@sequoiaboi said (#37):
incompleteness giving logos a form of expression that resembles habits, rather than something
set in stone, as in mathematically backtrackable
Like with most new-age reasonings this looks interesting (and, yes, somewhat convincing) at first glance, but upon close inspection is just half-understood concepts lumped together that have nothig to do with each other.
Let us start with "incompleteness" or, rather, Gödels Incompleteness theorems: mathematical systems are based on "axioms", basic facts (or assertions) that are so obvious that we "just know them to be true". There are, for instance, Euclids axioms as the foundation of geometry and there are Peanos axioms as the foundation of arithmetic (and, by extension, number theory). A system created by such base propositions ("axioms") and the resulting propositions created by applying logical deduction rules to combine them may be "complete" or not and it may be "free of contradictions (=consistent)" or not.
What Gödel found was that such an - any - axiomatic system can be complete or consistent, but not both. A system may be "complete" (for Gödel that was: able to build a system where arithmetic operations were possible), but then it is possible to find - by deductively creating propositions from the axioms and already deduced propositions - a proposition that is neither provable to be true nor provable to be false. Even worse, you can find a proposition which can be deduced from the axioms and that states about itself it can't be deduced from the axioms at all. That is a contraodiction. And if you extend the axiomatic system so that this contradiction is alleviated, you have a new system where you will find another proposition which will do the same to the new system. That game can go on infinitely.
Gödel responded with this in particular to Hilberts "program", which mainly drove mathematics in the twenties of the twentieth century. Hilbert tried to safeguard mathematics in a "constructionist" way against the "intuitionists" by formalizing it. Gödel showed that this formalization was in a strict way impossible to achieve.
What does that mean for natural laws? As far as i can see: nothing. All our science is basically a model we use to not only explain but also extrapolate reality. We do not "know" what i.e. an electron is, but we have a "model of an electron" and with this model we can not only explain what is going on but we can also predict what will be going on under certain circumstances. Sometimes we find circumstances our model does not correctly predict (or doesn't predict well) and then we modify our model, so that it incorporates these new circumstances too and predicts them correctly as well. This way we "err our way up". But ultimately the model is always - and will always be - a model. It may or may not get closer and closer to reality (and in fact i believe it would be very difficult to create a model that predicts so much correctly and is still not "very close to reality" - but that is not the point), but it will better and better explain the observable as well as predict future observations.
Now, there are - and always will be - competing models to explain reality. I don't want to talk about "evolution theory" as my wish to discuss bible verses with idiots with invisible friends is quite limited. Let us use "the inside of a mechanical clock" as an example instead: suppose we both don't know how a watch works and we have no way of taking it apart to look inside. We can watch it from outside and we will observe the hands revolving in certain patterns, we will notice the "tic-toc" sound it makes when it runs and also, that it sometimes need to be rewound or otherwise ti will stop working until it is rewound again.
Now, one way to explain all that will be a mechanism driven by a spring (hence the need of rewinding it from time to time) and some cogwheels. It won't matter (for most of the part) if the cogwheels in our model will be exactly the same as in reality, but with such an explanation we could explain most of what we observe about the clock. We could even predict "if it works according to that model it should stop working after X hours of running without being rewound again" and if that is true our model is good, if it wrong we would have to modify our model (maybe there is a coil instead of a spring with a longer or shorter period of necessary rewinding instead?).
But we could also have very different models of how the clock works: a horde of angels are fond of rotating the hands and they do so in a certain pattern. But they need to constantly fight off a horde of goblins, who are usually busy sucking the winding energy from the spring and the "tic-toc" sound is comes from their sucking. When there is no tension to be sucked out they fight the angels and then the angels are busy and they cannot move the hands until the spring is rewound again.
What makes the first "theory about how a clock works" probably true and the second one rather ridiculous? It is a philosophical insight a scottish medieval monk came up with and it is named after him "Occams razor". Basically it says that of tow theories the one with less unobservable and unprovable things to presuppose is to be preferred.
This is why we don't use "god" in discussions about nature: we simply don't need "god" - any god - to explain it at all. We don't need the "unspeakable", the "hidden", the "ectoplasmic" or similar - we can explain nature and everything we can observe in it by nature and its laws itself. Are there things we cannot explain? Yes, there are. But "we cannot explain" is also something absolute - it does NOT mean we cannot explain it other than by a "god" or something similar. It just means we cannot explain it - period. This is the background of Ernst Haeckel speaking about the "housing shortage of god" (orig.: "Wohnungsnot Gottes") in the 19th century. But that only as an aside.
In an effort to draw more attention to this from the philosophically inclined and knowledgeable i call on @havfanridindis, who might be interested too.
krasnaya
@sequoiaboi said (#37):
> incompleteness giving logos a form of expression that resembles habits, rather than something
> set in stone, as in mathematically backtrackable
Like with most new-age reasonings this looks interesting (and, yes, somewhat convincing) at first glance, but upon close inspection is just half-understood concepts lumped together that have nothig to do with each other.
Let us start with "incompleteness" or, rather, Gödels Incompleteness theorems: mathematical systems are based on "axioms", basic facts (or assertions) that are so obvious that we "just know them to be true". There are, for instance, Euclids axioms as the foundation of geometry and there are Peanos axioms as the foundation of arithmetic (and, by extension, number theory). A system created by such base propositions ("axioms") and the resulting propositions created by applying logical deduction rules to combine them may be "complete" or not and it may be "free of contradictions (=consistent)" or not.
What Gödel found was that such an - any - axiomatic system can be complete or consistent, but not both. A system may be "complete" (for Gödel that was: able to build a system where arithmetic operations were possible), but then it is possible to find - by deductively creating propositions from the axioms and already deduced propositions - a proposition that is neither provable to be true nor provable to be false. Even worse, you can find a proposition which can be deduced from the axioms and that states about itself it can't be deduced from the axioms at all. That is a contraodiction. And if you extend the axiomatic system so that this contradiction is alleviated, you have a new system where you will find another proposition which will do the same to the new system. That game can go on infinitely.
Gödel responded with this in particular to Hilberts "program", which mainly drove mathematics in the twenties of the twentieth century. Hilbert tried to safeguard mathematics in a "constructionist" way against the "intuitionists" by formalizing it. Gödel showed that this formalization was in a strict way impossible to achieve.
What does that mean for natural laws? As far as i can see: nothing. All our science is basically a model we use to not only explain but also extrapolate reality. We do not "know" what i.e. an electron is, but we have a "model of an electron" and with this model we can not only explain what is going on but we can also predict what will be going on under certain circumstances. Sometimes we find circumstances our model does not correctly predict (or doesn't predict well) and then we modify our model, so that it incorporates these new circumstances too and predicts them correctly as well. This way we "err our way up". But ultimately the model is always - and will always be - a model. It may or may not get closer and closer to reality (and in fact i believe it would be very difficult to create a model that predicts so much correctly and is still not "very close to reality" - but that is not the point), but it will better and better explain the observable as well as predict future observations.
Now, there are - and always will be - competing models to explain reality. I don't want to talk about "evolution theory" as my wish to discuss bible verses with idiots with invisible friends is quite limited. Let us use "the inside of a mechanical clock" as an example instead: suppose we both don't know how a watch works and we have no way of taking it apart to look inside. We can watch it from outside and we will observe the hands revolving in certain patterns, we will notice the "tic-toc" sound it makes when it runs and also, that it sometimes need to be rewound or otherwise ti will stop working until it is rewound again.
Now, one way to explain all that will be a mechanism driven by a spring (hence the need of rewinding it from time to time) and some cogwheels. It won't matter (for most of the part) if the cogwheels in our model will be exactly the same as in reality, but with such an explanation we could explain most of what we observe about the clock. We could even predict "if it works according to that model it should stop working after X hours of running without being rewound again" and if that is true our model is good, if it wrong we would have to modify our model (maybe there is a coil instead of a spring with a longer or shorter period of necessary rewinding instead?).
But we could also have very different models of how the clock works: a horde of angels are fond of rotating the hands and they do so in a certain pattern. But they need to constantly fight off a horde of goblins, who are usually busy sucking the winding energy from the spring and the "tic-toc" sound is comes from their sucking. When there is no tension to be sucked out they fight the angels and then the angels are busy and they cannot move the hands until the spring is rewound again.
What makes the first "theory about how a clock works" probably true and the second one rather ridiculous? It is a philosophical insight a scottish medieval monk came up with and it is named after him "Occams razor". Basically it says that of tow theories the one with less unobservable and unprovable things to presuppose is to be preferred.
This is why we don't use "god" in discussions about nature: we simply don't need "god" - any god - to explain it at all. We don't need the "unspeakable", the "hidden", the "ectoplasmic" or similar - we can explain nature and everything we can observe in it by nature and its laws itself. Are there things we cannot explain? Yes, there are. But "we cannot explain" is also something absolute - it does NOT mean we cannot explain it other than by a "god" or something similar. It just means we cannot explain it - period. This is the background of Ernst Haeckel speaking about the "housing shortage of god" (orig.: "Wohnungsnot Gottes") in the 19th century. But that only as an aside.
In an effort to draw more attention to this from the philosophically inclined and knowledgeable i call on @havfanridindis, who might be interested too.
krasnaya