GST 112 - CHAPTER VI

 SOME ASPECTS OF CLASSICAL LOGIC

INTRODUCTION

In this lesson, we shall carefully look into the rudiments of the oldest aspects of logic known as ‘Aristotelian Logic’. It was named after Aristotle [384 – 322 BC] who is properly famed with the founding of Western Logic. We will be looking at how propositions are derived and other determining factors. Aristotelian Logic can also be called Classical or Traditional Logic. Let us begin this study with the concept of categorical propositions.


Categorical and Non-Categorical Propositions:

A propositionsimply put, is a ‘statement’ or ‘sentence’ that asserts or declares that something is the case and that the claim made may either be ‘true’ or ‘false’ but never both at the same time. A good proposition has ‘a subject term’, ‘a predicate term’ and ‘a copula’ which links the two terms. There is also a ‘quantifier’ e.g. all, some; which are usually attached to be categorical to the subject term. Now, when we say a proposition is categorical, it means that whatever it claims is claimed without qualification or condition e.g. if we claim that Jesus is Lord, we are not claiming this compared to some other personality or given some circumstances, thus a categorical proposition is, in a nutshell, one in which the truth or falsity of the claim made by it is not dependent on the fulfillment of any other condition. The opposite of this will give us the non-categorical proposition, which can usually be ‘hypothetical’ or ‘disjunctive’. The hypothetical non-categorical proposition presents a claim that is often a conditional e.g. If Nerisa fails the examination, she will repeat; while the disjunctive non-categorical proposition usually presents a claim with ‘alternatives’ e.g. He is either a liar or a coward. As seen, in the aforementioned example, the disjunctive proposition has one subject term with two predicate alternatives.

Categorical Propositions and Class Membership: 

A ‘class’is simply a collection of objects which have similar or an agreed set of characteristics. Living and non-living things can constitute distinct classes e.g. a political class, a class of triangles, a business class etc. In a class, there could be overlapping i.e. where members of one class are equally members of another. For instance, some members of the political class are equally businessmen/women and therefore make up the business class as well. This leads us to a concept known as Aristotle’s Syllogism, which is based on the critical consideration that the subject and the predicate terms of any given proposition belong in principle to two different classes of objects. Simply put, it states that, that which a proposition claims (either affirms or denies) is a function of the overlapping or dissimilarity between the subject class and the predicate class.


Quality and Quantity of a Proposition: 

The ‘quality of a proposition’ is simply a matter of whether the proposition affirms something or denies it. A proposition that affirms something is either called ‘affirmative/positive proposition’while that which denies something is called ‘negative proposition’. The concept of ‘quantity’ when dealing with propositions is a function of what the proposition refers to i.e. if it refers to every member of the class of items mentioned or to one/some. Now, when the proposition refers too ‘all’ the members of the intended class, it is called a ‘universal proposition’ e.g. All Lions roar. But if the proposition is made in reference to one or some members of a class, it is called a ‘particular proposition’e.g. Some adults are bad-tempered.



On the above premises, there exist four main varieties of proposition, namely: A, E, I and O propositions.


A – Proposition: 

This type of proposition is affirmativein quality and universal in quantity hence it is also called a Universal Affirmative Proposition. It is called ‘A – proposition’ because the letter ‘A’ is derived from the first vowel of the Latin word affirmo meaning, I affirm. E.g. All things work together for good.

E – Proposition: 

This type of proposition is negativein terms of quality and universal in terms of quantity. For this reason, we can also call it the ‘universal negative proposition’. Example: No Woman deserves to be beaten. This proposition has its origin from the first vowel of the Latin word ‘nego’ meaning, I deny.


I – Proposition: 

The I – proposition is affirmativein quality and particular in quantity. Here, the proposition is made on some members of a particular class and not all. It is derived from the second vowel of the Latin word ‘affirmo’. Example: Some students are lazy.


O – Proposition: 

This is a ‘particular negative proposition’ e.g. Some men are not faithful. It is negative in quality and particular in quantity. Derived from the second vowel of the Latin word ‘nego’.


ARGUMENT

An argument is simply a sequence of statements where one makes a claim based on the others. The function of logic here is to provide bases for inferring the claim i.e. ‘conclusion’ from the other statements. However, we must note that ‘not all sequence/streams of sentences are arguments’. Example: When Abraham was 100 years old he became the father of Isaac. It should also be noted that when we can draw the conclusion of an argument justifiably, such argument is regarded as VALID. Now what is validity?


VALIDITY

This refers to the truth value of an argument. Validity entails the quality of an argument to be evidentially true and proven to be exact beyond all doubts. One basic requirement for validity is that in an oral argument, if all the premisses are true then the conclusion must also be true. For Example:

All humans are gods

Victor is a human

Hence, Victor is a god

The first two sentences above are the premises and are at the same time true, thus the conclusion which is clearly seen in the last sentence is equally true.


SYLLOGISM

This is the unique pattern of deductive argument devised and propagated by Aristotle and it is made up of two premises and a conclusion. Now, how do we ascertain the validity of syllogisms?

Basically there are three [3] methods of ascertaining the validity or otherwise of any given syllogism and they include:

  1. Testing by valid forms (this method is cumbersome and was used mainly in the middle Ages)
  2. Testing by Analogy (it is mostly used to prove invalidity other than validity)
  3. Employing rules of validity: Some common rules of validity include: (a) rule regarding structure (b) rule of quantity (c) rule of quality (d) Corollary.
Some of these rules include:

  • A valid syllogism must possess only three terms [structural rule] and the violation of this rule is known as - A Four-term Fallacy
  • The middle term in any valid syllogism must be distributed at least once [quantity]. 
  • If a term is not distributed in the premises, it must not be distributed in the conclusion [quantity
  • No conclusion can be followed from two negative premises and an argument which has two negative premises is guilty of the 'fallacy of exclusive premises'. [quality
  • If either premise is negative, the conclusion must be negative [quality]. 
  • A negative conclusion cannot follow from two affirmative premises [quality
  • From two particular premises nothing follows [corollary
  • If either premise is particular, the conclusion is particular [corollary]

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