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The history of computers is often told as a history of objects, from the abacus to the Babbage engine up through the code-breaking machines of World War II. In fact, it is better understood as a history of ideas, mainly ideas that emerged from mathematical logic, an obscure and cult-like discipline that first developed in the 19th century. Mathematical logic was pioneered by philosopher-mathematicians, most notably George Boole and Gottlob Frege, who were themselves inspired by Leibniz’s dream of a universal “concept language,” and the ancient logical system of Aristotle.
Mathematical logic was initially considered a hopelessly abstract subject with no conceivable applications. As one computer scientist commented: “If, in 1901, a talented and sympathetic outsider had been called upon to survey the sciences and name the branch which would be least fruitful in [the] century ahead, his choice might well have settled upon mathematical logic.” And yet, it would provide the foundation for a field that would have more impact on the modern world than any other.
The evolution of computer science from mathematical logic culminated in the 1930s, with two landmark papers: Claude Shannon’s “A Symbolic Analysis of Switching and Relay Circuits,” and Alan Turing’s “On Computable Numbers, With an Application to the Entscheidungsproblem.” In the history of computer science, Shannon and Turing are towering figures, but the importance of the philosophers and logicians who preceded them is frequently overlooked.
A well-known history of computer science describes Shannon’s paper as “possibly the most important, and also the most noted, master’s thesis of the century.” Shannon wrote it as an electrical engineering student at MIT. His adviser, Vannevar Bush, built a prototype computer known as the Differential Analyzer that could rapidly calculate differential equations. The device was mostly mechanical, with subsystems controlled by electrical relays, which were organized in an ad hoc manner as there was not yet a systematic theory underlying circuit design. Shannon’s thesis topic came about when Bush recommended he try to discover such a theory.
Shannon’s paper is in many ways a typical electrical-engineering paper, filled with equations and diagrams of electrical circuits. What is unusual is that the primary reference was a 90-year-old work of mathematical philosophy, George Boole’s The Laws of Thought.
Today,
Boole’s name is well known to computer scientists (many programming
languages have a basic data type called a Boolean), but in 1938 he was
rarely read outside of philosophy departments. Shannon himself
encountered Boole’s work in an undergraduate philosophy class. “It just
happened that no one else was familiar with both fields at the same
time,” he commented later.
Boole is often described as a mathematician, but he saw himself as a philosopher, following in the footsteps of Aristotle. The Laws of Thought begins with a description of his goals, to investigate the fundamental laws of the operation of the human mind:
Boole is often described as a mathematician, but he saw himself as a philosopher, following in the footsteps of Aristotle. The Laws of Thought begins with a description of his goals, to investigate the fundamental laws of the operation of the human mind:
The design of the following treatise is to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation to establish the science of Logic ... and, finally, to collect ... some probable intimations concerning the nature and constitution of the human mind.He then pays tribute to Aristotle, the inventor of logic, and the primary influence on his own work:
In its ancient and scholastic form, indeed, the subject of Logic stands almost exclusively associated with the great name of Aristotle. As it was presented to ancient Greece in the partly technical, partly metaphysical disquisitions of The Organon, such, with scarcely any essential change, it has continued to the present day.Trying to improve on the logical work of Aristotle was an intellectually daring move. Aristotle’s logic, presented in his six-part book The Organon, occupied a central place in the scholarly canon for more than 2,000 years. It was widely believed that Aristotle had written almost all there was to say on the topic. The great philosopher Immanuel Kant commented that since Aristotle’s logic had been “unable to take a single step forward, and therefore seems to all appearance to be finished and complete.”
Aristotle’s central observation was that arguments were valid or not based on their logical structure, independent of the non-logical words involved. The most famous argument schema he discussed is known as the syllogism:
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
Aristotle also defined a set of basic axioms from which he derived the rest of his logical system:
- An object is what it is (Law of Identity)
- No statement can be both true and false (Law of Non-contradiction)
- Every statement is either true or false (Law of the Excluded Middle)
Aristotle’s axiomatic method influenced an even more famous book, Euclid’s Elements, which is estimated to be second only to the Bible in the number of editions printed.
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Source: The Atlantic
