Feynman explains the foundations of arithmetic

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Discussion Overview

The discussion revolves around Richard Feynman's explanations of the foundations of arithmetic, particularly how these concepts can be derived from basic principles, potentially in relation to Peano's axioms. Participants explore references to Feynman's work and recall specific lectures or writings that address the derivation of arithmetic operations from fundamental concepts.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant recalls Feynman explaining arithmetic concepts derived from basic principles, similar to Peano's axioms, but cannot locate the source.
  • Another participant suggests a passage from "Second Philosophy: A Naturalistic Approach" as a possible reference, noting that Feynman is mentioned in a context related to causal theory, but expresses doubt that Feynman actually made the assertion.
  • A participant mentions Feynman's lectures at Cornell, highlighting his engaging style and a specific joke related to multi-dimensional concepts.
  • One participant shares a memory of Feynman explaining arithmetic by starting with sets and natural numbers, detailing how addition is derived and subsequently leading to multiplication and other operations.
  • A later reply questions whether this memory might be linked to chapter 22 of the Feynman Lectures on Physics, suggesting a specific volume and providing a link to the online version.

Areas of Agreement / Disagreement

Participants express varying recollections of Feynman's explanations and reference different sources, indicating that no consensus exists on the specific content or location of the explanation in question.

Contextual Notes

Some participants express uncertainty about the accuracy of their memories regarding Feynman's explanations and the sources they reference, indicating potential limitations in recalling specific details or contexts.

Liberty Bell
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A long time ago I read an explanation Richard Feynman did on how the concepts of arithmetic can be derived from basic principles, along the lines of Peano's axioms, but I don't remember where it was. Thanks.
 
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Perhaps this passage in the book: Second Philosophy: A Naturalistic Approach

https://books.google.com/books?id=d8MSDAAAQBAJ&pg=PA125&lpg=PA125&dq=feynman+peano+axiom+talk&source=bl&ots=2iH-vUOtlI&sig=zbWg3x1RsoK2stfhO0bK62yOqNY&hl=en&sa=X&ved=0ahUKEwiy0dHAxIHWAhVp0YMKHaERC1AQ6AEINTAC#v=onepage&q=feynman peano axiom talk&f=false

From reading the passage, Feynman is mentioned in the Causal Theory example as a person someone has heard of and then makes some assertion about. I don't believe Feynman said it though. It appears that Kripke gave this as an example of a causal theory and then went on to relate how Peano's name got associated with the Peano Axioms.

Here's Feynman talking about Math and Physics at Cornell for the Messenger Lectures:



and they are classic Feynman. I love the multi-dimension joke.
 
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Maybe my mind is playing tricks on me, but I remember him doing an explanation like his algebra lecture but going "further back," starting with sets and natural numbers, and explaining how the concept of "addition" is derived, and from there how you can create the concept of multiplication and other arithmetic operations.
 
Liberty Bell said:
Maybe my mind is playing tricks on me, but I remember him doing an explanation like his algebra lecture but going "further back," starting with sets and natural numbers, and explaining how the concept of "addition" is derived, and from there how you can create the concept of multiplication and other arithmetic operations.
Might you be remembering elements from chapter 22 (Algebra) in volume 1 of the Feynman Lectures on Physics?

Caltech online version: http://www.feynmanlectures.caltech.edu/I_toc.html
 
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