Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 5:59 PM Jason Resch wrote: > On Mon, Dec 17, 2018 at 12:03 AM Bruce Kellett > wrote: > >> On Mon, Dec 17, 2018 at 4:30 PM Jason Resch wrote: >> >>> On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett >>> wrote: >>> On Mon, Dec 17, 2018 at 1:50 PM Jason Resch

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 12:05 AM Brent Meeker wrote: > > > On 12/16/2018 9:36 PM, Jason Resch wrote: > > > > On Sun, Dec 16, 2018 at 10:22 PM Brent Meeker > wrote: > >> >> >> On 12/16/2018 4:39 PM, Jason Resch wrote: >> >> >> >> On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker >> wrote: >> >>> >>>

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 12:03 AM Bruce Kellett wrote: > On Mon, Dec 17, 2018 at 4:30 PM Jason Resch wrote: > >> On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett >> wrote: >> >>> On Mon, Dec 17, 2018 at 1:50 PM Jason Resch >>> wrote: >>> On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 12:00 AM Brent Meeker wrote: > > > On 12/16/2018 9:30 PM, Jason Resch wrote: > > > > On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett > wrote: > >> On Mon, Dec 17, 2018 at 1:50 PM Jason Resch wrote: >> >>> On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett >>> wrote: >>> >>>

Re: What is more primary than numbers?

On 12/16/2018 9:42 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 10:27 PM Brent Meeker > wrote: On 12/16/2018 4:43 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 6:02 PM Brent Meeker mailto:meeke...@verizon.net>> wrote: On

Re: What is more primary than numbers?

On 12/16/2018 9:36 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 10:22 PM Brent Meeker > wrote: On 12/16/2018 4:39 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker mailto:meeke...@verizon.net>> wrote: On

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 4:30 PM Jason Resch wrote: > On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett > wrote: > >> On Mon, Dec 17, 2018 at 1:50 PM Jason Resch wrote: >> >>> On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett >>> wrote: >>> >>> Are you claiming that there is an objective

Re: What is more primary than numbers?

On 12/16/2018 9:30 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett > wrote: On Mon, Dec 17, 2018 at 1:50 PM Jason Resch mailto:jasonre...@gmail.com>> wrote: On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 10:27 PM Brent Meeker wrote: > > > On 12/16/2018 4:43 PM, Jason Resch wrote: > > > > On Sun, Dec 16, 2018 at 6:02 PM Brent Meeker wrote: > >> >> >> On 12/16/2018 2:04 PM, Jason Resch wrote: >> >> >> >> On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett >> wrote: >> >>> On

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 10:22 PM Brent Meeker wrote: > > > On 12/16/2018 4:39 PM, Jason Resch wrote: > > > > On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker wrote: > >> >> >> On 12/16/2018 1:56 PM, Jason Resch wrote: >> >> >> >> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker >> wrote: >> >>> >>>

Re: What is more primary than numbers?

On Monday, December 17, 2018 at 1:21:15 AM UTC, Bruce wrote: > > On Mon, Dec 17, 2018 at 11:36 AM Jason Resch > wrote: > >> On Sun, Dec 16, 2018 at 4:14 PM Bruce Kellett > > wrote: >> >>> On Mon, Dec 17, 2018 at 9:04 AM Jason Resch >> > wrote: >>> On Sun, Dec 16, 2018 at 4:01 PM Bruce

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 9:39 PM Bruce Kellett wrote: > On Mon, Dec 17, 2018 at 1:50 PM Jason Resch wrote: > >> On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett >> wrote: >> >> >>> Are you claiming that there is an objective arithmetical realm that is >>> independent of any set of axioms? >>> >>

Re: What is more primary than numbers?

On 12/16/2018 4:43 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 6:02 PM Brent Meeker > wrote: On 12/16/2018 2:04 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett mailto:bhkellet...@gmail.com>> wrote: On Mon, Dec

Re: What is more primary than numbers?

On 12/16/2018 4:39 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker > wrote: On 12/16/2018 1:56 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker mailto:meeke...@verizon.net>> wrote: On 12/15/2018

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 1:50 PM Jason Resch wrote: > On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett > wrote: > > >> Are you claiming that there is an objective arithmetical realm that is >> independent of any set of axioms? >> > > Yes. This is partly why Gödel's result was so shocking, and so

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 7:21 PM Bruce Kellett wrote: > On Mon, Dec 17, 2018 at 11:36 AM Jason Resch wrote: > >> On Sun, Dec 16, 2018 at 4:14 PM Bruce Kellett >> wrote: >> >>> On Mon, Dec 17, 2018 at 9:04 AM Jason Resch >>> wrote: >>> On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 11:36 AM Jason Resch wrote: > On Sun, Dec 16, 2018 at 4:14 PM Bruce Kellett > wrote: > >> On Mon, Dec 17, 2018 at 9:04 AM Jason Resch wrote: >> >>> On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett >>> wrote: >>> On Mon, Dec 17, 2018 at 8:56 AM Jason Resch

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 10:01:18 PM UTC, Bruce wrote: > > On Mon, Dec 17, 2018 at 8:56 AM Jason Resch > wrote: > >> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker > > wrote: >> >>> >>> But a system that is consistent can also prove a statement that is false: >>> >>> axiom 1: Trump is a

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 6:02 PM Brent Meeker wrote: > > > On 12/16/2018 2:04 PM, Jason Resch wrote: > > > > On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett > wrote: > >> On Mon, Dec 17, 2018 at 8:56 AM Jason Resch wrote: >> >>> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker >>> wrote: >>>

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 5:53 PM Brent Meeker wrote: > > > On 12/16/2018 1:56 PM, Jason Resch wrote: > > > > On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker wrote: > >> >> >> On 12/15/2018 10:24 PM, Jason Resch wrote: >> >> >> >> On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker >> wrote: >> >>> >>>

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 4:14 PM Bruce Kellett wrote: > On Mon, Dec 17, 2018 at 9:04 AM Jason Resch wrote: > >> On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett >> wrote: >> >>> On Mon, Dec 17, 2018 at 8:56 AM Jason Resch >>> wrote: >>> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker

Re: What is more primary than numbers?

On 12/16/2018 2:04 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett > wrote: On Mon, Dec 17, 2018 at 8:56 AM Jason Resch mailto:jasonre...@gmail.com>> wrote: On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker

Re: What is more primary than numbers?

On 12/16/2018 1:56 PM, Jason Resch wrote: On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker > wrote: On 12/15/2018 10:24 PM, Jason Resch wrote: On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker mailto:meeke...@verizon.net>> wrote: On

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 10:53:18 PM UTC, agrays...@gmail.com wrote: > > > > On Sunday, December 16, 2018 at 10:01:55 PM UTC, Jason wrote: >> >> >> >> On Sun, Dec 16, 2018 at 3:39 PM wrote: >> >>> >>> >>> On Sunday, December 16, 2018 at 8:58:33 PM UTC, Jason wrote: On

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 10:01:55 PM UTC, Jason wrote: > > > > On Sun, Dec 16, 2018 at 3:39 PM > wrote: > >> >> >> On Sunday, December 16, 2018 at 8:58:33 PM UTC, Jason wrote: >>> >>> >>> >>> On Sun, Dec 16, 2018 at 2:14 PM wrote: >>> On Sunday, December 16, 2018 at

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 3:38:59 PM UTC-6, agrays...@gmail.com wrote: > > > > On Sunday, December 16, 2018 at 8:58:33 PM UTC, Jason wrote: >> >> >> >> On Sun, Dec 16, 2018 at 2:14 PM wrote: >> >>> >>> >>> On Sunday, December 16, 2018 at 2:11:06 AM UTC, Jason wrote: On

Re: What is more primary than numbers?

Keep in mind that what an "abstraction" is means different things to mathematical nominalists, constructivists, platonists. - pt On Sunday, December 16, 2018 at 3:37:44 PM UTC-6, Brent wrote: > > Numbers are an abstraction and generalization from counting. But > counting takes seeing some

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 9:04 AM Jason Resch wrote: > On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett > wrote: > >> On Mon, Dec 17, 2018 at 8:56 AM Jason Resch wrote: >> >>> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker >>> wrote: >>> But a system that is consistent can also prove a

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 4:01 PM Bruce Kellett wrote: > On Mon, Dec 17, 2018 at 8:56 AM Jason Resch wrote: > >> On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker >> wrote: >> >>> >>> But a system that is consistent can also prove a statement that is false: >>> >>> axiom 1: Trump is a genius. >>>

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 3:39 PM wrote: > > > On Sunday, December 16, 2018 at 8:58:33 PM UTC, Jason wrote: >> >> >> >> On Sun, Dec 16, 2018 at 2:14 PM wrote: >> >>> >>> >>> On Sunday, December 16, 2018 at 2:11:06 AM UTC, Jason wrote: On Sat, Dec 15, 2018 at 8:06 PM wrote:

Re: What is more primary than numbers?

On Mon, Dec 17, 2018 at 8:56 AM Jason Resch wrote: > On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker wrote: > >> >> But a system that is consistent can also prove a statement that is false: >> >> axiom 1: Trump is a genius. >> axiom 2: Trump is stable. >> >> theorem: Trump is a stable genius. >> >

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 3:28 PM Brent Meeker wrote: > > > On 12/15/2018 10:24 PM, Jason Resch wrote: > > > > On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker > wrote: > >> >> >> On 12/15/2018 6:07 PM, Jason Resch wrote: >> >> >> >> On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker >> wrote: >> >>> >>>

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 8:58:33 PM UTC, Jason wrote: > > > > On Sun, Dec 16, 2018 at 2:14 PM > wrote: > >> >> >> On Sunday, December 16, 2018 at 2:11:06 AM UTC, Jason wrote: >>> >>> >>> >>> On Sat, Dec 15, 2018 at 8:06 PM wrote: >>> On Sunday, December 16, 2018 at 1:41:08

Re: What is more primary than numbers?

Numbers are an abstraction and generalization from counting.   But counting takes seeing some things a similar enough to be counted, yet not identical.  I can count the dogs in my yard because what's a dog and what's not seems clear. But it's hard to count trees in my yard:  Is that a bush or

Re: What is more primary than numbers?

On 12/15/2018 10:24 PM, Jason Resch wrote: On Sat, Dec 15, 2018 at 11:35 PM Brent Meeker > wrote: On 12/15/2018 6:07 PM, Jason Resch wrote: On Sat, Dec 15, 2018 at 7:57 PM Brent Meeker mailto:meeke...@verizon.net>> wrote: On

Re: What is more primary than numbers?

On Sun, Dec 16, 2018 at 2:14 PM wrote: > > > On Sunday, December 16, 2018 at 2:11:06 AM UTC, Jason wrote: >> >> >> >> On Sat, Dec 15, 2018 at 8:06 PM wrote: >> >>> >>> >>> On Sunday, December 16, 2018 at 1:41:08 AM UTC, Jason wrote: On Sat, Dec 15, 2018 at 7:28 PM wrote:

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 9:29:47 AM UTC, scerir wrote: > > A *numerus* (literally: "number"*i*) was the term used for a unit of the > Roman > army .. In the Imperial Roman > army (30 BC – 284

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 2:11:06 AM UTC, Jason wrote: > > > > On Sat, Dec 15, 2018 at 8:06 PM > wrote: > >> >> >> On Sunday, December 16, 2018 at 1:41:08 AM UTC, Jason wrote: >>> >>> >>> >>> On Sat, Dec 15, 2018 at 7:28 PM wrote: >>> On Saturday, December 15, 2018 at

Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

> On 15 Dec 2018, at 00:12, Philip Thrift wrote: > > > > On Friday, December 14, 2018 at 5:00:33 PM UTC-6, Brent wrote: > > > On 12/14/2018 2:59 AM, Bruno Marchal wrote: > >> On 13 Dec 2018, at 21:24, Brent Meeker > > >> wrote: > >> > >> > >> > >> On 12/13/2018 3:25 AM, Bruno Marchal

Re: What is more primary than numbers?

On Sat, Dec 15, 2018 at 11:44 AM Jason Resch wrote: > > *Pure numbers may not correspond to point in time and space, but their > relationships do. * > Where and when did 2+2=4 happen? Does that relationship between 2 and 4 ever change? > *> Doesn't the fact that "John Clark is conscious of

Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

On Sunday, December 16, 2018 at 11:27:50 AM UTC-6, Bruno Marchal wrote: > > > > On 15 Dec 2018, at 00:00, Brent Meeker > wrote: > > > > > > > > On 12/14/2018 2:59 AM, Bruno Marchal wrote: > >>> On 13 Dec 2018, at 21:24, Brent Meeker > wrote: > >>> > >>> > >>> > >>> On 12/13/2018 3:25

Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

> On 15 Dec 2018, at 00:00, Brent Meeker wrote: > > > > On 12/14/2018 2:59 AM, Bruno Marchal wrote: >>> On 13 Dec 2018, at 21:24, Brent Meeker wrote: >>> >>> >>> >>> On 12/13/2018 3:25 AM, Bruno Marchal wrote: > But that is the same as saying proof=>truth. I don’t think so. It

Re: Towards Conscious AI Systems (a symposium at the AAAI Stanford Spring Symposium 2019)

> On 14 Dec 2018, at 12:01, Philip Thrift wrote: > > > > On Friday, December 14, 2018 at 4:49:33 AM UTC-6, Bruno Marchal wrote: > >> On 13 Dec 2018, at 21:05, Brent Meeker > >> wrote: >> >> >> >> On 12/13/2018 3:18 AM, Bruno Marchal wrote: Automating Gödel'’s Ontological Proof of

Re: What is more primary than numbers?

On Sunday, December 16, 2018, Philip Thrift wrote: > > > On Saturday, December 15, 2018 at 7:41:08 PM UTC-6, Jason wrote: >> >> >> >> On Sat, Dec 15, 2018 at 7:28 PM wrote: >> >>> >>> >>> On Saturday, December 15, 2018 at 11:04:55 PM UTC, Jason wrote: On Saturday, December

Re: Black holes and computational complexity

On Friday, December 7, 2018 at 11:45:30 AM UTC-6, Mason Green wrote: > > Leonard Susskind thinks there may be a link between the size of a black > hole’s interior (which grows with time) and its computational complexity > (which does likewise). > > At the end of the article there’s even a

Re: What is more primary than numbers?

On Sunday, December 16, 2018 at 3:29:47 AM UTC-6, scerir wrote: > > A *numerus* (literally: "number"*i*) was the term used for a unit of the > Roman > army .. In the Imperial Roman > army (30 BC –

Re: What is more primary than numbers?

A numerus (literally: "number"i) was the term used for a unit of the Roman army https://en.wikipedia.org/wiki/Roman_army .. In the Imperial Roman army https://en.wikipedia.org/wiki/Imperial_Roman_army (30 BC – 284 AD), it referred to units of barbarian https://en.wikipedia.org/wiki/Barbarian

Re: What is more primary than numbers?

On Saturday, December 15, 2018 at 7:41:08 PM UTC-6, Jason wrote: > > > > On Sat, Dec 15, 2018 at 7:28 PM > wrote: > >> >> >> On Saturday, December 15, 2018 at 11:04:55 PM UTC, Jason wrote: >>> >>> >>> >>> On Saturday, December 15, 2018, wrote: >>> On Saturday, December 15, 2018