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The Laws of Thought summary

Name: The Laws of Thought
Rating: 4.2 (70 reviews)
Author: Tom Griffiths

Tom Griffiths

The Quest for a Mathematical Theory of the Mind

4.2 (70 ratings)

19 mins

Brief summary

The Laws of Thought delves into the principles and foundations of logical thinking, exploring how we can use structured reasoning to solve problems and make decisions, enhancing both personal and professional cognitive skills.

Topics

The Brain Neuroscience Mathematics Critical Thinking & Problem Solving Learning

Table of Contents

The Laws of Thought
Summary of 7 key ideas

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Key idea 1 of 7

What’s in it for me? Uncover the laws that govern our minds.

Some 300 years ago, a small group of prominent thinkers set out to uncover the laws that governed the world around them. Newton, Descartes, Hobbes, Leibniz – they were all on a quest for the Laws of Nature, a way of applying mathematical theories to ascertain how things work.

Fast forward to today and laws that govern our world – from gravity to acceleration – are taught in every physics classroom around the world. But what about the world inside of us? Those enlightenment figures were also looking for the Laws of Thought.

That quest would ultimately lead to formal logic, cognitive science, Bayesian models of the mind and even the neural networks that power today’s AI. And this Blink will take you through that whirlwind of a thinking journey.

So, ready to think hard about thinking? Then let’s get started!

The early days of formal logic

Gottfried Wilhelm Leibniz might be the smartest man who ever lived. Born in 1646 in Leipzig, Germany, he developed calculus in tandem with Isaac Newton. But however hard he tried, he couldn’t figure how to use maths to describe our minds.

Leibniz was working off Aristotle, whose own research was based on the syllogism – an argument with two premises and a conclusion that follows from the premises if they are true. Here’s an example: Every healthy person is happy. Some healthy people are rich. Therefore some rich people are happy. If the premises are true, so is the conclusion.

Aristotle identified 14 types of syllogisms, using a mix of intuition and proofs. But Leibniz wanted to go further; he wanted a mathematical theorem that captured the validity of syllogisms. He wanted what we today call a formal system.

Several great minds were with him on this quest – Descartes included. But it would be a 17-year old English schoolteacher who made the next breakthrough, over a century later.

Walking through a field one day, George Boole had a sudden realization: human thought could be expressed in algebraic form. The trick was to restrict your variables so that they can only be equal to 0 or 1. In this way Boole developed algebraic statements to capture logical statements like “Every A is B.”

Major philosophers would build on Boole’s insights over the next century to develop an increasingly complete system of formal logic, which came to be known as propositional logic.

But hang on, you say – why does this even matter to us? Well, as living beings one of our chief problems is knowing what to believe. If we know some things are true, what else can we trust to be true? Formal logic offers a way to answer this. It reduces semantics to syntax, meaning it reduces the problem of finding truth to following a set of rules. In this way it presents a step in demystifying the nature of thought. But this is far from the end of our journey.

The rise of behaviorism

The first half of the twentieth century saw the emergence of psychology, a new and unusual science in which the subject matter could be neither seen nor touched

Early psychologists worked around this problem by observing people’s behavior, and then inferring backward to arrive at the thoughts and feelings behind that behavior. One early experiment by Wilhelm Wundt involved measuring the time between a participant hearing a sound and pressing a button, on which basis he made inferences about the nature of the mind.

The first computers

In 1833, English mathematician and inventor Charles Babbage started working on his Analytical Engine, a machine that could carry out any arithmetic calculation using instructions provided by punch cards. This would have been the earliest form of what we now call a computer. But Babbage died before he could complete it

Some hundred years later, Alan Turing, a fellow at King’s College Cambridge, picked up the baton, with his conception called the Turing machine. The machine’s design involved a moving head and an infinitely long piece of tape. The head could read or write either a 0 or a 1 on the tape, and could move through a number of finite states.

The cognitive revolution

The 1950s saw the explosion of cognitive science. A string of key papers propelled the discipline forward, as researchers grappled with the task of explaining the mind scientifically. One approach that emerged was that of rules and symbols – formal systems based on logic.

American scholars Allen Newell and Herbert Simon introduced the physical symbol hypothesis, whereby a collection of symbol structures could be produced that describes objects and their behaviors in the physical world.

Fuzzy boundaries

One of the hardest blows to the rules and symbols approach to describing the mind came from the highlands of Western New Guinea. In 1968 California native Eleanor Rosch travelled there to study the local Dani people.

The Dani only had two words for colours: “mola” and “mili”. She enrolled some of the community’s members in a color memory experiment that had previously been conducted by Roger Brown on Harvard undergraduates.

Neural networks

The perceptron. Sounds like science fiction, right? Well at the time, it was. This was a machine designed by researcher Frank Rosenblatt – an artificial visual system that could classify a range of images based on the visual input received by an artificial retina – much like what our brains do with the light patterns received on our own retinas.

The perceptron’s design involved three layers. First there were sensory units that would activate in response to light patterns. These would be connected to association units, which would sum up the signals received by the sensory units and activate if they passed some predetermined threshold. Finally, the association units would be connected to response units, which would do the same thing, summing and thresholding, and ultimately give a classification of the image presented to the artificial retina. The perceptron could recognize a shape as a triangle, for example, or state if a shape appeared on the left part of an image.

Bayesian inference

We all use probability in our daily lives. We gauge how likely it is for it to rain tomorrow, or what the chances are of getting a job promotion. As more information reaches us, like a menacing cloud or an encouraging email, we adjust our probabilities accordingly.

How do we capture this mathematically? This problem was solved in the eighteenth century, by the Reverend Thomas Bayes and the Marquis Pierre-Simon Laplace. Both men solved the problem independently, but we now refer to this kind of reasoning as Bayesian inference.

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What is The Laws of Thought about?

The Laws of Thought (2026) is a deep dive into the world of cognitive science – the quest to understand the laws that govern our minds. It gives a broad and detailed account of the history of the discipline, starting with the foundations of formal logic before moving through behaviorism, early computational theories, semantic research, artificial neural networks, and finally probability theory. By offering insights into three main approaches to understanding the mind, it offers an intricate picture of the Laws of Thought.

Who should read The Laws of Thought?

Anyone who ever thinks about how the mind works
AI users curious about where the tech came from
Philosophy buffs grappling with the great questions of life

About the Author

Tom Griffiths is the Henry R. Luce Professor of Information Technology, Consciousness and Culture in the Departments of Psychology and Computer Science at Princeton University. He directs the Computational Cognitive Science Lab and the Laboratory for Artificial Intelligence at Princeton, and his award-winning research has been published in Science, Nature, and the Proceedings of the National Academy of Sciences, among other publications. He is the co-author of the book Algorithms to Live By.

Categories with The Laws of Thought

Education Psychology Personal Development Science

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