either yoga is healthy or eating is nourishing.Ergo, it should be executed everyday.

2. Complex Constructive Dilemma

Premises: If A, then CIf B, then D

either ABut

or BConclusion: Ergo, C or D.

Example:

If stones are hard, then it is durable.If plastics are non-biodegradable, then it could last a long time.But either stones are hard or plastics are non-biodegradable.Ergo, then it is durable or it could last a long time.

3. Simple Destructive Dilemma

Premises: If A, then C and Deither not C

Butor not D

Conclusion: Ergo, not A

Example:

If angels are from heaven, then they use their wings and befriend people. But they will neither use their wings nor befriend people.Ergo, they are not from heaven.

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

Example:

If Maria is hungry, then she must eat her sandwichIf her classmates are hungry, she must give it to them.But Maria will eat neither she will eat her sandwich nor give it to her classmates. Ergo, she will make neither herself nor her classmates hungry.