Thanks, Brian, that was beautiful. (especially that little 2-liner: * Therefore, perhaps proof of truth is an unattainable goal in math. Perhaps proof of truth is an unattainable goal anywhere.*
...considering an infinite complexity - Nature (mostly still unknown to us) with ingredients unrestricted as pros and cons...) JM On Mon, Jun 15, 2015 at 11:15 AM, Brian Tenneson <[email protected]> wrote: > I had forgotten I wrote this a while back, from my FB feed "on this day." > Seems relevant. > > Can truth ever be proven? Here's something I wrote in a discussion I'm > having. > > Structure does not cause something to be non-fictional, nor does lack of > structure cause something to be fictional. A theorem in one formal system > might be false in another, a lot like how different video games have > different rules. Even if you "prove" something about all formal systems, > that "proof" has been carried out in a larger formal system; so there is an > inherent circularity, or more accurately, an inherent interdependency. It's > like being in a video game trying to prove that something is true of all > video games but that meta-game proof is being conducted in one of the video > games the proof is about. Thus, the concept of proof needs to be anchored > to something true but by this rationale, proof is merely anchored to itself. > > Therefore, perhaps proof of truth is an unattainable goal in math. Perhaps > proof of truth is an unattainable goal anywhere. > > If I were to say that both confirming and denying the statement "there is > no such thing as truth" implies that there is truth, I am still formulating > that theorem "there is truth" within yet another formal system which, on > the surface of things, gets us nowhere. It is like inventing a two-player > game with, from an outside point of view, a bizarre set of rules, and > claiming that checkmating someone in that game amounts to producing not > just truth but proof of truth. The people outside our fishbowl looking in > on us must be very amused, just as are the people outside their fishbowl > looking in on them. > > Formal systems show us that our usual formal systems (the ones we use to > communicate, inform, and persuade in English for instance) have the same > relationship to truth that Earth does to the center of the universe. No > formal system is provably true and correct, though there are formal systems > that might conform to what we perceive. Formal systems can only be proved > relatively true compared to other formal systems. > > At least until that anchor is found. > > That reduces math to a grand symphony. Grand symphonies aren't inherently > true or false and there is no hope in my mind of proving the grand symphony > that is math to be true. Another way to look at is is a grand poem that > makes up its own rules and even explicitly acknowledges that fact. > > The question of whether concepts referenced by the poem actually exist is > to open the door to many formal systems we might walk into in order to > answer the question. Moreover, it will be true in some but not others that > that concept exists. A really broad interpretation of existence would be > that something exists if it is referenced by a grammatically-correct > statement made in at least one formal system. > > -- > 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/d/optout. > -- 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/d/optout.
