It seems the truth vs provability distinction is actually the heart of decision theory.
I came across this paragraph from Bruno Marchal today, which strikingly reminds me of Vinge’s “Hexapodia as the key insight”:
Talking about Smullyan’s books, I recall that “Forever Undecided” is a
recreational (but ok … not so easy, nor really recreational)
introduction to the modal logic G (the one Solovay showed to be a sound
and complete theory for the Godel-Lob (Gödel, Löb, or Goedel, Loeb)
provability/concistency logic. G is the key for the math in the TOE
approach I am developing. The logic G is the entry for all
arithmetical “Plotinian Hypostases”.
Bruno is a prolific participant on the “everything-list” that I created years ago, but I’ve never been able to understand much of what he talked about. Now I wonder if I should have made a greater effort to learn mathematical logic. Do his writings make sense to you?
EDIT: it seems I was partly mistaken. What I could parse of Marchal’s mathy reasoning was both plausible and interesting, but parsing is quite hard work because he expresses his ideas in a very freaky manner. And there still remain many utterly unparseable philosophical bits.
Thanks for taking another look. BTW, I suggest if people change the content of their comments substantially, it’s better to make a reply to yourself, otherwise those who read LW by scanning new comments will miss the new content.
I came across this paragraph from Bruno Marchal today, which strikingly reminds me of Vinge’s “Hexapodia as the key insight”:
Bruno is a prolific participant on the “everything-list” that I created years ago, but I’ve never been able to understand much of what he talked about. Now I wonder if I should have made a greater effort to learn mathematical logic. Do his writings make sense to you?
No, they look like madness.
But logic is still worth learning.
EDIT: it seems I was partly mistaken. What I could parse of Marchal’s mathy reasoning was both plausible and interesting, but parsing is quite hard work because he expresses his ideas in a very freaky manner. And there still remain many utterly unparseable philosophical bits.
Thanks for taking another look. BTW, I suggest if people change the content of their comments substantially, it’s better to make a reply to yourself, otherwise those who read LW by scanning new comments will miss the new content.