First Lectures on the logic of thought by J. E. Barrett
THE NATURE AND AIM OF LOGIC.
A definition of Logic. Logic may be defined as the science which directs the operations of the mind in the attainment of truth.
What do we mean by truth? An assertion is said to be true when it corresponds to the reality of which the assertion is made. But the verbal statement is merely the outward expression of the thought within. It is our thoughts which are properly said to be true or erroneous.
For present purposes, therefore, we may define truth as the conformity of the intellect with its object. Thus if I see a white horse, and judge 'That horse is white’, my judgment is said to be true, because my thought corresponds with the thing about which I amjudging.
The aim of all our mental operations is to attain true judgments. If I endeavour to establish a geometrical proposition, my object is to arrive in the end at a judgment, which is in conformity with reality. Now there are certain definite ways in which, and in which alone, our thinking faculty must proceed if it is to achieve its task of faithfully representing the real order. Reflection enables us to observe the operations of the mind; and hence we are able to know and to catalogue these common types of mental action. In this way we learn the rules, which we must observe in reasoning, if we are to arrive at a true result. For, as experience shows us, it is very easy to argue in a way that will bring us, not to truth, but to error.
It was a boast of the Sophists in ancient Greece that they could make the worse appear to be the better cause. They managed this end by skilfully violating the rules which men must observe, if their conclusions are to be true.
Another definition may be given of Logic, in which the science is considered in a different aspect. Logic is the science which treats of the conceptual representation of the real order; in other words, which has for its subject-matter things as they are represented in our thought.
The difference between this definition and that which we gave in the first instance, is that this definition expresses the subject-matter of Logic, while the former expresses its aim. We shall find as we proceed that the science can scarcely be understood, unless both these aspects are kept in view.
The work of Logic therefore is not to teach us some way of discovering new facts. First Francis Bacon, later Descartes, and finally, despite his admitted genius, John Stuart Mill* failed to recognise this simple fact and drove logic from the confines of its valid form into the realm of the physical sciences. The discovery of things belongs to the special sciences, each in its own sphere. Logic’s purpose, on the other hand, is to assist us in the attainment of truth, because it treats of the way in which the mind represents things, and thus shows us what are those general conditions of right thinking, which must be observed whatever subject we are considering.
*Mills actually established a magnificent philosophy of evidence by perfecting Aristotle’s method of inductive reasoning, which we will examine later.
Is Formal Logic then a science in its own right? Where we have a systematic body of securely established principles and of conclusions legitimately drawn from these principles, there we have a science. Thus in the science of Astronomy we start from certain general laws, and have a body of conclusions derived from these. Mere facts not brought under general laws do not constitute a science. We are rightly said to have a science of Logic, for, as we shall see, it consists of a body of principles and legitimate conclusions, such as we have described.
Divisions of Logic. The simplest act of the mind in which it can attain truth is the judgment — the act by which the mind affirms or denies something about something else. That which is affirmed (or denied) of the other is called an attribute: that to which it is said to belong (or not to belong) is called a subject.
Hence we may define a judgment as the act by which the mind affirms or denies an attribute of a subject.
A judgment however gives the mind a complex object: for it involves these two parts — subject and attribute. We must therefore take account of a more elementary act of the mind than judgment, viz.: Simple Apprehension.
Many popular philosophies, of language for example, trip up because they fail to discern what is Simple Apprehension from the more complex act of Judgment.
Simple apprehension is the act by which the mind without judging, forms a concept of something. Thus if I should conceive the notion of a triangle, without however making any judgment about it, I should be said to have formed a simple apprehension of a tri angle. David Hume built much of his system on blatantly denied this fact. He insisted that immediately the mind conceived of triangle it had an image of its exact type and size, i.e. scalene or isosceles. Sadly nobody tried him with a myriagon!
However, the words true or false cannot be applied to simple apprehensions, just as we cannot say that the words in a dictionary are true or false. Following Hume, some philosophers indeed deny that the mind ever forms a simple apprehension; they hold that in every case some judgment is made. We need not even enter into this question. We can at least analyse the judgment into simple apprehensions: for every judgment requires two concepts, one in which the mind expresses the subject, and the other in which it expresses the attribute. Thus in the example given above, I must have a concept of horse, and one of whiteness, in order to say 'The horse is white’. These are the elements which go to constitute the complex act of judgment, and they can be considered in isolation from it. Logic therefore must deal with the concept.
There is a third process of the mind, namely Reasoning or Inference. This is defined as the act, by which from two given judgments, the mind passes to a third judgment distinct from these, but implicitly contained in them.
Thus if I say
This flower is a rose;
or if I argue
The world displays the harmonious ordering of many parts;
I am said in each case to infer the third judgment. An inference of the form which we have employed in these examples, is called a syllogism. The two judgments given are known as the premisses. The judgment derived from them is the conclusion.
It is of these three acts of the mind that Logic treats: and the science falls correspondingly into three main divisions, — the Logic (1) of the Concept, (2) of the Judgment, (3) of Inference.
Language: Since Logic deals with thought, it necessarily takes account to some extent of language — the verbal expression of thought. It does so however from quite a different point of view to that of Grammar.
Grammar is concerned with words as such. It is the art by which the words employed in significant speech are combined according to the conventional rules of a language. Hence in it each of the nine parts of speech is treated independently, and rules are given for their respective use. On the other hand, the simplest object of which Logic takes account is the Concept. In its consideration of words, therefore, it does not deal with any of those parts of speech, which taken by themselves are incapable of giving us an independent concept. It is conversant not with nine, but with two forms only of significant utterance, viz.: the Name, the verbal expression of the Concept, and the Proposition, the verbal expression of the Judgment.1
The proposition consists of three parts.
These are, (1) the Subject — that of which the assertion is made: (2) the Predicate — that which is affirmed or denied of the Subject: and (3) the Copula — the verb is or are which connects the Subject and the Predicate. The Subject and the Predicate are called the Terms (from the Latin terminus — a boundary) of the proposition: and the predicate is said to be predicated of the subject.
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