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.
