Varieties of Categorical Syllogism Mark Anthony D. Abenir, MCD Department of Philosophy & Humanities University of Santo TomasTopic Outline 1. Enthymeme 2. Epichereme 3. Polysyllogism 4. Sorites 5. DilemmaEnthymeme • Comes from the Greek terms enthymos which Means “in the mind.” • Is an abridged syllogism in which one of the premises or conclusion is not expressed but implied or understood in the mind. There are 3 Kinds: 1. Of the First Order 2. Of the Second Order 3. Of the Third Order Enthymeme of the 1st Order • The supreme good is infinitely lovable.
Transcript
Varieties of Categorical
Syllogism
Mark Anthony D. Abenir, MCD
Department of Philosophy & Humanities
University of Santo TomasTopic Outline
1. Enthymeme
2. Epichereme
3. Polysyllogism
4. Sorites
5. DilemmaEnthymeme
• Comes from the Greek terms enthymos which
Means “in the mind.”
• Is an abridged syllogism in which one of the premises
or conclusion is not expressed but implied or
understood in the mind. There are 3 Kinds:
1. Of the First Order
2. Of the Second Order
3. Of the Third Order
Enthymeme of the 1st Order
• The supreme good is infinitely lovable.
• But, God is the supreme good.
• Hence, God is infinitely lovable.
• Major premise is omitted.
• Example: God is the supreme good. Hence,
God is infinitely lovable
.Enthymeme of the 1st Order
• A Prayerful person is pious.
• But, Some monks are prayerful.
• Hence, Some monks are pious.
• Some monks are pious since some of them are prayerful.
Enthymeme of the 2nd Order
• Cancers are life-threatening.
• But, Leukaemia is cancer.
• Hence, Leukaemia is life-threatening.
• Minor premise is omitted.
• Example: Cancers are life-threatening. Hence,
Leukaemia is life-threatening
.• Example: Due to the fact that a traitor
is a liar, hence, Judas is a liar.
Enthymeme of the 2nd Order
• A traitor is a liar.
• But, Judas is traitor.
• Hence, Judas is a liar.• Conclusion is omitted.
• Example: Anything worth pursuing is worth
our time. But truth is worth pursuing.
Enthymeme of the 3rd Order
• Anything worth pursuing is worth our time.
• But, Truth is worth pursuing.
• Hence, Truth is worth our time.• All crimes are punishable by law and
corruption is a crime.
Enthymeme of the 3rd Order
• All crimes are punishable by law.
• And, corruption is a crime.
• Hence, Corruption is punishable by law.Epichereme
Comes from the Greek word epi cheir which
means “on hand.”
Syllogism in which one or both premises are
supported by proofs. The accompanying proof is
the explanation of the given premise. There are
2 Kinds:
1. Simple
2. Compound• Only one premise is accompanied by a
proof or explanation.
Simple Epichereme
• Love is unexplainable for it is mysterious.
• But, God is love.
• Hence, God is unexplainable.
• Anything mysterious is unexplainable.
• But, Love is mysterious.
• Hence, Love is unexplainable.Simple Epichereme
• Human beings are intelligent for
they are endowed with rationality.
• But, Daphne is a human being.
• Hence, Daphne is intelligent.
• Any being endowed with rationality is intelligent.
• But, Human beings are endowed with rationality.
• Hence, Human beings are intelligent.
• Both premises are accompanied by a proof or explanation.
Compound Epichereme
• Whatever is spiritual is immortal
because a spiritual being is incorruptible.
• But, the human soul is spiritual because
it is capable of grasping immaterial forms.
• Hence, The human soul is immortal.
• Whatever is spiritual is immortal because
a spiritual being is incorruptible.
Compound Epichereme
• Anything incorruptible is immortal.
• But, A spiritual being is incorruptible.
• Hence, Whatever is spiritual is immortal
l• The human soul is spiritual because it is
capable of grasping immaterial forms.
Compound Epichereme
• Anything capable of grasping immaterial
forms is spiritual.
• But, The human soul is capable of
grasping immaterial forms.
• Hence, The human soul is spiritual.Polysyllogism
Syllogism which is composed of several
syllogisms so related to one another that the
conclusion of one serves as the major
premise of the other.Polysyllogism
• The more one is close to God, the more one suffers.
• The more one suffers, the more one understands life.
• The more one understands life, the more one relates
to people.
• The more one relates to people, the more one
understands himself/herself.
• Ergo, The more one is close to God, the more one
understands himself/herself.
Sorites Abridged form of polysyllogism wherein the
intermediate conclusions are left out.
1. Aristotelian Sorites
2. Goclenian Sorites• The predicate of the preceding premise
becomes the subject of the following.
Aristotelian Sorites
• All A is B
• All B is C
• All C is D
• All D is E
• Ergo, All A is E.
Aristotelian Sorites
• Philosophers are wide readers;
• Wide readers are intelligent;
• Intelligent people are creative;
• Creative people are producers of good ideas.
• Ergo, Philosophers are producers of
good ideas.
The subject of the preceding premise becomes
the predicate of the following. In the
conclusion, the subject of the last premise is
united with the predicate of the first.
Goclenian Sorites
• All A is B
• All C is A
• All D is C
• All E is D
• Ergo, All E is B
.Goclenian Sorites
• One who will not sacrifice truth for power is a responsible person.
• One who is a paragon of honesty will not sacrifice truth for power.
• One who is worth emulating is one who is a paragon of honesty.
• Ergo One who is worth emulating is a responsible person.
Dilemma
Comes from the Greek dis (twice) and lemma
(assumption).
• Also known as horned argument.
• It is a form of argument whose major premise is a
disjunctive or conditional proposition, and whose
minor premise shows that whichever alternative the
opponent chooses, is conclusively against him/her. Kinds of Dilemma
Simple
Constructive
Complex
ConstructiveKinds of Dilemma
Simple
Destructive
Complex
DestructiveSimple Constructive
• Either you were asleep or you were
not;
• If you were, you deserve punishment
(for dereliction of duty).
• If you were not, you deserve
punishment (for being incompetent).
• Ergo, in either case, you deserve
punishment.Simple Constructive
• I must either jump or stay;
• If I jump, I shall die (immediately
from the fall).
• If I stay, I shall die (slowly from
the fire).
• Ergo, in either case, I shall die.Complex Constructive
• If a candidate is a reelectionist, then
she has nothing new to offer.
• If a candidate is not a reelectionist,
then she is not yet equipped in
political matters.
• But, she is either a reelectionist or
not.
• Therefore, in either case, she has
nothing new to offer or she is not yet
equipped in political matters. Simple Destructive
• If Mario studies Medicine, he will
have to study really hard and he
will have to pay high tuition fees.
• But, Mario either will not study
really hard or he will not be able
to pay high tuition fees.
• Therefore, Mario will not study
Medicine.Simple Destructive
• If I am to pass the examination, I
must study all night and I must
also be mentally alert as I write.
• But it’s either I do not study all
night or I am not mentally alert
as I write.
• Therefore, I will not pass the
examination.Complex Destructive
• If medicine prices are to be stabilized, then the
government must have control over the stocks of
pharmaceutical drugs.
• If greater pharmaceutical drugs production is to be
realized, the government should encourage greater
cooperation among pharmaceutical industries.
• But the government either does not have control over
the stocks of pharmaceutical drugs or does not
encourage greater cooperation among pharmaceutical
industries.
• Ergo, medicine prices are not stabilized or greater
pharmaceutical drugs production is not realized.Rules of the Dilemma1. The disjunctive enumeration must
be complete.
• Either the weather is cold or sunny.
• If it’s cold, I can’t go out because I’ll get colds.
• If it’s sunny, I can’t go out because I don’t want
to get dark.
• In either case, I won’t be able to go out.
• An exclusive disjunction is the best.
• Inclusive disjunctions are open to “escape
between the horns.”2. In the conditional proposition, the
consequents must flow with logical
necessity from the antecedents.
• If I take up medicine, I will not be able
to earn soon.
• If I take up a two year course, I will not
be able to earn a lot.
• But, either I take up medicine or a two
year course.
• I won’t be able to earn soon or I won’t
be able to earn a lot.
• If not, one can “take the dilemma by the
horns.”3. The dilemma must not be open to
rebuttal.
• If open to rebuttal, the purpose of a counterdilemma is to present a conclusion different
from that of the original. Ideally, the counterdilemma is built out of the same material that
the original dilemma contained.3. The dilemma must not be open to
rebuttal.
• Either the test is easy or not easy;
• If it is easy, I will not be challenged at all;
• If it is not easy, I will not be able to answer it;
• Ergo, either I will not be challenged at all or I
will not be able to answer it.
• Either the test is easy or not easy;
• If it is easy, then you will be able to answer it;
• If it is not easy, then you will be challenged by
it;
• Ergo, either you will be able to answer the test
or you will be challenged by it.3. The dilemma must not be open to
rebuttal.
• If Atty. Juan loses this case, then he must pay
me by the judgment of the court.
• If Atty. Juan wins this case, then he must pay
me (by the terms of the contract).
• But, he must either win or lose this case.
• If I win this case, I shall not pay you (by the
judgment of the court).
• If I lose this case, I shall not pay you (by the
terms of the contract).
• But, I must either win or lose this case.
• Therefore, I do not have to pay you.
Thursday, February 28, 2008VARIETIES OF CATEGORICAL SYLLOGISMThe previous chapter focused on the simple categorical syllogism. The present chapter deals with other varieties of categorical syllogism which in some arguments will prove useful in arriving a conclusion. These varieties include the enthymeme, the epichereme, the polysyllogism, the sorites and the dilemma.
The Enthymeme
The enthymeme is an abbreviated or shortened type of categorical syllogism in that one of its premises or its conclusion is left unexpressed. Enthymemes are of three categories, distinguished on the basis of the missing [art of an argument.
1.Missing Major – enthymemes are of the missing major category when the major premise of an argument is not expressed.
For example,
Africans are men,Therefore, they are mortal beings.
2.Missing Minor – enthymemes belong to the missing minor category when the minor premise of an argument is omitted. For example,
Men are mortal beings,Therefore, Africans are mortal beings.
3.Missing Conclusion – enthymemes whose conclusion is not expresses belong to the missing conclusion category. For example,
Men are mortal beings,Therefore, Africans are men.
Enthymemes are categorical syllogism because of the presence of three syllogism terms. In the example for each category, above the syllogistic are men,” “Africans,” and “mortal beings.”
To check to which category an enthymeme belongs it will be helpful reconstruct in its full syllogistic form. Then, on the basis of the syllogistic term one can easily determine the category of an enthymeme. Using the example, above, its full syllogistic form is as follows:
Men are mortal beings,but Africans are men;therefore, they (Africans) are mortal beings.
The Epichereme
The epichireme is a type of categorical syllogism whose premise or premise are provided with proofs. The proof is often joined with the premise with a causal connective such as “for,” because,” “since,” “due to,” and so on. For example,
Demagogues are persistent and aggressive because they are intensely-motivated,but because of their commitment to their cause communists are Demagogues,therefore, communists are persistent and aggressive.
In this example each premise has a proof. In the major premise the proof is “because they are intensely-motivated.” In the minor premise the proof is “because of their commitment to their cause.” Here are other examples:
1.Human beings will die because of their corruptible nature; but because of the presence of germs human beings are stalked with illnesses; therefore, anyone stalked with illnesses will die.
2.This city needs Darwin Selarda as mayor. Only a strong-hearted person can fight corruption. Only a man with keen business acumen can improve the economy. Only an upright person can bring back the dignity of the citizenry. Mr. Selarda has all these qualifications. Therefore, we must elect him as our next mayor.
The Polysyllogism
The polysyllogism is a chain of syllogisms which are constructed in a manner that the conclusion of the first syllogism serves as the premise of the next, and so on. The word “polysyllogism” is derived from the Greek word poly which means “many”. For the syllogism to be valid each individual syllogism must be valid by observing the rules of simple syllogism. Just one invalid individual syllogism in the series will render the whole chain of syllogism invalid. For example,
Animals are subject to death,but men are animals,therefore, men are subject to death,but Asians are men,therefore, Asians are subject to death,but Filipinos are Asians,therefore, Filipinos are subject to deathbut Cebuanos are Filipinos,Therefore, Cebuanos are subject to death,But Sergio Osmeña is a Cebuano,Therefore, Sergio Osmeña is subject to death.
The Sorites
The sorites is an abridged polysyllogism in which the intermediate conclusions are omitted. The word “sorites” is derived from the Greek word soros, which means “heap.”
The simple sorites is either Aristotelian which is progressive in form or Goclenian which is regressive. The classical Aristotelian sorites is a series of simple syllogism so arranged that the predicate-term of each premise is the subject-term of the following premise, and the subject-term of the first premises is the subject-term of the conclusion. The extension of the predicate-term of each succeeding premise is increasing. For example,
Every Cebuano is a Filipino,Every Filipino is an Asian,Every Asian is a man,Every man is a mortal being,Therefore every Cebuano is a mortal being.
In the Goclenian sorites the same premises occur, but their sequence is reversed. Here, the subject-term of each premises is the predicate-term of the following premise, and the
predicate-term of the first premise is the predicate-term of the conclusion. In contrast to Aristotelian sorites, the predicate-term of each premise shows a decreasing extension. To illustrate,
Every man is a mortal being,Every Asian is a man,Every Filipino is an Asian,Every Cebuano is a Filipino,Therefore, every Cebuano is a mortal being,
The Dilemma
The dilemma is a type of syllogism which combines the conditional and the disjunctive propositions. The major premise consists of two or more additional propositions. The minor premise is a disjunction proposition that their affirms the antecedents or denies the consequents of each of the simple conditional propositions. The dilemma is either constructive or destructive in form.
Constructive Dilemma
The dilemma is a type of syllogism which combines the conditional and the disjunctive propositions. The major premise consists of two or more additional propositions. The minor premise is disjunctive proposition that either affirms the antecedents or denies the consequents of each of the simple conditional propositions. The dilemma is either constructive or destructive in form.
Review of the Type of Propositions
a)Categorical Propositions – are propositions that either affirms or denies something without any qualification or condition.Examples:•Darwin is tall.•The weather is not good•Some men are honest individuals.
b)Conditional Propositions – are propositions that makes an assertion but qualified by a condition.Examples:•If the weather is fine, then we shall go boating.•If mother approves, then I will go to the dance party.•Election of officers will be held, only when fifty percent are in attendance.
c)Disjunctive Propositions – are propositions which presents two or more alternatives one of which is true.Examples:•He is either asleep or awake.•Juan will take up either engineering, architecture or medicine.
•Either we have a national language or we do not.
d)Conjunctive Propositions – are propositions which presents two alternatives which cannot be true simultaneously or at the same time.Examples:•She cannot be single and married too.*Mothers cannot be caring and uncaring at the same time.•It is impossible for a day to be sunny and at the same time rainy.
The dilemma is constructive in form when the minor premise is a conditional proposition that affirms a member of the disjunctive major premise. It is either simple or complex. It is simple constructive dilemma when the conditional premise infers the same consequent from all the antecedents presented in the disjunctive proposition. For example,
He must tell the truth or tell a lie – he has no other choice.If he will tell the truth, he will be damned for braking the law of man;If he will tell a lie, he will be damned for breaking the law of God;Therefore, he will be damned.
The constructive dilemma is complex when the conditional premise infers a different consequent from each of their antecedents given in the disjunctive proposition. The President of a country was in such a dilemma when he was urged to pardon a rapist about to be executed by lethal injection;
The President will either allow him to be executed or pardon him.If he will do the first, he will get the ire of the people who wanted the rapist executed.If he will do the second, he will get into trouble with the people who were against the death penalty;
Therefore, he will either get the ire of the trouble who were for execution, or get into trouble with the people who were against the death penalty.
Destructive Dilemma
The Dilemma is destructive in form when the minor premise denies the consequents of the conditional major premise. It is either simple or complex.
It is simple destructive dilemma when the conditional major premise infers more than one consequent from the same antecedent. The disjunctive proposition denies the consequents alternatively in the minor premise, and the antecedent is denied in the conclusion. For example
If I am to buy that piece of land, I must do two things – I must work hard to earn the needed amount and I must appeal to defer full payment.But either I will not work hard to earn the needed amount, or I will not make an appeal to defer full payment.
Therefore, I will not be able to buy that piece of land.
The destructive dilemma is complex when the conditional major premise infers a different consequent from each antecedent. The disjunctive minor premise these consequents alternatively. For example.
If we are to avoid global warming, then we must protect our forests; and if we must protect our forests, then we must stop indiscriminate logging.We will either not protect our forests or not stop indiscriminate logging.Therefore, we will either not avoid global warming or not protect our forest.
THE HYPOTHETICAL SYLLOGISM
Definition and Kinds
DefinitionA hypothetical syllogism is a syllogism whose first premise is either a sequential proposition or that which presents alternatives, one member of which is affirmed or denied in the second premise, and the other member is consequently affirmed or denied in conclusion. This is to say that the first premises of a hypothetical syllogism is a hypothetical proposition that either expresses a sequential relationship or presents alternatives one of which must be true. Sequential relationship is expressed in the proposition,” If you have poor eyesight, then you cannot join the team.” Alternatives are presented in these propositions: “He is either for you or against you,” and “He cannot be married and can be single too.”It should be noted that, unlike in the categorical syllogism, there is no major and minor premises in the hypothetical syllogism because there is no major or minor term. Thus, it is proper to distinguish the premises as either the first premise, or the second premise.
KindsThere are three kinds of hypothetical syllogism – the conditional, the disjunctive and the conjunctive. Each of these kinds is distinguished on the basis of the type of hypothetical proposition its first premise is. Thus, a conditional syllogism has for its first premise a conditional proposition (“If… then …”), the disjunctive syllogism has the disjunctive proposition (“either.. or…”), and the conjunctive syllogism has the conjunctive proposition )”not both… and …”).
A. Conditional syllogism. The conditional syllogism is the kind of hypothetical syllogism whose premise or premises are conditional propositions. The conditional proposition is a compound proposition one part of which states the condition, called the antecedent, and the other part states the consequent or assertion the validity of which is dependent on the condition aforesaid. The conditional syllogism may either be mixed or pure in kind.
1. Mixed conditional syllogism. The mixed conditional syllogism consists of a conditional proposition for its first premise and a categorical proposition for its second premise which affirms the antecedent or denies the consequent of the first premise.
There are two valid procedures with which the mixed conditional syllogism can be constructed. One valid procedure is to affirm the antecedent of the first premise in the second premise and to also affirm its consequent in the conclusion. For example,
If he studies well, then he will pass this course;but he studies well,therefore, he will pass this course.
The other valid procedure is to deny the consequent of the first premise in the second premise and to also deny its antecedent in the conclusion. For example,
If man has control over his emotion, then he will have peace;But he will have peace,Hence, man has no control over his emotions.
Procedures other than these two are not valid, as in the case of the following:
1. If he studies well, then he will pass this course;but he will pass this course,therefore, he studies well.
2. If man has control over this emotion, then he will have peace;but he will have peace;therefore, man has control over his emotion.
From the illustration, above, two rules governing the mixed conditional syllogism can be deduced. These are:
1. If the antecedent is true and is affirmed, then the consequent is also true and must be affirmed.2. If the consequent is false and is denied, then the antecedent is also false and must be denied.
These two rules are valid as long as the sequence between the antecedent and the consequent is valid.
2. Pure conditional syllogism. The pure conditional syllogism consists of conditional propositions in both premises and consequently, has a conditional proposition for its conclusion. This is, therefore, the true hypothetical syllogism for nothing definite is arrived at by this kind of argument or reasoning. As such it has little scientific value, for science aims in attaining knowledge which is certain or definite.
The procedure and the rules of the mixed conditional syllogism to the pure conditional syllogism with one exception: the condition stated in the second premise must be retained
in the conclusion. Below are valid examples.
1. If man has control over his emotions, then he is responsible for what he says;but if man is rational, then he will have control over his emotions;therefore, if man is rational, then he is responsible for what he says.
2. If man has control over his emotions, then he is responsible for what he says;but if man is not rational, then he is not responsible for what he says;hence, if man is not rational, then he has no control over his emotions.
Fallacies of conditional syllogism. There are four possible fallacies on the conditional syllogism which can be committed in the second premise or in the conclusion. In the second premise these two fallacies are possible:
1. denying the antecedent, and2. affirming the consequent.
In the conclusion, the two possible fallacies are:
1. affirming the antecedent (when the second premise denied the consequent), and2. denying the consequent (when the second premise affirmed the antecedent).
B. Disjunctive Syllogism. The disjunctive syllogism is a syllogism whose first premise is a disjunctive proposition, its second premise is a categorical proposition which either affirms or denies one or more alternatives of the first premise, and whose conclusion either affirms or denies the remaining alternatives. The disjunctive proposition is a proposition which presents a number of alternatives and asserts that one of them is true. The disjunctive syllogism is of two kinds – the strict disjunctive and the broad disjunctive.
1. Strict disjunctive syllogism. The strict disjunctive syllogism has for its premise a disjunctive proposition of which only one of its alternative is true. It s second premise is a categorical proposition which either affirms or denies one or more but not all of the alternatives of the first premise. Its conclusion either (a) denies the alternatives which were not affirmed in the second premise, or (b) affirms alternatives which were not denied in the second premise. Below are valid examples.
1. His car is either red, blue or green;but his car is red;therefore, his car is either blue nor green.
2. His car is either red, blue or green;but his car is not red;therefore, his car is either blue or green.
It should be noted that the first example concludes with the denial of alternatives not affirmed in the second premise, using the “neither… nor…”phrase. The second example, on the other hand, concludes with an affirmation of alternatives not denied in the second
premise, making use of the “either… or…”phrase.
Broad disjunctive syllogism. The broad disjunctive syllogism has for its first premise a disjunctive proposition of which more than one of its alternative may be true. Its only valid procedure is for its second premise to deny one or more but not all of the alternatives in the first premise, and to affirm the remaining alternatives in the conclusion. For example,
His pen is either black, red, violet, or green;but his pen is neither black nor red:therefore, his pen is either violet or green.
C. Conjunctive Syllogism. The conjunctive syllogism is the kind which has a conjunctive proposition for its first premise, whose second premise is a categorical proposition which affirms one of the alternatives of the first premise, and whose conclusion denies the other alternatives. The conjunctive proposition I the type which denies the possibility of two alternatives at the same time, as in: :You cannot be married and can be single too.”
In constructing a conjunctive syllogism, only one procedure is valid. The second premise affirms one alternative of the first premise, and the conclusion denies the rest of the alternatives. Care must be taken that the alternatives presented in the first premises are mutually exclusive, otherwise the process of exclusion cannot be made. The following syllogism serve as examples:
1.He cannot be inside and can be outside of the country too; but he is inside the country; therefore, he is not outside the country.
3.A person cannot be a real Marxist, a good Christian or a devout Muslim at the same time; but this person is a real Marxist; therefore, this person is neither a good Christian nor a devout Muslim.
A. Identify the following according to the varieties of Categorical Syllogism
__________________________a.God loves all sinners; the mayor is a sinner.__________________________b.The weather is bad; so I will stay home__________________________c.Norsunians are intelligent because they study everyday.But Jack is intelligentTherefore, jack is a Norsunian.__________________________d.Animals are living things,Dogs are animals,Therefore, dogs are living things.But Dalmatians are dogs
therefore, dalmatians are living things__________________________e.Every Norsunian is a Filipino,Every Filipino is an Asian,Every Asian is a man,Every man is a mortal being,Therefore, every Norsunian is a mortal being__________________________f.Gloria must either tell the truth or tell a lie – she has no other choiceIf she will tell the truth, she will be punished for breaking the law of man,If she will tell a lie, she will be punished for breaking the law of God,Therefore she will be punished.
B.Give one example of the Following Varieties of CS
a)Enthymemea.Missing major
b.Missing minor
c.Missing conclusion
b)Epichereme
c)Polysyllogism
d)Soritesa.Aristotelian
b.Goclenian
e)Dilemmaa.Constructive Dilemma
b.Destructive Dilemma
II. Hypothetical Syllogism
A.Give one example of each following kinds of hypothetical syllogisma.Conditional syllogism•Mixed conditional syllogism•Pure conditional syllogismb.Disjunctive Syllogism•Strict disjunctive syllogism
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