Lesson3-Special forms, syllogisms

LESSON 3 E

INDUCTION AND OTHER FORMS OF SYLLOGISMS

Induction is a method of inference that proceeds from the relationships of particular truths towards a universal truth.

In reality, human knowledge started from the inductive process since what man experiences are particular realities and man will have to grasp first the particular truths of reality before he can abstract these to universal truths. From these universal truths man is able to further improve his knowledge of the particular as deduced from universal truths and principles.

The conclusions of induction are less probable and are a far cry from the certainty of the conclusions of deduction. However, the synthesis of the different human experiences and the body of human knowledge that has evolved and survived the test of time lends credit to the validity of the inductive process. This was further reinforced by the conclusions of deductive inferential thinking that validated and was often intertwined and has complemented the conclusions of inductive inferential thinking.

Type of Analogy Tests

1. Single Approach. Example: Fish: Shoal :: Swine:________
2. Paired Approach. Example: Gynophobia: Women::_________:___________
3. Elimination Approach. Example: Eyes, Ears, Mouth, Nose, Feet
4. Number Series or Completion Approach. Example: Three, Twelve, Forty-eight, _________
5. Abstract Reasoning Approach. Example:  ABCD, BCDE, CDEF, DEFG,__________

Note: The Key in answering analogy test is to determine the relationships that exist between and among the items and to complete the sentence.

Examples: A group of fish is a shoal as a group of swine is a drift. The answer to #1 is Drift

              Eyes, ears, mouth and nose are found in the head while feet is not. Feet is the answer to # 3.

Types of Induction

1 Essential Induction when the mind grasps in experience the necessary link between a subject and its property. It makes use of formal principles, which are so clear that they do not need any proof for they are self-explanatory and self-evident truths. These principles are:

1. The principle of Identity. Everything is itself.

     Ex.: A school is a School.

2. The principle of excluded middle. A thing either is or is not.

     Ex.: A school is either a school or not a school

                        3.  The principle of non-contradiction. Nothing can be and not be at the same

time or respect.

     Ex.: A school cannot be a school and not a school at 

           the same time.

4. The principle of sufficient reason. Everything that exist has sufficient reason 

            for its existence.

      Ex.: A school is a place of learning.

2. Empirical Induction is the generalization of the connection between the subject and the predicate based not on the essential link between them but on the repeated occurrence of the observed phenomenon.

2 kinds of Empirical Induction

1.      Complete or perfect induction. The generalization rest on the knowledge of each instance covered. This is otherwise known as the induction by simple enumeration because it is simply the summation of all individual cases observed.

Example: Since Dr. Marin, Dr. Garcia , Prof. Manad, Prof. Gonzales and the rest of the faculty members of PNU are Master’s degree holders, We can conclude that all PNU teachers are master’s degree holders.

2.      Incomplete induction. The conclusion takes the instances as a sample of the class and generalizes from the properties of the sample to the properties of the class.

Example:  Since 80 % of survey respondents said that they prefer LRT to Jeepney’s as mode of transportation, we conclude that LRT is preferred as a mode of transportation by the public.

Examples of Incomplete Induction

·        Analogy is a form of induction, which seeks to establish a conclusion on something that is yet unknown to a thing based on similarities. Example: Peso is to Philippines as dollar is to United States of America.

·        Generalization is a form of induction that seeks to establish a conclusion about a whole group or population based on some samples. Example: We conclude that Filipinos are hospitable based on the result of the survey.

·        Causal Relation is a form of induction, which seeks to establish a conclusion based on the connection between cause and effect. Example: Based on our past experiences, Metro Manila becomes flooded whenever it is hit by a typhoon.

OTHER FORMS OF SYLLOGISMS

The five special forms of syllogisms are Enthememes, Epichiremes, Polysyllogisms, Sorites and Dilemmas.

1.ENTHYMEME

            Enthymemes are shortened forms of syllogism in which one of the premises or the conclusion is not expressed but implied.

            3 kinds of Enthymeme

1.      Enthymeme of the first order- the major premise is omitted

Example: Peter is free because he has a will

The syllogism is as follows:

 (All beings that have a will are free)

 But Peter has a will

Therefore, Peter is free

2.      Enthymeme of the second order- where the minor premise is omitted.

Example: Since all training programs are contributors to

human development then care-giving  is a contributor to human development.

                   

The syllogism is as follows:

All training programs are contributors to human development

                    (But care giving is a training program)

  Therefore, care giving is a contributor to human  

  development

3.      Enthymeme of the third order- where the conclusion is omitted

Example: All intelligent beings are beings that have

  morality and man is an intelligent   being

The complete syllogism is as follows:

All intelligent beings are beings that have morality

But man is an intelligent being;

 (Therefore, man is a being that has morality)

2. EPICHIREME.

Epichireme is another form of syllogism wherein a proof is joined to one or both premises. The proof is an explanation of the given premise. It is normally connected to the premise by such causal clauses as for, because, since, and insofar as. An epichireme makes use of an enthymeme for its premise thus there are actually more than one argument in an epichireme.

Two types of Epichireme

1.      Simple Epichireme- where one of the premises is accompanied by a proof or an explanation

Example: All human beings are rational

 because all men have a soul

               But doctors are human beings;

               Therefore, doctors are rational.

2.      Compound Epichireme- where both of the premises are accompanied by proofs or explanations. Actually the syllogism is made up of three arguments; the main syllogism and the two enthymemes that act as premises.

Example: All research works are beneficial to students

 because students learn to look for primary   sources of information

But all things beneficial to students are the   tasks of education

 since education is for total human development of 

 the students

                               therefore, some tasks of education are research

       works.

3.  POLYSYLLOGISM

             A Polysyllogism is a series of syllogism that are so related that the conclusion of the first becomes the major premise of the second syllogism and so on. When there are only two syllogism that are connected as such, it is known as Episyllogism.

            Example: 1. Every human being is a rational being;

                               But students are human beings;

                           2. therefore, students are rational beings

                               But All rational beings are free

                           3.Therefore, some free beings are students;

                              No slaves are free beings;

                              Therefore, some slaves are not students.

4. SORITES

            A Sorite is a shortened polysyllogism wherein the conclusions are suspended or not stated except the last.

            2 kinds of Sorites

1.      Aristotelian Sorites- a sylogism that uses the predicate of the preceding premise as the subject of the next premise and so on and so forth.

Example: All good students are good learners

                  But all good learners are rational beings

                  But all rational beings are responsible beings

                  But all responsible beings perform are good

performers of their civic duties;

                        But all good performers of their civic duties are

good citizens;

                        Therefore, all good students are good citizens.

2.      Goclenian Sorites. This employs the opposite form of the Aristotilian sorite. The subject of the preceding premise becomes the predicate of the next premise and so forth.

Example:    All responsible teachers are role models;

                  But effective teachers are responsible teachers;

                  But all efficient teachers are effective teachers;

                  But all awardees are efficient teachers;

                  Therefore, all awardees are role models.

Rules for the validity of Sorites

1.      All the premises must be universal except for the first. If the first premise is particular the conclusion must be particular.

2.      All the premises must be affirmative except for the last. If the last premise is negative, the conclusion should be negative.

3.      There must be sequence between and among the premises.

5. DILEMMA

A dilemma is a horned argument. This is an argument that gives two alternatives or choices both of which are detrimental to the one who will make the choice. The structure of the dilemma is so arranged that both alternatives will result into a conclusion that is both unfavorable to the one choosing thus pinning him down.

The major premise is a conditional hypothetical proposition and the minor premise is a disjunctive proposition or vice versa. The conclusion is either a categorical or a hypothetical proposition.

Kinds of Dilemma

1.      Simple constructive dilemma- where the conclusion is a simple and an affirmative proposition.

Example: Either, you give a report or you improve your

extra- curricular involvement;

              if  you give a report you’ll gain additional credit.

              if  you improve your extra- curricular activities

       you’ll gain additional credit.

                               Therefore, in any case, you’ll earn additional credit.

2.      Compound constructive dilemma-where the conclusion is a compound and an affirmative proposition.

Example:

    If I continue my studies then I will finish my degree.

                             and If I work then I will earn money to support my family.

   But either I continue my studies or work;

  Therefore, either I will finish my studies or I will earn money to support my family.

3.      Simple destructive dilemma- where the conclusion is a simple and negative proposition.

Example: The man trapped at the 20^th floor of a burning

                                   building will either not jump or he will not stay.

             If the man doesn’t jump, he will not survive because of the fire;

             If the man doesn’t stays, he will not survive because of the fall;

            Therefore, the man will not survive.

4.      Compound destructive dilemma-where the conclusion is a compound and negative proposition.

Example:

      In politic, if I’ll be honest then my colleagues will not like me

                        If I’ll be corrupt then people will not vote for me again;

                        But in politics, either I’ll be honest or I’ll be corrupt

                        Therefore, either my colleagues will not like me or the

people will not vote for me again.

Rules for a Valid Dilemma

1.       All the possible alternatives of the disjunction must be stated.

2.       The consequent of the conditional proposition must necessarily follow from the antecedents. There must be a valid sequence.

3.       Present alternatives that cannot be taken in two different respects, that is, it may not be interpreted both in its positive and negative perspective.

Ways to Defeat a Dilemma

1.      Going between the horns. Point out that there is another alternative not presented in the disjunction and its consequent is different or opposite the stated consequent. Or point out that there is another possible consequent for the given antecedent.

Example: Either you concentrate on relationship or on task

 If you concentrate on relationship then your efficiency will suffer.

      If you concentrate on task then your social life will suffer.

Thus, either your efficiency will suffer or your social life will suffer

This dilemma may be countered by pointing out that a balance between relationship and task will improve both your efficiency and social life.

2.      Grasping the dilemma by the horn. Point out that there is no sequence between the antecedent and the consequent. Or point out that the opposite of the consequent can also be the consequent of the given antecedent.

Example: Either I give the students a lecture or give them activities

              But If I give the students a lecture, I will be wasting

 time since they normally get bored and don’t listen.

                                If I give them activities, I will be wasting time for

they normally don’t cooperate and participate.

                                Therefore, in either case, I will be wasting time.

This dilemma may be countered by pointing out that “If I give a lecture then my students will learn and if I give activities, students will learn. So, in any case it will not be wasting time because students will learn”.

3.      Rebutting the dilemma. Point out an opposite conclusion in a counter-dilemma by reversing the original dilemma. If the perspective is negative, use a positive perspective and vice versa in a counter -dilemma.

Example:  If I tell a lie my teachers will be angry with me.

                If I tell the truth my classmates will be angry with me

                                  But either I tell a lie or l tell the truth

                                  In any case people will be angry with me.

                   Rebuttal: If I tell a lie my classmates will not be angry with me

                                If I tell the truth, my teachers will not be angry with me

                                But either I tell a lie or I tell the truth;

                                In any case, people will not be angry with me.