George Boole is now regarded by many scientists as one of the prominent mathematicians and logicians of the nineteenth century, yet we should remember that he did not receive recognition during his lifetime. Among his most famous works, it is quite possible for us to single out the following ones: The Laws of Thought, Mathematical Analysis of Logic, Calculus of Finite Differences and many others (Hale, 1985, p. 22). To a certain extent, his ideas laid the foundations for the development of information technologies and programming languages but at that time they were perceived as something impractical and inapplicable to any field of human activity. It should be borne in mind that for a considerable amount of time Boole was not very much interested in exact sciences, he was mostly attracted by humanities but later he evinced to mathematics and logic. But his liking for classic philosophy did not go in vain because Booles logic partly relies on Aristotle and Plato.
Probably, it would be more prudent for us to illustrate Booles views on the relations between mathematics and logic, because this is the cornerstone of his approach. It was traditionally believed that these two notions were two separate sciences and their rules were practically incompatible with each other. On the one hand, the famous scholar did not try to merge them into a single entity; however, he argued that logical mechanisms could be described by means of mathematical symbols. Consequently, it was also permissible to apply mathematical operations to logic (Bell, 1961, p. 44). According to him, every statement can be presented in the form of an equation. It was he who introduced such symbols as x and y into logical science. Subsequently, this idea was used by the first developers of information technologies because every algorithm demonstrates that a logical operation or syllogism is a form of the equation.
In addition to that George explored such issue as the theory of probability and he tried to apply his principles. In part, his attempts gave rise to the so-called probability algebra. The key method, which George Boole employed, was system analysis; though at that time it was not popular among scholars and logicians. He argued that every phenomenon could be subdivided into constituent parts or subsystems and it was of crucial importance to determine the relations between them. From his standpoint, in this way, the probability of any event could be determined. Nonetheless, it should be taken into consideration that he did not elaborate his argument, and later his theory of probability was subjected to criticism. Furthermore, George Boole dedicated several treatises to quantitative research methods, namely mathematical analysis. Again, it is worth mentioning that he did not fully develop his ideas but later many sociologists adopted his views. He intended to prove that every phenomenon could be presented in a numerical way. Although, this belief is now hotly debated, it would be an exaggeration to say that modern quantitative research methods take their origins in George Booles works and particularly in the Laws of Thought.
To conclude, George Booles impact on the development of mathematical science cannot be underestimated. Although his works were not received well by the coevals, we may say that later they immensely influenced cybernetics, programming. Moreover, we should not forget about quantitative research techniques that also strongly depend on Booles ideas.
References
- Bell, E.T, (1961). Men of Mathematics. Stand St. Andrews University Press, London.
- Mc Hale, D, (1985). George Boole: His Life and Work. Boole Press Dublin