A Logical Report

Ben Burton - H01

This report is on logic, which is “the use and study of valid reasoning.” It comes in many forms and is fond mainly in the subjects of philosophy and mathematics. It also applied in programming and computer science. The main types of logic include formal (or often called deductive) reasoning and informal (inductive) reasoning. A good example of formal reasoning would be most mathematical reasoning.

In western philosophy, the earliest logic was developed in ancient Greece by Aristotle. His Aristotelian logic is the basis of almost all European logic. His greatest contribution, perhaps, was the use of syllogisms. These are logical arguments that involves 3 statements which follow the form of if statement A is true, and statement B is true, then, therefore, statement C must be true as well. Statements A and B share a term, which allows for the inference of the final statement C.

Syllogism was king up until the 19^th century, when a focus on symbolic, or mathematical, logic took the main stage. George Boole introduced symbolic logic and the beginnings of Boolean operators in An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. After this point, there are more contributions to symbolic logic, such as the invention of quantifier notation by Gottlob Frege. Then, Bertrand Russel and Alfred North Whitehead published Principia Mathematica, a three volume work on the foundation of mathematics. The development of symbolic logic slowed down after 1931.

Nowadays, most people may, after hearing the word ‘logic,’ would probably think of logical circuits in the context of computers. The basis of all logical circuits is based on simple logic gates which are representations of Boolean logic functions. Boolean logic consists of many operators, with the most fundamental being the ‘and’ (a∧b), ‘or’ (a∨b), and not ( ¬a). The combination of these logic gates is the basis of every digital device, and allows for an extremely wide variety of possibilities and applications. A recent example of a popular medium to work with Boolean operators comes from the game Minecraft, where players can use ‘redstone’ to create anything from a light to logic arrays to full-blown computers. It gives many people a view of how computers work at their most fundamental level.

As our technology advances, we are running in to the possibility of creating machines that could carry on a conversation so well that even a human would be fooled. This benchmark is often referred to as the Turing Test, named after Alan Turing, who proposed the test. This raises some interesting questions about the nature of intelligence; should we be able to create a machine that could perfectly impersonate the way a human behaves, could we consider such a machine to be a sentient being? Even now, we are pursuing technologies, for example IBM’s Watson, that would make pretty convincing humans. There is a high possibility that, in the nearish future, this will be a great problem for us to face. It will certainly take a lot of thought to both treat these possible beings fairly, while also not becoming some sort of apocalyptic world, as Hollywood often likes to portray Still, logic is a field that makes humans be humans, it makes machines be machines, and it gives us all the tools we need to advance and thrive as a culture.