On 1/20/2014 5:00 PM, LizR wrote:
On 21 January 2014 06:42, meekerdb <[email protected] <mailto:[email protected]>> wrote:On 1/20/2014 1:11 AM, LizR wrote:On 20 January 2014 18:51, meekerdb <[email protected] <mailto:[email protected]>> wrote: You seem not to appreciate that this dissipates the one essential advantage ofmathematical monism: we understand mathematics (because, I say, we invent it). But if it's a mere human invention trying to model the Platonic ding and sich then PA may not be the real arithmetic. And there will have to be some magicmath stuff that makes the real arithmetic really real. Surely the real test is whether it works better than any other theory. (The phrase "unreasonable effectiveness" appears to indicate that it does.)Would it work any less well if there were a biggest number?I don't know. I would imagine so, because that would be a theory with an ad hoc extra clause with no obvious justification, so every calculation would have to carry extra baggage around. If I raise a number to the power of 100, say, I have to check first that the result isn't going to exceed the biggest number, and take appropriate action - whatever that is - if it will... what would be the point of that?
Just make it an axiom that the biggest number is bigger than any number you calculate. In other words just prohibit using those "..." and "so forth" in your theorems.
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 [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
