Mind Blown by Godel and Now I challenge him!

My roommate in college recommended a book called "Godel, Escher, Bach: An Eternal Golden Braid" but I never read it. He was then and is now a brilliant guy with whom I have enjoyed debating many philosophical issues. I just recently started reading about Godel's Incompleteness Theorem and my mind was blown! As is my tendency, when I encounter an intellectually stimulating idea it does one of three things to me: 1) fits perfectly with my existing paradigm and thus is elegantly integrated into my belief system (which immediately makes me quite happy) 2) disproves and replaces something in my existing paradigm and thus is integrated into my belief system albeit initially uncomfortably (which eventually makes me happy) 3) challenges but doesn't disprove something in my existing paradigm and thus requires my active rumination until it is integrated or discarded (either of which leaves me a bit intellectually-emotionally conflicted for a while). Now I'm pretty savvy about math (Mensa member, Stuy grad, 750 math SAT) but currently I simply do not have the education to understand advanced math (number theory etc.). *So my mega-math-savvy friends need to help me out here, please.* Nevertheless, I am about to challenge one of the most established ideas in the Philosophy of Mathematics. (My ignorance & hubris are explained at the end of this post.) Godel claims - "There exist statements that are true but not provable". Which, intuitively to most people, sounds like bullcrap. He gives mathematical examples of logical statements that are true every time you test them but "unprovable" in that there are an infinite number of tests and thus no definitive way to "test them all" which leads to his conclusion that such a statement is "true but not provable". I argue that what is at issue is a misunderstanding of language (semantics). It seems to be a misunderstanding of the concept of "infinity". Of course infinity is infinite. Of course you can't make a closed set of rules about infinity. That would be like saying "there are a limited number of ideas to be thought of" because, of course, every idea could be integrated into a newer, bigger idea just as you can always add the number 1 to any number to make a bigger number. More to the point, Godel seems to think something "having been true every time it was tested" is exactly equal to "is and will always be true". I don't think that is universally useful and, more importantly, I draw a valuable distinction. As such, I think there should be "True1" which would be the most pure definition of truth and there should be "True2" which could have a lower burden. It's the difference between saying a "True2" statement like: this convict will kill you because "he has been proven to be a murderer before and thus will necessarily continue to kill" (which may or may not be true in the future) and saying getting guillotined will kill you because "separating your brain from your heart & lungs will prevent the oxygen from getting to your brain". Now this is not to say that a "True1" statement need be an un-disprovable tautology. If you could prove that a disembodied head could survive (q.v. the jars in "Futurama") then that would disprove the statement that "getting guillotined will kill you". I strongly believe in the concept of falsifiability being necessary in intellectual discourse. Therefore, I choose to define the most useful version of the word "true" (i.e. "True1") in this way: "that which is consistent with reality and also is provable for every case". In this way there is no such paradox nor anything counter intuitive (which I, by no means, think should be a requirement). Consequently, I would rewrite Godel's logical statements such that they communicated the difference between what I call "True2" which is "having proven to be entirely consistent with reality but with no fundamental proof for why it should always be the case" (which is like finding even nearly infinite correlations but still no causality) and the substantially higher burden of 'truth' which I call "True1" that is defined as "having proven to be entirely consistent with reality AND ALSO coherent with a fundamental proof for why it must always be consistent with reality". Ultimately this issue intertwines with some of my grander thoughts on human decision-making and intellectual progress. While I don't have the following all worked out just yet, here are some things to consider: a) Any statement can be infinitely questioned down to fundamental issues that are virtually unponderable. The fun example is the child who has a seemingly infinite series of "Why" questions. At some point the parent just has to say "Because I said so. Now eat your dinner.". Similarly, in all human interaction, there is a heuristic of "we gotta move on" otherwise you would be paralyzed at every moment, paranoid and asking whether you can trust even the most basic of elements of life. b) For any philosophy to be useful it must recognize the "we gotta move on" dynamic. However, I am not arguing that everyone needs to have the same threshold because I, of course, appreciate the benefits of specialization & division-of-labor. c) For any productive debate, the most fundamental ground rules must be enforced. Some of my favorite rules:  • Terms must be defined and consistent.  • Evidence must be given priority over theory.  • Predictions proven to be true must be give priority over retro-actively created theories of how/why things happened before.  • "Goal Posts" defining who "won" must be set early on and be immovable unless by mutual consent.  • Sophistry (e.g. Schopenhauer's 38 Ways to Win an Argument) must be discouraged and seen as a sign of weakness (because someone who knows he is right need not use such specious techniques). This all plays into my idea for www.wiki-debate.com / www.DebateSherpa.com where I plan to eventually "connect the echo-chambers". d) Humans each have their own algorithm for decision-making and these are by no means 100% universal and consistent. But I believe there is a flow-chart to be made of how people integrate new information into their belief systems. I think there is a general triage of questions with their own subroutines:    1- Is this for me? Do I recognize this as relevant to me in any way?    2- Is this urgent? ("Look out!")    3- Is this important? ("Fire!")    4- Is this interesting?    5- Is this true? (crucial sub-routine for determining this is: Authority? Track record? Bias? Impact for acceptance? Coherence with other accepted views? Future benefit?) e) This post is already too long otherwise I'd go into detail of how I generally prefer to engage & challenge ideas when I am probably, relatively speaking, too ignorant to do so rather than read in-depth research that I fear will "track" my thinking into unoriginal paths. Since I value creativity & originality so highly I often risk embarrassment with my ignorance & hubris. DAN'S GENERIC DISCLAIMER: I'm not entirely sure everything I wrote here is correct or even if everything here is original. If you find identical or even similar thoughts elsewhere please alert me to them (especially if they disprove my assertions). Thank you.

My solution to the "Incalculable Derivatives" Accounting Problem!

I just solved the "Incalculable Derivatives" Accounting Problem! When a well-known, well-respected "Whale" (Casino term for a big gambler) shows up in Vegas he often gets to gamble on credit extended by the Casino. But there is a maximum he can bet on credit before the casino will demand a wire-transfer payment. The casino decides what amount the whale is good for on-credit and beyond that it's no more Mr.Nice Guy. If only Wall Street were so wise! Here's my solution - Government/SEC should mandate that ALL future derivatives have a "maximum value". e.g. a Call Option could then be a right to buy a given security at a certain strike price (as normal) but the change would be that the right can be exercised no more than X amount "in the money" (where X is an extremely big number). So Google stock is trading at $550 a share and this extreme derivative call option (for a single share) has a strike price of $10,000 with an expiration date of 3 months from now. Because it is so "out of the money" it trades for $0.01 and some bank is selling millions of these options because it's so utterly sure Google won't rise above it. Without my idea, if Google goes to $20,000 per share just before expiration then each option that the bank sold for $0.01 it will now have to pay out at $10,000. Consequently, if the bank sold millions it would be "on the hook" for tens of billions in losses. But with my idea, X could be "ten thousand times the original price of the derivative". So any investment in a derivative could get a 10,000 ROI but no more. In that specific Google hypothetical example the X number is "10,000" which is multiplied by the price "$0.01" which would equal $100. So when the option was exercised the strike price would "reset" to $100 less than the current price (which would then be $19,900). For over 99.999% of derivatives, well over 99.999% of the time, this wouldn't make a difference to either party (buyer or seller) because X would be such an extremely big number. And for when the markets go crazy, there is a maximum loss/gain that would limit absurd swings that serve no value to the economy. Consequently, all future "toxic assets" would have a known upside & downside for much more effective accounting! When one bank wants to write uncovered calls (or any "naked" derivatives) it would have to list publicly (to the rest of the market) what its maximum downside pay-out would be. Then we wouldn't have the problem of "incalculable derivatives". And hopefully, that would lead to more judicious investing.