Chapter 1: Prior Analytics(~ 350 BCE) Aristotle
This is my commentary and summary on Chapter 1 of Harry R. Lewis’ book Ideas That Created the Future: Classic Papers of Computer Science which sheds light on Prior Analytics written by Aristotle around 350BCE.
In ancient times there were multiple systems of logic in use. Among them, Aristotelian logic and Stoic logic were the two most prominent ones. In this article, I discuss some important ideas from one of Aristotle’s 1st writings on logic which can be traced back as one of the first building blocks towards modern-day computer science.
Aristotle was a great systematizer and his writings reflect the same. Prior Analytics consists of a lot of definitions for terms that are used in compounding ways. Colloquially used words such as ‘belong’ or ‘term’ are used in an unpopular/new context. Which makes his work not an easy read by any stretch. However, logicians who later built upon Aristotle’s work have greatly simplified it with the introduction of Mathematical notations and it’s become relatively easier to understand through that lens.
One of the most well-known transitive logic concepts, which goes as “If B belongs to A and C belongs to B. Then it necessarily follows that C belongs to A.” was put forth by Aristotle in Prior Analytics. Another important idea that was put forth by him was “If B belongs to A and B does not belong to C. Then we can’t infer anything between A and C.” The second concept can be a little less intuitive than the first. These axioms were part of Aristotle’s work which laid a foundation towards inferring conclusions from data that only depended on the form of the arguments and not on things like the emotional weight put forth by the presenter or things not captured by the data.
As an example, let A represent the set of all vehicles, B represents the set of 4-wheeled vehicles. We immediately see that B belongs to A since the set of all 4-wheeled vehicles is going to be in the set of all vehicles. Now, if C represents the set of all yellow-colored 4-wheeled vehicles. We see immediately that it belongs to B since B’s criteria of ‘4-wheeled’ vehicles would allow for all ‘yellow 4-wheeled’ vehicles. Now for understanding the relationship between A and C we have two points of view. In the first one, we can reason out the relation between A and C as we did between A and B or B and C. In the second one, we can apply the transitive logic concept and say that since B belongs to A and C belongs to B then necessarily C has to belong to A. The second point of view is considered as making an argument based on form.
Now, in the above example if C were to just belong to a set of ‘2-wheeled’ vehicles it does not belong to B. In this example, C does belong to A but we can come to that conclusion only from a single point of view which is by directly comparing A and C. The fact that B and C aren’t related does not help us in understanding the relation between A and C. C very well could have been representing a set of ‘houses’ in which case it would be unrelated to B as well as A. These two principles are at the very core of the logical systems inside modern computers that help them understand the relevance or irrelevance of inputs during computation.
Aristotle’s work put forth a foundation that allowed us to measure seemingly abstract things and make forth comparisons between different objects. With 0’s and 1’s computers can represent, store and compute an enormous variety of things with an almost perfect level of consistency and integrity which is ensured by modern logical systems. Modern logical deduction has its root in Aristotle’s work. Therefore, Aristotle is considered a contributor to the development of modern computer science.
References
- Prior Analytics ( 350 BCE), Aristotle
- Ideas That Created the Future: Classic Papers of Computer Science, Harry R. Lewis