Re: A different take on the ontological status of Math
On 15 Jan 2014, at 21:03, Chris de Morsella wrote: Stephen -- I like how he derives the natural numbers from some basic set operations on an empty set. One question though how does the empty set itself arise. Arithmetic is equivalent to finite set theory (hereditary finite set theory, HFST). Of course, like RA and PA assumes the existence of 0, and HFST has to assume the empty set. Now set theory assumes also an infinite set. While an empty set contains; it is not the same thing as nothing. It is a container; it envelopes, contains, encompasses. OK. Even if something exists that contains nothing it is itself something – a minimal something perhaps – but never the less it is not a formless nothing, but rather it is a conceptual entity that contains nothing. Not trying to be obdurate, driven by curiosity to understand. Yes. Nothing would be more like an empty model. But in first order logic, we usually suppose that the model are not empty. We suppose that we are talking on something. That is why AxP(x) - ExP(x) is a predicate tautology. Nothing type of theories have to define things which presuppose some non trivial axioms. Usually it leans, like in comp, non physical things. But you need still a Turing complete theory, to have computer, for example. Bruno Cheers, Chris From: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com ] On Behalf Of Stephen Paul King Sent: Saturday, January 11, 2014 6:48 AM To: everything-list@googlegroups.com Subject: A different take on the ontological status of Math Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
RE: A different take on the ontological status of Math
Stephen -- I like how he derives the natural numbers from some basic set operations on an empty set. One question though how does the empty set itself arise. While an empty set contains; it is not the same thing as nothing. It is a container; it envelopes, contains, encompasses. Even if something exists that contains nothing it is itself something - a minimal something perhaps - but never the less it is not a formless nothing, but rather it is a conceptual entity that contains nothing. Not trying to be obdurate, driven by curiosity to understand. Cheers, Chris From: everything-list@googlegroups.com [mailto:everything-list@googlegroups.com] On Behalf Of Stephen Paul King Sent: Saturday, January 11, 2014 6:48 AM To: everything-list@googlegroups.com Subject: A different take on the ontological status of Math Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: A different take on the ontological status of Math
On 11 Jan 2014, at 16:06, Platonist Guitar Cowboy wrote: On Sat, Jan 11, 2014 at 3:47 PM, Stephen Paul King stephe...@provensecure.com wrote: Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ Last I understood, you advocate some kind of process, here becoming interpretation. I don't see how that fits with some set theoretical foundation. Could you elaborate? I don't think sets are necessary for some comp foundation and arithmetic suffices already in throwing us down a rabbit hole. PGC Yeah, I just commented there. It is nice, but not quite original. Also, the idea to extract all sets from the empty set, is just like providing the common axiomatic of sets with the reflexion and comprehension axioms, but all axiomatics of sets subsumes all sets. Then if Stephen allows to found becoming on math, like me and Kauffman, then he accepts the idea that the illusion of change can be explained by a static block reality, which, as you point out, contradicts what he just said. On the contrary Kauffman is going, like Tegmark, nearer and nearer to the comp theory. Bruno -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: A different take on the ontological status of Math
On Sun, Jan 12, 2014 at 4:43 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 11 Jan 2014, at 16:06, Platonist Guitar Cowboy wrote: On Sat, Jan 11, 2014 at 3:47 PM, Stephen Paul King stephe...@provensecure.com wrote: Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ Last I understood, you advocate some kind of process, here becoming interpretation. I don't see how that fits with some set theoretical foundation. Could you elaborate? I don't think sets are necessary for some comp foundation and arithmetic suffices already in throwing us down a rabbit hole. PGC Yeah, I just commented there. It is nice, but not quite original. Also, the idea to extract all sets from the empty set, is just like providing the common axiomatic of sets with the reflexion and comprehension axioms, but all axiomatics of sets subsumes all sets. Then if Stephen allows to found becoming on math, like me and Kauffman, then he accepts the idea that the illusion of change can be explained by a static block reality, which, as you point out, contradicts what he just said. On the contrary Kauffman is going, like Tegmark, nearer and nearer to the comp theory. I found Kauffman's development quite interesting. In particular getting the expression RR=~RR for an imaginary universe and presumably GG=GG for a real universe. But quantum mechanics demands a complex universe. It must be a simple step to go from separate real and imaginary universes to a complex universe. Should I be amused that Kauffman did not take that step? I conjectured about doing that in my Metaverse String Cosmology paper. It would be nice to but some math around it with a suitable reference. Richard Bruno -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
A different take on the ontological status of Math
Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: A different take on the ontological status of Math
On Sat, Jan 11, 2014 at 3:47 PM, Stephen Paul King stephe...@provensecure.com wrote: Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ Last I understood, you advocate some kind of process, here becoming interpretation. I don't see how that fits with some set theoretical foundation. Could you elaborate? I don't think sets are necessary for some comp foundation and arithmetic suffices already in throwing us down a rabbit hole. PGC -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: A different take on the ontological status of Math
By the way 2014/1/11, Platonist Guitar Cowboy multiplecit...@gmail.com: On Sat, Jan 11, 2014 at 3:47 PM, Stephen Paul King stephe...@provensecure.com wrote: Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ Last I understood, you advocate some kind of process, here becoming interpretation. I don't see how that fits with some set theoretical foundation. Could you elaborate? I don't think sets are necessary for some comp foundation and arithmetic suffices already in throwing us down a rabbit hole. PGC -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- Alberto. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: A different take on the ontological status of Math
The mathematical entity GG wraps right around itself. Just so does our language and apparent existence wrap around itself and give us the possibility that we are ‘nothing more’ than our own description of our own description, a kind of illusion that generates its own illusion. Lovely! The sort of beauty we can only hope underlies the sometimes all too apparent ugliness of reality. On 12 January 2014 03:47, Stephen Paul King stephe...@provensecure.comwrote: Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
Re: A different take on the ontological status of Math
Note however that Kauffman does not go into axioms involved for set theory, whichever version he is referencing I can't make out, and steps to the side of that. The article would loose a bit of its metaphorical slickness if he had, I'd guess... PGC On Sat, Jan 11, 2014 at 10:45 PM, LizR lizj...@gmail.com wrote: The mathematical entity GG wraps right around itself. Just so does our language and apparent existence wrap around itself and give us the possibility that we are ‘nothing more’ than our own description of our own description, a kind of illusion that generates its own illusion. Lovely! The sort of beauty we can only hope underlies the sometimes all too apparent ugliness of reality. On 12 January 2014 03:47, Stephen Paul King stephe...@provensecure.comwrote: Dear Friends, I highly recommend Louis H. Kauffman's new blog. His latest post speaks to the Becoming interpretation of mathematics that I advocate: http://kauffman2013.wordpress.com/2014/01/11/is-mathematics-real/ -- Kindest Regards, Stephen Paul King -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out. -- You received this message because you are subscribed to the Google Groups Everything List group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
