Bruno Marchal wrote: > Le 22-août-06, à 08:36, Tom Caylor a écrit : > > > I believe that we are finite, but as I said in the "computationalsim > > and supervenience" thread, it doesn't seem that this is a strong enough > > statement to be useful in a TOE. It seems that you cannot have YD > > without CT, but if true I would leave Bruno to explain exactly why. > > > > I am not sure I have said that YD needs CT. CT is needed to use the > informal "digital" instead of the "turing", "java" "python" seemingly > restriction. > For someone not believing in CT, "digital" could have a wider meaning > than "turing emulable". > Now CT needs AR. CT is equivalent with the statement that all universal > digital machine can emulate each other.
i.e "If a Universal Digital macine exists, it can emulate another one". No ontological commitment there. > To make this precise (or just > to define universal machine/number) you need to believe in numbers. To make something precise you need a precise *definition*. For a formalist, there is nothing to numbers except definitions (axoms, etc),. The numbers themselves do not have to exist. So there is still no necessary ontological commitment in CT. > (But just in the usual sense of any number theorist). Which will depend on whether the individual number theorist is a Platonist, Formalist, or whatever. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list -~----------~----~----~----~------~----~------~--~---
