Re: Infinitesimals

2019-11-11 Thread Lawrence Crowell
ll >> wrote: >> >> We can think of infinitesimals as a manifestation of Gödel's theorem with >> Peano number theory. There is nothing odd that is going to happen with this >> number theory, but no matter how much we count we never reach "infinity." >>

Re: Infinitesimals

2019-11-11 Thread Philip Thrift
On Monday, November 11, 2019 at 3:28:05 AM UTC-6, Bruno Marchal wrote: > > > > Personally, despite I am logician, I don’t really believe in non standard > analysis. I find the Cauchy sequences more useful, and directly > understandable (the “new” infinitesimal requires an appendix in either >

Re: Infinitesimals

2019-11-11 Thread Bruno Marchal
> On 10 Nov 2019, at 20:09, Lawrence Crowell > wrote: > > On Sunday, November 10, 2019 at 6:17:10 AM UTC-6, Bruno Marchal wrote: > >> On 9 Nov 2019, at 02:22, Lawrence Crowell > > wrote: >> >> We can think of infinitesimals as a manifestation of Gödel

Re: Infinitesimals

2019-11-10 Thread Philip Thrift
On Sunday, November 10, 2019 at 1:09:41 PM UTC-6, Lawrence Crowell wrote: > > On Sunday, November 10, 2019 at 6:17:10 AM UTC-6, Bruno Marchal wrote: >> >> >> On 9 Nov 2019, at 02:22, Lawrence Crowell >> wrote: >> >> We can think of infinitesimals

Re: Infinitesimals

2019-11-10 Thread Lawrence Crowell
On Sunday, November 10, 2019 at 6:17:10 AM UTC-6, Bruno Marchal wrote: > > > On 9 Nov 2019, at 02:22, Lawrence Crowell > wrote: > > We can think of infinitesimals as a manifestation of Gödel's theorem with > Peano number theory. There is nothing odd that is going to

Re: Infinitesimals

2019-11-10 Thread Bruno Marchal
> On 9 Nov 2019, at 02:22, Lawrence Crowell > wrote: > > We can think of infinitesimals as a manifestation of Gödel's theorem with > Peano number theory. There is nothing odd that is going to happen with this > number theory, but no matter how much we count we nev

Re: Infinitesimals

2019-11-08 Thread Lawrence Crowell
We can think of infinitesimals as a manifestation of Gödel's theorem with Peano number theory. There is nothing odd that is going to happen with this number theory, but no matter how much we count we never reach "infinity." We have then an issue of ω-consistency, and to comple

Infinitesimals

2019-11-03 Thread Philip Thrift
*Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond* https://arxiv.org/abs/1205.0174 *Infinitesimals, Imaginaries, Ideals, and Fictions* https://arxiv.org/abs/1304.2137 *Leibniz vs Ishiguro: Closing a quarter-ce