February 25, 2026
The Laws of Thought: The Quest for a Mathematical Theory of the Mind
Tom Griffiths
Director of the Computational Cognitive Science Lab and the Princeton Laboratory for Artificial Intelligence
The Laws of Thought: The Quest for a Mathematical Theory of the Mind
Tom Griffiths
Director of the Computational Cognitive Science Lab and the Princeton Laboratory for Artificial Intelligence
George Bustin, introducer, and Tom Griffiths
Minutes of the 20th Meeting of the 84th Year
President George Bustin convened the 20th meeting of the Old Guard’s 84th year. Ninety-nine persons attended the session, including John Cotton’s guest, Riten Patel. Sarah Ringer read the minutes of the previous meeting. Frances Slade let the invocation.
George Bustin introduced the speaker, Tom Griffiths, Henry R. Luce Professor of Information Technology, Consciousness, and Culture at Princeton University and Director of the university’s Cognitive Science Lab and the Laboratory for Artificial Intelligence established in 2024. A native of the United Kingdom, he earned his B.A. from the University of Western Australia and his PhD from Stanford University. In 2019, the National Academy of Sciences selected him for the Troland Research Award in experimental psychology for his work on how humans and machines make decisions, a prestigious recognition of researchers no older than 40.
Professor Griffiths opened by suggesting that while many of us may know the story of how logic and mathematics have been used to help us understand more and more about the physical universe, fewer know the story of efforts to discover whether or how logic and mathematics can be used to help us decode that other great mystery: how the human mind works. He admitted that cognitive science has yet to converge on a theory of the mind comparable in power and utility to our standard theories about the physical universe, but that he would summarize efforts to eventually get there as described in much greater detail in his recent book, which was available to those interested at the end of the meeting.
In 1679, the great genius Gottfried Leibniz, co-inventor of calculus, attempted to make Aristotle’s syllogisms universally applicable so that they could be manipulated and analyzed arithmetically, but he failed. However, in 1668 the Rev. John Wilkins had also tried to do just that by numbering, categorizing, and ordering 3,240 concepts, to each of which he had assigned a symbol. However, his assigned numbers were arbitrary and his proposed language could be applied only to “formal” systems, such as the game of chess with its fixed rules and could not be used to address “informal” systems, such as fencing, or the capabilities of the human mind such as learning and using language, or the ability to quickly categorize, or to instantly sense a probable danger or challenge.
Enter John Boole, born in 1815 to a shoemaker and his wife Mary in Lincoln, England both of whom placed a very high premium upon education for their offspring. Deeply steeped in algebra and Leibniz’ approach to calculus, their son John would eventually produce a book that cemented him as one of the key founders of future computer and cognitive science. His goal: “to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation, to establish the science of logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and finally, to collect from the various elements of truth…brought to view during the course of these inquiries some probable intimations concerning the nature and constitution of the human mind.”
Half of Boole’s book was about logic, the other half about probabilities. Estimating probabilities, as the human mind frequently does subliminally during the course of daily life, presented a major challenge, but it eventually turned out that the Reverend Thomas Bayes and the French mathematician LaPlace worked out a way, now known as the Bayesian Inference, to calculate probabilities.
It is one thing to deal with problems or matters you can feel and touch, quite another to tackle challenges, like understanding how the mind works. Psychologists like William James, the brother of novelist Henry James, and much later, B.F. Skinner, attempted to understand the human mind solely by observing the behavior of patients. But psychologist Jerome Bruner, who was blind during part of his life, decided that such a “behaviorist” approach limited our ability to learn how the mind really works. As he discovered during his blindness, not everybody experiences the world in the same way. So he went looking for an alternative method to study the mind and eventually found that alternative in John von Neumann here in Princeton who was attempting to develop a computer with a stored memory that could be explored by whatever instructions it was given, much like the human mind. This was the spark that helped ignite a cognitive science that would attempt to express hypotheses about a wide range of cognitive problems—language, reasoning, categorization, and the structure of the world—that could then be tested against human behavior emulating some of the mathematical approaches in the physical sciences that theorize about unobservable entities to make precise predictions about observable phenomena.
From the mid-20th century on, many scientists have contributed to and refined how we might apply the methods of mathematics and logic to thought and apply them to a wide range of problems such as reasoning, categorization, problem-solving, and particularly language. The most visible consequence so far, of course, has been the dramatic emergence of AI large-language models trained on the probabilities of sequences of words in a language. Experience so far demonstrates that probability and logic really are the “Laws of Thought,” shared by all intelligences whether artificial or human.
There are some meaningful differences between humans and AI. Our minds are shaped by human limitations: time, computation and bandwidth. Nevertheless, AI systems require far more data and power and generalize less well.
The fact that babies can learn a language from much less data than these AI systems indicates that humans must have some predisposition toward learning things that is not currently captured by AI. Our minds also approximate Bayesian solutions to the problems posed by our environment, giving us an intuitive sense of the similarity between things, or the structure of categories, or the right words to use. Human minds and AI may prove to quite different kinds of minds.
Nonetheless, we should continue to think about how to create intelligent systems. Aerodynamics doesn’t just help us understand bird flight—it also helps us build jet airplanes. Such aspirations for AI may well exceed our own mind’s capabilities.
Respectfully submitted,
Ralph Widner
George Bustin introduced the speaker, Tom Griffiths, Henry R. Luce Professor of Information Technology, Consciousness, and Culture at Princeton University and Director of the university’s Cognitive Science Lab and the Laboratory for Artificial Intelligence established in 2024. A native of the United Kingdom, he earned his B.A. from the University of Western Australia and his PhD from Stanford University. In 2019, the National Academy of Sciences selected him for the Troland Research Award in experimental psychology for his work on how humans and machines make decisions, a prestigious recognition of researchers no older than 40.
Professor Griffiths opened by suggesting that while many of us may know the story of how logic and mathematics have been used to help us understand more and more about the physical universe, fewer know the story of efforts to discover whether or how logic and mathematics can be used to help us decode that other great mystery: how the human mind works. He admitted that cognitive science has yet to converge on a theory of the mind comparable in power and utility to our standard theories about the physical universe, but that he would summarize efforts to eventually get there as described in much greater detail in his recent book, which was available to those interested at the end of the meeting.
In 1679, the great genius Gottfried Leibniz, co-inventor of calculus, attempted to make Aristotle’s syllogisms universally applicable so that they could be manipulated and analyzed arithmetically, but he failed. However, in 1668 the Rev. John Wilkins had also tried to do just that by numbering, categorizing, and ordering 3,240 concepts, to each of which he had assigned a symbol. However, his assigned numbers were arbitrary and his proposed language could be applied only to “formal” systems, such as the game of chess with its fixed rules and could not be used to address “informal” systems, such as fencing, or the capabilities of the human mind such as learning and using language, or the ability to quickly categorize, or to instantly sense a probable danger or challenge.
Enter John Boole, born in 1815 to a shoemaker and his wife Mary in Lincoln, England both of whom placed a very high premium upon education for their offspring. Deeply steeped in algebra and Leibniz’ approach to calculus, their son John would eventually produce a book that cemented him as one of the key founders of future computer and cognitive science. His goal: “to investigate the fundamental laws of those operations of the mind by which reasoning is performed; to give expression to them in the symbolical language of a Calculus, and upon this foundation, to establish the science of logic and construct its method; to make that method itself the basis of a general method for the application of the mathematical doctrine of Probabilities; and finally, to collect from the various elements of truth…brought to view during the course of these inquiries some probable intimations concerning the nature and constitution of the human mind.”
Half of Boole’s book was about logic, the other half about probabilities. Estimating probabilities, as the human mind frequently does subliminally during the course of daily life, presented a major challenge, but it eventually turned out that the Reverend Thomas Bayes and the French mathematician LaPlace worked out a way, now known as the Bayesian Inference, to calculate probabilities.
It is one thing to deal with problems or matters you can feel and touch, quite another to tackle challenges, like understanding how the mind works. Psychologists like William James, the brother of novelist Henry James, and much later, B.F. Skinner, attempted to understand the human mind solely by observing the behavior of patients. But psychologist Jerome Bruner, who was blind during part of his life, decided that such a “behaviorist” approach limited our ability to learn how the mind really works. As he discovered during his blindness, not everybody experiences the world in the same way. So he went looking for an alternative method to study the mind and eventually found that alternative in John von Neumann here in Princeton who was attempting to develop a computer with a stored memory that could be explored by whatever instructions it was given, much like the human mind. This was the spark that helped ignite a cognitive science that would attempt to express hypotheses about a wide range of cognitive problems—language, reasoning, categorization, and the structure of the world—that could then be tested against human behavior emulating some of the mathematical approaches in the physical sciences that theorize about unobservable entities to make precise predictions about observable phenomena.
From the mid-20th century on, many scientists have contributed to and refined how we might apply the methods of mathematics and logic to thought and apply them to a wide range of problems such as reasoning, categorization, problem-solving, and particularly language. The most visible consequence so far, of course, has been the dramatic emergence of AI large-language models trained on the probabilities of sequences of words in a language. Experience so far demonstrates that probability and logic really are the “Laws of Thought,” shared by all intelligences whether artificial or human.
There are some meaningful differences between humans and AI. Our minds are shaped by human limitations: time, computation and bandwidth. Nevertheless, AI systems require far more data and power and generalize less well.
The fact that babies can learn a language from much less data than these AI systems indicates that humans must have some predisposition toward learning things that is not currently captured by AI. Our minds also approximate Bayesian solutions to the problems posed by our environment, giving us an intuitive sense of the similarity between things, or the structure of categories, or the right words to use. Human minds and AI may prove to quite different kinds of minds.
Nonetheless, we should continue to think about how to create intelligent systems. Aerodynamics doesn’t just help us understand bird flight—it also helps us build jet airplanes. Such aspirations for AI may well exceed our own mind’s capabilities.
Respectfully submitted,
Ralph Widner