"No rule without an exception, except this rule." by Stefan Weckbach

Interesting. If you are right, then a former ‚less fundamental' (space in GR) could turn out to be 'more fundamental' than we thought - if your approach takes space and time as an independent background like Newton did. Does it do so?

Andrew, you claim very much with your comment... You claim e.g. that

1. I have not read Gödel's work

2. I do not understand it

3. My essay is a loose paraphrase of what Gödel was bringing up

All three points you made are false.

Even for the case that Gödel's work would turn out to be - for whatever hitherto unknown reasons - false, my essay does not in any way depend on the correctness of Gödel's work. The latter just reassures my conclusions, it is not in opposition to my conclusions. I think you misunderstood what I intended to say with the realm of fundamental truth. This is not merely a realm of logical / mathematical tautologies, but an existential realm that incorporates consciousness as a fundamental ingredient. Not all tautologies are fundamental truths, but according to my essay, all fundamental truths are perceived (and are) as self-evident tautologies in the realm of fundamental truth. Self-evidently, this realm must be located beyond space and time, since space and time could turn out to be just temporary appearances. They are, in my opinion, for the reasons I layed out in my essay, not fundamental truths, since in my opinion, a fundamental truth should be timeless.

I have not found any hints in Gödel's official mathematical work that states that truth must be in union with consciousness, what my essay says is independent from what Gödel brought up with his work. Therefore the points you made are twice devoid of any meaning for the conclusions in my essay. Gödel's work is important, but for me, Gödel is not the one and only authority when it comes to the question "what is fundamental".

Good luck also for you!

Hi Georgina, thanks for reading and of course for commenting! Your effort of commenting is appreachiated by me.

I indeed took the terms frog's view and bird's view from Max' paper. They encode a huge problem not yet solved, the dichotomy between the subject (consciousness) and the object (matter), between relative, subjective truths (in reference to what is fundamental) and the necessity for the existence of such fundamental truths, means the fact that there is an external world independent of relative, subjective truths (objective truths) and whether or not these objective truths come out of literally nothing in the sense I defined it in the essay.

Many accounts on these problems assume the realm of what is most fundamental to be infinite. I am not quite sure if Max does also, but I take both possibilities into account. If mathematics is infinite, then one cannot speak meaningfully of an 'outside' for the black box I described as gedankenexperiment, hence there cannot be a bird's view, since then, the mathematical landscape is infinitely infinite, so to speak. Otherwise, if what is most fundamental would be finitely describable (albeit in a coarse-grained manner), one could refer to an 'outside' meaningfully in the sense whether or not there are further objective reasons for this most fundamental thing (in the case of Max's paper it would again be mathematics) to be fundamental at all.

If maths is finite, I think this would be a surprise for everybody. But I conclude just this in my essay: mathematics is a finitely, physical construct, as physical as one assumes matter, enery, wave functions and laws of physics to be physical. I consider 'infinity' from a logical point of view as merely an alternative term to express that something is fundamentally undefined - and undefinable (at least in our limited world).

You raise the question of many worlds. Many worlds fall naturally out of a global wave function, the latter seen as fundamental. The question is whether or not such a global wave function does exist ontologically. I cannot exclude this, but I doubt it, due to the arguments I gave in my essay against the exclusiveness of the complete formalizability of all that exists.

I like your painting analogy. This is what we normally do by inferencing due to antivalent thinking. The point I wanted to make in my essay is that you never can picture such a painting objectively with only antivalent thinking at hand. The best example for this impossibility seems to me the very essay contest here, where different assumptions are hold about what is true and what is false.

My own approach stems from the considerations of what properties a realm must have that does not suffer from the dichotomy of true and false propositions. My conclusion is that falseness as an option should evaporate into 'thin air' for at all being able to meaningfully speak about a 'most fundamental' as the basis for objective reality. Just consider what an angel in a spiritual realm ('heaven') would experience: she wouldn't experience the possibility that her realm could be just a fake, a kind of computer animation (since then it wouldn't be heaven anymore but just like earth...). She wouldn't experience this possibility, but not due to an error in her perception, but due to the fact (the truth) that this realm refers not anymore to 'time', but to eternity. Eternity in this sense means eternal truth without falseness in it. So the reason why you can't objectively paint this realm is that there is only 'white' in it, but no black.

You state that "I think the truth can be arrived at by finding all of the falsehoods and putting them out of the way. Which is how the scientific method at its best works." Albeit there is some truth in this statement, personally I wouldn't fully agree, since obviously there are situations where you aren't able to unequivocally identify some falsehood in the sense of a decisive proof for a counterexample, or a decisive proof for a certain assumption to be true at all. The problem is not that we can't observe in many cases *how* nature behaves, the problem is to unequivocally prove for at least some cases *why* it does so.

Thanks again for your thoughtful comment and good luck in the constest!

Kind regards, Stefan

Hi Georgina, i found your article and am going to read it now with much eager and will reply here and at the other site. It takes much time for the second bunch of essays to go online. I hope your essay contribution will be published soon, so i can also read your 'official' contribution to the essays current theme.

Hi Georgina, thanks for leading me to your 2 page article, which i just read. I have to think about it at bit longer, but just want to mention my spontaneous thoughts about some issues you raised.

Your attempt to model human intelligence and scientific progress as a result of a hive mind of a swarm of intelligent beings is interesting. I think it has pro's and con's. the pro's are surely that the progress in sciences was due to a huge swarm of beings, working on the question how nature works, falsifying some options and finding out that other options obviously do work and have some truth in them. But I would not glorify such a 'swarm intelligence' - and do not automatically assume that you indeed do. For me, the con's about the 'swarm intelligence' are directly before our very eyes. Different to, say birds, or flies, humans have the ability to some (assumed) unlimited imagination. That's an advantage, but I also see a certain danger, in that certain 'memes', 'ideas', 'trends' become dominant, trends that are not healthy for mankind. I could mention for example the glorification of money, but moreover, the glorification of science, the glorification of certain hypothesis of science, and in general, the glorification of the *assumption* that science can solve all problems human kind will probably face in the future. I see a trend that many unproven things are taken at face value and that more and more scientists cannot anymore discriminate between logical and physical / ontological necessities. Surely, the latter is impossible in general, but that's exactly the reason why one should handle hypothesis' as hypothesis', and not as some discovered truths.

It's the human ability to imaginate a full blown version of a wishfull future that is also a danger to mankind. Since most of us easily accept rose gardens and science-fiction like versions of ultimate reality, most of us tend to forget (or not even investigate) how such versions came about in the first place. A prime example for me is Max's mathematical universe - but to apologize to him I have to say that his new book (life 2.0) is a good piece of responsible science when it comes to probable future challenges. But let's briefly check what the mathematical universe is at its core. For me, it is a hypothesis that is able to camouflage itself as an established fact. It does so by using Curry's paradox. The latter are propositional statements of the form 'if this sentence is true, then Santa Claus does exist'. Obviously this sentence is true - hence Santa Claus *has* to exist. Examining the logical structure of Curry's paradox a bit closer (what I will not do here) reveals that it is just a kind of tautology of the form "if Santa Claus exists, then Santa Claus exists". Max's mathematical universe hypothesis uses (I think not deliberately) an instant of Turing's halting problem to appear as a proven fact. It states that all existent things are completely captureable by mathematics, even consciousness. This may all be true, but *until* we have captured consciousness in this manner, it remains an instant of the halting problem. Nonetheless, Curry's paradox enables that many recipients of Max's hypothesis to switch from "if this sentence is true, than all things that exist are exlusively and completely describable by mathematics" to the 'truth' of the second part of such a conditional proposition. Worse, you can also switch from "if this sentence is true, then all things that exist *are* exclusively only mathematics." to the 'truth' that "all things that exist *are* exlusively only mathematics". As I have mentioned, I see a tendency in theoretical physics to overlook such kinds of mechanics by not carefully discriminating between logical possibilities and ontological necessities. But I think I move on heretical grounds, since most professionals as well as non-professionals are convinced that mathematics is a kind of 'God-like' entity in a platonic heaven.

Your comments on entanglement and variables are also interesting. In this field, a similar self-confirming pattern as I described in my essay about the 'paradigma' of 'strict determinism' can be observed for a probabilistic interpretation of quantum mechanics. Once the premise is established that this theory is not about universal determinism, but rather about contingent single events in nature which are in most cases not predictable ('explainable'), but nonetheless statistically well defined, one must come to the following conclusion about the statistical method of the theory itself: if a huge trial of measurement outcomes is analyzed for possible deviations from the well defined standards of the theory, the theory should be capable of discriminating between random errors whose probability distributions are known and systematic errors, which can be excluded. The latter however, is not guaranteed by any probabilistic theory, because the theory concludes from observable events to counterfactual events and after that the other way round. This means, it presupposes to have taken into account all possible parameters and therefore assumes to know all governing laws of the counterfactual events. Moreover, even estimating the size of the expected random errors of huge trials of measurement outcomes on the basis of such a theory depends on what one assumes to be part of the theory. Putting it differently, the estimation of expected errors was put into the theory in the first place (necessarily without being falsifiable by 'further' measurements) on the basis of necessarily only measurable facts, and therefore the estimation of expected errors in the measured data base also becomes part of the output of the measurements when it comes to analyze the gathered data. This is again an extrapolation from known or assumed-to-be-known things to things that cannot be known for sure due to Moore's theorem.

Hi Lawrence, thanks for your excellent comments and your thoughts envoled in them. I will give my answers subsequently in this reply according to the points you made.

According to Russell's barber, this paradox necessarily presupposes that *none* of the other men (wich means the group of men in the village *except* the barber) are allowed to shave those other men of the village. Otherwise the barber wouldn't be a barber - *according to Russell's definition*. So, Russell's whole definition of a barber is *ill-defined*, since this is not what a barber must be defined, even for the case that there is only one barber in the village. The point is, that Russell's definition of the barber as "no men in the village are allowed to shave other men - except the barber" (this is the real fixed-point that can be extracted from the context in which Russell's definition seems to be true) does *not imply* that people are *not* allowed to shave themselves. Therefore the barber can shave himself.

What you say about Gödel's theorem and provability is interesting. It all crucially relies on whether or not logics is able to capture some fundamental truths. If logic and with it the mathematical systems which produced Gödel's results in the first place are inconsistent, then of course everything is provable with the help of these systems. So, the presupposition that logics is consistent demands that there are some true statements within those systems which are not provable with the help of these systems.

Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that a system is *not* inconsistent and incomplete. So would the latter proof be a stronger one, in the sense that the system under consideration should be considered as consistent, but incomplete? This is a senseless question, since we observed from the very start that the system generated a contradiction, leading to *everything* at the end of the day. If you can't make anymore a reliable distinction with a certain system, it is then senseless to further use this system.

Gödel's results are only *fundamentally* true under the following two presuppositions:

1. logics is consistent

2. Mathematics is eternal and infinite

If one of these two presuppositions is false, Gödel's results have no fundamental impact whatsoever. In my essay I argue that the second point may be false in the sense that our traditional view of mathematics as an eternal platonic realm is difficult to reconsile with Gödel's results, since every extension of a mathematical system critically hinges on what one considers to be a necessary additional axiom - for making such an extension not only *consistent*, but *eternally true*.

The problem is, if there exists an infinite, non-denumerable number of truths within this mathematical landscape, then also Moore's theorem should hold and every physically or mathematically defined final theory of everything would be a final theory of nothing - when refered to the question why our universe is what it is - and why mathematics is what it is. The suggested advantage of an eternal landscape of mathematics is that it seems to justify that there exists something at all, rather than nothing. What brings me back to the very beginning, since even the quest for the existence of God is in some form an instance of unprovability - in the same sense the eternal mathematical landscape is. In this sense, people knew all along, long before Gödel's results, that there may be things which cannot be logically proven nor disproven, but nonetheless could be true. Surely, the mathematical universe hypothesis, for example, does rest on empirically gathered data, means, on the truth that nature indeed incorporates a certain amount of mathematics. But it is also true that it incorporates a certain amount of consciousness. Max's (the latter I appreciate in very many respects) claim of the MUH rests (beneath others) on the assumption that even consciousness is fully formalizable by mathematics. I doubt this by saying that mathematics can at the maximum merely establish correlations between some brain actions and some mathematical patterns.

The question of how to properly interpret such correlations is a fundamental one. I am currently working on this, but cannot present yet any robust results. Trying to describe a strictly deterministic system in terms of axioms seems to be impossible to me other than taking it at face value and therefore as a true axiom that all that exists is indeed 'merely' a strictly deterministically acting system. It could turn out that a superposition of states yields *less* information about the system then the parts of the system themselves. Therefore it is crucial for me to look how one can incorporate an observer into quantum mechanics, the latter being independent of a strict determinism, but nonetheless being able to have some limited free-will at hand to decide between two mutually exclusive options. And you are right about closed systems. As I described in my essay, it may turn out that defining ultimate reality solely in terms of formal systems may itself be just a closed system. I am working on stepping out of such a system in a logically and meaningful manner in terms of how to properly interpret a global wave function. If I succeed, I surely will publish what I found.

Oh, of course it should be

"Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that *this* system is *not* inconsistent and incomplete."

Instead of

"Otherwise one potentially could prove a system to be inconsistent and incomplete, but could also prove that a system is *not* inconsistent and incomplete."

"If you can't make anymore a reliable distinction with a certain system, it is then senseless to further use this system."

The latter statement is, for avoiding misunderstandings, of course in reference to what the system can and has to say about 'more or less fundamental' things. For example non-euclidean geometry us indeed useful for examining the consequences of GR, but it doesn't (and cannot) say anything about whether or not gravity is merely a statistical description of something else (as annotated in the Contest Guidelines).

I hope to have clarified some rather uncouthed formulations in my previous post. If not - just ask.

Hi Lawrence... and of course I have once more forgotten to answer an important part of your comment, because there are so many issues involved in your comment. So here is my answer to your remarks concerning rule F:

This rule is perfectly consistent and not paradoxical. Try to imagine it like this:

There are 1000 doors. Behind every door, there is a certain rule. Behind the first 999 doors, there are arbitrary rules, with each an exception. Behind door number 1000, there is a rule that captures a regularity common to all the other rules behind the 999 doors, namely that each of these rules have an exception.

The paradoxical character of Rule F only comes about due to the semantical issue of the usage of the word "exception" in the second part of rule F. If you imagine door number 1000 (behind where rule F resides) and compare it to the other rules, it has no exception, since all rule F is about is a compressed commonality all the 999 other rules have. For rule F to have an exception itself would depend on at least one of the 999 other rules having *no exception*, right? Then rule F could indeed no more considered as truly describing a commonality all the 999 other rules have.

In this sense, the fact that *no* rule of those 999 rules has *no* exception (caution, double negation!), necessitates that rule number 1000 (rule F) *has* indeed *no* exception. Remember, Rule F is exclusively only about the 999 other rules' exceptions. In the form I wrote it down in my essay, it may seem that it is also about some exceptions for Rule F itself, because Rule F is as well as all the other 999 rules a rule. Despite the undeniable fact that rule F is indeed a rule, it is clear that it refers the whole lot only to the 999 other rules' exceptions, not to an exception that it has itself - albeit rule F indeed does refer to itself in the form I wrote it down in my essay. But this self-reference is harmless and non-paradoxical.

Replace one of the 999 rules with a rule that has *no exception* - and rule F is forced *to have an exception*. Globally seen, in this system, when just one of the 999 rules are replaced in the manner described, there will always be one rule without an exception. Surely it is not guaranteed that such a replacement results again in the original rule F. This depends on what one does insert as a new rule behind the one of those 999 doors.

Hi Jochen, thank you for your comment and all the very important questions and remarks therein.

Firstly I want to mention that I do not believe in mathematical infinities as ontologically real facts - be it physically or as a platonic fact. This concept of infinities is suspect to me, I view the notion of 'infinite' as an alternative term for 'undefined'.

Although I did not explicitely write about the issue of infinity in my essay, an aspect of it seems to me the problem of infinite recursive reasoning, especially about what is fundamentally true in physics and nature.

To remove any misunderstandings, I certainly believe two things: firstly that there is a true ontology behind all phenomena and hence I consider it as true that "this machine halts" should be either true or false - as long as if follows the valid definitions of turings halting problem and all the subsequent consequences derived from it. Even for the case of Chaitin's results I would say that a machine defined according to his framework must either halt or not - to whatever objective reasons.

So truth is not exclusively a subjective, relative concept, in my opinion. The question is rather whether or not our contemporary picture of reality as exclusively only following the first three causes of Aristotle (as mention in my essay and in footenote 2) is complete or not. And surely, I think that also this question has a definite answer, independent of whether I can know it or not.

I think that for coming closer to truth for whether or not the ontological reality merely encompasses the first three Aristotelian causes, one has to consider the possibility that the first three causes of Aristotle are merely limiting cases of the fourth cause Aristotle gives.

As you surely are aware of, the question about the truth or falsity of any theory that purports to having captured all 'necessary' ingredients to be a complete theory for at least all physical phenomena (and therefore for the contemporarily purported ontological framework of exclusively *non-subjective* causes) must necessarily be causally closed. With 'causally closed' I do not only mean that it encompasses all three Aristotelian causes, it even may incorporate true irreducible randomness - the latter in the sense of some timeless or time-dependent quantum fluctuations.

According to the picture of such a causally closed system, one cannot label other reasons for the modal ontology for whole existence (ultimate reality) than merely refer to either randomness - which must then be governed by some eternal mathematics (probabilities etc.) or to a strict determinism, or eventually to both.

Nevertheless, as you rightfully wrote in your own essay, understanding something is (at least in parts) equivalent to give a step-by-step description. By such a step-by-step analysis I come to the conclusion that for the cases that such a causally closed explanation for the ontological status of ultimate reality should be fundamentally true, it implies the following truths:

1. If someone claims that ultimate reality is strictly deterministic, this implies that she or he had to come to this conclusion just the way she / he did, and no jota other. It further implies that consciousness is an inevitably ontological phenomenon. It also implies that I had no other chance then to write exactly these lines of reasoning to you.

2. If someone claims that ultimate reality is irreducibly random at its core ('quantum fluctuations and the like), this either necessitates an eternal realm where at least the probabilistic framework of mathematics resides, or - vaguely in the spirit of the MUH - it implies that 'quantum fluctuations and the like' *are* in some sense the mathematics with which we assumed to merely *describe* those fluctuations. In fact, this mathematics then couldn't be anymore the traditionally fixed mathematics, but must have a random element. Hence, this kind of 'platonic realm' would be kind of dynamical in which mathematical truths are randomly generated by the mysterious power of mathematics to generate truly random values. Alternatively one could understand randomness in mathematics as an infinite sea of prefixed mathematical relations of any conceivable combination. So, if someone claims that ultimate reality is irreducibly random, what she / he means is either irreducible randomness in the absence of any platonic mathematical realm (ex nihilo truths), or that there has to exist an eternal platonic mathematical realm consisting of infinitely many prefixed mathematical relations of any conceivable combinations.

3. If someone claims that ultimate reality is a mixture of determinism and irreducible randomness, this necessitates that either this mixture came about ex nihilo, or that determinism and 'irreducible' randomness can be reduced to an eternally existing platonic mathematical realm consisting of infinitely many prefixed mathematical relations of any conceivable combinations. Alternatively one could interpret the mentioned claim as being a mixture of eternally prefixed mathematical relations and some ex nihilo created new mathematical relationships. This would necessitate that the eternal prefixed part of mathematics cannot be complete, since otherwise every 'new ex nihilo created' mathematical relationship would already be contained within the eternal prefixed part of the platonic mathematical realm. It is obvious that the latter possibility is completely indistinguishable from an infinite, prefixed platonic realm of mathematics. Any purported claim that it should nonetheless be distinguishable due to the very fact that there is indeed a dynamical external world out there that 'proves' that the platonic mathematical realm has to be understood as a *dynamical* realm - is anthropical reasoning, based on the fact that mathematics is indeed able to give a *coarse-grained* step-by-step description of some physical dynamics.

Let me resume point 3 a bit more detailed.

If it is true that the real meaning of mathematics has to be understood as a dynamical realm of mathematical relationships, this necessitates ex nihilo creations of mathematical relationships which are genuinly irreducibly random. The latter in the sense that every such creation at point t in time could have reasonably been also another relationship, other than that which has been created ex nihilo. So, if it is indeed true - and for the sake of my following arguments I will adopt the truth of the claim - that the real meaning of mathematics is that the latter is of a dynamical ontology which executes ex nihilo creations, then the big question is how this dynamics and especially its ex nihilo creative part is able to facilitate at all observers which can capture this truth. Surely and obviously, this must be impossible, since all we are talking about here is conditionally restricted by merely assuming that the claim in question is indeed true. We are not talking about that we unequivocally have found that this claim *must* be true. It does not help to push the lack of objectifiability for this claim a level up the chain of step-by-step descriptions. Even if we *assume* that there is a multiverse out there and in some multiverses observers indeed unequivocally can capture the truth of the claim in question - this would again not only be merely an assumption, but due to the very axioms of the claim in question, in every 'branch' of such a multiverse, observers could merely conclude what we conclude in our branch.

To make my long story short here: For explaining what generated some dynamics for a physical world to exist at all, one is left with some mysterious power of mathematics to do that and / or with some creation ex nihilo.

If we allow ex nihilo creations, we either allow the existence of a God in the traditional sense, or we allow what I called in my essay 'nothing' as an ontological fact. So the only way to escape both possibilities is to adopt that there necessarily has to exist something eternally from which the existence of our physical world can be derived. This could be the mysterious power of a platonic realm of mathematics - or simply the eternal existence of physical stuff, for example some steady-state universe.

Surely one can also assume that an eternally existing, finite landscape of platonical mathematical relationships, together with some ex nihilo creation, should be the ontologically real deal. But in my opinion, this would merely increase the mysterium of existence - especially the mysterium why there should be eternal existence of something and at the same time there should be the fact of ex nihilo creations.

In a very deep sense, the combination of eternal mathematics with ex nihilo creations merely resembles what human beings have figured out millennia ago, namely the possibility that there could exist an eternal thing - God - that is able to bring about some ex nihilo creation. Albeit the eternal realm of mathematics together with some ex nihilo creation of randomness seems to be able to explain some coarse-grained regularities of nature, I think it completely fails to explain the existence of consciousness and its ability to indeed capture some coarse-grained truths about ontological reality. Take for example the truth that every object falls down to earth or all the other physical facts that enable us to build all sorts of machines that follow in their behaviour at least a coarse-grained model we have about the behaviour of nature. How could this be related to your result that a model facilitated by human consciousness can at all capture some coarse-grained truths about external reality? It is because such coarse-grained models indeed are able to incorporate some coarse-grained truths of external reality and therefore aren't anymore merely models, but truths. The latter surely only if we exclude that there could be possible some miracles that could immediately contradict these truths, miracles either produced by God or by some random ex nihilo creation. If we exclude the latter two options, then our coarse-grained truths are at least true as long as as our accompanied laws of nature are true.

The question then is under what conditions these laws of nature could be only temorarily true. It could well be that these laws of nature can change with time (albeit surely within some rather large time-spans). I cannot exclude this possibility. At least in my essay I gave a minimal interpretation of what it could reasonably mean that those laws of nature could only be temporarily true. This would be the case if mathematics itself would be only temporarily true.

Regarding to the empirical content of physical theories and Popper, I would say that falsifying a certain prediction of a theory falsifies the theory as it stands. Surely there is the possibility to adapt the theory somewhat to incorporate the result of some experiment. One then had to look for another prediction of the adapted theory to be tested for its empirical content. As far as explanations are involved in the original, non-adapted version of the theory, I think it is not always easy to hold such explanations when the theory is adapted to the result of the first experiment. At least if such an explanation is equal to a fundamental principle one assumes to have discovered in nature. So, generally, I think that the falsificationist credo crititcally hinges on whether or not a certain theory has stated such a fundamental principle - or has stated rather a trivial prediction which is rather non-conclusive to decide whether or not the theory has any empirical content.

Concering what you wrote as

"However, I think you're selling logic short. Not all logic is deterministic---there are probabilistic logics, fuzzy logic, etc. Some systems of logic (paraconsistent logics) are even capable of dealing with inconsistencies---although they're a little out there for my taste. I'd want to keep the principle of explosion. And your leap from the examples you give to stipulating that 'every rule has an exception' seems a little quick, and far, to me."

I am aware of these logical systems. They are all concerned with issues like consistency and provability. Using one or the other of these systems surely depends on situative circumstances, not on eternal truths, as long as one does not mix them up into a kind of eternally fixed, logico-mathematical landscape of exclusively only relative truths. But even in doing so, the truth that all truths are somehwat relative must then itself be a fundamental truth. As I tried to lay out in footenote 6 of my essay, it seems to me to be impossible to unequivocally prove such a logico-mathematical landscape to have any ontological reality other than existing in the minds of people that believe in it. Even for the case that such a logico-mathematical landscape unavoidably necessitates the existence of consciousness, the fact of the latter's existence cannot be modeled other then by admitting that there is consciousness which is able to assume something non-conclusive about itself, namely that it should be a product of the assumed logico-mathematical landscape. Stated differently: I think that such a logico-mathematical landscape does merely exist in the imagination of someone who states that it must exist independently of him / her. It is a model of what lies at the very foundations of ultimate reality and the fact that a model is in fact a step-by-step description, as well as mathematics is, the believer in such a logico-mathematical landscape step-by-step infers that heself must be part of such a landscape, since all he has at hand are step-by-step descriptions which lead him in a self-confirming manner to the conclusion that step-by-step descriptions must be the ultimate foundation of reality. On the basis that such step-by-step description is not possible for the believer's own realm of consciousness, he concludes that such a step-by-step description nonetheless must nonethless exist objectively when adding an additional realm of step-by-step dynamics by means of a dynamically behaving logico-mathematical landscape. The latter then surely contains the exact step-by-step description of the believer's own contents of consciousness - including the assumption that such an additional realm has to exist 'independent' of whether or not he believes in it.

The crucial point here is, that in the framework of such a believer, his own belief in his very framework has been brought about by his very framework in manner that is in no way controllable by himself, because neither a deterministic step-by-step dynamics nor ex nihilo creations nor pseudo-randomness leave any room for a kind of limited free-will that is able to decide between two mutually exclusive alternatives. The framework may be consistent, but is incompatible with the kind of free-will I mentioned and with every-day life that demands that we are fully responsible for deciding between two mutually exclusive alternatives.

In my essay, I take consciousness serious in regards to every-day experience and responsibility in the sense that I assume it as a thing that at least has its roots not in the realm of time and space, and also not in the realm of some eternal mathematical landscape.

As you may have noticed, I purport the view that mathematics is merely of temporal truth, since in my framework the existence of mathematics is the result of a free-will based decision of an observer that I identify with the more traditional concept of God (hence, not some artifical God, produced by some omegapoint or something like that). My concept of God is that whatever we call this God, it is fundamentally non-formalizable truth far beyond ex nihilo randomness or mathematically tracable relationships. Of course, the fundamental relationships that are true in the realm of such a God are at the one hand indeed anthropically inferred truths, as for example the existence of love and some kind of free-will, but on the other hand go parallel with the absence of any necessity to describe the real intentions of such a God exhaustively in terms of step-by-step descriptions - with the exception that these intentions can to different degrees be *felt* by human beings. For example when they share love, are happy or even lucky.

Regarding my Rule F, I invented it as a reductio ad absurdum for every attempt to take a viable TOE that exlusively only follows the path of mathematical step-by-step descriptions to ever say something conclusively why human beings have at all the experiences they have, why they at all are existent and feel what they feel. I think as long as such questions are not considered to be valid, one cuts out an important factor of reality. Surely, no TOE in the sense of a scientific, physical explanation of existence is ever conducted to answer those questions, because they are theological in nature. But on the other hand, as I hopefully made clear, the assumption of an eternal realm of mathematics together with some ex nihilo creations is likewise a kind of theological explanation, because they purport to explain human feelings as the result of some mathematical dynamics without ever being able to unequivocally proving it. Every such purported proof must, in my opinion remain in the realm of mere correlations between some brain activities and some mathematical descriptions of what one assumes is causing certain Qualia.

My rule F can be stated without the flavour of self-reference by simply saying "No rule without an exception, but not for rule F" (in a comment above to Lawrence Crowell I explained how to better grasp the content of such a rule, for its only content is about rules and exceptions, means content and form are interchangeable without altering the invariant truth of it). I do not purport that such a rule indeed does exist (although I cannot exclude it), this rule is just a placeholder to question our rigid rule-dependend models of reality and suggest that this thinking can be transcended. In my essay, I made such an attempt to transcend it by pointing to the question what truth is and in which sense its existence is necessary to sufficiently explain existence itself. Self-evidently my conclusion is that at the very foundation of ultimate reality, there should be some fundamental truth, if we at all are able to speak meaningfully about ultimate reality. And self-evidently existence itself is a truth. And self-evidently, if 'nothing' would be indeed possible, this would be also a truth. I further think that 'nothing' as I defined it in my essay and an assumed eternally existing mathematical lanscape are completely equivalent when it comes to the question 'what is the ultimate truth?'. I conclude this because although the popularily purported view of ultimate reality being a mathematical landscape that must be considered as eternal, the latter is the very reason that the whole content of this mathematical landscape, as well as its included properties of conistency, inconsistency, provability and unprovability are at the end of the day not only not just relative truths, but by the very definition of 'relative truth' as abstract relationships that make no distinction between consistency and inconsistency - they are as random as the existence of such a mathematical landscape itself. With randomness I mean here that there is no cause (none of the four Aristotelian causes) that could support this landscape's existence to be eternal and reasonable. Note that these conclusions are made from the bird's perspective, looking at this landscape at a whole (from the frog's perspective there are indeed reasons to assume such a landscape, namely the fact that nature can be at all desribed mathematically). From this bird's perspective I conclude that, although mathematics is concerned with symbol manipuation, nothing within this whole landscape necessitates that there should be a criterion like consistency or inconsistency. I could well also assume that there is an eternal landscape that produces arbitrary different symbols, phenomena and subjective impressions no observer could extract any meaning out of them (like the stone you mentioned in your reply to my comment on your essay page) which are *not* concatenated or permutated, but appear to a potential observer as far beyond our notion of randomness. For excluding the latter scenario (furtherly called 'weird scenario'), platonists had to explain why mathematics comes with the feature of consistency and inconsistency at all. Obviously, my statement that "appear to a potential observer as far beyond our notion of randomness" presupposes that we have this model of randomness at hand, to compare it with the latter scenario. Therefore, by comparing this scenario with the contents of a traditional platonic realm with some randomness in it or not, I see only empirical arguments against the 'weired scenario', but no logical ones. The reason why there aren't such logical arguments at hand is rooted in the problem of induction - the observation of an observed rule does not imply that this rule is eternal or fundamental. Therefore the assumption of the existence of an eternal platonic realm is just an induction, an extrapolation. What guarantees that this platonic realm does not suddenly chance into a 'weird scenario'? I think the only answer that one can give to this question is that logics - altough necessarily not in its antivalent form - must play a crucial role at the heart of ultimate reality. Dropping the assumption that there is a realm of existence without antivalent logics (in the sense of a realm of fundamental truths as outlined in my essay), leaves us with antivalent thinking and the possibility of the 'weird scenario'. This 'weird scenario' then could be equivalently be considered as 'nothing' - playing some weird tricks on us by 'randomly' producing a seemingly consistent world. So the asumption of an eternal platonic realm of mathematics - with or without randomness - is just an extrapolation, an induction, as well as its feature of consistency and its very unchangeable properties are: if mathematical values can be created ex nihilo, can they also again vanish into 'nothing', one is tempted to ask. More serious, if mathematical consistency depends on some values created ex nihilo, can the very feature of mathematics, namely consistency, also vanish into 'nothing'? What guarantees that this landscape isn't just a lucky fluke - together with our universe? Well, these have been the questions I was concerned about in my essay, albeit due to restrictions of characters, I couldn't write them all down, but have done it with this rather epic comment!

Hi Branco, thanks for your comment.

Regarding

"If nothing is surrounded by anything then that is something."

That's also my point of view.

"Nothing surrounded with nothing (before the Big Bang) is a singularity (undefined state). Accordingly, Big Bang is false theory."

Well, nothing, according to my essay, can be defined. It 'is' simply total non-existence. As I defined it, there doesn't even exist a singularity - if you mean by 'singularity' the traditional meaning of a kind of black hole's internal structure or some GR-singularity.

If there has been nothing (again as I defined it) before the Big Bang, this simply means that 'nothing' as I defined it is possible. The consequences would be that one cannot exclude that such a 'nothing' has produced a Big Bang. Nothing can produce everything - if one believes in it. And if one believes in such a 'nothing', how can one exclude that the things which it has produced by it cannot vanish again into 'nothing' - perhaps in the next 3 minutes?

To stay on logical grounds, 'nothing' has nothing to do with the possibility that there could have been a Big Bang - except for the case that someone seriously believes in 'nothing'.

Hi Joe Fischer, thanks for reading my essay and for your comment!