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THE LEGACY OF ARISTOTLE

Part 2

Logic


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LOGIC


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LOGIC

Aristotle was the first to systematically study and

catalogue the rules of correct logical reasoning

His logic is important because it dominated all western

thought, including scientific thought, until the 19th century

CE; it also had enormous influence on the development

of Jewish, Christian and Muslim philosophy. It is stillinfluential today.

Although othertypes of logical systems exist, Aristotelian

logic is still a powerful tool used to teach reasoning skills

in numerous academic disciplines.


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In his logic, Aristotle explicitly established three laws oflogical thought.

Law # 1: law of identity: each thing is inseparablefrom itself and its being one just meant this(Metaphysics, 7, 17). A thing is just itself and notsomething else: e.g. a soccerball is a soccerball andnot a kitchen stove.

* Sometimes this is expressed as A = A.

Note: the fact that we can use a book fora doorstop does notmean it is not a book. Its use does not contradict the law of

identity. What a thing is and how it is used are two differentissues.


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Law # 2: the law of contradiction: the same attribute

cannot at the same time belong and not belong to the

same subject and in the same respect (Metaphysics,4, 3). E.g. my cup cannot be blue and not-blue at the

same time

A cannot be A and not-A at the same time in the

same way/respect.

Note: things may have and not have the same attributes in different

ways: e.g. man is the most intelligent creature compared to

animals but he is not intelligent compared to God. So man is

both intelligent (compared to animals) and not intelligent

(compared to God). There is no contradiction because intelligentis being used in different ways.


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Law # 3: the law of the excluded middle or excludedthird : there cannot be an intermediate between twocontradictories, but of one subject we must either

affirm ordeny any one predicate [statement](Metaphysics 4, 7).

A statement about a topic must eitherbe true orfalse.It cannot be both, i.e. there is no middle between

them. It cannot be neither

true no

rfalse.

Note: It is eithertrue that Socrates is mortal orit is not true thathe is not mortal. He is not both. Norcan he be neithermortal norimmortal.

Anotherexample: It is eithertrue that there is a rubberduck in

my bath tub orit is not true. Norcan we say neitherof thesechoices is true.


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ReflectionsontheRulesofLogic

According to Aristotle, the laws of logic are not man-made

prescriptions but are rules ofreality, i.e. if we violate them we will

reach false conclusions about the real world.

They are necessary (unchangeable, non-arbitrary) and not

normative (changeable and arbitrary) rules.

A traffic law is a normative rule, i.e. the government can change it.

The law of non-contradiction is necessary, i.e. if you try to violate it

you get into trouble with reality; no government can change it. E.g., it

is true that eitherthere is orthere is not a carcoming towards you

as you cross the street; it cant be both are true orneither.


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Aristotles systemization of thought laid the basis forscientific

progress which requires careful, systematic, step-by-step habits

of thinking, i.e. of inquiring, investigating, evaluating, comparing

and contrasting and drawing conclusions.

It also improved society in general because logic teaches people

to regard theirown and otherpeoples thinking critically in an

objective and systematic way. They become more self-critical, i.e.

learn to evaluate the validity of theirown thoughts.

Aristotles logic taught people that orderly critical, and objective

thought can give us knowledge about reality, that correct human

thought processes are adapted to the real world and capable of

discovering truth. Reality and truth are directly available to us if

we use these logical tools correctly.


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The SyllogismThe Syllogism To help us reason correctly, Aristotle invented the syllogism. A

syllogism is a three-part reasoning process beginning with 2premises and ending with 1 conclusion.

Aristotle works mainly with categorical syllogisms which affirm ordeny something. There are othertypes of syllogisms but thesewill not concern us here.

The value of studying and learning to work with syllogisms is thatwe learn to break ourideas down into simple parts and byputting them into syllogistic form we can make sure we aredeveloping a logical argument. Here is an example of asyllogism:

(1) No reptiles have fur;

(2) All snakes are reptiles;

(3) Therefore, no snakes have fur.


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Here is anotherexample the most famous syllogismof all time:

(1)A

ll men are mo

rtal;

(2) Socrates is a man;

(3) Therefore, Socrates is mortal.

Here we see the essential requirements of asyllogism:

(a) 3 statements: 2 premises (1) and (2) and a

conclusion (3)(b) 3 terms; each is used twice: men/man, mortal,

Socrates


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(c) each statement has a subject (what the statement is about)

e.g. All men in the statement All men are mortal.

(d) and a predicate (what is being said about the subject) e.g. aremortal in the statement All men are mortal.

(e) the subject of the conclusion is the minor term, e.g. Socrates

in the statement Therefore Socrates is mortal.

(f) the predicate of the conclusion is the major term, e.g. mortal

in the statement Therefore Socrates is mortal.

(g) the term that appears in premises (1) and (2) but not in the

conclusion is the middle term.

(h) the premise with the majorterm is the major premise

(i) the premise with the minorterm is the minor premise.


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Analysing a syllogism

To analyze a syllogism follow the steps in this order:

Step 1: Identify the conclusion

Step 2: Identify the minorand majorterms in the

conclusion

Step 3: Identify the majorand minorpremises

Step 4: Identify the middle term (it is not in the

conclusion but is the same in the first two premises.)


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To identify these parts we use:

*S forthe minorterm;

*P for

the major

term; and* M forthe middle term (repeated in both premises)

Forexample:

(1) All men (M) are mortal (P);

(2) Socrates (S) is a man (M);

(3) Therefore, Socrates (S) is mortal (P).

The majorpremise is All men are mortal.

The minorpremise is Socrates is a man.

NOTE: we could have switched the places of the first two premises:


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(1) Socrates (S) is a man (M);

(2) All men (M) are mortal (P);

(3) Therefore, Socrates (S) is mortal (P).

Now (2) is the majorpremise and (1) is the minorpremise.

Practice exercise # 1: Analyze the following syllogisms forS,M, P

and the major

and minor

premise.

1) Lions are meat-eaters;

(2) Leo is a lion;

(3) Therefore Leo is a meat-eater.

1) No computeris alive;

(2) Humans are alive;

(3) Therefore, no humans are computers


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NOTE:

(a) P is always the predicate of the conclusion but it is not always the

predicate of the majorpremise.

(b) S is always the subject of the conclusion but it is not always the

subject of the minorpremise.

(c) The middle term M can be anywhere in the first two premises; it can

be both subjects, both predicates orone of each. Forexample:

(1) All horses (P) have hooves (M);

(2) No humans have hooves (M);

(3) Therefore, no humans are horses (P).

*** In this case P is the predicate of the conclusion (as it always is) butis the subject not the predicate of the majorpremise.


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Anotherexample:

(1) All fruit is nutritious;

(2) Some nutritious things are tasty (S);

(3) Therefore, some tasty things (S) are fruit.

*** In this case the minorterm (S) is the subject of the conclusion

(as it always is) but is now the predicate of the minorpremise.

The purpose of this explanation is to show that there is some

flexibility in the construction of a syllogism.


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How To Construct a Syllogism

The

re a

re 3 basic steps to const

ructing a co

rrect syllogism:

(1) You must know the conclusion you are trying to prove, and put it

into logical form. Doing this will give you yourS (minorterm) and P

(majorterm). E.g. Justice is a virtue.

(2) Find a good middle term. This is the key to writing successful

syllogisms. The middle term joins the S and P. E.g. giving people

theirappropriate reward.

(3) Set up the first two premises that logically lead to the conclusion.


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Practice # 2: Write a syllogism (and label the parts S, P, and M) to

reach the following conclusion:

(1)

(2)

(3) Therefore, cake is not healthy.

Example 2:

(1)

(2)

(3) Therefore, people are imperfect.


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Remember:

(a) A syllogism cannot have two negative premises. We cannot

reach any conclusion from (1) No dogs are cats; (2) No cats are

nice;

(b) If a syllogism has a negative premise, the conclusion must be

negative.

(1) No tree is edible;

(2) Some trees are green;

(3) Therefore, some green things are not edible.

(c) Make sure the middle term (M) is distributed. If it is not, we have a

fallacy orlogical error. We shall ignore the technical reasons for

this name and use a simple test: are the two groups being joined

by the middle term (M) separate even though they share a

quality? Forexample:


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(1) All teenagers are two legged;

(2) All ostriches are two-legged;

(3) Therefore, all teenagers are ostriches.

Obviously the two groups are still separate even though they share the

quality of being two-legged.

In the Socrates is mortal syllogism, we can see that mankind and

Socrates are not separate groups. Here is anotherexample of anundistributed middle:

(1) All penguins are black and white;

(2) Some old films are black and white;

(3) Therefore, some old films are penguins.

This is obviously false.


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Four Types of Syllogisms

There are 4 types of syllogisms depending on if the first premise

affirms ordenies something, and how much it affirms ordenies, i.e.

all, some, ornone.

(1) All S are P (universal affirmation)** All men are mortal

Called A

(2) No S are P (universal negation) No men are birds

Called E

(3) Some S are P (particularaffirmation) Some dogs chase cats

Called I

(4) Some S are not P (particularnegation) Some dogs do not swim

* called O


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Here is an A type syllogism, i.e. a universal affirmation. It has 2universal premises; a universal premise applies to all members ofa kind orclass.

1) All cats hunt mice;

2) All Manxs are cats;

3) Therefore, all Manxs hunt mice.

Example # 2 of a universal affirmative with a singularaffirmativestatement:

(1)A

ll educated people canread and w

rite;

(2) Sam is an educated man; [Sam is singular, i.e. one]

(3) Therefore, Sam can read and write.


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Note: the 2 universal premises require a universal conclusion;

the affirmative conclusion also requires 2 affirmative premises.

Here is an E type syllogism, a universal negation: the premise is a

universal negative:

1) No members of the dog family have wings;

2) Wolves are members of the dog family;

3) Therefore, no wolves have wings.

Note: a negative premise requires a negative conclusion.

A syllogism cannot have 2 negative premises. If one

premise is negative, the conclusion must be negative.


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Here is a I type syllogism: it is a particular affirmation:

(1) Some vases are beautiful;

(2) All vases are useful;

(3) Therefore, some useful things are beautiful.

(1) Some computers are out-of-date;

(2) All out-of-date things should be replaced;

(3) Therefore, some things that should be replaced are

computers.

Note: the particularpremise requires a particularconclusion. We

cannot have two particularpremises.


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Here is an O type syllogism with a negative particular premise:

1) Some buildings are not tall;

2) All houses are buildings;

3) Therefore, some houses are not tall.

(1) Some cats have no tails;

(2) All cats are mammals;

(3) Therefore, some mammals have no tails.

Note: the negative conclusion requires a negative premise; aparticularpremise needs a particularconclusion.


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Practice # 3: Write an example of an A, E, I, O type syllogism andlabel the parts S, M, P and the minorand majorpremise.

Practical Uses of Syllogisms

Syllogisms can be used to construct valid arguments. If you think youhave a valid argument to make about something, you can try puttingit into syllogism form to see whetherit is valid.

Syllogisms do not always have to be about very simple topics,although we always try to keep them as simple as possible.

(1) Making people work without pay is morally wrong;

(2) Slavery is making people work without pay;

(3) Therefore, slavery is morally wrong.


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(1) Giving people theirproperreward is a virtue;

(2) Justice gives people theirproperreward;

(3) Therefore, justice is a virtue.

We shall now look at two examples of complex

syllogisms:

(1) All created things (M) receive divine bounties that

should be developed (P);

(2) We human beings (S) are created things (M);

(3) Therefore, human beings (S) must develop theirdivine bounties (P)


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Here is anotherexample:

(1) All living creations (M) undergo outward changes without

changing theirinneressence (P); (2) Human beings (S) are living creations (M);

(3) Therefore human beings (S) undergo outward changes withoutchanging theirinneressence (P).

Practice # 4: Complete the syllogism:

1. All fragile things are breakable things.Some glasses are fragile things.Therefore

2. All mammals are warm-blooded animals.All whales are mammals.Therefore


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3. All books are things with pages.

Some books are mysteries.Therefore

4. All flowers are pretty objects.

All pansies are flowers.

Therefore

5.No animals are plants.

All sheep are animals.

Therefore


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