Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 11 Jun 2018, at 18:08, John Clark wrote: > > On Mon, Jun 11, 2018 at 5:16 AM, Bruno Marchal > wrote: > > ​> ​why in the world did you say " With mechanism, obviously a soul, or a > first person experience can be duplicated from a third person pov. But not > fro

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, Jun 11, 2018 at 5:16 AM, Bruno Marchal wrote: ​> ​ >> why in the world did you say " With mechanism, obviously a soul, or a >> first person experience can be duplicated from a third person pov. But not >> from a first person pov”? > > > ​> *​* > *I think this has ben explained many times,

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 11 Jun 2018, at 03:56, John Clark wrote: > > On Sun, Jun 10, 2018 at 6:49 AM, Bruno Marchal > wrote: > > ​>>​that is one (of many) problems with your “proof”. You start off by > assuming a physical mechanism can duplicate everything > > ​>​False. I start from

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 11 Jun 2018, at 01:44, Russell Standish wrote: > > On Sun, Jun 10, 2018 at 12:49:17PM +0200, Bruno Marchal wrote: >> >>> On 8 Jun 2018, at 16:26, John Clark wrote: >>> >> >>> and didn't even know where the sun went at night. You've recommended many >>> many books on this list but only

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sun, Jun 10, 2018 at 6:49 AM, Bruno Marchal wrote: ​>>​that is one (of many) problems with your “proof”. You start off by >> assuming a physical mechanism can duplicate everything > > *​>​False. I start from the assumption that I can survive from a digital > emulation of my brain at some leve

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sun, Jun 10, 2018 at 12:49:17PM +0200, Bruno Marchal wrote: > > > On 8 Jun 2018, at 16:26, John Clark wrote: > > > > > and didn't even know where the sun went at night. You've recommended many > > many books on this list but only a very small number of them were written > > by authors who

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 8 Jun 2018, at 16:26, John Clark wrote: > > On Fri, Jun 8, 2018 at 6:31 AM, Bruno Marchal > wrote: > > >> I said information was as close as you can get to the traditional > >> religious concept of the soul and still remain within the scientific > >> method. I

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Fri, Jun 8, 2018 at 6:41 AM, Bruno Marchal wrote: ​>>​ >> Today "you" means the man who is currently experiencing H, tomorrow "you" >> means the man who is currently experiencing W and remembers experiencing H >> yesterday; and tomorrow "you" also means the man who is currently >> experiencing

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Fri, Jun 8, 2018 at 6:31 AM, Bruno Marchal wrote: >> I said information was as close as you can get to the traditional > religious concept of the soul and still remain within the scientific > method. In the past I pointed out exactly what those similarities and > differences were, I will repe

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 7 Jun 2018, at 19:40, John Clark wrote: > > On Thu, Jun 7, 2018 at 10:23 AM, Bruno Marchal > wrote: > > ​> ​I know perfectly well what the personal pronoun “you” will mean, as its > meaning will not change. > > Of course it will change. Today "you" means the ma

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 7 Jun 2018, at 16:44, John Clark wrote: > > On Wed, Jun 6, 2018 at 3:15 PM, Brent Meeker > wrote: > > ​> ​I don't want to get into arguments about pronouns, > > Then you don't want to talk about Bruno's ideas because personal pronouns are > vitally important

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Thu, Jun 7, 2018 at 10:23 AM, Bruno Marchal wrote: ​> *​* > *I know perfectly well what the personal pronoun “you” will mean, as its > meaning will not change.* > Of course it will change. Today "you" means the man who is currently experiencing H, tomorrow "you" means the man who is currently

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Wed, Jun 6, 2018 at 3:15 PM, Brent Meeker wrote: > ​> ​ > I don't want to get into arguments about pronouns, Then you don't want to talk about Bruno's ideas because personal pronouns are vitally important to it, they are the rug that Bruno uses to cover the gaping holes in Bruno's logic. >

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 6 Jun 2018, at 21:15, Brent Meeker wrote: > > > > On 6/6/2018 3:04 AM, Bruno Marchal wrote: >> >> But in Helsinki, as a computationalist, you know in advance that whatever >> you will live is a definite unique experience, of W or of M. You lost >> unicity in the 3p view, indeed, but a

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 7 Jun 2018, at 00:39, John Clark wrote: > > > On Wed, Jun 6, 2018 at 6:04 AM, Bruno Marchal > wrote: > > ​>​ in Helsinki, as a computationalist, you know in advance that whatever you > will live is a definite unique experience > > ​But as a ​computationalist​

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

Just wondering, John.  Did you learn capitalization at the Wharton School of Business? Brent On 6/6/2018 3:39 PM, John Clark wrote: On Wed, Jun 6, 2018 at 6:04 AM, Bruno Marchal > wrote: ​>​ /in Helsinki, as a computationalist, you know in advance that

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Wed, Jun 6, 2018 at 6:04 AM, Bruno Marchal wrote: ​>​ > *in Helsinki, as a computationalist, you know in advance that whatever > you will live is a definite unique experience* > ​But as a ​ computationalist ​ YOU don't know today what the goddamn personal pronoun "*YOU*​" will mean tomorrow

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On 6/6/2018 3:04 AM, Bruno Marchal wrote: But in Helsinki, as a computationalist, you know in advance that whatever you will live is a definite unique experience, of W or of M. You lost unicity in the 3p view, indeed, but as human survivor, you keep it, and feel to be only one of the two c

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 4 Jun 2018, at 17:04, John Clark wrote: > > On Mon, Jun 4, 2018 at 6:14 AM, Bruno Marchal > wrote: > > ​>>​There is absolutely nothing unique about that silly personal diary of > yours and there is nothing unique about your memories either because because > YO

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, Jun 4, 2018 at 6:14 AM, Bruno Marchal wrote: ​>>​ >> There is absolutely nothing unique about that silly personal diary of >> yours and there is nothing unique about your memories either because >> because YOU HAVE BEEN DUPLICATED and that is what the word "duplicated" >> means. > > > ​>

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 3 Jun 2018, at 22:36, John Clark wrote: > > On Sun, Jun 3, 2018 at 9:33 AM, Bruno Marchal > wrote: > > >> If you believe that is not possible then you must believe the most > >> important part of us is supernatural and can not be duplicated because it > >> is n

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sun, Jun 3, 2018 at 9:33 AM, Bruno Marchal wrote: > >> If you believe that is not possible then you must believe the most >> important part of us is supernatural and can not be duplicated because it >> is not amenable to the scientific method or even to logic. In other words >> you believe in

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 1 Jun 2018, at 19:52, John Clark wrote: > > On Fri, Jun 1, 2018 at 4:09 AM, Bruno Marchal > wrote: > > >>> The 1p-you is defined by the sequence of memories personally accessible​ > > >> That does not define a unique object if the world contains 1p-you > >> dup

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Fri, Jun 1, 2018 at 4:09 AM, Bruno Marchal wrote: > >>> >>> *The 1p-you is defined by the sequence of memories personally >>> accessible​* >> >> > >> That does not define a unique object if the world contains 1p-you >> duplicating machines as it does in your thought experiment , > > > >*How co

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 30 May 2018, at 21:56, John Clark wrote: > > > > On Wed, May 30, 2018 at 12:31 PM, Bruno Marchal > wrote: > > > ​> ​The 1p-you is defined by the sequence of memories personally accessible > > ​That does not define a unique object if the world contains 1p-you

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Wed, May 30, 2018 at 12:31 PM, Bruno Marchal wrote: ​> ​ > The 1p-you is defined by the sequence of memories personally accessible > ​ That does not define a unique object if the world contains 1p-you duplicating machines as it does in your thought experiment ​, therefore it is nonsensical t

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

Others, I thanks John Clark for giving me the opportunity to sum up the basics. Of course anyone can ask for a precision. I train my pedagogy. Grayson, don’t hesitate to read my sum up here: http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html Download the slides, and re

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Wed, May 30, 2018 at 5:46 AM, Bruno Marchal wrote: ​> ​ > *Just try to refute step 3 without eliminating the distinction between > first and third person view,* > Just try explaining what unique thing the personal pronoun “you” refers to in a world that contains first person view duplicating

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 29 May 2018, at 17:34, John Clark wrote: > > On Tue, May 29, 2018 at 10:48 AM, Bruno Marchal > wrote: > > ​> ​You, Sir, are definitely a troll. Your answer here is just a bunch of > begging the question, and of spreading misinformations, + blatant > inconsisten

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Tue, May 29, 2018 at 10:48 AM, Bruno Marchal wrote: ​> ​ > *You, Sir, are definitely a troll. Your answer here is just a bunch of > begging the question, and of spreading misinformations, + blatant > inconsistencies, on the very subject of computability. Whatever I would > answer would be used

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 28 May 2018, at 18:09, John Clark wrote: > > On Sun, May 27, 2018 at 6:15 AM, Bruno Marchal > wrote: > > > You ask me examples of computations? > No, I did not ask you that. I asked you for an example of a computation made > WITHOUT THE USE OF MATTER THAT OBEYS

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sun, May 27, 2018 at 6:15 AM, Bruno Marchal wrote: > *> You ask me examples of computations?* No, I did not ask you that. I asked you for an example of a computation made WITHOUT THE USE OF MATTER THAT OBEYS THE LAWS OF PHYSICS. > > *> OK, that is fair enough.Let me give you some example. In

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 26 May 2018, at 01:43, John Clark wrote: > > On Thu, May 24, 2018 at 1:18 PM, Bruno Marchal > wrote: > > > I have provided definition of computations, and explicit examples, > > I’m not interested in your definitions, examples are VASTLY more important. > Defi

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Thu, May 24, 2018 at 1:18 PM, Bruno Marchal wrote: *> I have provided definition of computations, and explicit examples,* I’m not interested in your definitions, examples are VASTLY more important. Definitions can't conjure anything into existence except for more definitions. Definitions o

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 24 May 2018, at 01:05, John Clark wrote: > > On Wed, May 23, 2018 at 8:59 AM, Bruno Marchal > wrote: > > > You were changing the mathematical definition of computations given > > independently by Church, Post, Turing, Markov >> ​>​I don't know what definition

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 23 May 2018, at 16:31, Lawrence Crowell > wrote: > > On Monday, May 21, 2018 at 7:42:50 PM UTC-5, spudb...@aol.com wrote: > The answer is right in front of us. Quantum collapse indicates that a photon > must pass through a slit, and become either a wave or a particle. But the > answer g

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Wed, May 23, 2018 at 8:59 AM, Bruno Marchal wrote: *> You were changing the mathematical definition of computations given >>> independently by Church, Post, Turing, Markov * >> >> ​>​ >> I don't know what definition you're referring to > > ​> ​ > *See any (serious) textbook in logic.* > ​In

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Monday, May 21, 2018 at 7:42:50 PM UTC-5, spudb...@aol.com wrote: > > The answer is right in front of us. Quantum collapse indicates that a > photon must pass through a slit, and become either a wave or a particle. > But the answer gets more complex, with Wigner's 4 body solution, with the >

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 22 May 2018, at 01:37, John Clark wrote: > > On Mon, May 21, 2018 at 7:33 AM, Bruno Marchal > wrote: > > > You were changing the mathematical definition of computations given > > independently by Church, Post, Turing, Markov , > > I don't know what definition

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

d Bob. -Original Message- From: John Clark To: everything-list Sent: Mon, May 21, 2018 7:37 pm Subject: Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ? On Mon, May 21, 2018 at 7:33 AM, Bruno Marchal wrote: > You were changing the math

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, May 21, 2018 at 7:33 AM, Bruno Marchal wrote: *> You were changing the mathematical definition of computations given > independently by Church, Post, Turing, Markov ,* I don't know what definition you're referring to but if it doesn't have something about actually obtaining an answer

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 18 May 2018, at 21:02, John Clark wrote: > > On Fri, May 18, 2018 at 7:36 AM, Bruno Marchal > wrote: > > ​>​ a Turing Machine knows nothing excepts what state it should go into, if > it should write a 1 or a 0, and if it should move left or right or halt. > Th

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Fri, May 18, 2018 at 7:36 AM, Bruno Marchal wrote: > ​>​ >> a Turing Machine knows nothing excepts what state it should go into, if >> it should write a 1 or a 0, and if it should move left or right or halt. >> That's it. And yet it can calculate anything that can be calculated >> provided t

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 18 May 2018, at 01:37, John Clark wrote: > > On Wed, May 16, 2018 at 6:29 AM, Bruno Marchal > wrote: > > ​​>> ​A Turing Machine knows no theories > > ​> ​I have no clues why you say so. > > I say so because a Turing Machine knows nothing excepts what state it

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Wed, May 16, 2018 at 6:29 AM, Bruno Marchal wrote: ​ >> ​>> ​ >> A Turing Machine knows no theories > > > ​> ​ > I have no clues why you say so. > I say so because a Turing Machine knows nothing excepts what state it should go into, if it should write a 1 or a 0, and if it should move left or

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 13 May 2018, at 21:53, John Clark wrote: > > > > On Sat, May 12, 2018 at 4:21 AM, Bruno Marchal > wrote: > > > ​> ​I use computer for “universal Turing machine”. That notion assumes (and > is Turing-equivalent with (very) elementary arithmetic). > > ​A Turin

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, May 14, 2018 at 8:38 PM, smitra wrote: ​> ​ > But then, without a solid mathematical model that describes experimental > outcomes, how can one draw any nontrivial conclusions from experiments at > all? > ​ > By observation. We may be very surprised that the cannonball swerved to the left

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On 15-05-2018 02:06, John Clark wrote: On Mon, May 14, 2018 at 7:01 PM, Russell Standish wrote: ​> ​How do you establish that the proof has no error? Why are we supposing that the ZFC axiom correctly describes the mathematical system? How do you establish that the computers haven't made an err

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, May 14, 2018 at 7:01 PM, Russell Standish wrote: > > * ​> ​How do you establish that the proof has no error? Why are we > supposing that the ZFC axiom correctly describes the mathematical system? > How do you establish that the computers haven't made an error?* It seems to me you're tr

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, May 14, 2018 at 11:41:34AM -0400, John Clark wrote: > On Sun, May 13, 2018 at 9:06 PM, Russell Standish > wrote: > > > > > you already said, quite wisely, that if you had correctly used the ZFC > >> > axioms to produce a proof the Goldbach Conjecture was true but then a > >> > computer fo

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sun, May 13, 2018 at 9:06 PM, Russell Standish wrote: > > you already said, quite wisely, that if you had correctly used the ZFC >> > axioms to produce a proof the Goldbach Conjecture was true but then a >> > computer found a number that violated Goldbach you would place the >> blame on >> > t

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sun, May 13, 2018 at 03:53:43PM -0400, John Clark wrote: > > And you already said, quite wisely, that if you had correctly used the ZFC > axioms to produce a proof the Goldbach Conjecture was true but then a > computer found a number that violated Goldbach you would place the blame on > the ZFC

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sat, May 12, 2018 at 4:21 AM, Bruno Marchal wrote: ​> ​ > I use computer for “universal Turing machine”. That notion assumes (and is > Turing-equivalent with (very) elementary arithmetic). > ​ A Turing Machine knows no theories and it operates under the laws of physics not because it assume

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 11 May 2018, at 23:32, John Clark wrote: > > On Fri, May 11, 2018 at 12:18 PM, Bruno Marchal > wrote: > > ​> ​If you started with the basic axioms of number theory and proved the > Goldbach Conjecture is true, and you were convinced you had not made an error >

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Fri, May 11, 2018 at 12:18 PM, Bruno Marchal wrote: ​> ​ >> If you started with the basic axioms of number theory and proved the >> Goldbach Conjecture is true, and you were convinced you had not made an >> error in the proof, and then the next day a computer found a huge even >> number that w

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 10 May 2018, at 19:11, John Clark wrote: > > On Thu, May 10, 2018 at 10:36 AM, Bruno Marchal > wrote: > > ​>> ​if you can not then the word "model" has no meaning. Unlike the > Continuum Hypothesis the Goldbach Conjecture is subject to the potential of > expe

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Thu, May 10, 2018 at 10:36 AM, Bruno Marchal wrote: > ​>> ​ >> if you can not then the word "model" has no meaning. Unlike the >> Continuum Hypothesis the Goldbach Conjecture is subject to the potential of >> experimental falsification, if logicians eventually proved that it is true, > > > *

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 8 May 2018, at 18:01, John Clark wrote: > > On Mon, May 7, 2018 at 8:12 PM, Russell Standish > wrote: > > >​>​ I think you're confused about the difference between what a model says > and what reality says. One model may say you can safely march across that >

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, May 7, 2018 at 8:12 PM, Russell Standish wrote: > > > >> ​>​ >> I think you're confused about the difference between what a model says >> and what reality says. One model may say you can safely march across that >> bridge and another model might say the bridge will collapse, but it makes

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 8 May 2018, at 02:20, Lawrence Crowell > wrote: > > On Monday, May 7, 2018 at 11:51:46 AM UTC-5, Bruno Marchal wrote: > >> On 7 May 2018, at 03:19, Brent Meeker > >> wrote: >> >> >> >> On 5/6/2018 6:40 AM, Bruno Marchal wrote: >>> On 2 May 2018, at 02:28, Lawrence Crowell >>> >

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 8 May 2018, at 01:32, John Clark wrote: > > On Mon, May 7, 2018 at 12:58 PM, Bruno Marchal > wrote: > > ​> ​in some model CH is true (Gödel) and in some model CH is false (Cohen). > > That is incorrect. Godel showed that if the CH is false it would not produce

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Monday, May 7, 2018 at 11:51:46 AM UTC-5, Bruno Marchal wrote: > > > On 7 May 2018, at 03:19, Brent Meeker > > wrote: > > > > On 5/6/2018 6:40 AM, Bruno Marchal wrote: > > > On 2 May 2018, at 02:28, Lawrence Crowell > wrote: > > On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote: >> >>

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, May 07, 2018 at 07:32:21PM -0400, John Clark wrote: > > And I think you're confused about the difference between what a model says > and what reality says. One model may say you can safely march across that > bridge and another model might say the bridge will collapse, but it makes > no di

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Mon, May 7, 2018 at 12:58 PM, Bruno Marchal wrote: > ​> ​ > in some model CH is true (Gödel) and in some model CH is false (Cohen). > That is incorrect. Godel showed that if the CH is false it would not produce any contradictions in Zermelo–Fraenkel set theory plus the Axiom Of Choice (ZFC),

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 7 May 2018, at 16:38, John Clark wrote: > > ​If the Real numbers exist then the Continuum Hypothesis is either true or it > is not. That does not follow. Cunter-exemple: Intuitionist analysis admit Real Numbers, but certainly not with the CH being true or false. You assume classical l

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 7 May 2018, at 12:52, Lawrence Crowell > wrote: > > On Sunday, May 6, 2018 at 9:16:13 PM UTC-5, Russell Standish wrote: > On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote: > > But don't you take all arithmetic theories to include the axioms that say > > every number has a suc

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 7 May 2018, at 03:19, Brent Meeker wrote: > > > > On 5/6/2018 6:40 AM, Bruno Marchal wrote: >> >>> On 2 May 2018, at 02:28, Lawrence Crowell >> > wrote: >>> >>> On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote: >>> An interesting proof by

Re: Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

​If the Real numbers exist then the Continuum Hypothesis is either true or it is not. But are the Real numbers really real? No less a mathematician than Gregory Chaitin (of Chaitin's Omega fame) is on record as saying the real numbers do not exist. If he's right and they don't exist then the Conti

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sunday, May 6, 2018 at 9:16:13 PM UTC-5, Russell Standish wrote: > > On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote: > > But don't you take all arithmetic theories to include the axioms that > say > > every number has a successor? > > Just because every number has a successor d

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Sun, May 06, 2018 at 06:19:01PM -0700, Brent Meeker wrote: > But don't you take all arithmetic theories to include the axioms that say > every number has a successor? Just because every number has a successor does not entail the existence of ω. This is otherwise known as "potential infinity" v

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On 5/6/2018 6:40 AM, Bruno Marchal wrote: On 2 May 2018, at 02:28, Lawrence Crowell > wrote: On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote: An interesting proof by Hamkins and a lot of discussion of its significance on John Baez's

Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

> On 2 May 2018, at 02:28, Lawrence Crowell > wrote: > > On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote: > An interesting proof by Hamkins and a lot of discussion of its > significance on John Baez's blog. It agrees with my intuition that the > mathematical idea of "finite" is not

Re: Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

On Tuesday, May 1, 2018 at 3:37:15 PM UTC-5, Brent wrote: > > An interesting proof by Hamkins and a lot of discussion of its > significance on John Baez's blog. It agrees with my intuition that the > mathematical idea of "finite" is not so obvious. > > Brent > > This gets into the rarefied atm

Fwd: Re: Is the Continuum Hypothesis a) really true or really false, or b) something else ?

An interesting proof by Hamkins and a lot of discussion of its significance on John Baez's blog.  It agrees with my intuition that the mathematical idea of "finite" is not so obvious. Brent Forwarded Message On Tue, May 1, 2018 at 1:13 PM, James wrote: On Tue, May 1, 2018