## Peano - Show Peano using backwards c for implication ("inverse contains"), upside down semicolons, and upside down square root for power. - By volume 5, Peano is now writing in Latin instead of French. ![[history-of-logic-notation-20.png]] ![[history-of-logic-notation-21.png]] ![[history-of-logic-notation-22.png]] ![[history-of-logic-notation-23.png]] ![[history-of-logic-notation-24.png]] ![[history-of-logic-notation-25.png]] ## Frege ![[history-of-logic-notation-17.png]] ![[history-of-logic-notation-18.png]] ![[history-of-logic-notation-19.png]] ![[history-of-logic-notation-26.png]] ## Russell and Whitehead - The quote from Russell and Whitehead here is fantastic. - Include the line about "Paternal Aunt is the Relative Product of Sister and Father." - Two lines below this they mention that "Peano and Frege showed that the class whose only member is x is not identical with x." The fact that they feel the need to CITE someone on this point, let alone someone so recent, really shows how _informal_ mathematics had been for the several thousand years of its history until then. - At the top of 311 they mention that "types" are introduced to avoid contradictions. - On 312, below the boobs, the thousand page book on the History of Mathematical Notations says of Russel and Whitehead's Principia Mathematica that: "We don't have enough space to list all the notations in this book." (LOL) - On page 314, in the final page of the Logic section in the book, the author mentions that no topic in mathematics comes close to logic in terms of its ability to provide a universal language, no group has a harder notation problem to solve, and no group has thought about that problem more deeply. This fact continues today into the culture of programming, where the need to maintain large codebases which actually execute (unlike mathematics in a textbook) has led to intuitions about what constitutes a good notation that go so far beyond mathematics that it's scarcely possible to compare the two. Perhaps the most illustrative example is the fact that it was Unix, not mathematics, that finally had the sense to write function composition in the right order: f | g. ![[history-of-logic-notation-27.png]] ![[history-of-logic-notation-28.png]] ![[history-of-logic-notation-29.png]] ![[history-of-logic-notation-30.png]] ![[history-of-logic-notation-31.png]] ![[history-of-logic-notation-32.png]] ![[history-of-logic-notation-33.png]] ![[history-of-logic-notation-34.png]] ![[history-of-logic-notation-35.png]] ![[history-of-logic-notation-36.png]] ![[history-of-logic-notation-37.png]] ![[history-of-logic-notation-38.png]] ## Judgement Stroke 0: Now, my dearest one, after all of the above, do you--- 1: Yes. For the love of god yes. 0: What question did you think I was about to ask? 1: Creation story. I see the point. Holy hell that was a lot. 0: Good, because--- 1: You don't need to convince me! I got it. I mean the horse logic alone probably would have convinced me. 0: In summary? 1: I can summarize. 0: Go ahead. 1: In summary, a creation story isn't the worst thing in the world. Actual history is worse. History is literally everything that's ever happened. If I learned anything from this file, it's that bibles probably wouldn't be so popular if they started with everything that ever happened. I mean Christ! Who wants to hear that? 0: Oh c'mon, you had fun in this file. 1: I know, I know. But still. Please no more history without a narrative. It hurts. 0: No more horse logic? 1: No more horse logic. 0: Any suggestions on where we should go next? 1: Let's get back to the creation story. 0: Say the magic words. 1: Please? 0: Not magical enough. _(Narrator: 1 flips back through the current file for a moment.)_ 1: Here. ![[magic-words-frege.png]] 0: Still not magic enough. 1: I hate you. _(Narrator: 1 leaves, heading in the direction of the the previous file, before returning with something in hand.)_ 0: What do you have to say for yourself? 1: The most magical words I know. 0: I'm listening. 1: ![[magic-words-horse-logic.png]] _(Narrator: 0 and 1 are immediately swept away to the next file, as if by magic.)_