Hi Brent, I don't like these types of truth predicates since they are Platonic in their assumptions, as if statements do not even involve or relate to finite entities like ourselves or, more relevant to my own work, real world computers. Consider a paper by Lou Kauffman that considers a local notion of truth values that can oscillate: http://homepages.math.uic.edu/~kauffman/TimeParadox.pdf
On Sat, Dec 21, 2013 at 5:28 PM, meekerdb <[email protected]> wrote: > On 12/21/2013 1:26 AM, Jason Resch wrote: > > If there exists a mathematical theorem that requires >> a countable infinity of integers to represent, no finite version can exist >> of it, in other words, can its proof be found? >> > > If its shortest proof is infinitely long, or if the required axioms > needed to develop a finite proof are infinite, (or instead of infinite, so > large we could not represent them in this universe), then its proof can't > be found (by us), but there is a definite answer to the question. > > > The other possibility is that there are mutually inconsistent axioms that > can be added. As I understand it, that was the point of > http://intelligence.org/wp-content/uploads/2013/03/Christiano-et-al-Naturalistic-reflection-early-draft.pdf > A truth predicate can be defined for arithmetic, but not all models or > arithmetic are the same as the standard model. > > Brent > > -- > 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/1NWmK1IeadI/unsubscribe. > To unsubscribe from this group and all its topics, 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. > -- Kindest Regards, Stephen Paul King Senior Researcher Mobile: (864) 567-3099 [email protected] 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 [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.
