The Religious Sentiment. Daniel G. (Daniel Garrison) Brinton
principles of reaching the laws of phenomena by inductive methods. Many say that the mind can go no further than this, that the truth thus reached, if not the highest, is at least the highest for man. It is at best relative, but it is real. The correctness of this statement may be tested by analyzing the processes by which we acquire knowledge.
Knowledge reaches the mind in two forms, for which there are in most languages, though not in modern English, two distinct expressions, connaitre and savoir, kennen and wissen. The former relates to knowledge through sensation, the latter through intellection; the former cannot be rendered in words, the latter can be; the former is reached through immediate perception, the latter through logical processes. For example: an odor is something we may certainly know and can identify, but we cannot possibly describe it in words; justice on the other hand may be clearly defined to our mind, but it is equally impossible to translate it into sensation. Nevertheless, it is generally agreed that the one of these processes is, so far as it goes, as conclusive as the other, and that they proceed on essentially the same principles.12 Religious philosophy has to do only with the second form of knowledge, that reached through notions or thoughts.
The enchainment or sequence of thoughts in the mind is at first an accidental one. They arise through the two general relations of nearness in time or similarity in sensation. Their succession is prescribed by these conditions, and without conscious effort cannot be changed. They are notions about phenomena only, and hence are infinitely more likely to be wrong than right. Of the innumerable associations of thought possible, only one can yield the truth. The beneficial effects of this one were felt, and thus by experience man slowly came to distinguish the true as what is good for him, the untrue as what is injurious.
After he had done this for a while, he attempted to find out some plan in accordance with which he could so arrange his thoughts that they should always produce this desirable result. He was thus led to establish the rules for right reasoning, which are now familiarly known as Logic. This science was long looked upon as a completed one, and at the commencement of this century we find such a thinker as Coleridge expressing an opinion that further development in it was not to be expected. Since then it has, however, taken a fresh start, and by its growth has laid the foundation for a system of metaphysics which will be free from the vagaries and unrealities which have thrown general discredit on the name of philosophy.
In one direction, as applied logic and the logic of induction, the natural associations of ideas have been thoroughly studied, and the methods by which they can be controlled and reduced have been taught with eminent success. In this branch, Bentham, Mill, Bain, and others have been prominent workers.
Dealing mainly with the subjects and materials of reasoning, with thoughts rather than with thinking, these writers, with the tendency of specialists, have not appreciated the labors of another school of logicians, who have made the investigation of the process of thinking itself their especial province. This is abstract logic, or pure logic, sometimes called, inasmuch as it deals with forms only, “formal logic,” or because it deals with names and not things, “the logic of names.” It dates its rise as an independent science from the discovery of what is known as “the quantification of the predicate,” claimed by Sir William Hamilton. Of writers upon it may be mentioned Professor De Morgan, W. Stanley Jevons, and especially Professor George Boole of Belfast. The latter, one of the subtlest thinkers of this age, and eminent as a mathematician, succeeded in making an ultimate analysis of the laws of thinking, and in giving them a symbolic notation, by which not only the truth of a simple proposition but the relative degree of truth in complex propositions may be accurately estimated.13
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
The most acute recent discussion of this subject is by Helmholtz, in his essay entitled, “
George Boole, Professor of Mathematics in Queen’s College, Cork, was born Nov. 2, 1815, died Dec. 8, 1864. He was the author of several contributions to the higher mathematics, but his principal production is entitled: