In my mind, there seems to be a deep connection between quantum theory and the conclusions arrived at by Godel. — Question
Does quantum mechanics obey causality? — Question
There is no such thing as a non-computable physical law. — tom
Well, causality is intertwined with the philosophical concept of the Principle of Sufficient Reason, which basically states that everything that has a reason for happening has also a cause, with the converse being true also. Thus if QM does not obey causality then it is either beyond our capacity to understand the cause of such event or de facto QM doesn't obey causality.Not sure what you might consider obeying causality, and I think different interpretations will give different answers to this. — noAxioms
There is no such thing as a non-computable physical law. — tom
Can you explore that further or point me to some sources stating that? I'd appreciate it. — Question
Non computability comes from negative self reference. Even just self-reference makes it hard make a correct working model for something.Classical mechanics takes a good stab at it, achieving non-computability-in-practice. This is because of phenomena such as sensitive dependence on initial conditions, leading to chaos — tom
We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.
Well, that's Turing's Halting problem for you...What would it even mean for a physical law to be non-computable? — tom
So, a computer can calculate without ordering causality? Seems fishy to me. Anyway, what about quantum wave function's? They seem to obey causality in some sense, as for computability, I don't think so...I think the link is basically computability. It's not about causality. — ssu
So, a computer can calculate without ordering causality? Seems fishy to me. Anyway, what about quantum wave function's? They seem to obey causality in some sense, as for computability, I don't think so — Question
No, I think you misunderstood.So, a computer can calculate without ordering causality? Seems fishy to me. Anyway, what about quantum wave function's? They seem to obey causality in some sense, as for computability, I don't think so... — Question
So you would call the world a formal system? This is part of what Gödel pointed out: There is a difference between formal deduction and existence of an entity.In my mind, there seems to be a deep connection between quantum theory and the conclusions arrived at by Godel. — Posty McPostface
The sentence cannot be deduced and hence does not exist in the system.From a viewpoint inside the formal system the model is the a posteriori observation required to determine the state of the G-sentence. — Arisktotle
So you would call the world a formal system? — Heiko
This is part of what Gödel pointed out: There is a difference between formal deduction and existence of an entity. — Heiko
Godel's theorems only apply to formal systems, as per Godel. — MindForged
Well, if the world is a formal system of sorts, then what's wrong with trying to find a link between the two? — Posty McPostface
Yes, why not? — Posty McPostface
This is part of what Gödel pointed out: There is a difference between formal deduction and existence of an entity. — Heiko
Gödel showed that there is at least one true - and hence in the sense of mathematics: existing - sentence that cannot be deduced from any set of axioms and thus not be part of any formal system.Could you expand on that? What do you mean by the difference here? — Posty McPostface
We are talking about formal systems of symbols here. The word "symbol" already indicates representation. Formalism was more or less concerned with making "glyphs"(no better word) the kind of object mathematics deals with: "correct syntax = true statement". In mathematics - like MindForged pointed out - it seems (up to now, yet again) to be the case that correct syntax is a guarantee for a true statement. Otherwise there would be a contradiction. This has happened before and may happen again.Do you agree with MindForged previous post for the matter? — Posty McPostface
I'm not that much into idealism that I'd say there really must be a contradiction-free set of laws of nature as otherwise things could not happen as they do. Of course omniscience and potential omnipotence are absolutely positive so this is the only assumption one can seriously work with. — Heiko
That is incorrect since it is covered by the syntax of the system. — Arisktotle
Oh... the syntax was a metaphor. "2=3" ain't true either and looks like some equation nontheless. When using "syntax" in the sense I did this does not mean " 'Number = Number' is a valid expression ". One can easily write a computer-program that could deduce any valid a+b=c for natural numbers gramatically.The Gödel-sentence would never have been debated, would it have been excluded a priori by the syntax-checker of the active system. — Arisktotle
It is not true in the formal system as it cannot be deduced.It is true though that it has no semantic value and therefore does not exist as a theorem. — Arisktotle
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