This he did by showing that the laws of correct thinking can be expressed in algebraic notation, and, thus expressed, will be subject to all the mathematical laws of an algebra whose symbols bear the uniform value of unity or nought (1 or 0) – a limitation required by the fact that pure logic deals in notions of quality only, not of quantity.
This mathematical form of logic was foreseen by Kant when he declared that all mathematical reasoning derives its validity from the logical laws; but no one before Professor Boole had succeeded in reaching the notation which subordinated these two divisions of abstract thought to the same formal types. His labors have not yet borne fruit in proportion to their value, and they are, I believe, comparatively little known. But in the future they will be regarded as epochal in the science of mind. They make us to see the same law governing mind and matter, thought and extension.
Not the least important result thus achieved was in emphasizing the contrast between the natural laws of mental association, and the laws of thinking which are the foundation of the syllogism.
By attending to this distinction we are enabled to keep the form and the matter of thought well apart – a neglect to do which, or rather a studied attempt to ignore which, is the radical error of the logic devised by Hegel, as I shall show more fully a little later.
All applied logic, inductive as well as deductive, is based on formal logic, and this in turn on the “laws of thought,” or rather of thinking. These are strictly regulative or abstract, and differ altogether from the natural laws of thought, such as those of similarity, contiguity and harmony, as well as from the rules of applied logic, such as those of agreement and difference. The fundamental laws of thinking are three in number, and their bearing on all the higher questions of religious philosophy is so immediate that their consideration becomes of the last moment in such a study as this. They are called the laws of Determination, Limitation and Excluded Middle.
The first affirms that every object thought about must be conceived as itself, and not as some other thing. “A is A,” or “x = x,” is its formal expression. This teaches us that whatever we think of, must be thought as one or a unity. It is important, however, to note that this does not mean a mathematical unit, but a logical one, that is, identity and not contrast. So true is this that in mathematical logic the only value which can satisfy the formula is a concept which does not admit of increase, to wit, a Universal.
From this necessity of conceiving a thought under unity has arisen the interesting tendency, so frequently observable even in early times, to speak of the universe as one whole, the το παν of the Greek philosophers; and also the monotheistic leaning of all thinkers, no matter what their creed, who have attained very general conceptions. Furthermore, the strong liability of confounding this speculative or logical unity with the concrete notion of individuality, or mathematical unity, has been, as I shall show hereafter, a fruitful source of error in both religious and metaphysical theories. Pure logic deals with quality only, not with quantity.
The second law is that of Limitation. As the first is sometimes called that of Affirmation, so this is called that of Negation. It prescribes that a thing is not that which it is not. Its formula is, “A is not not-A.” If this seems trivial, it is because it is so familiar.
These two laws are two aspects of the same law. The old maxim is, omnis determinatio est negatio; a quality can rise into cognition only by being limited by that which it is not. It is not a comparison of two thoughts, however, nor does it limit the quality itself. For the negative is not a thought, and the quality is not in suo genere finita, to use an expression of the old logicians; it is limited not by itself but by that which it is not. These are not idle distinctions, as will soon appear.
The third law comes into play when two thoughts are associated and compared. There is qualitative identity, or there is not. A is either B or not B. An animal is either a man or not a man. There is no middle class between the two to which it can be assigned. Superficial truism as this appears, we have now come upon the very battle ground of the philosophies. This is the famous “Law of the contradictories and excluded middle,” on the construction of which the whole fabric of religious dogma, and I may add of the higher metaphysics, must depend. “One of the principal retarding causes of philosophy,” remarks Professor Ferrier, “has been the want of a clear and developed doctrine of the contradictory.”14 The want is as old as the days of Heraclitus of Ephesus, and lent to his subtle paradoxes that obscurity which has not yet been wholly removed.
Founding his arguments on one construction of this law, expressed in the maxim, “The conceivable lies between two contradictory extremes,” Sir William Hamilton defended with his wide learning those theories of the Conditioned and the Unconditioned, the Knowable and Unknowable, which banish religion from the realm of reason and knowledge to that of faith, and cleave an impassable chasm between the human and the divine intelligence. From this unfavorable ground his orthodox followers, Mansel and Mozley, defended with ability but poor success their Christianity against Herbert Spencer and his disciples, who also accepted the same theories, but followed them out to their legitimate conclusion – a substantially atheistic one.
Hamilton in this was himself but a follower of Kant, who brought this law to support his celebrated “antinomies of the human understanding,” warnings set up to all metaphysical explorers to keep off of holy ground.
On another construction of it, one which sought to escape the dilemma of the contradictories by confining them to matters of the understanding, Hegel and Schelling believed they had gained the open field. They taught that in the highest domain of thought, there where it deals with questions of pure reason, the unity and limits which must be observed in matters of the understanding and which give validity to this third law, do not obtain. This view has been closely criticized, and, I think, with justice. Pretending to deal with matters of pure reason, it constantly though surreptitiously proceeds on the methods of applied logic; its conclusions are as fallacious logically as they are experimentally. The laws of thought are formal, and are as binding in transcendental subjects as in those which concern phenomena.
The real bearing of this law can, it appears to me, best be derived from a study of its mathematical expression. This is, according to the notation of Professor Boole, x2=x. As such, it presents a fundamental equation of thought, and it is because it is of the second degree that we classify in pairs or opposites. This equation can only be satisfied by assigning to x the value of 1 or 0. The “universal type of form” is therefore x(1-x)=0.
This algebraic notation shows that there is, not two, but only one thought in the antithesis; that it is made up of a thought and its expressed limit; and, therefore, that the so-called “law of contradictories” does not concern contradictories at all, in pure logic. This result was seen, though not clearly, by Dr. Thompson, who indicated the proper relation of the members of the formula as a positive and a privative. He, however, retained Hamilton’s doctrine that “privative conceptions enter into and assist the higher processes of the reason in all that it can know of the absolute and infinite;” that we must, “from the seen realize an unseen world, not by extending to the latter the properties of the former, but by assigning to it attributes entirely opposite.”15
The error that vitiates all such reasoning is the assumption that the privative is an independent thought, that a thought and its limitation are two thoughts; whereas they are but the two aspects of the one thought, like two sides to the one disc, and the absurdity of speaking of them as separate thoughts is as great as to speak of a curve seen from its concavity as a different thing from the same curve regarded from its convexity. The privative can help us nowhere and to nothing; the positive only can assist our reasoning.
This elevation of the privative into a contrary, or a contradictory, has been the bane of metaphysical reasoning. From it has arisen the doctrine of the synthesis of an affirmative and a negative into a higher conception, reconciling them both. This is the maxim of the Hegelian logic, which starts from the synthesis of Being and Not-being into the Becoming, a very ancient doctrine, long since offered as an explanation of certain phenomena, which I shall now touch upon.
A thought and its privative alone – that is, a quality and its negative – cannot lead to a more comprehensive thought. It is devoid of relation and barren. In pure logic this is always the case, and must be so. In concrete thought it may be otherwise. There are certain propositions in which the negative is a reciprocal quality, quite as positive as that which it is set over against. The members of such a proposition are what are called “true contraries.” To whatever they apply as qualities, they leave no middle ground. If a thing is not one of them, it is the other. There is no third possibility. An object is either red or not red; if not red, it may be one of many colors. But if we say that all laws are either concrete or abstract, then we know that a law not concrete has all the properties of one which is abstract. We must examine, then, this third law of thought in its applied forms in order to understand its correct use.
It will be observed that there is an assumption of space or time in many propositions having the form of the excluded middle. They are only true under given conditions. “All gold is fusible or not,” means that some is fusible at the time. If all gold be already fused, it does not hold good. This distinction was noted by Kant in his discrimination between synthetic judgments, which assume other conditions; and analytic judgments, which look only at the members of the proposition.
Only the latter satisfy the formal law, for the proposition must not look outside of itself for its completion. Most analytic propositions cannot extend our knowledge beyond their immediate statement. If A is either B or not B, and it is shown not to be B, it is left uncertain what A may be. The class of propositions referred to do more than this, inasmuch as they present alternative conceptions, mutually exhaustive, each the privative of the other. Of these two contraries, the one always evokes the other; neither can be thought except in relation to the other. They do not arise from the dichotomic process of classification, but from the polar relations of things. Their relation is not in the mind but in themselves, a real externality. The distinction between such as spring from the former and the latter is the most important question in philosophy.
To illustrate by examples, we familiarly speak of heat and cold, and to say a body is not hot is as much as to say it is cold. But every physicist knows that cold is merely a diminution of heat, not a distinct form of force. The absolute zero may be reached by the abstraction of all heat, and then the cold cannot increase. So, life and death are not true contraries, for the latter is not anything real but a mere privative, a quantitative diminution of the former, growing less to an absolute zero where it is wholly lost.
Thus it is easy to see that the Unconditioned exists only as a part of the idea of the Conditioned, the Unknowable as the foil of the Knowable; and the erecting of these mere privatives, these negatives, these shadows, into substances and realities, and then setting them up as impassable barriers to human thought, is one of the worst pieces of work that metaphysics has been guilty of.
The like does not hold in true contrasts. Each of them has an existence as a positive, and is never lost in a zero of the other. The one is always thought in relation to the other. Examples of these are subject and object, absolute and relative, mind and matter, person and consciousness, time and space. When any one of these is thought, the other is assumed. It is vain to attempt their separation. Thus those philosophers who assert that all knowledge is relative, are forced to maintain this assertion, to wit, All knowledge is relative, is nevertheless absolute, and thus they falsify their own position. So also, those others who say all mind is a property of matter, assume in this sentence the reality of an idea apart from matter. Some have argued that space and time can be conceived independently of each other; but their experiments to show it do not bear repetition.
All true contraries are universals. A universal concept is one of “maximum extension,” as logicians say, that is, it is without limit. The logical limitation of such a universal is not its negation, but its contrary, which is itself also a universal. The synthesis of the two can be in theory only, yet yields a real product. To illustrate this by a geometrical example, a straight line produced indefinitely is, logically considered, a universal. Its antithesis or true contrary is not a crooked line, as might be supposed, but the straight line which runs at right angles to it. Their synthesis is not the line which bisects their angle but that formed by these contraries continually uniting, that is, the arc of a circle, the genesis of which is theoretically the union of two such lines. Again, time can only be measured by space, space by time; they are true universals and contraries; their synthesis is motion, a conception which requires them both and is completed by them. Or again, the philosophical extremes of downright materialism and idealism are each wholly true, yet but half the truth. The insoluble enigmas that either meets in standing alone are kindred to those which puzzled the old philosophers in the sophisms relating to motion, as, for instance, that as a body cannot move where it is and still less where it is not, therefore it cannot move at all. Motion must recognise both time and space to be comprehensible. As a true contrary constantly implies the existence of its opposite, we cannot take a step in right reasoning without a full recognition of both.
This relation of contraries to the higher conception which logically must include them is one of the well-worn problems of the higher metaphysics.
The proper explanation would seem to be, as suggested above, that the synthesis of contraries is capable of formal expression only, but not of interpretation. In pursuing the search for their union we pass into a realm of thought not unlike that of the mathematician when he deals with hypothetical quantities, those which can only be expressed in symbols – , √1 for example, – but uses them to good purpose in reaching real results. The law does not fail, but its operations can no longer be expressed under material images. They are symbolic and for speculative thought alone, though pregnant with practical applications.
As I have hinted, in all real contraries it is theoretically possible to accept either the one or the other. As in mathematics, all motion can be expressed either under formulas of initial motion (mechanics), or of continuous motion (kinematics), or as all force can be expressed as either static or as dynamic force; in either case the other form assuming a merely hypothetical or negative position; so the logic of quality is competent to represent all existence as ideal or as material, all truth as absolute or all as relative, or even to express the universe in formulæ of being or of not-being. This perhaps was what Heraclitus meant when he propounded his dark saying: “All things are and are not.” He added that “All is not,” is truer than “All is.” Previous to his day, Buddha Sakyamuni had said: “He who has risen to the perception of the not-Being, to the Unconditioned, the Universal, his path is difficult to understand, like the flight of birds in the air.”16 Perhaps even he learned his lore from some older song of the Veda, one of which ends, “Thus have the sages, meditating in their souls, explained away the fetters of being by the not-being.”17 The not-being, as alone free from space and time, impressed these sages as the more real of the two, the only absolute.
The error of assigning to the one universal a preponderance over the other arose from the easy confusion of pure with applied thought. The synthesis of contraries exists in the formal law alone, and this is difficult to keep before the mind. In concrete displays they are forever incommensurate. One seems to exclude the other. To see them correctly we must there treat them as alternates. We may be competent, for instance, to explain all phenomena of mind by organic processes; and equally competent to explain all organism as effects of mind; but we must never suppose an immediate identity of the two; this is only to be found in the formal law common to both; still less should we deny the reality of either. Each exhausts the universe; but at every step each presupposes the other; their synthesis is life, a concept hopelessly puzzling unless regarded in all its possible displays as made up of both.
This indicates also the limits of explanation. By no means every man’s reason knows when it has had enough. The less it is developed, the further is it from such knowledge. This is plainly seen in children, who often do not rest satisfied with a really satisfactory explanation. It is of first importance to be able to recognize what is a good reason.
I may first say what it is not. It is not a cause. This is nothing more than a prior arrangement of the effect; the reason for an occurrence is never assigned by showing its cause. Nor is it a caprice, that is, motiveless volition, or will as a motor. In this sense, the “will of God” is no good reason for an occurrence. Nor is it fate, or physical necessity. This is denying there is any explanation to give.
The reason can only be satisfied with an aliment consubstantial with itself. Nothing material like cause, nor anything incomprehensible like caprice, meets its demands. Reason is allied to order, system and purpose above all things. That which most completely answers to these will alone satisfy its requirements. They are for an ideal of order. Their complete satisfaction is obtained in universal types and measures, pure abstractions, which are not and cannot be real. The formal law is the limit of explanation of phenomena, beyond which a sound intellect will ask nothing. It fulfils all the requirements of reason, and leaves nothing to be desired.
Those philosophers, such as Herbert Spencer, who teach that there is some incogitable “nature” of something which is the immanent “cause” of phenomena, delude themselves with words. The history and the laws of a phenomenon are its nature, and there is no chimerical something beyond them. They are exhaustive. They fully answer the question why, as well as the question how.18
For it is important to note that the word “law” is not here used in the sense which Blackstone gives to it, a “rule of conduct;” nor yet in that which science assigns to it, a “physical necessity.” Law in its highest sense is the type or form, perceived by reason as that toward which phenomena tend, but which they always fail to reach. It was shown by Kant that all physical laws depend for their validity on logical laws. These are not authoritative, like the former, but purposive only. But their purpose is clear, to wit, the attainment of proportion, consistency or truth. As this purpose is reached only in the abstract form, this alone gives us the absolutely true in which reason can rest.
In the concrete, matter shows the law in its efforts toward form, mind in its struggle for the true. The former is guided by physical force, and the extinction of the aberrant. The latter, in its highest exhibition in a conscious intelligence, can alone guide itself by the representation of law, by the sense of Duty. Such an intelligence has both the faculty to see and the power to choose and appropriate to its own behoof, and thus to build itself up out of those truths which are “from everlasting unto everlasting.”
A purely formal truth of this kind as something wholly apart from phenomena, not in any way connected with the knowledge derived through the senses, does not admit of doubt and can never be changed by future conquests of the reasoning powers. We may rest upon it as something more permanent than matter, greater than Nature.
Such was the vision that inspired the noble lines of Wordsworth: —
“What are things eternal? – Powers depart,
Possessions vanish, and opinions change,
And passions hold a fluctuating seat;
But, by the storms of circumstance unshaken,
And subject neither to eclipse nor wane,
Duty exists; immutably survive
For our support, the measures and the forms
Which an abstract intelligence supplies;
Whose kingdom is where time and space are not.”
There is no danger that we shall not know what is thus true when we see it. The sane reason cannot reject it. “The true,” says Novalis, “is that which we cannot help believing.” It is the perceptio per solam essentiam of Spinoza. It asks not faith nor yet testimony; it stands in need of neither.
Mathematical truth is of this nature. We cannot, if we try, believe that twice two is five. Hence the unceasing effort of all science is to give its results mathematical expression. Such truth so informs itself with will that once received, it is never thereafter alienated; obedience to it does not impair freedom. Necessity and servitude do not arise from correct reasoning, but through the limitation of fallacies. They have nothing to do with
“Those transcendent truths
Of the pure intellect, that stand as laws
Even to Thy Being’s infinite majesty.”
It is not derogatory, but on the contrary essential to the conception of the Supreme Reason, the Divine Logos, to contemplate its will as in accord and one with the forms of abstract truth. “The ‘will of God’” says Spinoza, “is the refuge of ignorance; the true Will is the spirit of right reasoning.”
This identification of the forms of thought with the Absolute is almost as old as philosophy itself. The objections to it have been that no independent existence attaches to these forms; that they prescribe the conditions of thought but are not thought itself, still less being; that they hold good to thought as known to man’s reason, but perchance not to thought in other intelligences; and, therefore, that even if through the dialectical development of thought a consistent idea of the universe were framed, that is, one wherein every fact was referred to its appropriate law, still would remain the inquiry, Is this the last and absolute truth?
The principal points in these objections are that abstract thought does not postulate being; and that possibly all intelligence is not one in kind. To the former objection the most satisfactory, reply has been offered by Professor J. F. Ferrier. He has shown that the conception of object, even ideal object, implies the conception of self in the subject; and upon this proposition which has been fully recognized even by those who differ from him widely, he grounds the existence of Supreme Thought as a logical unity. Those who would pursue this branch of the subject further, I would refer to his singularly able work.19
The latter consideration will come up in a later chapter. If it be shown that all possible intelligence proceeds on the same laws as that of man, and that the essence of this is activity, permanence, or truth – synonymous terms – then the limitation of time ceases, and existence not in time but without regard to time, is a necessary consequence. Knowledge through intellection can alone reach a truth independent of time; that through sensation is always relative, true for the time only. The former cannot be expressed without the implication of the conceptions of the universal and the eternal as “dominant among the subjects of thought with which Logic is concerned;”20 and hence the relation which the intellect bears to the absolute is a real and positive one.
THE EMOTIONAL ELEMENTS OF THE RELIGIOUS SENTIMENT
SUMMARY
The Religious Sentiment is made up of emotions and thoughts. The emotions are historically first and most prominent. Of all concerned, Fear is the most obvious. Hope is its correlate. Both suppose Experience, and a desire to repeat or avoid it. Hence a Wish is the source of both emotions, and the proximate element of religion. The significance of desire as the postulate of development. The influence of fear and hope. The conditions which encourage them.
The success of desire fails to gratify the religious sentiment. The alternative left is eternal repose, or else action, unending yet which aims at nothing beyond. The latter is reached through Love. The result of love is continuance. Illustrations of this. Sexual love and the venereal sense in religions. The hermaphrodite gods. The virgin mother. Mohammed was the first to proclaim a deity above sex. The conversion of sexual and religious emotion exemplified from insane delusions. The element of fascination. The love of God. Other emotional elements in religions.
The religious wish defined to be one whose fruition depends upon unknown power. To be religious, one must desire and be ignorant. The unknown power is of religious interest only in so far as it is believed to be in relation to men’s desires. In what sense ignorance is the mother of devotion.