Philosophy: Logic

1.  Categorical syllogisms

 Logic is a branch of philosophy that concerns rules and principles for valid and coherent reasoning. It is treated in what Aristotle called syllogism. We have material logic (looks for the truth of the content) and formal logic (concerned with the validity of the structure of reasoning without considering the content. Ex:

All stones are fire,

Every fire is water

Therefore all stones are water.

We shall not develop material logic. Our focus is on formal logic.

There is no truth in the content of this syllogism but the structure of this reasoning is valid. We may also have a syllogism whose content is true but the structure of the syllogism is invalid: ex:

Some Africans are Rwandans

Yet you are Rwandan

Therefore you are African.

1. 1.       Rules of Syllogism:

 One should know the components of a syllogism before applying the rules:

 Example of a syllogism:

 Human beings are mortal

Socrates is a human being

Therefore Socrates is mortal.

 We have 3 concepts in this syllogism (Human beings (1), Socrates (2), mortal (3). They are also called terms. Underlined “Human being” and Socrates in both 2 statements are subjects. Mortal in both 2 statements are predicates. The non underlined “human being” concept is a predicate. It is also the middle term because it serves as a link between mortal and Socrates. It is the concept which should never come in the conclusion.

 A judgment or a proposition is a relationship of agreement or disagreement between 2 concepts (a subject and a predicate) which are linked by a copula (a verb to be) or similar verb.

 The three statements are each called a proposition or a judgment. The 2 first judgments:

Human beings are mortal

Socrates is a human being,

are called premises because they introduce and support the last one.

That last proposition:

Socrates is a human being

is called the conclusion, not because it is last but because it is the outcome or the consequence of the link between the 2 premises. It is the necessary implication of the link between the 2 premises. That link of necessity is the one which rules of formal logic tends to protect and assure. This is an other way of saying that if you agree with the link between the 2 premises above, you can not deny the conclusion unless you are a liar.

This labeling is true only for this syllogism because of its disposition. The conclusion may not necessarily come at the last position. Ex:

 Socrates is mortal

Because Socrates is a human being and

Human beings are mortal

 The three propositions connected logically to produce a sound conclusion are called reasoning or an argument. The reasoning can be valid or invalid. Formal logic therefore provided rules for valid reasoning. Many operations are involved but the time we have can not allow us to develop every notion of formal logic. But few things have to be known necessarily in order to perform minimum analysis of syllogism:

1. 1.       A. Extension and Comprehension.

 Extension: A concept may be universal (U) or particular (A).  This is its extension.

Universality means: every thing without exception is under consideration

Particularity means: only a part of the set is under consideration.

 Comprehension: A concept may be positive (I) or negative (E). This is its comprehension.

 The extension of a concept which is subject is the extension of the judgment in which it belongs.

 Extension of a concept which is subject:

 Quantifiers: quantifiers are words which determine the extension.

 All, every, the totality… and all the words that consider the totality of the subject of interest are appropriate for universal concepts affirmative.

 Example: All human beings are mortal

The concept “all human beings” is universal because every human being is under consideration. The proposition: “All human beings are mortal” is universal affirmative.

 None of, no,…are the quantifiers for universal negative because the totality of human beings is excluded without exception.

 Example: No human being is a natural killer

This proposition is universal negative.

 Note that we don’t say “All human being are not natural killers”. This proposition is ambiguous and may mean: “Some human beings are natural killers”. It shows then that a quantifier with total exclusion.

 Particular propositions:

 Some, a part of, are quantifiers for particular propositions.

Example: Some KIE students are tall.

In this proposition which is particular affirmative, only a part of the set “KIE students” is considered. It is the same for particular negative.

Ex: Some KIE students are not tall.

This proposition is particular negative.

 Extension of predicates (laws of distribution)

 So far we have seen the extension of concepts that are subjects, and the extension of propositions which is the same as that of the subjects they hold. However, the extension of predicates follows this rule:

 A predicate of an affirmative proposition is particular. (It is not distributed)

 Ex: All human beings are mortal.

The predicate mortal here is particular because it is a predicate to an affirmative proposition.

Ex2: Some KIE students are tall:

The predicate “tall” is particular because it a predicate to an affirmative proposition.

 A predicate of a negative proposition is universal. (It is distributed)

 Ex: Some KIE students are not tall:

The predicate tall here is universal because it is a predicate to a negative proposition.

 Ex2: No human being is a natural killer

The predicate “natural killer” here is Universal because it is a predicate to a negative proposition.

 Rules of Syllogism:

1. A syllogism must have only 3 terms with univocal meaning. No concept with more than one meaning. (No equivocity, no ambiguity).

Ex: I ate a captain

      A captain is a soldier

      Therefore I ate a soldier.

This syllogism sins against this first law because the concept captain has 2 meanings. (One is a fish and an other is a soldier)

2. The middle term must not be present in the conclusion.

Ex: All men are animals, but all men are material, so all men are animals and material. (It sins against the second law)

3. No term should have greater extension in the conclusion than in the premises (because it would imply an other term). Ex: All imperialists are racists, but Africans are not imperialists, so Africans are not racist.

Here “racist” in the conclusion is a predicate to a negative proposition so it is universal while “racist” in the 1st premise it is a predicate to an affirmative proposition so it is particular. It has greater extension in the conclusion than in the premise. It sins against the 3rd rule.

4. The middle term should be taken at least once in its universal extension.

Ex of a sinning syllogism:

Some Africans are Rwandans

Yet you are a Rwandan

So you are an African

The middle term here is Randan(s). It is taken twice in particular because it is predicate affirmative proposition and it is not taken at least once in a universal extension.

5. Two negative premises no conclusion:

Ex: Europeans are not animals

      You are not European

     Therefore…..

There is no conclusion.

6. From two affirmative premises, only an affirmative conclusion can come out. Never a negative conclusion.

Ex. All Africans are sensitive

      You are a European

      So you are not sensitive

This sins against the 6th rule.

7. If one premise is negative, the conclusion is negative

Ex: All men are animals

      You are not an animal

      So you are not a man (this does not sin against this rule because one premise is negative and the conclusion is negative. It would sin if we said for instance in the conclusion: so you are a woman)

8. If one premise is particular, the conclusion is particular.

Ex: All Africans are sensitive

      Some Arabs are Africans

      So some Arabs are sensitive (It doesn’t sin against this rule because one premise is particular and the conclusion is particular. It would sin if we said for instance in the conclusion: So, Arabs are sensitive.)

9. If both premises are particular, no conclusion possible.

Ex: Some Africans are dangerous

      Some dangerous creatures live in the jungle,

      So,…

There is no conclusion possible.

From premises to conclusion, there should be a link of necessity. There should be no way of escaping the conclusion if one agrees with the link in the premises.

The above syllogisms are called categorical because they affirm or denies in a categorical way.

We also have hypothetical syllogisms.

1. II.                Hypothetical syllogism:

1. II.                A. Conditional syllogism:

If electricity is there you will get an electrical chock

Electricity is there so you will get an electrical chock

Or you did not get an electrical chock, so electricity is not there.

Ex 1: If electricity is there you will get an electrical chock by touching

Electricity is there so you will get an electrical chock by touching

Ex 2: If electricity is there you will get an electrical chock by touching

you did not get  an electrical chock by touching, so electricity is not there.

If electricity is there: this first part connected to if is called the antecedent.

you will get an electrical chock by touching: this part which is an outcome of the if proposition is called the consequent.

The only valid cases of conditional syllogisms are:

When the antecedent is affirmed (modus ponnens: as in Ex 1) and when the consequent is denied (modus tollens: as in Ex 2)

1. II.                B. Disjunctive syllogisms

Either you are a soldier or you are a civilian. You are a soldier, so you are not a civilian. Or you are a civilian, so you are not a soldier.

The validity of these syllogism is only true if the two propositions are mutually exclusive. If they are not mutually exclusive, only the denial of one proposition leads to the affirmation of the other but the affirmation of one does not lead necessarily to the denial of the other.

1. II.                C. Conjunctive syllogisms

 You are a student and a teacher. Teachers have a meeting so you have a meeting.

For these syllogism if you have 2 qualities, what is affirmed on one of the qualities is also affirmed to the other quality.

 Some people commit mistakes in their reasoning. These mistakes are called fallacies. When they are done willingly they are called sophism and when they are done unwillingly they are called paralogism.

1. III.             Fallacies

 We do have many fallacies but let us highlight some of them especially the common ones:

1. Ambiguity: Presenting concepts that appear to have same meaning but which may have 2 or more meanings. Ex: The cook feels the soup. We don’t know whether the cook is smelling at the soup or whether by passing he leaves the smell of soup behind him.
2. Petitio principia or begging the question. This is repeating the asked question instead of answering to it. Ex: A human being is a human being. This is a vicious circle.
3. Ignorancia elenchi or  Ignoring the question: this is answering to something else than what you are asked to answer. Ex: Why do you like politics? In fact I like to pray. (here you don’t answer what you are asked to answer)
4. Post hoc propter hoc or False cause: Sometimes to consider one of two events that follow each other as the cause of the other. Ex: He has just come out of girls’ dormitory at the same time with Mary so they are cooking something.
5. Fallacy of accident: To take an accident as essential: Ex: That dog is father and that dog is yours, so that dog is your father.
6. Composition: To take a part as a whole. Ex: This brave man is an American so Americans are brave people.
7. Division: To take a whole as a part: Ex: America is a rich nation so you are rich because you are an American. Rwandans committed genocide yet you are a Rwandan so you committed genocide.
8. Ad populum or appeal to the mass: to take something to be true because many people say so. Ex: Everybody knows that Kibungo people are skilled in witchcraft so each one takes it for granted that witchcraft exist because everybody says so.
9. Ad vereccundiam or Appeal to authority: Something does not become true because it is said by someone with authority in a given domain. Ex: saying it is true if Aristotle said so.
10.  Ad bacculum  or appeal to elderness or tradition: something is taken to be true if the old people said so. Ex: It is our tradition so it is true.
11. Double question: Ex: Have you stopped harassing your wife? If you answer yes it means you have stopped but you have been harassing her before. If you answer no it means you are still harassing her since you have not yet stopped harassing her. This kind of question is used in the court where clever lawyers try to get a weak person condemned.
12. Imperfect comparison: this is the case when for instance one extends a comparison to irrelevant characteristics. Ex: The earth is round like an egg, so it is yellow inside. (here the object of comparison does not concern all the characteristics of the egg but only the roundness but the one who compares claims to put equality between the earth and the egg.
13. Add hominem: Attacking the man: This is when you you may deny someone’s statement because of his/her reputation (ex: It a prostitute told you that adultery is bad, truth remains truth independent from the source.)
14. Poisoning the well!      

Imperfect syllogisms:

These are syllogisms that are not structured in the way we have seen.

Ex: Anthymeme: This boy will pass because he is intelligent. This syllogism would be:

All intelligent beings pass

This boy is intelligent

So this boy will pass.

Anthymeme is the normal and ordinary way people speak in every day life. One does not speak the way syllogisms are formally structured.

See other imperfect syllogisms in your notes in class (sorite, Epichereme, dilemma, polysylogism…), same as educational implication of studying logic…(Clear and valid reasoning , speech and presentation, convincing argumentation, rational and critical defense capacity,…)

Epichereme

Polysyllogism

Sorite

Dilemma

Argumentum ad absurdum

1. IV.              Developing a personal philosophy of Education:

Developing a personal philosophy of education requires to maintain the main characteristics of philosophy in mind: being open, rational, critical by living no stone unturned or unchecked, critical by taking nothing for granted, knowing that the enterprise of truth searching is a task that requires effort and time, being perennial or universal, capable of wondering on mysteries of life and become contemplative in front of the greatness of reality. These attitudes may allow somebody to walk on the road of philosophy. More over, as an educator, one should bear in mind that any helpful philosophy should be value grounded, for the simple reason that one’s mission is to build and not to destroy humanity: values such as honesty, honesty for the search of truth, which implies Socratic humility, where one does not pretend to know but works rather hard to uncover the mysteries of life. Values such as respect, justice, charity, humility, hard work, sense of duty and determination, gratuity and service motivation…are things that one needs in order to function and to be accepted in a society which expect much of you. A lover of philosophy can not at the same time love ugly and bad business. An educator who embraces philosophy is not only a good philosopher, but also a good psychologist and sociologist. He or she knows to reason by oneself but knows to understand and respect other members of societ

References:

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Dave R., (1999). Introducing Philosophy. New York: Icon Books Uk.

Spangler,M., (1980). Logic: an Aristotelian approach; New York : University Press America.

Stumpf, S., (1994). PHILOSOPHY, History and Problems: New York McGraw-Hill book Company.

Vernon, J., (1981). Argumentation. California: Wadswoth Publishing company,

Walsh,M.J., (1984) A History of philosophy, London: Chapman.

William F.Lawhead, (1999). The Philosophical Journey, an interactive approach:Mayfield Publishing Company.

George K. (2002) Philosophy of education. Kigali: KIE.