The laws of thoughtGeorge Boole
The laws of thought
by George Boole · first published 2013
15mentions
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2014–2026first – last mentioned
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Working through it now - reading the Laws of Thought by George Boole was a spiritual experience for me. The connection between natural language, logic, and math finally made sense to me. Before I had a hard time understanding the saliency of things like…
on “When did computer science theory get so hard?” ↗> a singularity would almost surely be preceded by a world in which machines are 0.01% intelligent (say) I'm not sure that fractional intelligence makes sense. Otherwise, Boole's Laws of Thought, mechanisms like clockwork, even books, even counting, and many other ideas would be seen as capturing some "fraction" of intelligence. I think it's a threshold, like Turing equivalence: either you can…
on “Don Knuth Plays with ChatGPT” ↗…fundamental, because, a machine built to flip a coin with always the same pressure, can be adjusted to always give heads, or tails. In such a setup there won't be probability. From George Boole's The Laws of Thought, p.244: "Probability is expectation founded upon partial knowledge. A perfect acquaintance with _all_ the circumstances affecting the occurence of an event would change expectation into certainty, and…
on “Probability (1963)” ↗People forget that Alan Turing's essay "Computing Machinery and Intelligence" was published in Mind, a major philosophy journal. People forget that Boolean algebra comes from a work called "The Laws of Thought," where Boole tries to describe the algebraic operations underlying thought. If you think that isn't something "philosophers do," this is an ancient goal stretching back to Aristotle's logic, up through…
on “What, exactly, do philosophers do?” ↗…effort to distill the essence of what humans (regular, average people) find reasonable and convincing. (To mention just one example, there is a reason one of George Boole's major works is called "The Laws of Thought".) Our strategies for understanding language also involve inference and unification that is similar to logic programming. This is not to say the exact semantics and evaluation strategy of Prolog is what…
on “Ask HN: Production Prolog in 2020?” ↗Thinking that you need to learn "Category Theory" in order write Haskell is like saying you need to read George Boole's 'Investigation of the Laws of Thought' (1854) in order to write a conditional statement. In other words, it's not. "Category Theory" is for mathematicians and people interested in highly abstract mathematical theory. It doesn't help you…
on “Learning Haskell is no harder than learning any other programming language” ↗…reasoning, depart; secondly, that the laws by which the process is conducted be founded exclusively upon the above fixed sense or meaning of the symbols employed." —George Boole, An Investigation of the Laws of Thought
on “The logic of Buddhist philosophy” ↗funfact: Boole titled his on book on his algebra "The Laws of Thought". AI & computation were old friends long before electro-computers.
on “The Subtle Power of Booleans: Programming with truth and statefulness” ↗…The True Method (1677) By Gottfried Wilhelm Leibniz Sketch of the Analytical Engine (1843) By L. F. Menabrea, with Notes by the Translator, Ada Augusta, Countess of Lovelace An Investigation of the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probabilities (1854) By George Boole Mathematical Problems (1900) By David Hilbert On Computable Numbers, with an Application to the Entscheidungsproblem…
on “Ideas That Created the Future: Classic Papers of Computer Science” ↗All computer science is AI, including before computers existed. Boole even called his logic the "Laws of Thought". It's just the goal-posts that move.
on “Why 2015 Was a Breakthrough Year in Artificial Intelligence” ↗Boole, "An Investigation into the Laws of Thought": https://books.google.com/books?id=DqwAAAAAcAAJ&printsec=fron...
on “Creating a Computer Science Canon (2003) [pdf]” ↗George Boole proposed something similar in The Laws of Thought: he considered a definition of c = a/b where a = c AND b (even if he didn't write it like that). Thus, 0/0 was an indeterminate value, and 1/0 was seen as an impossibility. Boole's example: if m means…
on “What's the difference between 0/0 and 1/0?” ↗Always has been. My favorite example: George Boole (Who we get Boolean from), had a road to Damascus experience as a teenager and later wrote "An Investigation of the Laws of Thought" where we get our 0s and 1s from, and truth operations, largely to prove God is Good. The concept of 0 and 1, absolute truth and false, was born from his spiritual views.
on “Pythagorean Theorem Found on Clay Tablet 1k Years Older Than Pythagoras” ↗Mathematics is not the only formal languages. Every profession soon invents its own jargon because natural language are too ambiguous. For some that’s enough. But science require more formalism. Boole’s Laws of Thought or Church’s The Calculi of Lambda-Conversion are mostly describing how to be so precise that the description of the problem equates its solution. But formal languages have their own issues.
on “Declarative Programming with AI/LLMs” ↗Boole was trying to improve logic for humans, "The Laws of Thought". So it has a connection to human problems, and eventually to practical matters. He could instead have been working on something much more abstract and much less useful. By which I'm trying to make an…
on “Mathematicians issue warning as AI rapidly gains ground” ↗