Everett Piper

[Everett Piper @devilsstaircase]

@DrYohanJohn There is a research program in the foundations of math which goes by the name "Reverse Mathematics". Many of the main results in this area establish that major theorems are in fact *equivalent* to certain axiom systems. Does this mitigate or complicate concerns about "observers?"

[Everett Piper @devilsstaircase]

@FennerTanswell Very much appreciated.

[Everett Piper @devilsstaircase]

@JDHamkins Is A contained in B? Does B need to be well-founded?

[Everett Piper @devilsstaircase]

@JDHamkins What's the intuition that covering *every* element in the larger structure B with the image of *some* elementary embedding from the smaller structure will give consistency strength? It seems closer to a compactness idea than an elementary embedding idea. I'm curious now, Sir.

[Everett Piper @devilsstaircase]

@JDHamkins How high are we talking? Rank-into-rank?

[Everett Piper @devilsstaircase]

@bertil_hatt @kareem_carr @PutOption This is interesting. Thank you.

[Everett Piper @devilsstaircase]

@kareem_carr Would you mind articulating a little more context for me? Is the above image offensive or censored in some way?

[Everett Piper @devilsstaircase]

@bertil_hatt @kareem_carr @PutOption Genuinely curious as to these limits. How do these programs recognize and enforce forbidden content? I agree these are issues but maybe I'm too naive to fully comprehend what you're stating. Photocopiers and word processors have, in some sense, already been capable of enforcment?

[Everett Piper @devilsstaircase]

@JDHamkins Also, I guess I'm rusty on this...but when creating a random predicate A on M by flipping a fair coin, do we consider this process as being carried out within M, or externally by us? Apologies in advance if this question is silly.

[Everett Piper @devilsstaircase]

@JDHamkins Let M be a countable non-standard model and random predicate A be given. By "standard cut" do you mean a predicate P(x,A) such that x is a (standard) natural number iff M|=P(x,A)?

[Everett Piper @devilsstaircase]

@DrYohanJohn These papers by Henning Voss get my spidey sense tingling. Perhaps they offer some insight to the "delay" aspect of this backwards-in-time. Thoughts, Yohan? https://t.co/4FXHj6DOMr
https://t.co/gljZOADRZS

[Everett Piper @devilsstaircase]

@DrYohanJohn Yohan, is this merely interesting to note, or do you view at as evidence in favor of adopting a dynamical systems perspective in neuroscience? Much appreciation for the NeuroLogos channel, btw. Very informative and insightful.

[Everett Piper @devilsstaircase]

@kareem_carr Appreciate the thread. My take, upon learning of Tai's Method, was that academics are far too isolated within their fields. I saw it as calling for cross-disciplinary integration, so as to minimize reinventing the wheel in every field. But I appreciate your more humanizing take.

[Everett Piper @devilsstaircase]

@ineshipolito @Macquarie_Uni Congratulations! I'm lucky to have encountered your work in the recent months. Kudos to you.

[Everett Piper @devilsstaircase]

@iapct Much appreciation to the man and his work. A sincere thank you for the volumes, I will cherish them.

[Everett Piper @devilsstaircase]

@KamerynJW Hmmm...interesting. Will have to ponder on this.

[Everett Piper @devilsstaircase]

@KamerynJW Are you tacitly assuming T is consistent? Or are you asking about well-known/researched mathematical theories T and S? It seems like letting T=PA+~"0=0" will get us anything we want, including Con(S). You have, however, been educating me on constructivism and LEM recently so....

[Everett Piper @devilsstaircase]

@DangDonovan @angryfermion Interesting little thread. I have some sympathies with your view, though I am hesitant. Are you saying that causal relationships are fundamental? Anyhoo, following now. Cheers!

[Everett Piper @devilsstaircase]

@LMichelleJ87 @teachforever54 Hmm. Never considered this before. Can you elaborate?

[Everett Piper @devilsstaircase]

@KamerynJW Good stuff. Also good stuff: Raffaella Cutolo's PhD Thesis "Berkeley Cardinals and the Search for V"