Re: Where do numbers and geometry come from ?

2012-09-07 Thread Bruno Marchal
On 06 Sep 2012, at 16:28, Brian Tenneson wrote: All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? I would say invented, as many different notion of sets can exist. You

Re: Re: Where do numbers and geometry come from ?

2012-09-07 Thread Roger Clough
Marchal Receiver: everything-list Time: 2012-09-07, 03:21:21 Subject: Re: Where do numbers and geometry come from ? On 06 Sep 2012, at 16:28, Brian Tenneson wrote: All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind

Re: Where do numbers and geometry come from ?

2012-09-07 Thread Stephen P. King
*Subject:* Re: Where do numbers and geometry come from ? Dear Roger, 　　　 Why is it that people persist in even suggesting that numbers are created by man? Why the anthropocentric bias? Pink Ponies might have actually crated them, or Polka-dotted Unicorns! The idea is just silly

Where do numbers and geometry come from ?

2012-09-06 Thread Roger Clough
Hi Stephen P. King Yes, of course, but I wanted a more obvious, dramatic example. The philosophy of mathematics says something like the numbers belong to a static or eternal world, change itself is a property of geometry. Numbers and geometry thus belong to the platonic world, which is

Re: Where do numbers and geometry come from ?

2012-09-06 Thread Brian Tenneson
All numbers can be defined in terms of sets. The question becomes this: do sets have ontological primacy relative to mankind or are sets invented or created by mankind? On Thu, Sep 6, 2012 at 5:11 AM, Roger Clough rclo...@verizon.net wrote: Hi Stephen P. King Yes, of course, but I wanted a

Re: Where do numbers and geometry come from ?

2012-09-06 Thread Stephen P. King
On 9/6/2012 11:09 AM, Brian Tenneson wrote: Correct me if I'm wrong but my understanding is that sets and membership cannot be defined in terms of a more primary mathematical concept. Functions can be defined in terms of this primitive called sets. Numbers are sets; natural numbers are

Re: Re: Where do numbers and geometry come from ?

2012-09-06 Thread Brian Tenneson
- *From:* Brian Tenneson tenn...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes this: do sets have ontological

Re: Where do numbers and geometry come from ?

2012-09-06 Thread Stephen P. King
...@gmail.com *Receiver:* everything-list mailto:everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes this: do sets have ontological primacy relative

Re: Where do numbers and geometry come from ?

2012-09-06 Thread Brian Tenneson
. - Receiving the following content - *From:* Brian Tenneson tenn...@gmail.com *Receiver:* everything-list everything-list@googlegroups.com *Time:* 2012-09-06, 10:28:51 *Subject:* Re: Where do numbers and geometry come from ? All numbers can be defined in terms of sets.� The question becomes