All relations are either qualitative or quantitative. Qualitative relations can be considered by themselves without regard to quantity. The algebra of such enquiries may be called logical algebra, of which a fine example is given by Boole.
Quantitative relations may also be considered by themselves without regard to quality. They belong to arithmetic, and the corresponding algebra is the common or arithmetical algebra.
In all other algebras both relations must be combined, and the algebra must conform to the character of the relations.
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§ 3Benjamin Peirce
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By the help of God and with His precious assistance, I say that Algebra is a scientific art. The objects with which it deals are absolute numbers and measurable quantities which, though themselves unknown, are related to "things" which are known, whereby the determination of the unknown quantities is possible. Such a thing is either a quantity or a unique relation, which is only determined by careful examination. What one searches for in the algebraic art are the relations which lead from the known to the unknown, to discover which is the object of Algebra as stated above. The perfection of this art consists in knowledge of the scientific method by which one determines numerical and geometric unknowns.
Omar Khayyam
Whoever thinks algebra is a trick in obtaining unknowns has thought it in vain. No attention should be paid to the fact that algebra and geometry are different in appearance. Algebras (jabbre and maqabeleh) are geometric facts which are proved by propositions five and six of Book two of Elements.
Omar Khayyam
Stand firm in your refusal to remain conscious during algebra. In real life, I assure you, there is no such thing as algebra.
Fran Lebowitz
As the mathematics are now understood, each branch — or, if you please, each problem, — is but the study of the relations of a collection of connected objects, without parts, without any distinctive characters, except their names or designating letters. These objects are commonly called points; but to remove all notion of space relations, it may be better to name them monads. The relations between these points are mere complications of two different kinds of elementary relations, which may be termed immediate connection and immediate non-connection. All the monads except as serve as intermediaries for the connections have distinctive designations.
Charles Sanders Peirce
It seems reasonable to suppose that conflict does exhibit many general patterns, that the patterns of conflict in industrial relations, international relations, interpersonal relations, and even animal life are not wholly different from one another, and that it is, therefore, worth looking for the common element. On the other hand, we should be surprised if there were no differences; the pattern of conflict in international relations, for instance, is not the same as in industrial or interpersonal relations. Just as it is important to perceive the similarities in different situations, so it is important to perceive the differences. These differences cannot be perceived, however, without a general theory to serve as a standard of comparison.
Kenneth Boulding
Peirce, Benjamin
Peirce, Charles Sanders
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