Wow. I guess I’m among the people who misunderstand Godel’s implications. I’ve always assumed that it meant that you cannot prove some of the more complex truths.
Unexpectedly, I don’t have to leave. So I’ll answer Half Man Half Wit’s question “what would you have us do?”. It seems nothing, because it seems you are already armed to the teeth with the knowledge of the pitfalls of formalism. But, maybe you know some applied scientists that need educating! I have serious problems with a lot of model builders especially in the field of Numerical Hydrodynamics and especially especially especially when they are used in Cosmology. This is largely because of something I discovered when working on Cellular Automaton fluid models of various sorts. It was a very Wittgensteinesque moment for me, rather shattering as I wasn’t yet free and clear of the notion that “everything is rational” and I placed much more faith in inference as a general and extensible tool than I do now.
In Cellular Automaton (CA) models, you generally have a lattice (the system), particles (the propositions), and collision rules and/or force fields (inferences). I found that when I applied reasonably sensible collision rules, be they random CM-rotation collisions or with a collision parameter, or whatever, I immediately got great results. I’d get Stokes-Navier satisfaction, Galilean invariance (or Lorentz if I wanted it), a perfect Boltzman velocity distribution, parabolic flow profiles for test pipes, equipartition of energy, you name it. That was not surprising to me, even if I was blown away by how pretty much the entire richness of fluid-flow Physics was inevitable from the most simplistic imaginable rules, as long as the rules conserved Momentum, Energy, and Mass.
But get this. For fun I screwed with the rules. I made rules like "if you’re two cells away from another particle that has the same even-/odd-ness in it’s array index as you do, then both turn “rightward” by a random number of degrees up to 180. If the even-/odd-ness doesn’t match then “leftward”. I made all sorts of incredibly stupid and non-physical rules up. You wouldn’t believe how crazy some of them were, like game of life rules involving the presence or absence of neighbors, or where collisions were handled differently if the system clock’s minute was divisible by some prime number. Whatever. I just ONLY made sure to conserve energy, mass, and momentum. Can you guess what happened? I’d get Stokes-Navier satisfaction, Galilean invariance (or Lorentz if I wanted it), a perfect Boltzman velocity distribution, parabolic flow profiles for test pipes, equipartition, you name it! It turned out that the specifics of the transport mechanisms and collision rules really didn’t matter one whit. Maybe this doesn’t surprise any of you, but for me it was almost a crisis of the soul! It was absolute proof that getting the right results in the model meant NOTHING about whether or not the rules I chose were physical ones, or even sane ones! What a blow to my ego! Of course previously, my models were the best, my models applied to EVERYTHING, my models were going to create new micro-fields, my models this, my models that.
So how is this Wittgensteinian?
System: The lattice. The empty pool table. Useless until you place one or more balls on it (propositions) and move them around and collide them (inferences). Empty systems are obviously trivial and uninteresting. [In Gödel’s proof he has to ignore them. They have to be sufficiently complex. There have to be enough propositions and they have to be sufficiently meaningful.]
Propositions: I take the particles themselves to be the propositions. That’s because EVERY bulk property, flow measurement, etc. is about particle location, mass, velocity, period. No exceptions. It’s not like you can “measure the density of the collision rules in a certain area”. If you have a parabolic flow profile it’s because the mass is transported in the way that it is, the particles are where they are, and for no other reason. So it obeys W.'s assertion that all meaning is in the propositions.
Inferences: We have “deduced from”, “descends from”, “a translation of”, “a consequence of” yada yada. So the collision and movement rules are the inferences, any force fields would be also, since a particle that moves along according to some rule is as a new proposition deduced from an old proposition (it’s previous location) according to a law of inference. Likewise with the collisions and force fields. New velocities “descend from” the old velocities using the collision rules to infer the new velocities. Etc. So that all works spotlessly (unless you can think of anything?)
So I screwed with the inferences in unimaginably dumb-seeming ways to no avail. I made one that was like square-dancing…particles would go arm in arm and rotate for a while, releasing after a random (or fixed) interval. No matter. The model remained perfectly physical. Occasionally I had to widen out the spacial or temporal statistical averaging to smooth the effects of particularly bazaar mysterious-action-at-a-distance rule-sets but that was the most I had to do.
So when cosmologists use hydrodynamical models to test whether they have an understanding of the physical laws I shudder and shake my head. I should write a paper on it, but the way things are getting it would probably be ignored anyway. Still…it’s such a scam.
So, that is the story of how I became somewhat convinced that Wittgenstein was right in practice as well as just in theory.
But is it really surprising in hindsight? No. Stokes-Navier fulfillment is DEFINED more or less along the lines of the conservation of mass, momentum and energy. Boltzman speed distributions are DEFINED as N-dimentional superpositions of random Gaussian distributions. Parabolic flow profiles (laminar flow) is DEFINED as drag being placed on a set of particles by collisions and impingements from an adjacent set, along with a no-slip boundary to give the zero velocity intercepts at the boundaries. So was it surprising that given these RULES ABOUT THE RULES, practically ANY set of “rules of inference” we all but irrelevant?
Did that make sense? What do you think? Is this really an applied experience of W. proposition that “it’s ALL in the propositions”?
Sorry, you’re right that W.'s idea pertain broadly. It’s just that G. was about the most diametric view going. There was a controversy over just this specific issue that was fairly long-lived among academics. It was that controversy that gave me the idea to explore it here. I mostly wanted to find out how many people really know what G. was about. He’s been exploited and distorted all out of context and importance by the jazz-philosophers in my opinion. I also got the idea from that fun thread
Where Godel came up at the very end. As for your complaint that it pertains generally, yes of course. It was immediately massively generalized by all commenters, but not by me. But sorry if that’s of concern. I personally, would be cool with tightening it right down on that one narrow topic too. “Was Godel right [at the one extreme] or W. [at the other] or both?”
Enough said.
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Words are symbols/metaphors and rely for their “meaning/truth” in entirely subjective individual interpretations. Each interpreter brings any and all meaning to the symbol. So-called “consensual reality” is just that, an ongoing public opinion poll on how words map to “reality”.
The idea works fine in everyday commerce, we all know the difference between a tire and a pumpkin and how to show up on time for a flight. Things get sticky when we talk about abstract concepts like truth, democracy or Tao that have no direct reference to the material world.
Our our unfortunate tendency is mistake the map for the territory when we venture in words beyond time and space. Look no further than GD.
The Tao that can be named is anybody’s guess or as Godel might put it, incomplete.