On Sat, Jun 4, 2011 at 1:51 PM, Jason Resch <[email protected]> wrote: > > > On Sat, Jun 4, 2011 at 12:06 PM, Rex Allen <[email protected]> wrote: >> >> On Sat, Jun 4, 2011 at 12:21 PM, Jason Resch <[email protected]> wrote: >> > One thing I thought of recently which is a good way of showing how >> > computation occurs due to the objective truth or falsehood of >> > mathematical >> > propositions is as follows: >> > >> > Most would agree that a statement such as "8 is composite" has an >> > eternal >> > objective truth. >> >> Assuming certain of axioms and rules of inference, sure. > > Godel showed no single axiomatic system captures all mathematical truth, any > fixed set of axioms can at best approximate mathematical truth. If > mathematical truth cannot be fully captured by a set of axioms, it must > exist outside sets of axioms altogether.
Then perhaps the correct conclusion to draw is that there is no such thing as "mathematical truth"? Perhaps there is just human belief. > The fractal is just an example of a simple formula leading to very complex > output. The same is true for the UDA: > for i = 0 to inf: > for each j in set of programs: > execute single instruction of program j > add i to set of programs > That simple formula executes all programs. Following those instructions will let someone "execute" all "programs". Or, alternatively, configuring a physical system in a way that represents those instructions will allow someone to interpret the system's subsequent states as being analogous to the "execution" of all "programs". >> Is extraordinary complexity required for the manifestation of "mind"? >> If so, why? >> > > I don't know what lower bound of information or complexity is required for > minds. Then why do you believe that information of complexity is required for minds? >> Is it that these recursive relations cause our experience, or are just >> a way of thinking about our experience? >> >> Is it: >> >> Recursive relations cause thought. >> >> OR: >> >> Recursion is just a label that we apply to some of our implicational >> beliefs. >> >> The latter seems more plausible to me. >> > > Through recursion one can implement any form of computation. But, ultimately, what is computation? > Recursion is > common and easy to show in different mathematical formulas, while showing a > Turing machine is more difficult. Many programs which can be easily defined > through recursion can also be implemented without recursion, so I was not > implying recursion is necessary for minds. Then what do you believe is necessary for minds? Rex -- 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?hl=en.
