The Traditional Formal Logic

A Short Account for Students

William Angus Sinclair

• Publisher: Routledge
• Year: 2019
• ISBN:
  9781000737141
• Edition: 1
• Topic: Philosophy
• Subtopic: Philosophy History & Theory

Originally published in 1937. A short account of the traditional logic, intended to provide the student with the fundamentals necessary for the specialized study. Suitable for working through individualy, it will provide sufficient knowledge of the elements of the subject to understand materials on more advanced and specialized topics. This is an interesting historic perspective on this area of philosophy and mathematics.

CHAPTER I

PROPOSITIONS

LOGIC, we all know, is a science or inquiry dealing with topics such as reasoning, inferring, and arguing, and especially with reasoning, inferring, and arguing aright. We may find it difficult to give an adequate definition of ‘ logic’ and ‘ logical’ but we feel confident that these words are properly used in sentences such as He is a clear and logical thinker, or That may be a logical conclusion but I don’t agree with it, or There is no regard for logic in your argument. All we can at present say is that logic is in some sense an examination of argument, statement, implication, inference, and the like.¹ It is important to understand that the traditional logic confines itself to statements and arguments that can be true or false, valid or invalid, and that it does not deal with the many other forms of speech that make no claim to be either true or false, such as commands, wishes, ejaculations, and so forth. In other words, it confines itself to sentences that have verbs in the indicative mood, or that can be restated as sentences having verbs in the indicative mood.

¹ It is important to understand that we may be able to argue and infer and conclude quite correctly without knowing anything about logic. There is often confusion on this point, and it is sometimes even alleged that a man ignorant of logic is on that account unlikely to be accurate in his thinking.

This confusion disappears on making clear the distinction between the carrying out of an activity and the study of that activity. The activity of a living organism, namely being alive, is different from the study of it, which is physiology ; similarly the activity of talking or writing grammatically is different from the study of it, which is grammar ; and similarly the activity of thinking and arguing logically is different from the study of it, which is logic.

Old Parr of Banbury lived for more than a hundred and fifty years though he knew no physiology ; Homer wrote grammatically though he had never heard of grammar ; and we can argue logically without knowing any logic.

Whether the study of an activity affects the efficiency with which we perform it, and in what way and how far, is another question.

Consider examples:

Some flowers are scarlet

All men are moralists

A wanderer is man from his birth

Not all stocks and shares are worth having

If supplies increase, prices fall

That is either a horse or a mule

It must have been raining for the pavements are wet.

The first point to be noticed is that these differ considerably in their degree of complexity, for the latter examples are comparatively involved and complicated in structure, whereas the first two are comparatively simple. It will be seen that the simplest kinds of statement to be found are similar in their structure to these first two examples,

Some flowers are scarlet
All men are moralists.

Statements of this simple kind are known as propositions, and as such are of fundamental importance for our present purpose, because the traditional logic maintains the convention that all statements and arguments, no matter how involved and complicated, can be analysed and shown to consist either of simple propositions, or of groups of simple propositions standing in some systematic relation to each other. Though we have not yet studied the structure of propositions, we can with moderate facility recognize to be propositions such examples as the two previously quoted, and others similarly simple.

We shall now investigate the nature and structure of propositions, but before doing so we must be clear on a most important point, namely that the truth or falsity of the propositions is at this stage irrelevant, for what is being examined is the structure of the propositions and not the truth or falsity of what they assert. This may be made clearer by reference to the similar conditions in the study of grammar, for the grammatical and syntactical structure of a sentence is independent of its truth or falsity. For instance, the word efficiently in the sentence This business is efficiently run is an adverb, and it remains an adverb whether the business in question is in fact capably managed or incompetently mismanaged. In a similar way, the truth or falsity of a proposition is irrelevant to a study of its structure. In the technical language of logic, it is the form of the proposition that is important for our purpose and not its matter.

STRUCTURE OF THE PROPOSITION

All propositions may be regarded as exhibiting a definite structure. Consider examples, such as

Some trees are conifers
Whales are not fish.

In these propositions there is, first, something spoken about, the subject of the discussion, namely trees or whales. Secondly, there is something said about the subject, ‘predicated’ of it, and therefore called the predicate.

The traditional doctrine insists on the convention of treating all propositions as stating a relation between two classes of entities, between a subject and a predicate.¹ Thus the proposition Some trees are conifers is treated as asserting that a certain relation holds between the class of entities called trees, which is the subject of the proposition, and the class of entities called conifers, which is the predicate of the proposition. In the second example a relation of a somewhat different kind is asserted to hold between whales which is the subject, and fish which is the predicate.

So there are three factors in every proposition. First, there is a class of entities spoken about, namely the subject; secondly, there is another class of entities, namely the predicate; and thirdly, there is the relation stated to hold between these two classes. This relation is indicated by a part of the verb to be (e.g. are or are not ) in conjunction with an adjective of quantity (e.g. all or some ) which is prefixed to the subject.

¹ A more detailed analysis shows that this involves two distinguishable conventions :

(a) The convention of treating a proposition as stating a relation between its Subject and its Predicate.

(b) The convention of treating Subject and Predicate as classes of entities.

The subject and predicate are called technically the terms of the proposition, and the part of the verb to be is called the copula. A proposition thus consists of two terms, namely the subject term and the predicate term, (commonly called more briefly the subject and the predicate), and of the copula and the quantitative adjective which serve in conjunction to indicate the relation in which these two terms stand to each other.

Very few of the statements of ordinary speech take forms in which the subject, the predicate and their relation are readily distinguishable, for ordinary speech is in a high degree complex, condensed and elliptical, since most statements in normal language consist not of one proposition, but of several involved one with another in comparatively brief wording. So for the purposes of logical study, (since the traditional logic maintains that any statement however complex consists of these simple units called propositions) the statements of ordinary speech must be analysed, and the constituent propositions disen...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Original Title Page
• Original Copyright Page
• Preface to the Fifth Edition
• Contents
• Introduction
• Chapter I Propositions
• Chapter II Symbols and Distribution
• Chapter III Immediate Inference
• Chapter IV Mediate Inference. Syllogism
• Chapter V Hypothetical Argument
• Chapter VI Disjunctive Argument. More Complex Arguments
• Chapter VII Logical Division and Definition
• Schematic Summaries
• Index