Dear Jason,
On Mon, Jan 20, 2014 at 8:58 AM, Jason Resch <jasonre...@gmail.com> wrote: > > > On Jan 19, 2014, at 11:51 PM, meekerdb <meeke...@verizon.net> wrote: > > On 1/19/2014 3:41 PM, Jason Resch wrote: > > > On Jan 19, 2014, at 3:31 PM, meekerdb < <meeke...@verizon.net> > meeke...@verizon.net> wrote: > > On 1/19/2014 9:45 AM, Bruno Marchal wrote: > > But why should that imply **existence**. > > > It does not. Unless we believe in the axioms, which is the case for > elementary arithmetic. > > > But what does "believe in the axioms" mean. Do we really believe we can > **always** add one more? I find it doubtful. It's just a good model for > most countable things. So I can believe the axioms imply the theorems and > that "17 is prime" is a theorem, but I don't think that commits me to any > existence in the normal sense of "THAT exists". > > > Axioms are a human invention which only approach the truth that was > already there. Our picking some axioms to believe in changes nothing. > > > You seem not to appreciate that this dissipates the one essential > advantage of mathematical monism: we understand mathematics (because, I > say, we invent it). > > > I would say we understand some things about sine mathematical objects > because we can simulate them in our mind (or on computers) and learn their > properties. > > For example, the general shape of the Mandelbrot set. > Great point! We could say that the entire Mandelbrot set "exists" but access to knowledge of some particular structure in it requires that we run the equations on a physical machine. The same thing can be said for any scape <http://en.wikipedia.org/wiki/Diaspora_(novel)> we wish to explore. We must perform work to acquire knowledge. Knowledge does not come for free. > > But if it's a mere human invention trying to model the Platonic ding and > sich then PA may not be the real arithmetic. > > > It certainly isn't, as it leaves inaccessible an infinite number of true > statements. However, when it can prove something, like that a certain > Turing machine halts at a certain step, we find it is in agreement with > other axiomatic systems and reality. > It is the access that matters most for us. > > And there will have to be some magic math stuff that makes the real > arithmetic really real. > > > I thought we were talking about truth not reality, though perhaps the two > are related. The Sanskrit word for truth also means that which exists. > > So what makes 2+2=4 true? I don't know, I suppose you might say "magic". > Hear Hear! > > Jason > > > > > Brent > > -- > 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> > http://groups.google.com/group/everything-list. > For more options, visit <https://groups.google.com/groups/opt_out> > https://groups.google.com/groups/opt_out. > > -- > You received this message because you are subscribed to a topic in the > Google Groups "Everything List" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/everything-list/TBc_y2MZV5c/unsubscribe. > To unsubscribe from this group and all its topics, 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. > -- Kindest Regards, Stephen Paul King Senior Researcher Mobile: (864) 567-3099 stephe...@provensecure.com http://www.provensecure.us/ “This message (including any attachments) is intended only for the use of the individual or entity to which it is addressed, and may contain information that is non-public, proprietary, privileged, confidential and exempt from disclosure under applicable law or may be constituted as attorney work product. If you are not the intended recipient, you are hereby notified that any use, dissemination, distribution, or copying of this communication is strictly prohibited. If you have received this message in error, notify sender immediately and delete this message immediately.” -- 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.
