On Mon, May 20, 2024 at 9:49 AM Rob Freeman <chaotic.langu...@gmail.com> wrote:
> Well, I don't know number theory well, but what axiomatization of > maths are you basing the predictions in your series on? > > I have a hunch the distinction I am making is similar to a distinction > about the choice of axiomatization. Which will be random. (The > randomness demonstrated by Goedel's diagonalization lemma? "True" but > not provable/predictable within the system?) > Here's how I tend to think about it: Solomonoff addressed this "random" choice of axioms by introducing a random bit string (the axioms of the theory) interpreted as an algorithm (rules of inference) which, itself, produces another bit string (theorems). However, this leaves undefined the "rules of inference" which, in my way of thinking, is like leaving undefined the choice of UTM within Algorithmic Information Theory. I've addressed this before in terms of the axioms of arithmetic by saying that the choice of UTM is no more "random" than is the choice of axioms of arithmetic which must, itself, incorporate the rules of inference else you have no theory. Marcus Hutter has addressed this "philosophical nuisance" in terms of no post hoc (after observing the dataset) choice of UTM being permitted by the principles of prediction. I've further addressed this philosophical nuisance by permitting the sophist to examine the dataset prior to "choosing the UTM", but restricted to NiNOR Complexity <https://groups.google.com/g/ait0/c/D1wd2fV6Ax4/m/fzZThQRyAAAJ> which further reduces the argument surface available to sophists. > On Mon, May 20, 2024 at 9:09 PM James Bowery <jabow...@gmail.com> wrote: > > > > > > > > On Sun, May 19, 2024 at 11:32 PM Rob Freeman <chaotic.langu...@gmail.com> > wrote: > >> > >> James, > >> > >> My working definition of "truth" is a pattern that predicts. And I'm > >> tending away from compression for that. > > > > > > 2, 4, 6, 8 > > > > does it mean > > 2n? > > > > or does it mean > > 10? > > > > > > > >> Related to your sense of "meaning" in (Algorithmic Information) > >> randomness. But perhaps not quite the same thing. > > > > > > or does it mean a probability distribution of formulae that all produce > 2, 4, 6, 8 whatever they may subsequently produce? > > > > or does it mean a probability distribution of sequences > > 10, 12? > > 10, 12, 14? > > 10, 13, 14? > > ... ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T682a307a763c1ced-M1ce471d20cc6a3bfdec9f397 Delivery options: https://agi.topicbox.com/groups/agi/subscription
