One of the most interesting things about technology is that it has two distinct strands to it. The obvious strand is what technology is usually associated with i.e. software programming and hardware like chips and transistors. The less obvious and more intriguing strand is the one which links technology to maths, logic and thence to philosophy. This outstanding article from the archives of The Atlantic focuses on the latter strand. [And if you like reading this article, you will love reading Claude Shannon’s biography by Jimmy Soni, “A Mind at Play”.]
In this article, Chris Dixon posits that it is Aristotle’s work that ultimately resulted – 2200 years after Aristotle’s death – in the computer. Befittingly, Dixon makes his case in a logical step-by-step fashion. Firstly, he references the two papers which are widely acknowledged as having laid the foundations of modern computer science: “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.”
Then in step 2, Dixon links Claude Shannon’s work with that George Boole: “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:
‘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.’”
In step 3, Dixon points out Boole himself had explained how his work was premised on what Aristotle did by inventing logic. Boole “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.’”
Chris Dixon then explains why Aristotle’s work is basically the guts of how any computer functions: “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:
In this article, Chris Dixon posits that it is Aristotle’s work that ultimately resulted – 2200 years after Aristotle’s death – in the computer. Befittingly, Dixon makes his case in a logical step-by-step fashion. Firstly, he references the two papers which are widely acknowledged as having laid the foundations of modern computer science: “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.”
Then in step 2, Dixon links Claude Shannon’s work with that George Boole: “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:
‘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.’”
In step 3, Dixon points out Boole himself had explained how his work was premised on what Aristotle did by inventing logic. Boole “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.’”
Chris Dixon then explains why Aristotle’s work is basically the guts of how any computer functions: “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.
You can replace “Socrates” with any other object, and “mortal” with any other predicate, and the argument remains valid. The validity of the argument is determined solely by the logical structure. The logical words — “all,” “is,” are,” and “therefore” — are doing all the work.
Aristotle also defined a set of basic axioms from which he derived the rest of his logical system:
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)
These axioms weren’t meant to describe how people actually think (that would be the realm of psychology), but how an idealized, perfectly rational person ought to think.” 2,200 years on, that idealized rational person is the smartphone in your and my pocket.
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