52 ideas that changed the world: 36. Logic

In this series, The Week looks at the ideas and innovations that permanently changed the way we see the world. This week, the spotlight is on logic:

Boris Johnson’s de facto chief of staff Dominic Cummings published a post on his blog in 2017 titled “Complexity and Prediction Part V”. The post linked to a paper, written by Cummings, that aimed to “sketch a new approach to education and training in general but particularly for those who go on to make important decisions in political institutions”.

At the foot of the post, Cummings quoted Hungarian-American mathematician John von Neumann on logician Kurt Godel, writing: “Godel’s achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time.”

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Following his appeal for “misfits” and “weirdos” to apply to work at No. 10 Downing Street, Cummings’s short-lived appointment of “superforecaster” Andrew Sabisky seems to have formed part of his effort to shift the goalposts in terms of how people “make important decisions” in the upper echelons of politics.

Cummings has clearly read Godel widely, citing him in various blog posts and papers on his personal website. He is not alone in considering him influential and in 1999, when Time magazine conducted a survey to determine the 20 most influential thinkers of the 20th century, the Austro-Hungarian logician came ninth.

Logic in 60 seconds

Logic is the study of how we arrive at premises based on a set of propositions or evidence.

More broadly, logic is the analysis and appraisal of arguments. In this definition, the premises may or may not support the conclusion; when they do not, this is characterised as a fallacy.

Historically, logic has been predominantly the preserve of philosophers and mathematicians. However, more recently, it has been studied as a part of cognitive sciences, which draws on computer science, linguistics and psychology.

Cummings’s academic background is in history, but based on his wide-ranging writing, it would appear that theories of logic and logicians themselves are now influencing our politics.

How did it develop?

The word “logic” derives from the Greek logos, meaning reason or plan. This etymology allows us to fairly easily pinpoint the origins of the concept in the Western world. For most, the study of logic was dominated by Aristotle right up until the late 19th century.

Aristotelian logic (often referred to as “categorical logic”) argues that logical statements relate to the “classes of things, and relationships between those classes”. An often cited example is the statement, “all men are mortals, Socrates is a man, therefore Socrates is mortal”.

What this essentially represents is “deductive reasoning”, where the argument is built on each step being deduced from what comes before. In Sophistical Refutations, Aristotle acknowledges that his work on logic was exploring uncharted territory. He wrote that prior to him, “nothing existed at all… on the subject of deduction we had absolutely nothing else of an earlier date to mention”.

The Franciscan friar William of Ockham, said to have devised the problem-solving principle Occam’s Razor, adapted Aristotelian logic in the 14th century, influencing the work of French philosopher Jean Buridan.

Buridan’s Summulae de Dialectica would become the primary textbook of logic at European universities for about two centuries. However, he is perhaps most famous for the “Buridan’s ass” paradox. This proposes a hypothetical situation in which a donkey that is equally hungry and thirsty is placed midway between a stack of hay and a pail of water. The paradox assumes the ass will always go to whichever is closer, it dies of both hunger and thirst since it cannot make any logical decision between the hay and water. The paradox exposes a problem in logical thought, for when there is no logical conclusion for what to do next, what is the ass to do?

During the same period, the Chinese philosopher Gongsun Long proposed the paradox “one and one cannot become two, since neither becomes two”, while at the same time, Indian logical scholarship began to develop theories indicative of modern philosophical logic. As a result of British colonial interests, this work began to draw the attention of many Western scholars, and influenced 19th-century logicians including Charles Babbage, Augustus De Morgan and George Boole.

In the mid-19th century, mathematical logic began to supplant Aristotelian logic in Western academia. In 1854, Boole published the catchily titled, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. This introduced mathematical logic, in which the foundations of mathematical problems are applied to the school of logic.

Boolean logic grew out of his writing, a branch of algebra in which all values are reduced to either true or false. This neat binary would later perfectly suit computer scientists as it can be easily represented through the binary of 1 (true) or 0 (false). It would later influence the development of the Turing machine, invented in 1936 by future Second World War codebreaker Alan Turing.

From 1910 to 1913, Alfred North Whitehead and Bertrand Russell published Principia Mathematica, a study that attempted to define so-called “symbolic logic”, a school of thought that attempts to derive logic from mathematics. Whitehead and Russell’s work, however, “did not satisfy everybody”.

In the 1920s, an English logician and philosopher, Frank Ramsey, showed how the system of Principia Mathematica could be revised. Commenting on the often confusing role of studying logic, Ramsey wrote: “Logic issues in tautologies, mathematics in identities, philosophy in definitions; all trivial, but all part of the vital work of clarifying and organising our thought.”

Cummings’s favourite logician Godel devised the First Incompleteness Theorem in the early 1930s. This established that logic like Russell and Whitehead’s Principia Mathematica cannot prove every mathematical truth. As The Economic Times notes, Albert Einstein is reported to have told a colleague that in the later years of his life, he used to come to the Institute of Advanced Study at Princeton University merely “to have the privilege to be able to walk home with Godel”.

Writing in Prospect magazine, emeritus professor of philosophy at the University of Southampton, Ray Monk, notes that “the general idea that there are truths that cannot be proved has an appeal far beyond logic”. This, Monk says, led Godel to be labelled “the romantic’s favourite mathematician” by American mathematician Jordan Ellenberg.

One of the most famous philosophers of the 20th century, Ludwig Wittgenstein, devoted his early writing to the field of logic. Tractatus Logico-Philosophicus, the only full length work published by Wittgenstein in his lifetime, was written as notes while the Austrian philosopher was serving as a soldier in the First World War and outlined a theory that would influence the logical positivist philosophers of the “Vienna Circle”.

The Vienna Circle was a group of around 13 philosophers – including Godel – who met regularly at the University of Vienna throughout the late 1920s and early 1930s with the aim of making philosophy scientific with the help of modern logic.

The group released a manifesto in 1929 in which it outlined the use of mathematical logic to clarify philosophical problems. The Vienna Circle members were also empiricists, believing that there is knowledge only from experience. Einstein, Russell and Wittgenstein are named in the manifesto as its “leading representatives”.

Heading into the 21st century, the combination of logic and improvements in data collection began to influence a new generation of “predictive sciences”. Another influence on Cummings, Canadian-American political science writer Philip Tetlock, devised the notion of “superforecasting”, a combination of exploiting “diverse sources of information”, while constantly “critiquing each other’s logic”.

In July 2011, Tetlock co-founded the Good Judgement Project, which aimed to “harness the wisdom of the crowd to forecast world events” by “developing coherent and logical probabilities”. The project spawned a book, Superforecasters: The Art and Science of Prediction, which Cummings has advised people to read, rather than “political pundits who don’t know what they are talking about”.

How did it change the world?

Theories of logic may seem academic and abstruse, a criticism that is easily levelled when trying to wrap your head around Aristotelian theory or the Vienna Circle’s manifesto.

However, the first study of logic, when, as Aristotle wrote “nothing existed at all… on the subject of deduction”, began a process of clarifying how we evaluate arguments and reasoning.

As Frank Ramsey notes, logicians work in “tautologies”, but the influence of their analytical framework is clear in a figure like Dominic Cummings, whose extensive writing makes regular reference to logicians like Godel and who employs the framework of their thinking in his plans for education and prediction.

The blog post in which Cummings cited Godel promised to devise a “new approach” to how decisions are made in politics and in sticking to his threat to hire weirdos like Sabisky, Cummings appears to be following through.

Ramsey may have said that logicians deal in the “trivial”, but it is the second part of that quote – that they are “part of the vital work of clarifying and organising our thought” – where their impact lies.