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## Philosophy & Logic

### Philosophy and Logic

### De Morgan and Hamilton

### Jevons, Babbage and Shannon

George Boole – original thinker and man of genius – came along in the mid-nineteenth century and after him nothing was the same. He could be described as the originator of mathematical logic. Boole showed that a mathematical approach could be applied to logic, making it amenable to calculation. He took the principles of logic and reduced them to a simple form of algebra, now widely known as Boolean algebra.

Throughout the history of thought, from the Greek philosopher Aristotle (384-322 BC) to the German mathematician Godfried Wilhelm von Leibniz (1646-1716) logicians and philosophers had tried to understand the principles governing logical thought. They wanted to symbolise and formalise these principles and in turn apply them in mechanical and automatic ways in order to analyse a wide range of human, linguistic, scientific and ethical situations.

Boole’s work on logic was concentrated during the middle years of his career. In 1847, at the age of 32, he published his ground-breaking book – *The Mathematical Analysis of Logic*. Feeling a deep need to build on this achievement, he later pushed the boundaries even further by publishing another book entitled *An* *Investigation of the Laws of Thought* in 1854. Boole himself understood the importance of the findings published in this latter book. On 2 January 1851 in a letter to William Thomson (later Lord Kelvin) he said:

"I am now about to set seriously to work upon preparing for the press an account of my theory of Logic and Probabilities which in its present state I look upon as the most valuable if not the only valuable contribution that I have made or am likely to make to Science and the thing by which I would desire if at all to be remembered hereafter . . . "

Boole’s thinking may have been spurred on by a heated controversy raging at the time between two formidable academics working in this area. They were the British mathematician and logician Augustus De Morgan (1806-71) and the Scottish philosopher and metaphysician Sir William Hamilton (1788-1856). Boole came up with an ingenious formulation that synthesised the approaches of both De Morgan and Hamilton. Indeed De Morgan praised Boole’s work on logic saying:

"Boole's system of logic is but one of many proofs of genius and patience combined . . . That the symbolic processes of algebra, invented as tools of numerical calculation, should be competent to express every act of thought, and to furnish the grammar and dictionary of an all-containing system of logic, would not have been believed until it was proved."

The English economist and logician William Stanley Jevons (1835-82) followed after Boole and, it could be said, simplified Boole’s system of logic. He developed the Logic Machine, a working mechanical computer that solved problems faster than the human mind. Charles Babbage (1791-1871), who was known to Boole, originated the concept of a programmable computer.

In the last century the American mathematician Claude Shannon (1916-2001) demonstrated how Boolean algebra could be connected to switching circuits in electrical engineering. Combined with miniaturisation this developed into the construction of computer hardware. So by applying mathematical principles to logic, Boole provided a platform for the processing and storing of information, something that later played a central role in how computers were constructed and how they were coded to handle data.

Philosophical and indeed psychological principles were closely linked with mathematical reasoning in Boole’s enormous contribution to modern science. In the first chapter of *The Laws of Thought* he said:

"the design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed . . . and finally, to collect from these inquiries some probable intimations concerning the nature and constitution of the human mind.’ In a letter to De Morgan after

The Laws of Thoughtwas published, Boole says ‘I do not so much care about the mere forms of Logic as about the philosophy of the connection between thought and speech."

In *The Laws of Thought* Boole takes texts by Baruch Spinoza (1632-77) and other philosophers and checks these texts from a logical point of view. So Boole strengthened the role of logic and this had an important impact on philosophy, particularly through Der Wiener Kreis (Vienna Circle) which came together in the early 1920s and developed analytic philosophy.

After Boole’s death in 1864 at the age of 49, a number of manuscripts were found showing that he intended to publish a further book in which his discoveries in logic were to inform his personal view of philosophy.