• The False Argument of Faith
    Being very straightfoward, everytime I enter in a religious debate with someone who "follows" some religion (catholic, protestant, orthodox, muslim, etc...) eventually, as a religious debate tends to end, the "faithful" one, ends appealing to the "Faith Argument", that i find stupid and misleading, because this argument is supported by no base. — Gus Lamarch

    If the practice of adopting system-wide premises is that stupid, then what exactly supports the fourteen axioms of propositional logic or the nine axioms of standard number theory?

    Can you show me one example of an axiomatic system that is not based on unsupported, speculative, and essentially arbitrary beliefs?

    It is not possible to do mathematics without axiomatic sytems, and without mathematics, you have no instrument to maintain consistency in scientific theories either. Hence, in your view, science also goes out of the window.

    In other words, your views are suitable only for aboriginal hunter-gatherer tribes who live off collecting elephant dung in a tropical rain forest.
  • Unanswerable question about human origins.
    First of all, Tegmarks premise there is not what is usually referred to as the theory of everything. — noAxioms

    I understand Tegmark idea of "Ultimate Ensemble theory of everything" (UE-ToE) as being a fully-fledged "theory of everything". I think that Tegmark really means a ToE with his idea of UE-ToE. What else would he mean to refer to?

    Tegmark's proposal about SASs is rather some kind of detail in his complete idea, which on the whole is, in my impression, a ToE.

    That 'holy grail' is a unified theory, and Tegmarks comment paves no way towards unifying gravity with quantum field theory. — noAxioms

    That unification attempt is the concept of ToE as seen through the lens of nuclear physics. They want the real details of the ToE. Tegmark's view is a metamathematical approach in which we are not necessarily interested in the details, and in which we treat the ToE as a black box with emergent properties.

    The ToE is the only subject-matter intersection between mathematics and physics, in a sense that it is the only place where both disciplines study the same subject.

    I am personally not particularly interested in the grand unification attempt in physics. I do not believe that Tegmark is either. Unification is obviously a legitimate research subject in physics, but I consider it to be a subject for physicists.

    But it points out that there is no distinction between mathematics that exists and mathematics that does not. — noAxioms

    It only works like that in the context of the ToE. That is what is so special about this theory. If a sentence is provable in the ToE, it is guaranteed to appear as a true fact in the physical universe. This is not the case for any other mathematical theory. It will not work for number theory, set theory, or another partial theory in mathematics, which are merely Platonic abstractions, divorced from the real, physical world.

    2+2=4 is true whether or not something physical performs the sum or not. — noAxioms

    The sentence "2+2=4" is true in the abstract, Platonic world of the natural numbers, which is one model (the standard one) of number theory. This model is not the physical universe. That would be impossible because number theory is not the ToE. Hence, "2+2=4" cannot be deemed (physically) true in the physical universe, unless you can argue that it is provable from the ToE. That is not possible without having access to all the details of the ToE. Proving anything from the ToE requires you to have a full copy of it. Hence, you cannot prove anything from the ToE.

    Still, even a black box ToE has emergent system-wide properties, for which we do not need access to its details. We know that the ToE is consistent, because it has a model, i.e. the physical universe. We also know that the physical universe contains true facts that are not provable from the ToE, and therefore, that there must exist other universes in which these facts are false. Hence, we know that the ToE is incomplete. Still, all of that still does not allow us to (inferentially) prove anything from the ToE. We do not know even one single theorem in the ToE. We only understand some of its emergent properties.

    That is the power of metamathematics, in which theories are just objects; just like numbers are objects in number theory. You can actually discover quite a bit about these objects without knowing (all of) their details.

    This has led me to a a different approach where being 'real' is not a property of something (like a rock say) but rather a relation. The rock is real to the water it diverts. But such a view is very different now than what Tegmark is proposing. — noAxioms

    We cannot seek to abolish the distinction between mathematics and science.

    Except for the ToE, all mathematics is divorced and deemed unrelated to the real, physical world. Partial theories concerning the real, physical world must first go through the hands of correspondence-seeking scientific bureaucracies, i.e. mostly: experimental testing.
  • Emphasizing Red Ink Christianity
    Therefore, Christian institutions should prioritize the words of Jesus (and the Gospels) over other scripture. — James Moore

    If you read the Sermon on the Mount, Matthew 5:17, it says:

    17 “Do not think that I have come to abolish the Law or the Prophets; I have not come to abolish them but to fulfill them. 18 For truly I tell you, until heaven and earth disappear, not the smallest letter, not the least stroke of a pen, will by any means disappear from the Law until everything is accomplished. 19 Therefore anyone who sets aside one of the least of these commands and teaches others accordingly will be called least in the kingdom of heaven, but whoever practices and teaches these commands will be called great in the kingdom of heaven. 20 For I tell you that unless your righteousness surpasses that of the Pharisees and the teachers of the law, you will certainly not enter the kingdom of heaven.

    Jesus clearly expected his followers to keep the Law and the Prophets, i.e. the commandments in the Torah, i.e. full Jewish Law.

    Many Christian theologians will come up with all kinds of excuses why there would be no need to keep the Law and the Prophets. For example, the Law forbids eating pork. Do you know of one Christian who does not eat pork? I don't. Still, we know that Jewish Law strictly forbids it. Did Jesus eat pork? No, because then the gospels would certainly have mentioned him breaking the Law. So, you can see followers of Jesus eating pork, while Jesus did not do that, and while the Law even forbids it, and while Jesus insists that his followers must keep the Law. Muslims do follow the Law and the Prophets, and also avoid eating pork. No excuses. In that sense, Muslims seem to be better followers of Jesus than Christians are.
  • What is love?
    Men aspire to women; women deign to be with men. — The Great Whatever

    This is the case only in societies infected with the romantic-love disease and with too much easy money floating around. Elsewhere, these things are always arranged, and very much so as a business transaction.

    You want a wife? Then pay the marriage gift. You want a one-night stand? Then pay the rental fee and for the room. If you want something, you will simply have to pay for it. How hard can that be?

    (Of course, I do not recommend to marry or even co-habitate with anyone in a divorce-rape jurisdiction. I live in SE Asia.)

    Furthermore, I would never see or ever talk with a woman who does not want to be with me, because I only ever see the ones who do. Hence, I do not give a flying fart about what arbitrary women may think about me. Since they are not candidates who were pushed through a particular arrangement procedure, they are totally irrelevant. If I need a woman for any such purpose, I just ask a local friend to do the legwork. Over here, they love doing that anyway. He may even bring his favourite niece! It is simply a question of "getting HR to thoroughly filter candidates" first.

    I do not date and I do not participate sexually in societies where people date. What kind of situation are you constructing if you start out by putting her on a pedestal? These guys actively transform themselves into a bunch of losers.

    Seriously, if you are good at business negotiations, and you can pay the reasonable price, then why wouldn't you get exactly what you want? You don't need to be a "higher-status" man for that, and frankly, it is not even particularly costly. Like with any business transaction, all you need to do, is to shut off and shut down all avenues for bullshitting, upfront. Prevent the system from allowing that, and you should be fine!
  • Unanswerable question about human origins.
    So, Kierkegaard advocated being an individual, but so did Thoreau. Both of them had a distaste for "sheepdom"...(people following in lockstep with one another). I think that's why both were critical of organized religion. — sydell

    Most people eat breakfast in the morning, but is it "sheepdom"? Lots of people enjoy playing or watching tennis, but is that "sheepdom"? Kierkegaard may have extensively criticized existing systems, but did he propose alternative ones? No, he did not do that either.

    As usual, his atheist morality remains the typical, random collection of single-concern issues, also known as the atheist system-less bullshit.

    Single-concern issues are not innocent.

    For example, look at the women's right issue. Out of context, the rhetoric may sound attractive. However, we are now in the long run of the erstwhile short-term decisions. The long-term result means that the these atheist populations have a very low birth rate and increasingly fail to reproduce. There simply was an entire system to consider geared at keeping families together.

    But then again, now that the system has decided to replace these shrinking atheist populations by immigrants, the problem is actually solving itself. These immigrants are certainly not atheist and seem to reproduce themselves fine. Still, it was a long detour to get there. If getting rid of atheist populations was the original goal, they could have achieved that much faster and much cheaper.

    Kierkegaard would have been proud to see his atheist followers dying out like they are doing now. They can now follow their leader Kierkegaard to hell, where they can collectively burn in the hands of their master, Satan.
  • Unanswerable question about human origins.
    Just as an instrumental way to try to reconcile quantum mechanics and general relativity without having to retool physics and/or mathematics, sure. — Terrapin Station

    We do not need to have a copy of the ToE to actually know quite a few things about it -- even without reconciling QM with GR.

    As a theory, i.e. an axiomatic system, the ToE is subject to the "theory of theories", i.e. metamathematics. That is undoubtedly why Gödel's incompleteness theorems so often pop up in this context.

    I don't think that the goal of ToE research is to retool physics and/or mathematics.
  • Unanswerable question about human origins.
    I don't see how that's not basically just making up arbitrary SciFi-like crap. — Terrapin Station

    I may not completely agree with Tegmark's "Ultimate Ensemble theory of everything" (ToE) but if you treat the unknown ToE like a blackbox, there are still quite a few meaningful things that you can say about it.

    Tegmark's approach may have its problems, but the Theory of Everything is actually a very legitimate mathematical and scientific subject:

    Prominent contributors were Gunnar Nordström, Hermann Weyl, Arthur Eddington, David Hilbert,[19] Theodor Kaluza, Oskar Klein (see Kaluza–Klein theory), and most notably, Albert Einstein and his collaborators. Einstein intensely searched for, but ultimately failed to find, a unifying theory.[20]:ch 17 (But see:Einstein–Maxwell–Dirac equations.) More than a half a century later, Einstein's dream of discovering a unified theory has become the Holy Grail of modern physics.

    It is in fact the only theory that is both abstract, Platonic (=mathematics) and empirical-scientific. All other theories can only be either.
  • Unanswerable question about human origins.
    And that we are able to craft this "mathematics" thing that allows us to model the system that produced us? — staticphoton

    Max Tegmark has made an interesting attempt at modeling the "Ultimate Ensemble theory of everything" (ToE):

    ... whose only postulate is that "all structures that exist mathematically exist also physically". This simple theory, with no free parameters at all, suggests that in those structures complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically "real" world. This idea is formalized as the mathematical universe hypothesis,[16] described in his book "Our Mathematical Universe".

    Tegmark tries to model us as "self-aware substructures" (SASs). If humanity has free will, then we are a very serious problem for any ToE, which will then necessarily be incomplete.

    In fact, we can even define the term "free will" in that manner: A being has free will, if there does not exist any theory that can correctly predict its behaviour.

    So, Tegmark's self-aware substructures (SASs) are actively sabotaging the completeness of his ToE by their mere existence. If our universe is then a model of Tegmark's ToE, and since it contains true facts that are not provable from his ToE, then there must be other models, i.e. universes, in which these facts are false.

    Tegmark agrees that there must be other universes:

    The MUH is related to Tegmark's categorization of four levels of the multiverse.[6] This categorization posits a nested hierarchy of increasing diversity, with worlds corresponding to different sets of initial conditions (level 1), physical constants (level 2), quantum branches (level 3), and altogether different equations or mathematical structures (level 4).

    I don't see, however, why Tegmark needs four levels in his approach. Gödel's incompleteness theorems are enough to predict that his ToE will have more than one model. It is our very presence, causing true but unprovable facts, that makes it inevitable.

    But then again, Tegmark's detailed interpretation of how it works, goes off in directions that are inconsistent with Gödel's incompleteness theorems:

    In[3] (sec. VII) he gives a more detailed response, proposing as an alternative to MUH the more restricted "Computable Universe Hypothesis" (CUH) which only includes mathematical structures that are simple enough that Gödel's theorem does not require them to contain any undecidable or uncomputable theorems. Tegmark admits that this approach faces "serious challenges", including (a) it excludes much of the mathematical landscape; (b) the measure on the space of allowed theories may itself be uncomputable; and (c) "virtually all historically successful theories of physics violate the CUH".

    I do not believe in Tegmark's "Computable Universe Hypothesis" (CUH).

    I believe that it is exactly the other way around.

    It is the very fact that our universe is not computable, i.e. that it is a model of the ToE which contains true facts but that are unprovable from the ToE, that determines the very nature of our universe. It is rather a multi-world system that very much looks like the religious take on heaven and hell.
  • Free will and scientific determinism
    what happens is all predestined or scientifically determined. — christian2017

    The (ToE) Theory of Everything cannot calculate what we will be doing, because we have free will. The idea is rather that God can skip ahead and see what we have done:

    According to this belief, a person's action is not caused by what is written in the preserved tablet (al-lawh al-mahfooz), but rather the action is written in the tablet because God already knows all occurrences without the restrictions of time.

    The idea that the ToE would be able to pre-calculate what we will be doing, is a serious problem, because in that case, there would be no true but unprovable facts (=unprovable from the ToE) in this universe, which would then be the only model of the ToE. The ToE needs to be incomplete for it to have multiple models (=universes), such as heaven and hell. Fortunately, our free will automatically implies incompleteness of the ToE. In that sense, we may even look at ourselves as the special ingredient that was needed to complete this universe.

    A Baby has free will but its actions are completely predictable. — christian2017

    Well, its actions still need to be fundamentally unpredictable, but it would be possible to know what it will do, by peeking ahead. If you can move forward/backward in time without restriction, you will also perfectly know what happened, or what will happen, while all of that is still fundamentally unpredictable.

    Modern science is clearly just a Platonic-cave shadow of the real ToE. Still, the real ToE may actually not be that much better either. The most accurate ToE will still be surprisingly lousy at predicting the future. The Preserved Tablet is deemed to be fully accurate by means of looking ahead (=by using a cheat sheet).

    Stephen Hawking said something similar in his lecture, Gödel and the end of physics:

    Some people will be very disappointed if there is not an ultimate theory that can be formulated as a finite number of principles. I used to belong to that camp, but I have changed my mind. I'm now glad that our search for understanding will never come to an end, and that we will always have the challenge of new discovery.
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    Since ~G says that G is provable then, if ~G is true, G is provable. Now ~G is true (in that model) therefore G is provable (in that model). It seems you disagree with this. Which part and why? — Andrew M

    Concerning "G is provable (in that model)", it should be phrased as "G is provable (in the theory of which M is a model)". Sentences are true or false in a model. Sentences are provable or unprovable in a theory.

    Concerning "Arithmetic unsoundness for models with ~G true", the very first remark to make is that the model is unsound. The model contains a sentence ~G as true, while it is false. That is unsound.

    Inconsistency, however, means that both ~G and G would be provable from the theory. This is not the case, because neither are provable. Hence, the theory is consistent but one of its models is unsound.

    The nonstandard model is indeed unsound but that does not make the theory inconsistent.

    • Unsound model: it has true sentences that are actually false.
    • Inconsistent theory: it is possible to prove a sentence as well as its negation.

    Concerning "Since ~G says that G is provable then, if ~G is true, G is provable", no. The model says this, but it simply says something wrong.

    G is not provable. ~G is also not provable. Therefore, ~G being true, is simply wrong in the model.

    It just means that the model is unsound, meaning, that it contains a statement that of which it says that it is true, while it is actually false.
  • The futility of insisting on exactness
    This video appeared on reddit recently. It offers some thoughts about whether we can ever go beyond being pragmatic about defining words. — frank

    This problem occurs in natural language, because natural language tries to establish correspondence with the real, physical world.

    This problem does not occur in formal languages, because a formal-language sentence does not "mean" anything. It just acquires (or does not) its truth status from other formal-language sentences that already have such status. Example: S1 is true, S2 is true, S3 is false. What is the truth status of S1 and not S2 or S3?

    It is a tremendous advantage that S1, S2, and S3 do not mean anything.

    Natural language obviously has its applications but is often useless in situations where you should rather use a meaningless formal language. In that case, the solution is simply to strip away all meaning.
  • What's the missing Cause?
    Btw, it's possible to be responsible but not guilty (i.e. blameworthy) e.g. defective brakes responsible for a car crash - makes no sense, however, to claim that the car or its failed breaks are to blame. — 180 Proof

    We may assume the existence of responsibility, guilt, and blame, and the subtle differences between them, but we do not seem to have a deeper explanation, i.e. justification, for these beliefs. They just appear out of the blue into our minds and behaviour. Even children understand blame. Is it innate? Even a feeling like shame would not make sense without free will.

    If free will exists, it fundamentally alters the nature of our universe.

    Free will means that our universe is a model of a necessarily incomplete theory. As this model then contains true facts that are not provable from its theory, it means that this theory has other models, i.e. other universes, in which these facts are false.

    Beings, who have the impression that they have free will, may pretty much automatically tend to believe that there are other worlds (such as a heaven and a hell) simply because they intuitively sense the mathematical hints which suggest such belief.
  • What's the missing Cause?
    There is no room for choice or 'free will'. — philsterr

    If free will does not exist, then an individual is not responsible for what he does. That would mean that there is no need for a legal system to judge anybody for his crimes. That is, however, not the mainstream belief. We rather seem to believe that people can be held accountable for what they do.

    In other words, free will seems to be deeply embedded in our beliefs.

    Of course, I have no explanation whatsoever for this basic belief. In fact, there is no explanation nor justification for any basic belief. We just seem to believe it.

    There is nothing special about the status of free will as a basic belief. Logic is a system of fourteen basic, speculative, and arbitrary beliefs with no further justification. Number theory is one of nine basic beliefs (Peano) that cannot be explained.

    These beliefs appear to us as arbitrary, but they are most likely rooted somewhere in our deeper nature:

    "Fitra" or "fitrah" (Arabic: فطرة‎; ALA-LC: fiṭrah), is the state of purity and innocence Muslims believe all humans to be born with. Fitra is an Arabic word that is usually translated as "original disposition," "natural constitution," or "innate nature."

    The belief in the existence of free will, and the fact that we act upon that belief, and even construct entire legal systems that assume it, are simply part of human nature, most of which cannot be explained, justified, or clarified. Humanity is largely a mystery to itself.
  • Material alternative to theism
    Conclusion: the world does not need anything spiritual in order to be explained — Gregory

    Why would any of that necessarily follow from your ramblings on Einstein and/or Hawking?

    Do you really believe that your simplistic view on their work would be universal?

    Try to say something "difficult", which requires understanding other concepts that are "difficult", which can then be considered somewhat original.

    Seriously, there are good reasons why liberal-arts people and their ramblings are derided and wholesale treated with contempt. What they do, is just too easy. When everybody and their little sister can also do it, why would you, or your ramblings, deserve any respect? The reason why you do not get any respect, is simply because you do not deserve any.
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    Therefore there can be no models where ~G is true. — Andrew M

    There are, and they are arithmetically unsound: Arithmetic unsoundness for models with ~G true.
  • The Destructive Beginning of Humanity
    I’m not suggesting an all or nothing, just that destruction is much easier than construction. — I like sushi

    Life is inherently violent.

    Inter-species violence is necessary for predators to feed off prey and to remove competition for prey from one's territory. Intra-species violence is an important ingredient in the allocation mating rights. This principle is euphemistically called "competition" in biology: https://en.wikipedia.org/wiki/Competition_(biology)

    Violence exists because it is necessary.

    There are rules in human society that seek to reduce violence. However, such rules can never be allowed to impede or obstruct the very principle of life, which always takes precedence. Therefore, the rulers in human society are continuously at risk of being smashed to smithereens. That is one reason why governing is a dangerous activity. If government tries to enforce rules that are contrary to the principles of life, it will sooner or later face an explosion of "natural" violence. I personally believe that we are again very close to a historical point at which the principles of life will regain the upper hand by attacking and destroying the ruling class.
  • Free will seems to imply that this is not the only world
    Do you agree that saying there are two universes that satisfy theory T does not necessarily imply that the two universes actually exist? That is my point. — leo

    Well, everything that is provable about one universe in the theory will also be provable about the other universe.

    For example, if it is provable from the theory that our universe exists, then it will be automatically provable that the other universe also exists. Another example would be the existence of a particular galaxy. If the theory proves that it exists in our universe, it also proves that it exists in the other universe. It will be exactly the same proof.

    For instance there could be a finite universe and an infinite universe that both satisfy a theory T, that doesn’t imply that both universes actually exist, it could be there is only one of them. — leo

    These universes will be "largely" isomorphic. For models of natural numbers:

    The elements of any model of Peano arithmetic are linearly ordered and possess an initial segment isomorphic to the standard natural numbers. A non-standard model is one that has additional elements outside this initial segment. The construction of such models is due to Thoralf Skolem (1934).

    In my impression, a finite universe and an infinite one cannot be isomorphic. But then again, models do not need to be perfectly isomorphic either. It is more about satisfying Skolem's construction constraints (which I haven't investigated in detail yet), mutatis mutandis. Not all other possible universes are sufficiently isomorphic with ours to be models of the same theory, just like not all sequences of numbers are sufficiently isomorphic with the set of natural numbers to be a model for arithmetic theory.

    What seems to be needed, to satisfy Skolem's requirements, is that a carbon copy of our entire universe is contained in the other universe, or the other way around.

    Our universe is finite, and our time is finite, because it progresses. If our time were infinite, it would not be able to progress by addition of time slices. If the other universe is infinite, its time will also be infinite, and therefore, will stand still. It is pretty much impossible that such two universes (a finite versus an infinite one) would be isomorphic in any way.

    Saying that something exists in the realm of mathematics does not imply that it is actualized in reality. — leo

    Agreed, unless it is about the ToE. If a proposition is provable in the ToE, then it will necessarily be true in our reality. We do not have a copy of the ToE. Therefore, we cannot use it to prove facts in our world. What I am doing here, is working the other way around: There are facts that even the ToE cannot prove, but that are nonetheless true in our reality. Hence, these facts must be false in nonstandard models of the ToE (In that case, we accept our universe as the standard model for the ToE). Hence, these nonstandard models must exist. Furthermore, everything that is provable in the ToE about our universe, is not only true in our universe but also in all these other nonstandard universes.

    I understand your argument, if we know that our universe satisfies a theory T and we have free will then we can conceptualize other universes that satisfy this theory T, but there is a missing step between existing as a concept and existing in reality. Unless you assume that everything that we can think exists beyond our thoughts. — leo

    The ToE has special status. The ToE can prove everything that is provable about our universe. Every provable theorem in the ToE corresponds to a true fact in our universe. Hence, if you can prove a claim from the ToE, then you can simply see it in our universe. It will be undeniably true.

    Other theories are merely Platonic abstractions that do not necessarily correspond with the reality of our universe. In fact, there is no reason to believe that they correspond with the real, physical world. We use empirical methods (by experimentally testing them) to infuse some correspondence in such theories. This is not necessary for the ToE, because the ToE automatically corresponds with our reality.
  • The Destructive Beginning of Humanity
    Do you agree that we grew from a destructive disposition rather than a more cooperative one? — I like sushi

    A herd, a troop, or a gang are collective defence mechanisms. A single buffalo cannot fend off a pride of lions, but a herd surely can. Before the discovery of fire, we probably did not eat meat, and therefore, we probably did not hunt. We still needed to fend off predators by forming gangs and defend against them collectively. It is not clear how mating worked back then, but it could have involved aggressive combat between males. Therefore, except for a possible mating season, I think that mankind was originally mostly cooperative. Therefore, I disagree.
  • Free will seems to imply that this is not the only world
    If I am understanding it correctly, your argument takes this form:
    1. There is a Theory of Everything (ToE).
    2. This world is the ToE’s model.
    3. If we have free will, then the ToE is not able to calculate what we will be doing.
    4. What we do is true in our universe but not provable from the ToE.
    5. The existence of true but not provable statements in the ToE means that the ToE is incomplete.
    6. Incompleteness of a consistent theory automatically implies the existence of more than one model.
    7. Therefore, if free will exists, then alternative worlds (that we may call heaven and hell) also necessarily exist.     — Marissa

    Yes, and you actually expressed it more clearly than me. I have a lot of trouble saying this succinctly, and I rarely feel that the idea came across correctly, but this time, I actually do. This is indeed what I meant to say. Thanks!

    In the meanwhile, I also discovered Tegmark's ultimate ensemble theory, which seems to say something similar. However, I probably disagree with Tegmark's view on the effect of Gödel's incompleteness theorems. He says we can simplify the universe to a "Computable Universe Hypothesis (CUH) which only includes mathematical structures that are simple enough that Gödel's theorem does not require them to contain any undecidable or uncomputable theorems."

    This is pretty much the opposite of what I argue. It is the existence of undecidable statements that leads to the idea of multiple universes. So, simplifying them away would go against that.

    I think that if free will exists, it doesn’t mean that heaven and hell are the alternative models. The alternative models to this world could be anything. — Marissa

    Agreed.

    The actual characteristics of these alternative universes do not result from Gödel's work. His work does not go as far as describing the complete difference between the various models. He just detects that they must be there.

    I don’t think it is safe to assume from the fact that we have been given free will that the other models are just where we go after we die. — Marissa

    Agreed.

    This is another proposition that goes far beyong Gödel's work. It is indeed not possible to reach any conclusion about this just with model theory. The tool is much more limited than that ...

    Basically, I don’t think this argument warrants the conclusion that heaven and hell exist. I definitely believe that the ToE being incomplete warrants other models of this world, but I would say something more along the lines of the multi-universe hypothesis. I would conclude that God has made other models, but they are not heaven and hell. I think they are more so just other universes like ours with slight variations. — Marissa

    Agreed.

    From model theory, there is indeed no answer to this remark. The heaven and hell concept would fit into the this multi-universe hypothesis, but any other system of universes would too. The limitations of model theory do not allow us to conclude anything else, merely by using model theory.

    I think your argument is a really good way to prove the multiple universes hypothesis which in turn helps to prove God’s existence. — Marissa

    I think that model theory does indeed not help directly proving that God exists. I think that, at most, it could prove that multiple universes exist.

    I actually do not even feel the need to prove that God exists. As far as I am concerned, you believe it or you don't. Personally, I instinctively believe that God exists, and that suits me absolutely fine. Seriously, I am not looking for a proof that God exists, simply, because it is of little use to me. There are questions on which I completely trust my instincts and where formal arguments would not even sway me.

    Furthermore, model theory is just a tool. It allows us to pick a few otherwise seemingly unimportant structural details from within the universe and draw surprising conclusions about them.

    It is a similar exercises as looking around you on earth and picking a few innocuous details from which you can decisively conclude that the earth must be a globe, and that it cannot possibly be flat:

    • Watch a ship sail off to sea
    • Climb a tree
    • Watch a sunset
    • Measure shadows across the country

    Once you are aware of the hypothesis that there is more than one world, there are most likely clues that you can see from within our world. These details will undoubtedly be innocuous. Otherwise, people would already have picked them up. I consider model theory to be one such clue, but there could be more.
  • Free will seems to imply that this is not the only world
    Okay, but then it seems you assume that this set of rules existed prior to the universe which would be an instantiation of these rules, whereas we have no evidence of these rules existing before, rather we attempt to infer a ToE from the universe we do observe. — leo

    These rules did not have to exist before.

    If you see a model M, then you can argue that they satisfy a theory T. Fine, but now you also see that there are facts in the model that cannot possibly be predicted by such T. That creates the situation that there are statements that are true in model M but not provable in theory T. According to model theory, this means that there must be at least one other model M' which also satisfies theory T but in which these facts are false. That is why these facts are true in M but not provable in T.

    The term "free will" in this context means: there are facts in this universe for which no theory about that universe could ever predict them. Hence, according to model theory, there are other universes that satisfy the theory that governs our universe.

    There are many universes consistent with an incomplete theory, but even if somehow we found a ToE, and even if somehow we knew that the rules of the ToE existed before the universe, it still wouldn't prove that there are other universes, because it seems to me the incompleteness of the theory only implies that many possible universes are consistent with the theory, not that these universes exist as more than possibilities. — leo

    According to model theory, if there are no other models that satisfy the theory, then all true facts in the single model will be provable/predictable from that theory. As soon as you detect a true fact in that model, however, that cannot possibly be predicted from its theory, then there must exist other models. Otherwise, such true but unprovable facts cannot exist.

    The theory of our universe is consistent, because otherwise it cannot have a model, i.e. our universe, which clearly exists. If free will exists, then our universe has true facts that are unprovable by any theory about it. Therefore, there must be other models, i.e. other universes.

    However if we have free will it seems to directly imply that we can create other worlds. — leo

    We cannot create these other worlds.

    However, without the existence of these other worlds, we cannot have free will. Our free will produces true facts in this universe that cannot possibly be proven in any theory about this universe. This is only possible, if there are other universes that satisfy the same theory as the one which our universe satisfies.

    It is the same for natural numbers. Gödel proves that there are true facts about natural numbers that are not provable from the theory of arithmetic. Therefore, there must exist carbon copies of these natural numbers, i.e. alternative models, in which these facts are false. The existence of these nonstandard models of arithmetic is not optional. A true fact that is not provable means that the same fact is false in another model.
  • Free will seems to imply that this is not the only world
    Shouldn't it be that a ToE is a model of the world rather than the other way around? — leo

    Well, in normal English, yes. In model theory, no. In model theory, a theory T is a set of rules, while a model M is a set of values, i.e. an "interpretation", that satisfy these rules.

    The universe itself is not a set of rules. It is a set of values that satisfy the rules of the ToE.

    Then the fact, that there are true facts in the universe (model), that cannot be proven from the ToE (theory), implies that there are other such models.
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    What I don't get is why the negation of G shouldn't be interpreted as saying that G is provable. Since G is saying that G is not provable, then it seems to me that to negate G is just to say that G is provable.

    We're obviously interpreting ~G differently, but I don't understand how you're interpreting it, nor what you think I'm specifically getting wrong in the above.     — Andrew M

    Yes, there is a problem there. In a nonstandard model it would say that G is provable, while it isn't. Wikipedia says the following about that problem:

    Arithmetic unsoundness for models with ~G true
    Assuming that arithmetic is consistent, arithmetic with ~G is also consistent. However, since ~G means that arithmetic is inconsistent, the result will not be ω-consistent (because ~G is false and this violates ω-consistency).

    ω-consistency is inconsistency at the level of a combination of universally quantified propositions:



    It is different from outright inconsistency:



    Having models with ~G true causes trouble, but does not end up rendering arithmetic inconsistent, only ω-inconsistent.
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    Is that the same as saying, "If, in a nonstandard model, G is false, then G is provable there"? — Andrew M

    No, provability means: true (or false) in ALL models. The lack of provability in theory T is caused by the existence of a mixture of true and false in its models. True in some models and false in others.
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    If that is correct, then it seems that ~G can't be true in any model of the theory, since G isn't provable. — Andrew M

    If, in a nonstandard model, G is false, then ~G is true there.
  • Why do people still have children?
    No need to evoke “final solutions” in regards to public education. Families can supplement public education with their own training. — NOS4A2

    Adding insult to injury, the politicians even collect taxes for that public-school depravity. I don't want to use it and I don't want to pay for it. There is only one solution for the problem of the arrogance of these politicians, because all respect is ultimately always based on the fear for reprisals.

    But then again, it is much more than a conflict between politicians and the people who are sick and tired of them. The reason why that kind of politicians exists, is because there is a demographic, a part of the population, that wants them around. Therefore, merely getting rid of these politicians is not enough to solve the problem. If that part of the population "democratically" uses their head count to harass other people, then the problem of their excess head count will need to be addressed.
  • Why do people still have children?
    I'm guessing you spend most of your time in shady parts of Thailand, as well. — Swan

    I only transit in Thailand when flying relatively far, and not even always, because Malaysia and Singapore are also large hubs. Talk to people in these places and you will quickly understand that they thoroughly despise your way of thinking, your view on life, your view on how society should work, and so on. After over a decade of living here, I ended up agreeing with them. As far as I am concerned, they are right while you are wrong.
  • Why do people still have children?
    That's a very weird distraction you're mounting there. Anyways, I don't think anyone outside the alt-right, with the exception of the people mocking them, is using the term "soy-boys", so this is rather a shibboleth. — Echarmion

    Lmao. Found the /r/The_Donald Reddit edgelord user. I don't know what university you went to, but. — Swan

    I reject both alt-right and radical left.

    Neither view reflects that I believe in the primacy of religious law.

    Furthermore, neither view is a documented system, but rather a hodgepodge of changing, circumstantial opinions. Their very structure is already utterly inferior. There is no need to even look at their content to condemn these things.

    "Alt-right" and "radical left" are very western ways of seeing things, that emerged in just the last decades, while I have largely switched to centuries-old, non-western ways of thinking on these matters. I have learned a lot from studying Islamic sources and from living 10+ years in a Buddhist country, to the extent that I consider concoctions such as "alt-right" and "radical left" to be mere bullshit.

    During the day, I spend most of my time with people who only speak an Asian language. Few people speak English over here.

    Absolutely nobody over here would believe in the "alt-right" and "radical left" bullshit. What's more, these terms reflect the worst of western society, i.e. that what is utterly wrong with it.
  • Why do people still have children?
    Is this an actual post or were you just playing alt-right bingo? — Echarmion

    My bingo is not necessarily "alt-right", but your criticism is certainly classified as "left":

    Liberal and left-leaning observers have found themselves doing something they never normally do: criticising Muslims. Specifically Muslim parents in Birmingham who have successfully pressured the local primary school to stop teaching their kids about homosexuality and transgenderism. Apparently it is outrageous for parents to exercise moral authority over their very young children and instead they should trust the state to impart the correct moral wisdom to their offspring. That’s the undertone of the coverage of this controversy: that officialdom knows better than a child’s own parents how that child should be raised and morally instructed. The parents of these pupils have been kicking up a storm over the school’s ‘challenging homophobia’ programme, which involves teaching the kids about gay relationships and the transgender lifestyle. They have protested outside the school with placards saying ‘No to the promotion of homosexuality to our children’ and ‘Education not indoctrination’.

    So, according to you these Muslim parents are "alt-right"?
    Not so sure about that, really.

    As far as I am concerned, the final solution for the problem of public-school indoctrination camps, i.e. die Endlösung der Indoktrinationsfrage, is to shut them down. We simply need a "final solution" for that problem.
  • Why do people still have children?
    What's wrong with human beings existing?

    Why on Earth even the whole discussion?     — ssu

    These "anti-natalists" are incredibly short-sighted. When they will be old and retired, the only reason why they would not starve to death, is because there will be a younger generation keeping the boat afloat. That is why I deeply resent state-run pension systems. It allows people like them to claim that they do not need children, because they expect someone else's children to pick up the bill. Fortunately, these state-run retirement systems are slated to go bust anyway. Good riddance!
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    So, per the earlier Wikipedia quote, what does it mean that the Godel sentence (G) is false in some (non-standard) model of Peano arithmetic? Since that implies that G is provable, isn't that an inconsistency? — Andrew M

    No, ~G would still not be provable, because to that effect G needs to be false in ALL models.
    Provability of G means: G is true in ALL models
    Provability of ~G means: G is false in ALL models
    If it is true in some and false in others, that means: it is not provable nor disprovable in the theory.

    Truth is attached to a model. Provability is attached to the theory, which may have more than one model. If a theorem has mixed truth status in the models then it will not be provable or disprovable in the theory.

    Example.

    Theory T has model M1 and M2.

    Sentence Sa is true in M1 and true in M2. Hence, Sa is provable in T.
    Sentence Sb is false in M1 and false in M2. Hence, ~Sb is provable in T.
    Sentence Sc is true in M1 and false in M2. Hence, Sc is not provable and ~Sc is not provable in T.

    What is a theory? A set of rules.
    What is a model? A set of objects (with operators on them)

    At first glance, PA arithmetic theory, which is a set of rules, describes just the natural numbers. However, that turns out not to be true. There are other sets of numbers that also satisfy the rules of PA. Hence, the natural numbers are considered the "standard" model, while these alternatives that also satisfy these rules, are considered "non-standard" models.

    Imagine that you try to describe a car by giving rules which objects must satisfy in order to be considered a car. It must have wheels. It must have a steering wheel. And so on. At this point, the set of Ford vehicles (model 1) satisfy the rules, but also the set of Harley-Davidson motorbikes (model 2).

    No matter how precisely you design the rules of PA arithmetic, there will always be other models than the natural numbers that will satisfy these rules. The set of objects described will be unique only up to an isomorphism. Any theory that is complex enough will exhibit the same problem of having multiple models. If a theorem is true in some models but false in other ones, then this theorem will not be provable in the theory. That is the basic idea of model theory.
  • Why do people still have children?
    There is a reason why poor folks or people with lower IQ's have more kids. — Swan

    IQ strongly correlates with the number of years of public-school indoctrination camp. It does not necessarily correlate with anything else. It is therefore mostly a measure for how often a local feminazi herded you into the school's lecture hall in order to listen to a transvestite pornstar expounding the virtues of gender fluidity. Next, you grow up to become a soyboy that no girl wants to have kids with, or an aggressive lesbian that no man would want in his house. Total number of kids: zero.
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    Does that just mean that non-standard models of Peano arithmetic are inconsistent? Or is there more to it than that? — Andrew M

    A model cannot be inconsistent. Only a theory could be.

    A model in PA is a carbon copy of the natural numbers. It is just a structure, which is a set, such as: 1,2,3, ... along with a collection of operators {+,-,*,/} that operate on that set. structure = two-tuple: (set, operators).

    The standard model of PA is ({1,2,3,...},{+,-,*,/})

    A theory is a collection of theorems, i.e. sentences about a model. PA is a theory. If PA is true in structure M, then M is a model of PA. If PA does not hold true in M, then it would simply not be a model of PA.

    Hence, if non-standard models of PA were inconsistent with PA, they would by definition not be models of PA.

    There is no such thing as the consistency of a model. They fit the bill (of the theory) or they don't.

    Can there be an alternative arithmetic model where the Godel sentence is neither true nor false? — Andrew M

    A theorem S will be unprovable in theory T, if S has a different truth status across T's models. I am not sure that model theory implies that this is the only possible reason for unprovability.

    I am not sure about the answer. I am not sure that the existence of nonstandard models is the only source of unprovability/undecidability in PA. This is about the limitations of model theory. This is a hard question!
  • Why do people still have children?
    From a logical point of view, there is no reason to have children. — John Pingo

    Life is a system.
    In that system it works exactly the other way around as you think.

    If you do not want children, and I want them, then your views will not be represented in the next generation, while mine will. Hence, in life-as-a-system your point of view is self-defeating while mine is self-perpetuating.

    Either you reason within a system, or else about a system, because in all other cases, you are doing system-less bullshit.
  • Attempt at an intuitive explanation (ELI12) for the weirdest logic theorem ever (Gödel-Carnap)
    But that contradicts the above premise that true sentences are provable. — Andrew M
    Alternatively, if the Godel sentence were true then it would not be provable. But that contradicts the above premise that true sentences are provable. Therefore it cannot be true. — Andrew M

    There is a complicating twist to this.

    A theory such as PA can have more than one model. Say that a theory has five models. A sentence could be true in one model but not in the other four models. Semantic completeness means: if a sentence is true in all models of the theory, then the sentence is also provable in the theory.

    So, what does it mean that a statement S is true but not provable in theory T? It simply means that theory T has other models than the one you are considering, say, the standard model, and that in at least one of these alternative models, S is blatantly false.

    Gödel's incompleteness theorems also imply the existence of non-standard models of arithmetic. The incompleteness theorems show that a particular sentence G, the Gödel sentence of Peano arithmetic, is not provable nor disprovable in Peano arithmetic. By the completeness theorem, this means that G is false in some model of Peano arithmetic.

    The standard model of PA is N, the natural numbers.

    You can create an example non-standard model for PA by axiomatizing the existence of a transfinite cardinal in PA in addition to N, the natural numbers. From the compactness theorem follows that this non-standard model is still a legitimate model of PA.

    But that contradicts the above premise that true sentences are provable. — Andrew M

    So, no, because such sentence could be true in one model of the theory and false in another. Therefore, true sentences are not necessarily provable. According to semantic completeness, provability means: true in all models of the theory (without exception).

    Note:

    Objects can only be defined uniquely up to unique isomorphism. So, all these models satisfying PA are isomorphic with the natural numbers, but are not necessarily the natural numbers. These carbon copies of the natural numbers each start at another transfinite cardinal, and start counting up from there.

    Everything you claim from the axiomatic PA definition of natural numbers -- for such claim to be provable in PA -- must also hold to be (logically) true for each of these carbon copies of the natural numbers. Otherwise, it will only be true for the original natural numbers, but not provable from their axiomatic definition (i.e. provable from PA).
  • Sub Blue Laws
    Libertarians are noted to threaten departure from certain conservative values with violence. Now do you see what i'm saying? — christian2017

    Ok. I thought that it just some baseless criticism on having a seven-day week with one day of rest. Sorry for that.
  • How should we carry out punishment?
    ou haven't escaped the fact that moral judgements begin with feelings — Isaac

    I am opposed to emotional judgments in law.

    Each time the text delivers that you should do X, your mind will deliver either a sense of agreement or a sense of dispute. — Isaac

    Religious people trust their scriptures. Therefore, this is not a problem.

    Notwithsatnding the above, you still have to translate the words, sentences and paragraphs into some understanding in your mind as to what to do. — Isaac

    The system verifies if a particular behaviour is permissible or impermissible. So, it has only one predicate function:

    verify(%behaviour,%permissible, %justification) --> valid/invalid
    • %behaviour: what you want to do
    • %permissible: yes, if deemed permissible. No, if not.
    • %justification: logical argument leading up to the assessment of permissibility

    So, you supply behaviour, purported permissibility, and justification to the system, which will then verify if the ruling is provable from religious law. Note that the system cannot produce %permissible or %justification by itself. It is not possible to automate the discovery of knowledge. Coq is merely a proof assistant. It is not possible to create a complete theorem prover.

    In other words, the system only verifies the answer provided by the rabbi or mufti. What you do with the answer, is completely up to you (as has always been, of course). A jurisprudential ruling is not and has never been binding.

    You're assuming, without any justification offered, that the human mind is not itself a system. Simply because you don't fully know it's workings does not mean it is demonstrably not a fully complete system. — Isaac

    Since the human mind is capable of rationality, it can certainly compute inference results in axiomatic systems. I have never said that it cannot be done, if only, because people do that every day. My take is rather that the human mind cannot be just an axiomatic system, since the human mind does things that mechanical systems cannot do.
  • How should we carry out punishment?
    Well, there is another problem with the Islamic system-: What does it accomplish, exactly, besides making the victim's family -since this is mostly about murder- feel better, if the person pays the money? — HereToDisscuss

    If it accomplishes that already, i.e. making the victim's family feel better, it would at least accomplish something.

    Them paying will not change their behaviour and won't deter them from doing such things in the future, and is only defendable if one commits to the assumption that punishment is carried out in order to get revenge, which in itself is suspect to heavy doubt and i would like you to justify why we should think of punishment in that way. — HereToDisscuss

    Diyya (victim compensation) (or forgiveness) is an optional alternative to qisas (equal retaliation), but it is not mandatory:

    Quran 5:45: We ordained therein for them: "Life for life, eye for eye, nose for nose, ear for ear, tooth for tooth, and wounds equal for equal." But if any one remits the retaliation by way of charity, it is an act of atonement for himself. And if any fail to judge by (the light of) what Allah hath revealed, they are (No better than) wrong-doers.

    The victim's family will not readily think of forgiveness (or victim compensation) as an act of atonement for themselves, if the perpetrator does not repent. Again, this system has thousands of years of mileage. It was already included in the Torah. I have never heard anybody with first-hand, practical experience with the system, heard complaining about it.

    Also, no, to convert it to formal language -which doesn't need to be done in pure code and i do not get the need to use Coq since classical logic would probably be fine, but that's another matter-, you need to figure out what the text meant by certain statements so that you can use them but that requires textual interpreation. — HereToDisscuss

    The manual approach to textual interpretation is not suitable for a purely mechanical verification procedure. We won't make progress if we keep doing that.
  • How should we carry out punishment?
    Any system that relies on a text written in a natural language is going to require textual interpretation. Textual interpretation is never going to be machine-mechanically verifiable, because the text simply doesn't contain the necessary information. — Echarmion

    It will be necessary to encode the text in formal language. The following example:

    All men are mortals.
    Socrates is a man.
    Therefore, Socrates is a mortal.

    results in the following translation alternative in the Coq proof assistant:

    assert Syllogism {
  all Socrates: univ, Man, Mortal: set univ |
      -- every man is mortal
      Man in Mortal
      -- Socrates is a man
      and (Socrates in Man)
      -- implies Socrates is mortal
      implies Socrates in Mortal
  }

check Syllogism

    The formalism is flexible, though. So, it may be possible to reduce the amount of boilerplate required in the encoding. There is indeed syntactic overhead (and even noise) to consider. Still, experience is gradually growing. I think it may become quite usable some day.

    When we get to legal matters, there is also the additional value judgement of applying a given law to a given set of circumstances, which is also not verifiable. — Echarmion

    "Additional value judgment" is exactly what we want to avoid.

    I stick to the Church-Turing thesis in that regard. If there does not exist a purely mechanical procedure to verify a justification, then the statement being justified is not formal knowledge.
  • Sub Blue Laws
    Many libertarians (conservatives) in some cases reject religion altogether. Some attribute the concept of the Sabbath or Blue laws as religious and in accordance with denying the notion of separation of church and state. — christian2017

    A single-concern argument is not the same as a complete moral system.

    Outside the context of a complete system, it is easy, peasy to argue whatever you want, and you will always be right.

    Instead, try to reason within a system or about a system. You will understand that it is not that easy to do.

    Atheists always seem to propose single-concern, system-less bullshit. That is not critical thinking!

    Take something complex and non-trivial instead, and then try to detect an inconsistency. That is hard and intelligent work. That is something that we can respect!
  • Can reason and logic explain everything.
    Well, yes. I suspect he or she is including science, but I think that facet has to be described/included, since I think this opens up more issues in deciding. — Coben

    Well, yeah. Immanuel Kant already pointed out at length in his "Critique of Pure Reason" that science is not pure reason. On the contrary, science seeks to explicitly systematize experimental observations.

    It is not possible to target the real, physical world and still hope to stick to pure reason. It cannot be done.
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