Thanks for your attention to this! The happy face is the outer box. So, line 3 of the cartoon proof is assumption 3.
If you want the full []([]C->C) to be inside a thought bubble, then just take every line of the cartoon and put into a thought bubble, and I think that will do what you want.
LMK if this doesn’t make sense; given the time you’ve spent thinking about this, you’re probably my #1 target audience member for making the more intuitive proof (assuming it’s possible, which I think it is).
ETA: You might have been asking if there should be a copy of Line 3 of the cartoon proof inside Line 1 of the cartoon proof. The goal is, yes, to basically to have a compressed copy of line 3 inside line 1, like how the strings inside this Java quine are basically a 2x compressed copy of the whole program: https://en.wikipedia.org/wiki/Quine_(computing)#Constructive_quines#:~:text=java
The last four lines of the Java quine are essentially instructions for duplicating the strings in a form that reconstructs the whole program.
If we end up with a compressed proof like this, you might complain that the compression is being depicted as magical/non-reductive, and ask for cartoon that breaks down into further detail showing how the Quinean compression works. However, I’ll note that your cartoon guide did not break down the self-referential sentence L into a detailed cartoon form; you used natural language instead, and just illustrated vaguely that the sentence can unpack itself with this picture:
I would say the same picture could work for the proof, but with “sentence” replaced by “proof”.
Thanks for your attention to this! The happy face is the outer box. So, line 3 of the cartoon proof is assumption 3.
If you want the full []([]C->C) to be inside a thought bubble, then just take every line of the cartoon and put into a thought bubble, and I think that will do what you want.
LMK if this doesn’t make sense; given the time you’ve spent thinking about this, you’re probably my #1 target audience member for making the more intuitive proof (assuming it’s possible, which I think it is).
ETA: You might have been asking if there should be a copy of Line 3 of the cartoon proof inside Line 1 of the cartoon proof. The goal is, yes, to basically to have a compressed copy of line 3 inside line 1, like how the strings inside this Java quine are basically a 2x compressed copy of the whole program:
https://en.wikipedia.org/wiki/Quine_(computing)#Constructive_quines#:~:text=java
The last four lines of the Java quine are essentially instructions for duplicating the strings in a form that reconstructs the whole program.
If we end up with a compressed proof like this, you might complain that the compression is being depicted as magical/non-reductive, and ask for cartoon that breaks down into further detail showing how the Quinean compression works. However, I’ll note that your cartoon guide did not break down the self-referential sentence L into a detailed cartoon form; you used natural language instead, and just illustrated vaguely that the sentence can unpack itself with this picture:
I would say the same picture could work for the proof, but with “sentence” replaced by “proof”.
Okay, that makes much more sense. I initially read the diagram as saying that just lines 1 and 2 were in the box.