文档介绍：The Calculus of Logic
e Boole
[Cambridge and Dublin Mathematical Journal, Vol. III (1848), pp. 183–98]
In a work lately published1 I have exhibited the application of a new and
peculiar form of Mathematics to the expression of the operations of the mind in
reasoning. In the present essay I design to offer such an account of a portion of
this treatise as may furnish a correct view of the nature of the system developed.
I shall endeavour to state distinctly those positions in which its characteristic
distinctions consist, and shall offer a more particular illustration of some fea-
tures which are less prominently displayed in the original work. The part of
the system to which I shall confine my observations is that which treats of cate-
gorical propositions, and the positions which, under this limitation, I design to
illustrate, are the following:
(1) That the business of Logic is with the relations of classes, and with the
modes in which the mind contemplates those relations.
(2) That antecedently to our recognition of the existence of propositions,
there are laws to which the conception of a class is subject,—laws which are
dependent upon the constitution of the intellect, and which determine the char-
acter and form of the reasoning process.
(3) That those laws are capable of mathematical expression, and that they
thus constitute the basis of an interpretable calculus.
(4) That those laws are, furthermore, such, that all equations which are
formed in subjection to them, even though expressed under functional signs,
admit of perfect solution, so that every problem in logic can be solved by refer-
ence to a general theorem.
(5) That the forms under which propositions are actually exhibited, in ac-
cordance with the principles of this calculus, are analogous with those of a
philosophical language.
(6) That although the symbols of the calculus do not depend for their in-
terpretation upon the idea of quantity, they nevertheless, in th