THE LAWS OF THOUGHT.

In each science there are certain principles or laws, which are recognized as fundamental within that science. Every conclusion which it claims to have demonstrated, depends for its validity on the truth of those principles. Such for instance are the definitions of Euclid in regard to Geometry (the science of abstract spatial extension), and the laws of motion in regard to the science of Mechanics.

In each case the principles have their own sphere of application. They are principles of this or that science, and beyond it they are not operative.

There are, however, certain laws, which are not confined within the limits of any one of the special sciences, but which apply to all that is, to all that has a right to the name of Being or Thing.

For instance the law of causality which lays down that every event must have a cause, is such a principle as this. It is not a law of one of the special sciences, but is true of all things. It belongs to that universal science of Metaphysics or Ontology, of which something has already been said.

Just as there are laws which apply to the whole realm of Being — to the real order in its full extent — so too there are laws which govern the whole of the conceptual order, and on which depends the validity of every judgment, whatever it may be.

These are the Laws of Thought, which form the subject of this most important lecture. They are three in number

(I) The Law of Contradiction, viz. Contradictory judgments (e.g. A is B, A is not B) cannot both be

(2) The Law of Identity, viz. Everything is what it is.

(3) The Law of Excluded Middle, viz.: Of two contradictory judgments (A is B, A is not B) the one

These three laws we shall proceed to consider in detail. But first, it will be well to ask ourselves in what sense they are termed laws. For the word 'law' is used in various senses. In its primary signification it means an ordinance imposed by a legitimate superior on the body politic, and carrying with it an obligation of obedience. But it is also employed to signify a uniform mode of acting observed by some natural agent. In this sense we use the term 'laws of nature,' e.g. the law of gravitation, the law that water under a certain pressure freezes at 320 F., etc.

Laws of nature are only called laws by analogy: there is of course, no question here of the obedience which one will ought to yield to another. The law is simply our description of the way in which the agent does in fact act.

It tells us what is, not what ought to be. In yet another meaning we use it to denote a norm or standard, to which we must conform in order to achieve some end. Thus we may speak of the laws of perspective. If we wish our drawing to be accurate, we must observe them. Otherwise, we shall not attain our object.

It is in this last sense that we employ the word, when we speak about the laws of thought. It is certainly the case that we are unable to judge a pair of contradictory propositions to be true, if we are conscious of the contradiction.

But it not infrequently happens that men unconsciously hold opinions, which are really contradictory the one of the other, though because they are expressed in different words, or from some confusion of mind, their mutual opposition is not recognized. Hence the laws of thought cannot strictly be termed laws in the second of the senses we have noticed above. But since in all our mental judgments our end and object is to attain truth, they are rightly termed laws in the last sense mentioned: for if they are not observed, our judgments are not true but false.

The Law of Contradiction.

The form in which we have given the principle of Contradiction, 'Contradictory judgments cannot both be true,' is that in which, with various slight modifications it is several times enunciated by Aristotle.¹

He, moreover, is careful to point out that where judgments are contradictory to each other, the predicate must be referred to the subject in the same way in each, and the point of time must be identical. "A refutation," he says, "occurs when something is both affirmed and denied of one and the same subject . . . and when it is denied in the identical respect, relation, manner and time, in which it has been affirmed."²

It might be true to say both that ‘the prime minister is capable,' and that 'the prime minister is not capable,' if the capacity referred to was in the one case capacity for government, in the other capacity for writing Greek verse: or if we were speaking of different periods in his life.

Mill adopts a more cumbrous phraseology. He gives the law as follows: 'The affirmation of an assertion and the denial of its contradictory are logical equivalents, which it is allowable and indispensable to make use of as logically convertible" (Exam. of Hamilton, p. 414).

This law, as we have said, is a ruling principle of the whole conceptual order. It applies to all that is thought. But the order of thought — of conceptual Being — is essentially a representative order. It manifests the order of things. And this law of thought is the conceptual expression of a fundamental necessity of the real order: to the logical principle corresponds a metaphysical principIe. This metaphysical law may be stated: "The same attribute cannot at one and the same time both belong and not belong to the same thing "(Arist. Met. III., c. 3, sect; 10).

Another form in which it is frequently expressed, is: "It is impossible for the same thing both to be and not to be, at the same time."³ How closely the logical principle represents the metaphysical will at once be seen, if we express the former as: "The same attribute cannot at one and the same time be both affirmed and denied of the same thing."

But the student should be careful to distinguish the various expressions of the law, and when dealing with logical questions not to state the principle in a metaphysical form, nor vice versa.

This law Aristotle declares to be the first of all axioms,

and the most certain of all principles (Met. X., c. 5, sect; I).

* The question will doubtless suggest itself, on what grounds this is asserted to be the first of all axioms. A brief examination will show us that the principle of Contradiction is the first Analytic proposition, which we attain through an analysis of our most primary notion — the notion of 'Being' or 'thing.'

This notion, which we apply equally to all entities whatever, calls for a brief consideration.

We are accustomed to name objects from their various determinations and perfections. We term one man a 'runner,' because the perfection denoted by the word 'to run,' characterizes him, and we call another a 'painter' for a similar reason. Further, we apply these denominatives to them, even though the perfection is not at the moment in a state of actualization.

The man is called a 'runner' or a 'painter,' not because he is actually running or painting, but because he has the capacity to do so: the capacity or potency remains even when he is not eliciting the act.

'Being' is a denominative of this type. It is applied to objects in virtue of that primary perfection signified by the verb 'to be,' namely 'to exist.' The notion which expresses this primary characteristic of 'Being' or 'actuality,' is clear to us from the dawn of our intelligence.

What then is the Analytic proposition which unfolds the intension of this term, which is the first principle to emerge from the consideration of our primary concept?

Its very simplicity prohibits our explaining it otherwise than by declaring its difference from its opposite, viz, that it is essentially opposed to non-existence.¹ Yet we cannot state the principle as 'A Being is that which is not non-existent,' for as we have noticed, 'Being' is applied not merely to that which does at present exist, but to such objects of thought as we see can exist. A chiliagon may be termed a 'thing' or a 'Being.' Our proposition must be expressed, 'A Being which is, cannot at the same time not be'; or as otherwise phrased, 'It is impossible for the same thing both to be and not to be at the same time.' Here then we have the principle of Contradiction, as the first of principles derived by analysis from the primary notion.

In regard of each Being, however, we must consider not merely its existence, but its nature: that which makes it what it is.

The principle may be enunciated not merely in reference to the former, but to the latter: for the nature of an entity determines the mode of its existence. As thus expressed, we get the form 'The same attribute cannot at the same time both belong and not belong to the same thing.' The logical expression, as we have seen, is identical with this, save that it refers to the mental act by which we judge about the thing: 'The same attribute cannot at the same time be both affirmed and denied of the same thing.'

¹It is to be observed that the principle of contradiction is a modal proposition de impossibili, and the principle of Excluded Middle a modal de necessario (ch. 3. 9).