What were the reasons leading to development of Boolean algebra?
Nowadays it's so fundamentally used that it almost seems like a triviality, but since it preceded the uses in electronics, then it's (more often) surprising as to why did Boole come to think of such system? Did he have some applications in mind? Or was he "suddenly" studying a simple algebra?
Is Boolean algebra just a reformulation or resyntaxing of earlier logic?
George Boole's project must be understood in the context of the development of symbolic algebra in England (mainly Cambridge) during the early 1800s (taking into account also Leibniz's Influence on 19th Century Logic).
See G.Boole, The Mathematical Analysis of Logic: Being an Essay Towards a Calculus of Deductive Reasoning (1847) :
They who are acquainted with the present state of the theory of Symbolical Algebra, are aware, that the validity of the processes of analysis does not depend upon the interpretation of the symbols which are employed, but solely upon the laws of their combination. [...] But the full recognition of the consequences of this important doctrine has been, in some measure, retarded by accidental circumstances. It has happened in every known form of analysis, that the elements to be determined have been
conceived as measurable by comparison with some fixed standard. The predominant idea has been that of magnitude, or more strictly, of numerical ratio.
Abstract algebra can "free itself" from the restricted domain of nubers and magnitudes and the process of "symbolizarion" can be applied to a wider domain.
That which renders Logic possible, is the existence in our minds of general notions,—our ability to conceive of a class, and to designate its individual members by a common name. The theory of Logic is thus intimately connected with that of Language. A successful attempt to express logical propositions by symbols, the laws of whose combinations should be founded upon the laws of the mental processes which they represent, would, so far, be a step toward a philosophical language. But this is a view which we need not here follow into detail.
Assuming the notion of a class, we are able, from any conceivable collection of objects, to separate by a mental act, those which belong to the given class, and to contemplate them apart from the rest. [...] Now the several mental operations which in the above case we have supposed to be performed, are subject to peculiar laws.
Such are the elementary laws upon the existence of which, and upon their capability of exact symbolical expression, the method of the following Essay is founded.
The laws we have to examine are the laws of one of the most important of our mental faculties. The mathematics we have to construct are the mathematics of the human intellect.
