Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas

343 | Tom Griffiths on The Laws of Thought

February 9, 2026

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  • The quest for the "Laws of Thought," as explored in the episode "343 | Tom Griffiths on The Laws of Thought" of *Sean Carroll's Mindscape: Science, Society, Philosophy, Culture, Arts, and Ideas*, seeks abstract, mathematical principles (like logic and probability theory) that govern ideal information processing at the computational level. 
  • Human cognition is best understood through the lens of **Resource Rationality**, where apparent irrationalities or heuristics are optimal strategies for achieving ideal Bayesian outcomes given finite cognitive constraints like time and energy. 
  • A major difference between human learning and current AI models (LLMs) lies in **inductive bias**; humans require vastly less data to learn complex tasks like language because they possess strong innate predispositions that AI models must artificially replicate through techniques like meta-learning. 
  • LLMs exhibit idiosyncratic biases, such as favoring answers whose numerical representations appear more frequently on the internet, suggesting their internal solutions can differ significantly from human-like reasoning despite producing similar outputs. 
  • The history of cognitive science shows a shift from purely logical/rule-based theories of thought (1950s) to spatial/geometric representations (1970s), which ultimately led to the development of neural networks as a computational framework for processing concepts as points in space. 
  • David Marr's three levels of analysis (computational, algorithmic, implementation) explain why there isn't a single 'Law of Thought,' as correct theories can coexist at different levels, with the computational level (logic/Bayesian inference) providing the most general principles for intelligence across systems. 

Segments

Sponsor Messages and LLM Arithmetic
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(00:00:00)
  • Key Takeaway: LLMs, in their natural state, often fail at simple arithmetic and counting tasks, mirroring human limitations, because the underlying program is optimized for human-like conversation rather than computation.
  • Summary: The host notes that LLMs often struggle with basic arithmetic and counting, similar to humans, because the model is optimized for sounding human rather than accessing the computer’s native calculation abilities. This highlights that ’thought’ encompasses distinct abilities, like conversation versus calculation, which can be optimized separately. The segment is interrupted by advertisements for Incogni and Jerry.
Defining the Laws of Thought
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(00:04:06)
  • Key Takeaway: The ‘Laws of Thought’ are best characterized at the abstract computational level, defining the ideal solution to problems minds must solve, primarily through logic and probability theory.
  • Summary: Sean Carroll frames the central problem as reconciling pristine logical rules with the constraints of embodied intelligence, energy, and uncertainty. Tom Griffiths explains that cognitive science analyzes systems at computational, algorithmic, and implementation levels, placing the ‘Laws of Thought’ at the most abstract computational level. Ideal solutions at this level involve logic for certainty and probability theory for uncertainty.
Historical Foundations: Logic and Syllogisms
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(00:07:17)
  • Key Takeaway: The historical pursuit of mathematical theories of thought began with Aristotle’s syllogisms, which Leibniz attempted to formalize using arithmetic (vector embeddings) and Boole later formalized using a distinct algebra focusing on binary true/false logic.
  • Summary: Griffiths traces the lineage of formal thought from Aristotle’s syllogisms to Leibniz’s unsuccessful attempt to map terms to numbers (a precursor to vector embeddings) to automate reasoning. George Boole later succeeded in formalizing Aristotle using algebra, leading to the 19th-century concept of ‘The Laws of Thought’ as parallel to the laws of nature.
The Shift to Probabilistic Reasoning
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(00:15:22)
  • Key Takeaway: The transition from classical logic (true/false) to modern thought involves probability theory, pioneered by Bayes and Laplace, which allows for graded degrees of belief about propositions and uncertain inference (induction).
  • Summary: Boole’s work included a section on probability theory to handle induction, reasoning from uncertain premises. Bayesian probability generalizes classical logic by assigning numerical degrees of belief to possible worlds, allowing for updating beliefs based on new evidence. This framework is considered the ideal solution for inductive problems faced by minds.
Resource Rationality and Heuristics
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(00:40:21)
  • Key Takeaway: Human biases and heuristics are often best understood not as failures of rationality, but as resource-rational strategies—the best algorithms for approximating ideal Bayesian inference given limited cognitive resources.
  • Summary: Griffiths explains that resource rationality redefines rationality for bounded agents, focusing on using the best algorithm to choose actions under constraints. Human strategies, or heuristics, are seen as sampling strategies or goal decomposition methods that approximate ideal reasoning efficiently. This framework explains why humans appear error-prone when compared against perfect, resource-unconstrained Bayesian ideals.
Inductive Bias in Learning
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(00:49:33)
  • Key Takeaway: The vast difference in data required for human language acquisition versus LLMs (years vs. millennia of data) is attributed to the strong, evolved inductive biases present in the human prior distributions.
  • Summary: Priors inform inductive inference across perception, language interpretation, and fundamental learning. LLMs require massive datasets because they start as near-blank slates, whereas human children leverage evolved constraints (inductive bias) to learn language quickly. Closing this gap requires understanding and engineering these prior distributions into AI systems.
AI Learning Paths and Jagged Intelligence
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(00:57:02)
  • Key Takeaway: AI systems trained on massive data may find solutions that are functionally similar to human language use but internally ‘weird’ or non-human-like, leading to jagged intelligence where performance is brittle outside trained domains.
  • Summary: The success of LLMs confirms Chomsky’s point that learning complex language requires enormous data, far exceeding human exposure. If AI is nudged toward human-like inductive biases via meta-learning, its solutions may become more interpretable and less prone to ‘jagged intelligence’—the phenomenon where systems fail spectacularly on problems adjacent to those they master.
LLM Biases and Training Objectives
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(01:04:51)
  • Key Takeaway: LLMs’ training objective (predicting the next token) fundamentally shapes their solutions, leading to behaviors like favoring high-probability answers even when incorrect for specific tasks.
  • Summary: AI systems trained on vast amounts of data may find solutions that look similar externally to human ones but are internally very different. Research suggests LLMs are highly sensitive to the probability of their outputs, demonstrated by their tendency to miscount letters based on the frequency of the resulting number in training data. Differences between the AI’s objective function and the problems human minds evolved to solve cause predictable mismatches in behavior.
Logic vs. Spatial Representation
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(01:08:38)
  • Key Takeaway: Psychological research revealed that human categorization relies on fuzzy, spatial structures rather than strict logical definitions, necessitating theories beyond classical logic.
  • Summary: The third thread in the laws of thought involves viewing thought as points in space, contrasting with earlier logical frameworks. Eleanor Roche’s work showed that human categories (like ‘furniture’) lack the strict definitions required by logic, exhibiting a gradient structure. This fuzziness suggested that representing concepts as points in space, where proximity defines category membership, offered a better theoretical fit.
Neural Networks and Spatial Computation
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(01:11:48)
  • Key Takeaway: Neural networks provide the computational mechanism for working with concepts represented as points in space by transforming input vectors into output vectors.
  • Summary: The problem of computation with spatial concepts was answered by neural networks, which translate vectors of input values into vectors of output values. Early work by McCullough and Pitts translated Boolean logic into neuron operations, but Minsky later halted research due to perceived limitations in single-layer networks. The development of backpropagation, utilizing Leibniz’s chain rule, enabled multi-layer networks capable of solving more complex, non-linear problems.
Marr’s Levels and Explanatory Pluralism
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(01:18:01)
  • Key Takeaway: A complete understanding of the mind requires mutually reinforcing explanations across Marr’s three levels: computational, algorithmic, and implementation, precluding a single, monolithic theory.
  • Summary: Marr’s levels—computational (the abstract problem), algorithmic (the process), and implementation (the physical realization)—show why a single theory of mind is insufficient. Logic and probability theory operate at the computational level, while artificial neural networks serve as an algorithmic approximation. It is unlikely that a one-to-one mapping exists between these levels, as multiple algorithms can approximate the same ideal computational solution.