Godel's first incompleteness theorem is not true but there's a Platonic ideal form that is true. Physics does in fact have a logical singularity as described by Godel - something true, but not provable.
Little known fact: physics is indeed a formal system, which is why theoretical physics works (e.g. Einstein).
Godel's first concludes that healthy formal systems include true but unprovable statements. I have no idea what this would look like for math - and you can try googling up an example yourself, let me know if you find any, and more importantly teach me your google-fu. However, in physics, it's quantum decoherence.
Without loss of generality, consider an electron in a superposition of spin up and spin down. Before collapse there is no fact of the matter regarding whether it will be spin up or spin down. After, it is true that it is spin down.
How does the electron know to pick spin down?
('How does it know' is a critical physics question. Easy example: the water knows to be held back because the dam's surface tells it to stop, and more importantly, where exactly to stop, and how much force is necessary to unstop.)
Picking up or down makes sense - it's aligning with a magnetic field. After it's picked we can just look. But how does the electron itself know it picked spin down?
We know nothing else picks for it, because then we'd be able to measure that thing and predict the choice. Without some internal process telling it which to pick, it should itself not know which to pick, and remain in a superposition...but this has the same problem, being as we could measure the process and predict it.
There is no process that tells the electron it has picked spin down. It is not a consequences of any law of physics. Yet, we can measure that it indeed did pick it, and it is therefore true.
Tuesday, July 5, 2016
So, the five answers: yes, no, I don't know, I don't care, and wrong question. Y/N/?/¯\_(ツ)_/¯/X
At first I found a strong sign of X on the libertarianism vs. determinism question when it turned out their consequences were identical. I've since found determinism isn't predictable and now it's time to show libertarianism is impossible. Mainly for perspective on how conflicted the original question was.
Either I can decide to pursue what I want, or I can't. Either I can choose what I want or I can't. These are mainly straightforward empirical questions - I would notice if I couldn't pursue the strategy I wanted, like I notice I don't control what I like or don't like. (Minimal control, anyway.) However, it doesn't matter, because either way free will is impossible.
Though I control my actions, my best action is determined/predicted by what I want. If it were not so determined, I would not be free - I would be doing something other than what I decide to do. Thus, I cannot be free either way.
In theory I could control what I want, but based on what? Look at the words - I would be able to want whatever I want. If I could fully control my wants, then how I arranged them would have to be determined by some not-me factor. The thing which I use to decide how I arrange things under my control is, by definition, my preferences. Having total control over my preferences is impossible, because there would be nothing to decide their disposition with.
Empirically, the 'want' part of the brain can be damaged, producing caricature vulcans. These folk don't make decisions, because there's no ought from is. Ultimately, to change what I want, I have to have some core value to use as a fulcrum to lever around the values lower in the hierarchy. (Or shallower in the onion.)
Hence, the desire for 'free will' is an evopsych thing, not a philosophy thing. It's about not being in physical chains. It's about my values not being overridden by someone else's. Not being in logical/causal chains is impossible.
at 1:37 PM