User blog comment:Syst3ms/YAUD/@comment-30754445-20180810132619/@comment-30754445-20180811231039

@Syst3ms

"...But deliberately confusing everyone? Come on, I know you're not stupid enough to actually think that."

You're right. I've phrased that rather poorly, and I am sorry.

Of-course I didn't mean that you're aiming to confuse people, or that you had any malicious intentions

What I meant was that you're deliberately set on a course of action that will inevitably cause confusion.

More specifically:

You're deliberately using familiar notations and terminology and then insist that that we should interepert them as something else (without really explaining what - exactly - is supposed to be the difference between real ordinals and the symbols you're using).

It seems to me (please correct me if I am wrong) that you''ve chosen this way because you want to enjoy the best of both worlds: On the one hand, you want to base your definitions on Username5243's own ideas (which definitely rely on ordinals). On the other hand, you want to be free of aligning your definitions with the precise way that actual ordinals behave.

And what I'm trying to tell you is, that you can't have it both ways. You're trying to achieve two incompatible goals at once (which is why your definitions end up looking very much like an OCF, even though you are trying really hard for it to be something else).

"You can call me inexperienced, noobish, too informal, or whatever you seem to equate to 'despicable'..."

Huh?

When did I ever say (or even hint) that being inexperienced or noobish or too informal is "despicable"? You putting words in my mouth?

Now it's my turn to repeat your own words back at you: Come on, I know you're not stupid enough to actually think that.

@Emlightened

" I believe the point Ale made is that the isomorphism isn't fixed, so you can't say that there's an ordinal \(\alpha\) such that \(\psi_M(x) = \alpha\).. "

Fair point. But in a sense, this is also true for ordinary OCF's as well.

For example, in Madore's ψ, there's really no need for Ω to be equal to "the first uncountable ordinal". The symbol Ω, really, is just shorthand for "something which is big enough for the collapse to work properly". We could set Ω=ω2 or Ω=ω1ck and it won't change the end result. If I'm not mistaken, we could even set Ω=BHO for Madore's ψ and it will still work as intended.