# What did Thomas Hobbes mean when he said reasoning is reckoning?

Date: 2019-03-27 · Author: Robert Scales · https://guidetoartificialintelligence.com/en/learn/what-did-hobbes-mean-by-reasoning-is-reckoning/

**Answer:** In Leviathan, published in London in 1651, the English philosopher Thomas Hobbes argued that reasoning is a kind of arithmetic, nothing more than adding and subtracting ideas expressed in words. That claim, that thinking might be calculation, is one of the oldest roots of the idea that a machine could think.

"Reckoning" is an old word for doing sums, the kind of counting a merchant does when checking a bill. When Thomas Hobbes wrote that reasoning is reckoning, he meant it literally: to reason is to add things together and take things away, only with words and ideas instead of coins. He put the idea in chapter 5 of *Leviathan*, a long book about human nature and government printed in London in 1651.

Hobbes was not building a machine and had no computer in mind. Still, his sentence is quoted again and again in histories of artificial intelligence, because it states, in plain language, the bet that the whole field has made: if thinking follows rules like arithmetic, then something other than a human brain might be able to follow them too.

## When and where Leviathan appeared

Hobbes (1588–1679) wrote *Leviathan* during the English Civil War, which ran from 1642 to 1651. He was living in France when he finished it, and he signed the book's dedication in Paris in April 1651. It was printed that year in London for the bookseller Andrew Crooke, at the sign of the Green Dragon in St. Paul's Churchyard. A revised Latin version followed in 1668.

Most readers know *Leviathan* for its politics. Hobbes argued that without a strong government, life would be a war of all against all, and that people therefore agree, in a kind of contract, to accept a powerful sovereign. Its famous title page shows a giant king whose body is made of hundreds of tiny people.

But the book opens with a long section called "Of Man", and that is where the ideas that matter for AI live.

## A body like a clock, a state like a machine

The very first page sets the tone. Hobbes compares a living body to a watch: the heart works like a spring, the nerves like strings, the joints like wheels. If life is just movement driven from inside, he asks, why not say that self-moving machines have a kind of artificial life? He then calls the state itself an "Artificial Man", a giant machine made by human skill.

This is a *mechanical* picture of nature, the view that people and animals can be explained as matter in motion, without an immaterial soul pulling the strings. Once you see the body that way, it is a short step to seeing the mind that way too.

## How reasoning works, according to Hobbes

Chapter 5, "Of Reason, and Science", makes the step. Hobbes says that whenever we reason, we either add parts to get a total or subtract one amount from another to find what is left. Multiplying and dividing, he adds, are only shortcuts for adding and subtracting.

What do you add when you reason in words? Names. Here is his scheme, laid out as a table:

| What a logician adds | What comes out |
|---|---|
| Two names ("Socrates", "a man") | A statement: "Socrates is a man" |
| Two statements | A syllogism, a small argument with a conclusion |
| Many syllogisms | A demonstration, or proof |

Subtraction works in the other direction: take a conclusion and one of its premises away, and you can work out the missing premise. Hobbes says geometers, lawyers and writers on politics all do the same thing in their own subjects. Where nothing can be added or subtracted, he concludes, reason has no work to do.

He then gives his definition: reason is

> "nothing but Reckoning (that is, Adding and Substracting)"

of the consequences of general names that people have agreed on. The agreement matters. For Hobbes, words must be pinned down by clear definitions first, the way a bookkeeper must know what each figure stands for. Start with vague or empty words and you will reach absurd conclusions, however carefully you reason.

> **Try it:** Pick a simple argument you heard this week, such as "All phones need charging; my phone is a phone; so my phone needs charging." Write it as Hobbes would: which two names were joined into each statement, and which two statements were joined into the conclusion? Then remove the conclusion and one premise, and see whether you can recover the other.

## Why it mattered

Hobbes's claim was short, and he did not develop it into a working system. Others did. The German thinker Gottfried Leibniz dreamed of a symbolic language in which arguments could be settled by calculating. In the 17th century Leibniz, Hobbes and René Descartes all wondered whether careful thinking could be reduced to a method as strict as algebra or geometry. That question runs straight through to the logicians of the 1800s and to the researchers who, in the 1950s, wrote the first programs that proved theorems.

In 2019 the idea is still alive in two forms. One is the rule-based approach: programs that store facts and definitions and combine them step by step, much as Hobbes described. The other, behind today's speech recognition and the AlphaGo system that beat top Go players, learns patterns from huge amounts of data rather than from definitions. Both are calculation, but only the first looks like Hobbes's bookkeeping.

Hobbes also left a useful warning. He noted that even skilled reckoners make mistakes, and that a sum is not correct just because many people approve it. The same holds for any system that reasons: the result is only as good as the definitions it starts from and the checking done afterwards.

## Can a machine reason just by adding and subtracting?

At the lowest level, a computer does little more than Hobbes described. Its chips combine and compare numbers, billions of times a second, and every program, from a spreadsheet to a voice assistant, is built from those simple operations. In that narrow sense, a machine reasons by reckoning all the time.

The harder question is whether that is *enough*. Hobbes assumed that the meaning was already fixed in agreed definitions, so only the arithmetic remained. Real life rarely hands us such clean definitions. Much of what makes people good at reasoning is deciding what the words should mean, noticing when a definition no longer fits, and knowing which facts matter. Researchers have spent decades on exactly that problem.

So the honest answer in 2019 is: machines can follow reasoning rules very well once the problem is stated precisely, as chess and Go programs show. Turning messy, everyday questions into that precise form is where much of the work remains, and where human judgment still does most of the heavy lifting.

## Sources

- Leviathan: https://www.gutenberg.org/ebooks/3207
- History of artificial intelligence: https://web.archive.org/web/20190301000000/https://en.wikipedia.org/wiki/History_of_artificial_intelligence
- Leviathan (Hobbes book): https://en.wikipedia.org/w/index.php?title=Leviathan_%28Hobbes_book%29&oldid=886683608