When one definition of determinism is equivalent to "completeness", but then another definition allows you to say "incomplete determinism", and you put pretty close to 0 effort into explaining how that's supposed to make sense, I can't imagine I'm alone in just thinking it's all nonsense from that point on. — flannel jesus

seems like you're mixing vocabularies a lot here and generating a lot of unnecessary ambiguity. — flannel jesus

Yeah, if you say determinism means completeness, then "incomplete deterministic" just sounds like "incomplete completeness". Seems like a nosnense term to me. — flannel jesus

So then when you were talking about incomplete determinism — flannel jesus

I don't think any of that goes any distance towards demonstrating what I said was incorrect. Incompatibilists say free will is incompatible with determinism, not oracles — flannel jesus

I guarantee you 95%+ of incompatibilists will say "screw oracles, free will is incompatible with determinism period". — flannel jesus

https://en.wikipedia.org/wiki/Predeterminism

Predeterminism is the philosophy that all events of history, past, present and future, have been already decided or are already known (by God, fate, or some other force), including human actions. Predeterminism is closely related to determinism.

https://en.wikipedia.org/wiki/Deterministic_system

In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.

https://en.wikipedia.org/wiki/Determinism

Determinism is the philosophical view that all events in the universe, including human decisions and actions, are causally inevitable.

what is this incomplete determinism? — flannel jesus

https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e. an algorithm) is capable of proving all truths about the arithmetic of natural numbers.

no, incompatibilism implies that if determinism is true, free will doesn't exist — flannel jesus

So one can imagine a world where determinism is true, this oracle is impossible. — flannel jesus

I really don't see that as free will in any meaningful sense. — flannel jesus

What makes you convinced thwarter is a genuinely possible program? Has anyone programmed one? — flannel jesus

If you give me a program, say its listing printed out on paper; and you give me its inputs; and you give me a lot of pencils, paper, and time; I can deterministically and with no ambiguity determine exactly what it's going to do. I can not imagine this being false, and therefore Rice must be full of beans! — fishfry

A chaotic system is deterministic yet unpredictable. Nothing to do with incompleteness. There's no free will, none whatsoever, in a chaotic system. — fishfry

Hmmm. Let me mull that over. I don't agree. Computability, by its nature, is deterministic. Whatever free will is, it is not computable. — fishfry

https://en.wikipedia.org/wiki/Rice%27s_theorem

In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable.

A semantic property is one about the program's behavior (for instance, "does the program terminate for all inputs?"), unlike a syntactic property (for instance, "does the program contain an if-then-else statement?"). A non-trivial property is one which is neither true for every program, nor false for every program.

The theorem generalizes the undecidability of the halting problem. It has far-reaching implications on the feasibility of static analysis of programs. It implies that it is impossible, for example, to implement a tool that checks whether a given program is correct, or even executes without error.

The theorem is named after Henry Gordon Rice, who proved it in his doctoral dissertation of 1951 at Syracuse University.

You are aware, I suspect, that as far as Islam in concerned, Christianity is false, right? Jesus is not god and and the Crucifixion story is a myth. So an Islamic person who has the experience of Allah and Mohammad is confirming his/her belief that Christianity is not the true religion. That is certainly what Muslims I have met have told me. Conversely, the Christian vison confirms that Islam is not true and Jesus is God. How do you resolve this psycho-cultural conundrum? — Tom Storm

At each subsequent time, the output can be predicted from the input. The output is pre-determined by the input. At any time t + x, the output has been pre-determined by the situation at time zero. — RussellA

Terrific, readable paper. Hamkins rocks. https://arxiv.org/pdf/2407.00680 — fishfry

Turing thus showed that the symbol-printing problem is undecidable by mounting a reduction to and through the undecidability of the circle-free problem. But let us illustrate how one may improve upon Turing with a simpler self-referential proof of the undecidability of the symbol-printing problem in the style of the standard contemporary proof of the undecidability of the halting problem. There was actually no need for Turing’s detour through the circle-free problem.

= Original ==

Namely, assume toward contradiction that the symbol-printing problem were computably decidable, and fix a method of solving this problem. Using this as a subroutine, consider the algorithm q which on input p, a program, asks whether p on input p would ever print 0 as output. If so, then q will halt immediately without printing 0; but if not, then q prints 0 immediately as output. So q has the opposite behavior on input p with respect to printing 0 as output than p has on input p. Running q on input q will therefore print 0 as output if and only if it will not, a contradiction.

== Narrative ==

Namely, assume toward contradiction that the symbol-printing problem were computably decidable, and fix a method of solving this problem. Using the oracle as a subroutine, consider the thwarter program which asks to the oracle whether any program p on input p would ever print 0 as output. If the oracle answers that it will print 0, then thwarter itself will not print 0; but if the oracle says that thwarter doesn't print 0, then thwarter does print 0. Running thwarter on itself as input will therefore print 0 as output if and only if the oracle says that thwarter will not, a contradiction.

He mounts an unusual kind of reduction, showing that if symbol-printing were decidable, then also the circle-free problem would be decidable, which he had already proved is not the case.

This is not a straightforward reduction of one problem to another, but rather an argument that if one problem were actually computably decidable, then so would be the other.

By the way, humans may or may not have free will.
Programs, by their very nature, do not have free will. — fishfry

You define the terms for the sake of progress? — frank

Somehow that doesn't follow from the impossibility of such an app since the app is impossible even in a pure deterministic universe. — noAxioms

Free will is about possibility. If you're going to make a choice, there must be multiple possibilities, as if time is a branching thing and you can choose the path you'll take. — frank

https://en.wikipedia.org/wiki/Incompatibilism

Incompatibilism is the view that the thesis of determinism is logically incompatible with the classical thesis of free will.

https://en.wikipedia.org/wiki/Predeterminism

Predeterminism is the philosophy that all events of history, past, present and future, have been already decided or are already known (by God, fate, or some other force), including human actions.

What would free will look like then? — Igitur

How odd! — Vera Mont

Nailed it, finally! — Vera Mont

https://en.m.wikipedia.org/wiki/Foundations_of_mathematics

This led, near the end of the 19th century, to a series of paradoxical mathematical results that challenged the general confidence in reliability and truth of mathematical results. This has been called the foundational crisis of mathematics.

The resolution of this crisis involved the rise of a new mathematical discipline called mathematical logic that includes set theory, model theory, proof theory, computability and computational complexity theory, and more recently, several parts of computer science.

Of course you were, rambling about the economic status of someone you know nothing about. Disingenuous and malicious, pretending his sour character attacks were his "haha humour". — Lionino

I don't know neither do I care about some fringe github application you pretend to know about, crank. — Lionino

https://en.wikipedia.org/wiki/Macsyma

Macsyma (/ˈmæksɪmə/; "Project MAC's SYmbolic MAnipulator")[1] is one of the oldest general-purpose computer algebra systems still in wide use. It was originally developed from 1968 to 1982 at MIT's Project MAC.

In 1982, Macsyma was licensed to Symbolics and became a commercial product. In 1992, Symbolics Macsyma was spun off to Macsyma, Inc., which continued to develop Macsyma until 1999. That version is still available for Microsoft's Windows XP operating system.

The 1982 version of MIT Macsyma remained available to academics and US government agencies, and it is distributed by the US Department of Energy (DOE). That version, DOE Macsyma, was maintained by Bill Schelter. Under the name of Maxima, it was released under the GPL in 1999, and remains under active maintenance.

$ sudo apt install maxima
Reading package lists... Done
Building dependency tree... Done
Reading state information... Done
The following additional packages will be installed:
aglfn gnuplot-data gnuplot-x11 liblua5.4-0 libpcre2-32-0 libwxbase3.2-1
libwxgtk3.2-1 maxima-share tex-common
Suggested packages:
gnuplot-doc texmacs maxima-doc xmaxima maxima-emacs wish debhelper
The following NEW packages will be installed:
aglfn gnuplot-data gnuplot-x11 liblua5.4-0 libpcre2-32-0 libwxbase3.2-1
libwxgtk3.2-1 maxima maxima-share tex-common
0 upgraded, 10 newly installed, 0 to remove and 0 not upgraded.
Need to get 23.7 MB of archives.
After this operation, 112 MB of additional disk space will be used.
Do you want to continue? [Y/n]Abort.

The multiverse I understand as a "place" where universes exist much as galaxies in the universe. — tim wood

As to the uni-verse, the predictions are for either a hot death or a cold death. — tim wood

Is there any way for a teleporter machine to randomly select an Earth out of an infinite number of them in a finite amount of time, or is there always going to be, practically speaking, only a finite amount of Earths for Alice to teleport to because of the limitations of the machine? — RogueAI

complaining about "ad hominem". Sprinkling a bit of hypocrisy in the sophistry, aren't we? — Lionino

Mathematical infinity has nothing to do with any study of the universe (except as it may appear in some of the mathematics that describe the physics of the universe). — tim wood

2x4+4x2+2 — Lionino

solve([2*x^4+4*x^2+2=0],[x]);
(%o1) 	[x=−i,x=i]

solve([2*u^2+4*u+2=0],[u]);
(%o1) 	[u=−1]

(defun solve1a (exp mult) 
  (let ((*myvar *myvar)
	(*g nil)) 
    (cond ((atom exp) nil)
          ((not (memalike (setq *myvar (simplify (pdis (list (car exp) 1 1))))
                          *has*var))
           nil)
	  ((equal (cadr exp) 1) ([b]solvelin[/b] exp))
	  ((of-form-A*F<X>^N+B exp) (solve-A*F<X>^N+B exp t))
	  ((equal (cadr exp) 2) ([b]solvequad[/b] exp))
	  ((not (equal 1 (setq *g (solventhp (cdddr exp) (cadr exp)))))
	   (solventh exp *g))
	  ((equal (cadr exp) 3) ([b]solvecubic[/b] exp))
	  ((equal (cadr exp) 4) ([b]solvequartic[/b] exp))
	  (t (let ((tt (solve-by-decomposition exp *myvar)))
	       (setq *failures (append (solution-losses tt) *failures))
	       (setq *roots    (append (solution-wins tt) *roots)))))))

Wrong. Everybody who lives in Europe knows why the far-right is rising. Funnily enough, it has nothing to do with the lack of religion, it has to do with the presence of (a certain) religion.

Keep European politics for people who have skin in the game. If someone is backpacking in Siberia or being a sexpat in Thailand they typically wouldn't have a lot of investment in what is going on across the glope. — Lionino

Is that why after I completely debunked your claim about birth rates one page ago you disappeared from the thread only to come back to repeat the same clownish nonsense that was already disproved — much in the same way that several of your claims throughout the site have been shown to be factually false or nonsensical? — Lionino

The set would have to countable, wouldn't it? You could count the worlds. There's a one-to-one correspondence with each parallel world and the natural numbers. How could the multiverse be uncountably infinite? — RogueAI

https://en.wikipedia.org/wiki/Spectrum_of_a_theory

Saharon Shelah gave an almost complete solution to the spectrum problem.

Roughly speaking this means that either there are the maximum possible number of models in all uncountable cardinalities, or there are only "few" models in all uncountable cardinalities.

Multiverse cosmology is not about set theoretic models. — fishfry

Are there a countable or uncountable infinity of worlds? — fishfry

https://en.m.wikipedia.org/wiki/L%C3%B6wenheim%E2%80%93Skolem_theorem

It implies that if a countable first-order theory has an infinite model, then for every infinite cardinal number κ it has a model of size κ, and that no first-order theory with an infinite model can have a unique model up to isomorphism. As a consequence, first-order theories are unable to control the cardinality of their infinite models.

https://victoriagitman.github.io/talks/2015/04/22/an-introduction-to-nonstandard-model-of-arithmetic.html

An easy application of the compactness theorem shows that there are countable nonstandard models of the Peano axioms, or indeed of any collection of true arithmetic statements.

By destroying people's freedom and ability to think, theism can cause untold damage. — Tom Storm

Nietzsche called one of his books “beyond good and evil” and belittled those with a “will to truth” as lying to themselves, and said “God is dead” to make his point thoroughly. — Fire Ologist

Nietzche having made predictions about the future based on his limited perspective isn't something I am all that interested in. — wonderer1

Suppose a substantial portion of our fellow social primates can't cope emotionally with having an atheistic perspective. Do you recognize that that doesn't have any bearing on whether God exists? — wonderer1

Sounds like fantasizing on your part, to me.

Do you see yourself as someone likely to commit suicide if you came to have an atheist perspective? If so, do you think that might just be a personal issue you have? — wonderer1

Europe no longer needed God as the source for all morality, value, or order in the universe; philosophy and science were capable of doing that for us.

Nietzsche believed that the removal of this system put most people at the risk of despair or meaninglessness.

For some time now our whole European culture has been moving as toward a catastrophe.

Absurdism is the philosophical theory that the universe is irrational and meaningless.

The three responses discussed in the traditional absurdist literature are suicide, religious belief in a higher purpose, and rebellion against the absurd.

Nietzsche often considered suicide due to his physical suffering. It was his philosophy which rescued him. — Joshs

Getting along with others is the most difficult challenge in life, and making progress at it is our responsibility, not the gods. — Joshs

There is nothing to understand. You are writing gibberish about free will and Gödel. — Lionino

https://arxiv.org/pdf/1401.1800

Gödel, Tarski, Turing and the conundrum of free will

Free will exists relative to a base theory if there is freedom to deviate from the deterministic or indeterministic dynamics in the theory ...