TonesInDeepFreeze

It is a fascinating subject. I wish I were up to speed to absorb and appreciate that paper.

We'll go with our continuing lead story: That's yet more dishonest obfuscation by you. For about the 1000th time: Inconsistency is having both a state...

I'm not tabling it for anything. It is flat out incorrect that The S-B tree is clear enough by the ostensive definition we have of it. (Eventually tho...

The mathematical axioms prove the existence of the S-B tree. The mathematical axioms also prove the existence of a complete ordered field with the car...

There are two separate matters: (1) The definitions of the operations. For addition, this is of the form: x=y = z <-> P where P is a formula in which ...

Keeping track of where the discussion stands: I wrote: That still stands, notwithstanding your reply (which ends with a lie).

Exactly. Meanwhile, with the other common definitions, we do define addition and multiplication of real numbers and that is not blocked by the fact th...

The crux of this is that there uncountably many reals but only denumerably many names. But it's difficult to reply point by point to your post, becaus...

Right. I was distracted by the dashed lines in the Wikipedia illustration. I recognize now that they're just for place keeping. For example, the squar...

I can only take your word for it that you've satisfactorily worked out that arithmetic. Don't forget that you have to manage not just finite sequences...

Of course, I agree that the computation is not the same as the result. / Also, back to an earlier juncture, it is decidedly not the case that I want t...

Thank you for that. Different authors of textbooks in mathematical logic define these terms somewhat differently. I go with Enderton, and this is for ...

Of course. Right there, you're committing the error of not distinguishing the name from the object. The expressions are not the number. '4' is not 4 a...

You are talking about two different subjects together: Mathematics and mathematical logic and, as I take your word for it, information theory. I have ...

I'll look at that link. / I know what 'instantiate' means. I just don't know what you mean by "the abstraction". Which abstraction? And I don't know w...

Still interested. I know what 'formalism' is in the philosophy of mathematics. But I don't know of formalism claiming "and entity is what it does".

I'm still interested. If you are earnest about communicating, then the least you could do is provide a resource for the definitions of your terminolog...

But P vs NP does make sense, so from your conditional we would have to infer that 4 is not identical with 2+2. (By the way, I have no idea why you thi...

You said the contrary at the outset and some time afterwards also. I don't know what you mean by "the instantiation of the abstraction". In any case, ...

Let's flag this right away: Here is what I posted: YOU said that most mathematicians don't "particularly care that much about the philosophy of mathem...

As I wrote, we don't ordinarily work with languages with uncountably many symbols. It's not even clear what "use" would mean with a language of uncoun...

An equation is a formula. An equation is a formula of the form: T = S where 'T' and 'S' are terms. You don't know what you're talking about. In ordina...

I know about intuitionism, platonism and formalism. Meanwhile, you need to learn the most basic mathematics rather than throwing around a bunch of ter...

They don't need to care about the philosophy of mathematics to know that 2+2 is 4. No, you are confusing what I said and meant with something you want...

Here's what you need to provide for your SB proposal: rigorous definition of 'is an SB_real' (then let SB_R = {x | x is an SB_real}) (and you'll have ...

That's a strawman. He didn't say that all discourse has to be at the level of a mathematics journal.

I'm not talking about defining a particular real number. I'm talking about defining the PROPERTY 'is a real number'. Such a definition is of the form:...

I'm still interested. Where can I read a "formalist interpretation" that "an entity is what it does".

Choo choo! All aboard the crazy train! That's pure extemporization. In ordinary mathematics, '=' is taken to have a fixed semantics such that: 4 = 2+2...

Sorry, but that's an invitation to a crazy train.

equivalence classes of Cauchy sequences of rationals. Yes. or Dedekind cuts. Yes. or decimal representations. (Actually, I think two sequences. A fini...

What is your definition of 'completely described'? Anyway: Phi is explicitly defined: Phi = (1+sqrt(5))/2 And: If x not= y, then 2 = card({x y}) Why a...

I take it that by 'describe' you mean in the sense of 'represent' as ordinarily understand to be a denumerable decimal (or binary, whatever) expansion...

What do you think a theory is? What do you think set theory is? What do you think an inconsistent theory is? (You claim ZFC+CH+~CH is not an inconsist...

From several textbooks and articles on mathematical logic and set theory. As far as I can tell (based on the page you mentioned, and the surrounding p...

I already told you. It's a collection of models (or "worlds" informally). Are you interested in understanding anything about theories, models, set the...

Your snark is ludicrous in context. You entirely skipped my specific and exact explanation, to instead try to gain a pathetic bit of snarky upper hand...

No, he mentions that there are separate universes. That is the multiverse: The collection of separate individual universes. He doesn't combine univers...

Meanwhile, https://thephilosophyforum.com/discussion/comment/766751 stands, and now we add: * You are utterly confused on even the most basic notions ...

That's a variation of your abysmal ignorance of the basics of the subject of models of theories. (1) and (2) are a contradiction. However, there is a ...

Wow. You most clearly demonstrated your ignorance of the basics of this subject, and continue to carelessly misappropriate Hamkins. Yes, ZFC+CH+~CH is...

That is an inconsistent theory. And even then it doesn't say what you say it does. You keep skipping the point that there is no apparent way to put yo...

Yes, I deleted that post, as I realized it failed to track with what you did say.

self-deleted. not needed.

Back to the very start: It is not correct that "according to set theory, all logically possible (consistent) collections exist". I've demonstrated tha...

And that quote is not at all tantamount to saying that we take as existing all the sets that are proven to exist according to different set theories. ...

First, you falsely put words in my mouth: Contrary to your mischaracterization of my remarks, I didn't opine as to naive set theory regarding the axio...

No one could predict that by "set theory" you meant your own personal concept (a concept that is not at all what people ordinarily mean by "set theory...

Your claim was: I refuted that claim: https://thephilosophyforum.com/discussion/comment/766312 Your reply does not refute my refutation, as well as th...

The axiom of regularity precludes that there exist non-empty sets that don't have a minimal element. Most saliently, the axiom of regularity precludes...