Chapter IV.

THE LAWS OF THOUGHT.

 

1. The Laws of Thought. 

2. The Law of Contradiction

3. The Law of Identity

4. The Law of Excluded Middle

5. Other Views as to the Source of the Laws of Thought

§ 1.  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 been said in Ch. 1, §3.

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: --

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

(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 must be true, the other false.

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 32o 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.

§ 2. 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 [N1].  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." [N2].  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, § 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." [N3].  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, § 1).

* 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.  It is absolutely simple. We cannot explain it by any that is simpler for its simplicity is ultimate. Indeed were there not primary notions of this kind, it would be impossible to explain anything. The mind would be lost in an infinite regress, as it endeavoured to find some idea which did not itself need elucidation.

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 [N4].  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.'

 

§ 3. The Law of Identity. This principle is often stated in the form A = A. This, however, is manifestly a formula, and not the enunciation of a philosophic principle. Locke (Essay, Bk. 4, c. 7) enunciates it as 'Whatever is, is,' and this form appears to be philosophically correct. Like the principle of Contradiction, this law is an Analytic proposition explicative of the concept of Being.  Its connection with that principle will appear plainly if we express it as 'A Being which is, is.' In this form we see that the only difference between the two is that in the one case we affirm that things which exist, exist : in the other, that things which exist, cannot not exist.

Like the principle of Contradiction also, it may be enunciated in reference to the nature, which determines the existence.  Leibniz has given expression to the law in this form. He words it 'Everything is what it is.' Leibniz's form will serve us also for the logical order, if it be understood as signifying that every subject of predication is what it is, i.e. that whatever attribute is affirmed of any subject, is in fact an attribute of that subject.

Mill somewhat unnecessarily introduces the question of verbal expression. He enunciates the law as: "Whatever is true in one form of words, is true in every other form of words, which conveys the same meaning" (Exam. of Hamilton, p. 409).

It is the universal practice at present to treat the principle of Identity separately from the principle of Contradiction.  Scholastic authors, however, do not admit its claim to rank as a really independent principle. At most they admit that it is a rudimentary form of the principle of Contradiction [N7]. They urge that the predicate of an Analytic proposition must in some way explicate the notion of the subject. This principle does not do so. The predicate and the subject are the same concept. It is mere tautology.

There is, it may be owned, some force in this objection. The principle tells us nothing. Yet we must remember that Being is a concept which does not admit of analysis properly so called. Hence perhaps justification may be found for a tautologous principle here, which could not be adduced in any other case. The form is permissible, because it is indicative of the fact, that we have arrived at the limits of all explanation. But in order for the principle to convey any information, and to be of any service, it must be developed into the law of Contradiction.

The separate treatment of the two principles first became usual after the time of Leibniz. It is true that Parmenides the Eleatic (circa BC. 490) had enunciated the principle Being is (eon emmenai) as the foundation of his philosophy. But Aristotle emphatically affirms that the law of Contradiction is the first of all principles: and his decision for long went undisputed. Among medieval authors the Spanish Scotist Antonius Andrew (ob. 1320) argues that the first place should belong to the principle 'Every Being is a Being' (Omme Ens est Ens, Qq. in Met. IV., Q. 4). But the authority both of St. Thomas (Met. IV., lect. 6) and of Scotus (Quaest. sup. Met. IV., Q. 3) was against him: and he is expressly refuted by Suarez (Disp. Met. III., §  3).  Leibniz however makes the principle of Identity, which he gives as 'Everything is what it is,' the first of the primitive truths of reason which are affirmative, and the principle of Contradiction, 'A proposition is either true or false' the first of the negative truths (Nouv. Ess. IV., 2, §  i). He further says, "the statement that a thing is what it is, is prior to the statement that it is not another thing" (Nouv. Ess. IV.. 7, §  9). Here as it would seem, is the real ground for the introduction of the principle of Identity as distinct from that of Contradiction. It appeared impossible that the primary analytic principle should be negative. If however, the view taken in the last section is accurate, the negative form is the necessary consequence of the primary character of the principle. We can only explain the perfectly simple by distinguishing it from that which it is not.

§ 4. The Law of Excluded Middle.  Aristotle enunciates this principle in the form given above, "Of two contradictory judgments, the one must be true and the other false" (Met. III., c. 8, sects 3, 4). He says also, "Between the two members of a contradiction, there is no middle term" (Met. III., c. 7, § i) [N5].

As a metaphysical principle, it is stated, 'A thing must either be or not be.' The truth of this is evident from the immediacy of the opposition between being and not- being. The truth of the logical principle is capable of demonstration as follows. Where we have two contradictories, we have affirmation and negation, is and is not.  If the member which constitutes the mental judgment corresponds with the reality, whether it be in affirmation or negation, then the mind has attained truth. Should it, however, not be in conformity with its object, the judgment is false. That is to say, the mind has either judged that what is, is not, or that what is not, is.

Wherever, therefore, the judgment is false, the contradictory judgment, whether it be the affirmative is, or the negative is not, will be true. Hence of two contradictories, the one must be true, the other false [N6].

The close connection between the logical principle and the metaphysical at once appears, when we reflect, that in affirmation, we are attributing a certain conceptual being to the subject; in negation, we assert that it does not possess this being (Ch. 3, § 2). All contradictories therefore present the alternative between being and not being.

The way in which the principle is expressed by certain logicians, "Of any two contradictory predicates, one must belong to every subject," is unsatisfactory. It supposes that the predicates, and not the propositions, are contradictory to each other, and is represented by the formula, 'A is either B or not-B.' But, as we have seen, the primary form of negation is the negative judgment, not an affirmative judgment with a negative predicate; and in the expression of a fundamental law, it is the primary form that we need.  Mill employs the following formula - "It is allowable to substitute for the denial of either of two contradictory propositions, the assertion of the other" (Exam. of Hamilton, p. 416).

It should be carefully noted that the law of Excluded Middle is in no way concerned with Contrary terms [N8]. We have explained Contrary terms as those which express the widest possible difference among classes belonging to the same genus, e.g. 'white, black,' 'convex, concave,' 'love, hatred.' There is, of course, a mean between terms such as these. Objects possessed of any other variety of colour are neither white nor black; a plane surface is neither concave nor convex; and indifference is neither love nor hatred. It is manifest, however, that an object must be either white or not white, convex or not convex; and that in regard to any particular individual, it is either true that we do or that we do not feel love towards him.

The principle has not passed unchallenged. Mill, in the interests of the empiricist philosophy, declared the law to be a mere generalization from experience. We have no grounds, he thought, for regarding it as necessary. Indeed he goes further, and maintains that "it is not even true except with a large 'qualification. . . . 'Abracadabra is a second intention,' is neither 'true nor false. Between the true and false there is a third possibility, the Unmeaning." Such an argument can scarcely be treated as serious. An unmeaning proposition is not a judgment at all. Of more moment perhaps is the Hegelian objection. The very basis of the Hegelian philosophy is the reconciliation of opposites. Becoming is supposed to owe its origin to the union of Being and Not-Being, and the whole of Nature is regarded as constituted by this dialectic development. Hegel himself argues against the principle of Excluded Middle by pointing out that between + A and -A lies A. As against this view, it is urged that in Hegel's system the opposites are in fact contraries not contradictories, and that the individual does not owe its origin to them, but that they are obtained by abstraction from the individual.  Thus if it be urged that at dawn we can say with equal truth 'It is day' and 'It is not day,' and that the state of dawn is constituted by these opposites, it is answered that the two moments are not, as alleged, contradictory opposites, but the contraries 'dark' and 'light': and that dawn is not in any sense constituted by a dialectic development out of darkness and light, though we can mentally abstract these concepts from the state of dawn.

§ 5. Other Views as to the Source of the Laws of Thought.  In other schools of philosophy, very various accounts are given as to the nature and origin of these laws. It seems well to notice here three theories differing widely from that set forth in the preceding sections. These views respectively regard the laws of thought (1) as subjective laws of the understanding, of whose objective, validity, however, we can have no rational guarantee, (2) as principles determining the growth of that 'ex perience,' which men erroneously distinguish into thought on the one hand, and things on the other hand, (3) as mere generalizations from experience.

The first view is that of Kant. Among English logicians it is explicitly taught by Mansel. He tells us that the principles of thought are "laws under which the mind is compelled to think, and which it cannot transgress, otherwise than negatively by ceasing to think at all."  "It may be," he adds, "that the conditions of possible thought correspond to conditions of possible being, that what is to us inconceivable is in itself non-existent. But of this, from the nature of the case, it is impossible to have any evidence" (Proleg. Logica, 7r, 72).  It is needless to point out that such a view as this leads directly to philosophic scepticism. The second view is represented by Mr. Bosanquet. We have already called attention to the theory held by the neo-Hegelian school of logicians, according to which the operations of the mind are vital functions by which the so-called 'real' world has been constituted.  It is under this aspect Mr. Bradley regards the laws of thought. He holds that we cannot say that these principles are merely laws of thought, if by that we mean thought as distinguished from things: "Since a separation between intelligence and experience is purely fictitious, there is nothing to be gained by cutting down the content of these principles to a minimum in the hope of restricting their reference to thought as opposed to things."  They are "the animating principles of growth" which govern the development of experience: and if we recognize them as "postulates of know ledge," this is because "on analysis of experience, they are found to be active factors in it from the first" (Logic, II. 205- 207).

Mill (Logic, I., p. 308. Exam. of Hamilton, p. 417) explicitly repudiates the view that these principles are subjective laws of the thinking faculty. He holds that they are conclusions derived from a constant experience of their truth. We have never as a matter of fact known any case where two contradictories have been simultaneously true.  Hence we rightly lay down a general but empirically discovered principle to that effect. As for the law of Excluded Middle, we have already seen that he holds that it needs qualification before it can be admitted as universally true.  It must, he admits, be owned that "we cannot now conceive the opposite of these laws to be true. But this inconceivability is of little value as a criterion of truth to those who know how artificial, modifiable, the creatures of circumstances and alterable by circumstances, most of the supposed necessities of thought are."  Constant experience of one character is, in his view, sufficient to lead us to regard its opposite as inconceivable.

 


Footnotes

[N1]  Met. III., c.6, § 10.

[N2] Soph. Elenchi.c.5 § 5.

[N3]  It 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).

[N4]  On Being and Not-being as the primary concepts of the understanding, see St. Thomas, Opusc. 44, Summa Totius Logicae, Tract 3, c. 1,  Ad videndum. cf. Summa Theol. I.. Q. 11 Art. a. ad 4

[N5]

[N6] Arist. Met. III., 7, §1;  St. Thomas, in Met. Iv., lect. 16.

[N7] Pesch. Instit. Logicae, vol. 3, § 1230. Ad usum principii identitatis quod attinet, illud a Peripateticis nunquam in sua propria forma adhibitum videmus. Est enim vagum et indeterminatum, et principiorum potius radicem continet et germen imperfectum.

[N8] Mr. Bosanquet's views as to negation lead him into this error. He holds that negation qud negation is void of all significance, and that the true value of a negative judgment is to be sought in its positive content. Hence he concludes that the principle of Excluded Middle relates to contraries (Logic, II. 2101. A full treatment of the import of the negative judgment and of the relation between contradictory and contrary propositions, will be found in St. Thomas, Opusc. De Quatuor Oppositis, cc. I, 2.


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