106 karma · joined December 5, 2024
I’m free to refuse to do business with a company for racial reasons but a company is not feee to refuse to do business with me due to my race.
EDIT: I’m pointing out one of the ways that “free association” for corporations is different than for people.
My point stands. Meta is suppressing speech while embracing it. It just happens that the suppression is welcomed by the group whose speech is being embraced.
It’s the insurer that was unreasonable in this case. No one buys into your view.
Weird that you think surgeons, anesthesiologists, hospitals, and nurses should work for free.
Should mechanics, teachers, police, firefighters work for free? Are you advocating for a communist type economic system?
I believe writing “after the riots of 2020” and framing what happened as “wokeness” qualifies as idiotic.
I made my points and haven’t responded further. I don’t believe I’ve said anything else that can be considered flamewar style commentary. I’ll keep in mind what you’ve said.
I think though that Trump truly is worse. If you made this comment in 2008 or 2012 and used Trump or McCain I’d say you are right. But what happens when a person truly is a vile disgusting human being? Then it no longer becomes the same shit. As an extreme example, Kerensky wasn’t as bad as the Bolsheviks. It wasn’t the same shit.
EDIT: Graham wrote, “Not a problem on the scale that the woke believe it to be, but a genuine one.”
He stated a limit on the level of racism. He gave a bound on it. He said it is less that what woke people think it is. CrissCross is being deliberately obtuse. This edit is for people who come across this thread. My comment pointed out that Graham didn’t justify this belief. I don’t know the level of racism and I’m not arrogant enough to try.
1. The axioms of PA_2 are recursively enumerable. 2. The full semantics of PA_2 are what cause categoricity.
It seems to me then that the crux of the matter is that the full semantics of PA_2 prevent there being an effective deductive system. I think Z_2 is constructed to get around the non effectiveness of the full semantics of PA_2 and is a weaker theory.
Anyway, thanks for the enlightenment.
...it's decidable - otherwise, it would be impossible to decide whether a proof is valid.
Isn't that the whole issue with PA_2 vs. PA? In PA_2 with "full semantics" there is no effective procedure for determining if a statement is an axiom. In my mind this is what I mean by the incompleteness results not applying to PA_2. They do apply to Z_2 since that is an effective (computable?) system.
But Z2 is usually studied with first-order semantics, and in that context it is an effective theory of arithmetic subject to the incompleteness theorems. In particular, Z2 includes every axiom of PA, and it does include the second-order induction axiom, and it is still incomplete.
Therefore, the well-known categoricity proof must not rely solely on the second-order induction axiom. It also relies on a change to an entirely different semantics, apart from the choice of axioms. It is only in the context of these special "full" semantics that PA with the second-order induction axiom becomes categorical.
https://math.stackexchange.com/questions/617124/peano-arithm...
Thanks for the knoweledge. I'm going to read up more on this stuff.
However, my understanding is that the incompleteness results apply to only recursively enumerable axiomatic systems. I can find references for this. If I take the standard model of ZFC and collect all true statements in the one model of PA_2 and make that my axiomatic system then I have an axiomatic system that is not recursively enumerable and contains PA_1. It’s not a nice set of axioms. It’s not computable. But it shows that one can have an axiomatic system that contains PA_1 for which the Incompleteness theorems don’t apply.
Andreas wrote “meaningless” not “nonsensical”. I’m not a pedant but the former term evokes in me the idea of “does not apply in this situation becausethe hypotheses of the incompleteness theorem are not satisfied”.
From a mathematical logic book is the following. It’s the set up for the Incompleteness theorems.
Suppose that A is a collection of axioms in the language of number theory such that A is consistent and is simple enough so that we can decide whether or not a given formula is an element of A.
PA_2 is not such a system and as such the Incompleteness Theorems don’t apply. Maybe we are talking past each other. You know more than me.