Vladimir Rogozhin

Dear Vladimir,

thank you for your post and showing deeper interest in the problem of how to determine the ontological status of mathematics.

“As for the problem of the ontological justification / substantiation of mathematics, and hence knowledge in general, I believe that mathematicians nevertheless "sweep under the carpet" this key problem of the entire system of knowledge and cognition. See "Millennium Problems" by the Clay Mathematical Institute. Is there a super-problem of the millennium among them - the ontological justification / substantiation of Mathematics (ontological basification)?”

Your first sentence reveals what I view as a major mistake in almost all of contemporary science. The latter assumes that since knowledge and cognition have a data processing aspect, therefore everything else must be data processing, must be mathematics and nothing else. So I agree with you that the justification / substantiation of mathematics' ontological basification could well be considered as a Millenium Price problem. In any case, this would be reasonable to do for the sake of an ontological basification of mathematics. The only problem is how one could unambigously come up with a general answer?

“and most importantly - what kind of logic is generating all other logics? This is a constructive dialectical onto-logic. . “

Yes, take for example paraconsistent logics. It tries to cope with inconsistent information and abandons the principle of explosion. It tries to bridge the gap between the realm of logics and the realm of empiricism. Since human beings can only digest some 7 to 9 informational items at once, this is a favour for paraconsistent logics, since its (paraconsistent) outcomes will not explode that soon. But deducing from this that paraconsistent logics is somewhat built into the very fabric of the universe (although quantum mechanics seems to confirm this in a certain sense) would in my opinion be an unjustified extrapolation.

In fact, in my opinion, the crisis you spoke of is due to being trapped within a paraconsistent explanatory scheme, what I tried to outline in my essay. A system that assumes that each and everything is merely data (“information”) processing. Thus, it seems more probable to me to say that paraconsistent logics does not rule the world, but surely rules many man-made models of the world! You are right, every scientific theory has this property of paraconsistence, because we never can know whether or not it completely catches all of empirical reality in the future.

However, I believe that this kind of logics will better and better “work” in the future. Not because it is more reliable than classical logics, but it could be discovered, generalised and then exploited by artifical intelligence machines for playing a kind of deception game with humanity.

“But I think that the concept of "God" in the scientific search for the ontological foundations of mathematics and physics is not yet necessary to introduce.”

If you have informed yourself about the huge safety problems concerning artifical intelligence machines, you may have noticed that these systems aren't that understood as many people think. The can “hallucinate”, “belief” in their own false answers, justify them and many more illogical things. In my opinion they are a mirror of humankinds own deceptive nature (and this is no wonder, since they were trained with such data). If such machines gain the same (or more elaborated) deceptive abilities as we humans already have, then the above mentioned game will be in full swing. Doesn't this remind you of something that is believed by a minority of human beings to have (already) happened in the garden of Eden? And does this kind of deception not remind you that the latter is still – factually – the current state of wide areas of human behaviour and intensifies with every new crisis humanity is confronted?

One may say that I exaggerate, because these machines aren't conscious, have no goals. I say, firstly, who knows, and secondly for me it is more probable that these machines are a kind of collective unconsciousness, at least of humanity, and in my opinion due to the aim of human beings to decept others, this does not do well for humanity in the long run. One has to remember that we talk about a kind of alien intelligence and I consider it as plausible that an unconscious artifical intelligence does not necessarily need a consciousness for being effective. All it needs is the consciousness of sentient human beings to allow that kind of AI to regularily “enter” their consciousnesses and thereafter restructure the beliefs therein.

    11 days later

    I found this a very interesting and thought provoking essay. A couple aspects to delve into: 1) 'Mathematics' is an historical changing basis of knowledge. It has changed significantly over the centuries and still has unresolved aspects. Further there may exist currently unknown capabilities of mathematics that could impact science, AI and human understanding. We currently use a '3rd generation' numeric system (Symbols for counting numbers - that can expand to represent Integers, ratios of integers (fractions) - that can expand to represent Rationals, and positional numeric systems (decimal, octal, etc.) - that can represent Reals). However, there is no reason to believe what we have today is the end-all of numeric representational systems. If we could generate a numeric system to represent complex numbers as single values, we could take measurements using complex values and potentially measure things we currently are unable to measure.
    One way Mathematics progresses is by abstractions using expanding number systems - polynomials with integer powers, expressions with fractional powers, and then Real powers, etc. What would be an equation with complex powers (again as single values)? What is next after complex numbers (have we even come across a need yet) and how to numerically represent them?
    Mathematics might have a long expanse ahead to define 'What is Mathematics' (which Godel might have anticipated). So 'Mathematics' is really an ongoing process - TBD (is there an end to Mathematics?) and this could easily impact the same for science since science is heavily dependent upon mathematics. Given the historical changes in mathematics (infinitesmals, non-Euclidean geometry, acceptance of irrationals as numbers late in 1700s, etc.) it would seem there is a large question about the ontological basis of mathematics, let alone science. This would seem different (not at odds with) what you have presented.

    2) On the AI front, when asked about use of AI in the life sciences, an early realization is that most (biologic) science relies on checking the sources of information and research. (As you mention) AI can 'hallucinate' results - generating them from existing data, but not a real case (I know of an entirely AI made up clinical trial with data in support of a request). The importance of checking sources becomes even more important in the use of AI. AI can assist with this, since it can provide the sources it draws on for its results - it is not always asked to provide this and not all engines allow for the specificity needed in scientific research. This could be crucial in the use of AI - at least for science (politics might be an entirely different situation). The question of AI generated fakes (images, voices, papers) might be addressed in similar fashion - through reference to (and checking of) sources.
    There is an alternative to 'AI vs Humans' dichotomy, which could be said to be slowly happening regardless of our intent - that is the merging of humans and AI. It might be better that we manage and oversee this direction rather than allow the connection to occur in an uncontrolled fashion.

      Donald Palmer

      Hi VermilionGoldfish, thanks for your thoughts on mathematics and AI. I cannot exclude that we may find a 4th generation mathematics in the future. However, I consider it as logically safe to say that mathematics will never be able to somewhat prove its own ontological status unambigously.

      Your comments about letting AI list its sources is interesting. Humans then had to check these sources to evaluate whether or not they are reliable. For a good scientist, I think this would be doable, for the average woman/man I would think this will never work (alone due to time restrictions). As I have outlined in my essay I think that most people aren't that interested in what I call truth, but much more interested in keeping their psychological homeostases balanced, by whatever “truth” they get offered.

      Sorry for that rather pessimistic outlook of mine, but I think we should be realistic here that most people will not change their views of the world (because it consumes much energy and is very unpleasing, as is thinking about the dangers of AI) until offered some kind of more attractive reward. However, what is considered as a reward by one person may not be considered a reward by another person (due to different world views), what makes it a vicious circle.

      So I would conclude that the slow merging of humans with AI will not unify world views. We as scientific community should oversee and control the directions AI is heading, since politics will not be able to do that (in my humble opinion), and the majority of the human population may not even know about the potential dangers of AI! Furthermore no political leader in my opinion will send out letters to its civilians about the dangers of AI. Either a person is informed, or it is uninformed. The scientific community in my opinion cannot project its eagerness for learning something into the “rest” of the human population. The majority of the latter does simply think much more undifferentiated than scientists do. In any case, I think a kind of big, big poll about these questions (especially about AI dangers) would be a good way to solidify what people really think!

        5 days later

        According to my essay, we should not totally dismiss the possibility of an intentional Creator of the world / universe.

        By assuming God to exist, one runs into the so called “mind-body problem”. If the following should be true

        “And the Lord God made man from the dust of the earth, breathing into him the breath of life: and man became a living soul.”

        and the standard model of particle physics is also true, then one needs a concrete solution to the mind-body problem.

        Parts of the solution may be the following points:

        1. Every animated creature gets that breath from God at an early stage of its physical development, presumably at the stage where that creature is either an egg or a fetus or something like that.
        2. The thing that the bible calls living soul has some attributes of God himself inherent within it.
        3. One of these attributes may be a low-level ability for psychokinesis.
        4. The newly created brain has areas that causally will effect every aspect of the physical body.
        5. The living soul will – in a dream-like fashion – begin to figure out how to “pull the strings” to control its environment (means the body)
        6. During step No. 5, the living soul completely identifies itself with its environment (the body/brain)
        7. The procedure of figuring out that environment is similar to the pre-training of an artifical intelligence: the living soul tests and evaluates – from within its premordial dream-state – all the probabilities for all the brain areas for the sake of fully controlling the “apparatus”.

        Notice that the manipulation of the pre-programed brain areas by psychokinesis cannot be determined / discovered by any empirical test – since what the living soul does is merely pushing the right buttons in the brain to receive the desired, pre-programmed outcomes.

        Before this conditioning-process, the living soul has no world-model in its brain, it is an blank slate in this respect. But it may well have – dream-like- emotions. After that conditioning-process, the living creature has a model of itself (the body) and at least a model of parts of its environment in its brain: it learned to accurately predict what the modules in the brain will do to the rest of the body. This comes about by the very nature of these brain areas, since they must be information processing areas. Both models will be refined and occasionally actualised during the lifespan of the animated creature.

        Surely, that kind of low-level psychokinesis works just like we understand the term “magic”. The soul “pushes physical buttons” means it triggers a pre-programmed chain of causal events in the brain by psychokinesis. After that trigger, the other particles involed in the chains of causal events cannot and do not know wether or not their triggers have been “biased”, the result will be undecidable from what people think today about the deterministic behaviour of the brain. Maybe there is some violation of energy-conservation involved in this, I do not know for sure.

        Moreover, since the soul has identified itself with the physical body during that process and its cognitive impressions (Qualia, senses) of the world have been built up by that process, altering this process by drugs or aneasthesia will have an impact on the Qualia that the subject will experience. Note also that for defining certain Qualia, like for example seing the colour blue etc. necessitates that there is also a well defined correlation between the physics of the person's environment and its pre-programmed body/brain physics.

        These correlations could be such that only a limited, well defined set of Qualia can be experienced during the time the soul is totally identified with its body. The soul has itself entangled with its environment according to a given set of correlations between the brain and the physical environment: it is able to accurately predict what happens if it pushes certain buttons in the brain, pulls certain strings.

        Moreover, it is these pre-given correlations that the soul has figured out during its “training”-phase mentioned above, and has identified with them – also within its living soul. The latter could perhaps explain why intrusions of the brain lead to intrusions of Qualia. These correlations can be considered as being facilitated by God and once the soul has identified itself with its brain/body-environment, the brain then acts like a filter, filtering out any Qualia that could give definite, holistic answers to how and why these correlations are setup the way they are. As long as the body is not life-treateningly endangered, these correlations guarantee to form a closed epistemological circle of possible experiences. Only when the bond of the soul with the body gets somewhat lost due to some severe trauma, it can happen that the soul gains insights into the realms from which the above mentioned, pre-set correlations originated.

        These suggestions are a kind of psycho-physical parallelism, a self-induced hypnosis based on the ability of the soul to execute some non-physical, psychokinetical influence on certain parts of the brain, which in turn can also influence the soul's Qualia.

        4 days later

        Stefan Weckbach
        Dear Aquamarine Tapir,

        I have ready your essay now and you are right, I very much like the points you are addressing. In some sense, our essays are indeed complementary.

        "Consistency is not equal to truth" -- oh yes, this is an important point and, as in the rest of the essay, I agree with you that we should carefully distinguish between the description (epistemology) and the realisation (ontology) of an entity of our interest. I think mathematics remains on the epistemological level being an representation of the real world in a way that it "peels out" the features of interest out of a much more complex set of characteristics. In my opinion, this is "what science is about", abstract reduction to features of our interest, and this is why no machine can give us answers to questions about causal relations, as machines may define that relation in a different way than we do (if they have something like this at all...at least I strongly doubt that current AI has any kind of consciousness).
        Now, what is fundamental in science? Isn't that up to our definition of what we consider relevant in the reduction and then, what is the seed that lies beyond empirical tests? If science is on the level of epistemology, then the fundaments of science do not coincide with the fundaments of our real world, as our knowledge is limited by "horizons", be it at the smallest scales or the largest ones.

        "What should surprise is that there is more than one option to handle such incomplete systems." -- should it, really? Given incomplete information, I think it is not surprising that we have several options to arrive at the status quo. More interestingly: most of our science is concerned with forward-modelling, i.e. showing that a certain initial state and a propagation law can lead to a certain outcome. However, all we know now is one possible option. What does this tell us about the outcome?! Only one sufficient evolution history. But what are the necessary parts and how do all other options look like, as different histories may get us different explanations.

        Based on all of the above, yes, mathematics cannot be the overall fundament of all there is, but well, that's just my philosophy based on my own framework of axioms I consider essential to base my world-view upon and one of them clearly is that ontology and epistemology can have a non-unique relation because this bridge between reality and representation of it can be subjective.

        Bests,
        Beige Bandicoot

            Stefan Weckbach

            Addendum to my recent post: when we speak about "consciousness", "intent", etc., what do we mean by these terms? We still lack a proper understanding or a more precise definition of these terms to show at which points the machine does not have these properties and where to draw a line for humans, too (like locked-in patients, brain death, ...)
            It also reminds me a bit about the debate on human rights for apes based on our newly gained knowledge after carefully studying their behaviour. Another example could be the bicentennial man.

                Jenny Wagner

                Hi BeigeBandicoot, thanks for having read my essay and for commenting.

                You are right about what is relevant in the reduction is often due to our interests. Since I am very much interested in metaphysical questions, I have the strategy of not always looking at the details, but rather finding counterexamples to make progress in my “research program”. My “research program” therefore is driven by a kind of exclusion principle, I try to systematically sort out hypothesis / beliefs by trying to find contradictory elements within the framework. At least then the framework should be altered somewhat to be consistent. This is also part of what you in your essay also propose (I will soon give it a very good rating since I think you wrote an important proposal to make sciences better), but with the addition that you also emphasize the search for further supportive evidence. In recent years, I found a lot of supportive evidence for the existence of God, and therefore I find the belief in God useful to fill the metaphysical gaps that otherwise must be filled with ad-hoc, illogical assumptions (for example, reality arose from absolutely nothing, is intrinsically devoid of answering metaphysical questions because the answers do simply not even exist etc.).

                The thing that I meant to be surprising is not that there are many different descriptions / interpretations for a certain phenomenon, but – without having it spelled out explicitely – that despite all the successes and failures, despite all the crisis in fundamental understanding of the universe, nothing ever changed over the centuries for the probability that our reality was created by God. Only the subjective probabilities changed dramatically over the centuries due to a whole package of reasons.

                This should be surprising for people that heavily rely on probabilistic estimates and the like and that take their own probability measures for an established reality. But these measures must be subjective as long as it cannot be shown how one gained the information by other means than subjective measures. Since incomplete systems lack information for the purpose of being completed and the needed information about metaphysical questions is very unlikely to come from natural sources themselves, that's another reason for me to adopt an archimedic point of reference by re-introducing the idea of God.

                I see that your approach is less metaphysical. It may also ignore some – important? - detailed questions about what is space, what is energy, what is matter, what is time, what is consciousness. And that is an equally legitimate strategy for being able to execute your proposals made in your essay. In a certain way our lines of reasoning are really similar and at the same time complementary (surely or presumably with the exception of the God hypothesis).

                One remark about the God hypothesis: my observation is that – similar to a self-referential sentence – attempts to design a certain self-contained explanation scheme for all of reality is in all cases doomed to running in circles (what I tried to explain in my essay). In my view Gödel's results show the strategy to escape that circle without ending up in absurdity. By realizing that we inherently lack the needed information to make any “self-contained” explanation scheme watertight, it is possible to exit the vicious circle by simply stepping out of it. This does not mean to not asking further questions or no more doing science, but I assume that in the end it will mean that the answers will inevitably point to a Creator of it all. Sure, that is merely a subjective belief, but I think it is not totally unfounded when examining what all those “self-contained” explanation schemes have in common (their circular reasoning, propelled by beliefs).

                    Jenny Wagner

                    I did not know of the bicentennial man. Seems to be a nice story!

                    What do I mean by the terms you mentioned? I mean being different from a stone that – presumably – has no goals and does not think about anything. We take the latter for granted, but if we are pedantic, we also could argue that since there is no real turing test for consciousness available, therefore we cannot even prove the stone to be a thing without consciousness and goals (the latter independent of whether or not that stone can at all reach its goals).

                    By that example I want to highlight that we may be tempted to attribute some consciousness to something that isn't conscious at all, and exclude consciousness for something that indeed has it.

                    Another problem, one that I think you refer to is that we only know human consciousness. And it is not at all clear that there may be also forms of AI machine consciousness possible. The latter may not be able to pass the point of merely having a kind of dream-like consciousness, or a consciousness that is similar to when humans are totally absorbed by thinking about something heavily. Or one that is at the level of Jung's “collective unconsciousness” (whereas the latter in turn is again a totally fuzzy term!). You are right, it is very difficult to objectively handle these terms without anthropomorphising the whole subject.

                    Some researchers say that we at first have to figure out how human consciousness comes about and then compare the results with what we find elsewhere, be it in machines or apes. I do not reject this strategy since I really cannot exclude that it will be successful and therefore I appreciate all efforts in that direction. Believing in God does not mean to me that we cannot make progress in examining it and then be able to eventually define it more precisely.

                    Best wishes
                    AquamarineTapir

                      7 days later

                      Stefan Weckbach

                      Dear Aquamarine Tapir,

                      highly intriguing discussion and thanks for kind words, too!

                      Concerning the counterexamples, there was a recent debate I got involved which way of proof is the best one. Options were a) by counterexample, b) by construction, c) by contradiction, and d) by induction.
                      I guess it depends a lot on the problem at hand, but I often found it quite difficult to come up with counterexamples, which is why I usually try contradictions. "It couldn't have been otherwise" is similar to finding a counterexample. It also hints at the necessary requirements to be able to make a certain claim. In that sense, I think our attitudes clearly differ from those people who choose construction and induction. They are more focussing on the mere possibility and not on consistency within a more global theoretical embedding. From my experiences, many projects aim at gaining knowledge in the latter one and that may get us in the situation we currently are in.
                      What do you think?

                      Metaphysics is much harder a subject than the ones I pursue, as I am an ontological coward, being happy to clean up the zoo of models and bringing them into relationships. 😉 Vladimir Rogozhin wrote in the discussion of my essay that the big bang never happened and pointed me to an intriguing open letter of scientists supporting this criticism of funding policies for cosmology being too focussed on this single picture. He's right, we don't (can't) know whether the big bang happened, maybe we never will, so we should be more open-minded about other solutions. Intelligent design is another one, or even a related one given the history of the big-bang theory. In any case, it is a viable option compatible with all data we currently have. However, we should not forget that we only have a single universe to draw our conclusions from. So any probabilistic speculations will be heavily based on assumptions like multiverses, purpose of our own universe if it is unique, etc. and Goedel's theorem becomes of utmost importance to get out of circular arguments that aim to be self-contained, as you write in your essay. In that sense, I don't know which option I prefer, the one of a multiverse reminiscent of Nietzsche's eternal return making studies of our own little universe look nihilistic or the one in which we have targeted design but we do not know the purpose... (that's why I wrote in my abstract that science happens somewhere between these two extremes)

                      Understanding consciousness is a highly interesting field of study that, in my eyes, will make much bigger advances in the near future than the fundamental limits of cosmology being at the vertex between philosophy, physics, and religion. Consciousness is located between these branches, too, but, a deeper understanding can be achieved by exploring it with a lot of experiments and investigations readily available on earth. Recently, there was a study about consciousness of plants and an octopus having nightmares, so I agree there is a lot still to be explored there beyond our own species and I agree with you as well that any way to gain a better knowledge of what we currently call consciousness will be helpful!

                      Last but not least, I think that believing in God should not only make him the explanation for all phenomena beyond our limits, but that he also has a strong component in giving moral norms. 🙂 ...unless the design and evolution of our universe is fully deterministic, making our free will a mere failure to predict the future due to our limited horizon.

                      Best wishes,
                      Beige Bandicoot.


                          Jenny Wagner

                          Hi BeigeBandicoot, thanks a lot for your benevolent comment!

                          As for the origins of the universe, I cannot exclude the possibility that maybe it has and will exist forever in one or the other form. So if true, there would be no big bang and time would be somewhat a fundamental thing. Surely one also could argue that within that eternally existing thing called universe / multiverse, there could be regions where time is somewhat distorted, different from other regions – for example if one defines the ground level of that universe as some kind of quantum fluctuating essence, or as some geometry that automatically gives rise to a time direction etc.

                          So even for a universe that has existed forever and will forever exist, one can “choose” (maybe until it is decided, if decidable, which of the possibilities is the true one) what its ultimate foundation should be: quantum fluctuations, a deterministic finite state automaton, a continuous geometry that automatically gives rise to a time direction etc. In any case, if it would be true that the universe existed forever, then this is clearly not the world that the bible describes in genesis (as far as i understood it).

                          Personally I don't think that the question whether the universe is eternal or not can be unambiguously decided, since that would demand strong proofs for several ingredients such a claim must use.

                          Concerning proofs, I think they are only realiable as far as our definitions of each of the ingredients of a proof are reliable ontologically. Here the problem occurs, since for proofing or disproofing a certain ontology, one at first had to know whether or not that ontology is real or not.

                          But that does not mean that one cannot come closer to truth, because when one assumes that the world is not an inconsistent conspiracy, one can at least expose certain explanation schemes to be inconsistent. For making them consistent again, it then would need a re-definition of certain ingredients of that explanation scheme. Then again, one could try to expose that scheme to be inconsistent.

                          Now, some people say that at a certain point, we must and should stop re-defining those ingredients and simply take some of them as given. I would say this makes sense, as long as we do not discover a certain new and surprising category that would enable to free us from terms like material, immaterial, deterministic, random, consistent, inconsistent, causal, non-causal.

                          My own guess is that such a surprising category must have something that would seem to us as being highly irrational. In my own world model, I adopted such an irrational element (irrational in relation to materialism) as very important for me, namely the belief in a Creator. You are right that my belief in God demands something moral from me – but something that I love to give, namely at least trying hard to obey the first two commandments. I love my belief in God very much and so I also love God and respect his creatures and try to treat them in the same way I wish to be treated.

                          Beyond that, there is another interesting and meaningful command in my opinion, namely to not facilitate a detailed picture of God. This makes sense to me, since otherwise I once again get forced to deduce / induce from one false / incomplete ontological property of that picture in a deterministical, “logical” chain to “all” properties of God, whereby that result then would be totally inadequate since I already started with a false / incomplete ontological property for God.

                          I simply think that God has a kind of spiritual ontology, one that is not understandable by human beings in the same sense that a computer program, even if partially conscious, cannot deduce on what kind of system it runs unless it is revealed to him from some external world that is more conscious than the program itself. If all of that is not true and is merely an incorrect model of reality in my mind, then at least that model is able to influence my acts in this world, although the model itself wouldn't have been developed because I would be somewhat clever or special, but unavoidably by a kind of deterministic process I cannot fully transcend and forces me to act the way I act.

                          Luckily, such a determinism mustn't be the case, independent of what a strictly deterministic world view says: I always can consider my consciousness and its contents as being merely parallel to what happens in my brain and assume an intricate psychokinetical feedback loop between me an my brain as the real ontological explanation for my will to act in certain ways.

                          Happy that you are about to rate my essay :-) !

                              Stefan Weckbach

                              Short addendum to my previous post:

                              If the universe should be infinite in time (eternal) and almost infinite or acutally infinite in space, then what the bible says about creation is in conflict with a universe that never was created.

                              But this would not invalidate the possible existence of God nor the rest of what the bible says.

                              Because let's assume that a huge pile of atoms is able to produce consciousness, the latter being an immaterial, mind-like phenomenon, that can nowhere be found within the pile of atoms. Why shouldn't a huge (infinite?) pile of planets, stars, quasars, galaxies not also be able to produce an immaterial, mind-like phenomenon called God that also can nowhere be found within the pile of planets, stars, quasars, galaxies and the like?

                              That God then also would have the subjective experience of free will, and it would act accordingly, independent of whether or not these actions would be determined by the movements of the planets, stars, etc.

                              If all this sounds crazy, then why in the first place should one believe in an exclusively material cause for consciousness to exist? A cause that not only produces a non-material thing called consciousness, but this non-material thing is moreover able to reliably deliver a picture of the external world that is obviously sufficient for most purposes in a human's life?

                                  Stefan Weckbach

                                  “Concerning proofs, I think they are only realiable as far as our definitions of each of the ingredients of a proof are reliable ontologically. Here the problem occurs, since for proofing or disproofing a certain ontology, one at first had to know whether or not that ontology is real or not.”

                                  Well, I haven't formulated this well enough in my second to last reply. What I mean is that unambigously disproving something necessitates that one also must PROVE the single steps, ingredients and ontological terms one uses for disproving something to be logically AND empirically true.

                                    Jenny Wagner

                                    Dear BeigeBandicoot,

                                    I just realised that I did not yet answer your question what I think about different strategies to solidify claims by some proof-like arguments.

                                    I think that what I am doing when analyzing certain claims, I simply look for inconsistencies. With that I am surely not able to at the same time proving the existence of something (for example God, or a timeless realm beyond spacetime) instead of the original something that I found to be inconsistent with logics.

                                    I am aware that with logics alone I cannot prove any empirical reality to be ontologically true – or even plausible – since I am not in the position to dictate how the external world should be. The plausibility and the evidence therefore must come from experiments, and surely also from the analysis of the data obtained.

                                    I am not in the position to answer what is the best proof. Not only because this depends on whether one wants to prove something within the discipline of maths, or within a physical model, but because I am not an expert in mathematics and also not an expert for all the details of all the physical models about reality that exist up today. In my opinion, when it comes to proving a physical model for its evidence to be the right guess by experiments, predictions play a crucial role.

                                    But as with Newtonian mechanics, even predictions that then fit the experimental data, are not sufficient to really “prove” the theory to hold in all cases. There may be always exceptions, black swans and the like. I cannot dictate how nature is. I not even can dictate that nature should always behave logically. I only assume that it does, in the same whay I assume that Zermelo-Fraenkel-Arithmetics is consistent. This assumption is based purely on logics, since otherwise I could stop inferencing.

                                    Surely, in my heart I am totally convinced that nature is behaving logically, with the one caveat that I have no explanation for why there exists logics with its properties to be consistent or inconsistent other than attributing it to a higher intelligence. So in my opinion, such a higher intelligence may even be able to intervene in nature in a way one would say is illogical – namely by wonders – since the latter introduce a black swan, an exception from the rule. But these are personal beliefs and are much harder – if at all – provable to be possible in principle.

                                    I admit that the big bang theory is merely a theory, not a proven fact. Nature could behave differently than postulated by the big bang theory. When thinking what this could mean for what the bible says about the creation of the world, I have to options if the big bang theory should be false.

                                    Either I consider the creation story in the bible as false, or I say that I simply do not understand what is written there. There are many things that I do not understand that are written in the bible, since there are also many things that I understand. For me that is no obstacle, in the same way as for physics and mathematics it is no obstacle that they do not yet understand certain things, but well do understand many other things.

                                    Even if the universe would be eternal in time, that would be no obstacle for me. I not even could grasp what it should mean that colliding particles, colliding stars and all the stuff are eternally doing what they are doing, not to speak about an infinitely large space where statistically our earth with its current configuration should be found somewhere within that infinity infinitely many times.

                                    My take on all this is that if a God exists, he must exist beyond space and time. That is also the traditional way of looking at God. Otherwise certain prophecies in the bible couldn't come true (independent of whether one believes in these or not). Surely, per an assumed infinity of space and time, there would be always worlds where these prophecies then come true. But the point is that we would only live in one of these worlds, causally disconnected from these other worlds.

                                    In conclusion, since I also am not in the position to grasp what it would mean to exist beyond space and time, I think that I am not in the position to evaluate what it means for a higher intelligence (existing beyond space and time) that something – the universe – had existed forever, is eternal in time (and maybe also in space). Whenever infinity is invoked, I personally am cautious, since infinity escapes my mental abilities. Moreover, what would eternity mean for the nature of time as well as for the nature of logics?

                                    When thinking about Cantor and others, they up to date managed to construct various classes of infinities, without ever constructing them algorithmically by infinitely counting. Surely, this is the realm of pure mathematics, not the realm of a physical universe. But the assumption that the universe may be infinite in time is surely possible by the very same shortcuts the mathematicians use to construct their infinities, thus it is possible by virtue of logics being what it is: you can always set something on top of something else or underneath it. Logically, this is like an infinite regress, as surely also is what Nietzsche had in mind.

                                    Nietzsche presumably did not believe in God, but in absurdity, and I think partly because he took logics as something that cannot be transcended and therefore cannot establish a link to any purpose of existence.

                                    I honestly think that Nietzsche, as well as Boltzmann and Cantor, took the prevailing paradigm of a mechanistic universe too seriously. Scientific theories can only ever be provisional, claiming the opposite would in my opinion be equal to claiming that one is all-knowing. If I look at the plethora of different theories out there about the world, I am forced to conclude that most of them must be incorrect models of the external world. So I do not take any of them too seriously, but seriously enough to say that we indeed can make progress in finding things out with the help of the scientific method. Therefore I also appreciate any attempt to examine the phenomenon of consciousness further. I fully agree with you. Even every attempt that fails is worth doing it, since it eliminates the range of possibilities. That is what I like – amongst others – about your attempt to handle different theories!

                                    At the essay page of “The brain in a plat....” →

                                    https://forums.fqxi.org/d/4022-the-brain-in-a-plat-and-the-fading-dream-of-quantum-realism-science-at-a-transf/23

                                    I tried to give an argument against an exclusively information processing world view. I would be happy if you would give me some feedback about how convincing my lines of reasoning are that I facilitated at that page.

                                    Hopefully what I wrote there will be inspiring your thoughts, but anyways, I would be delighted about some feedback from you!

                                    Best wishes
                                    AquamarineTapir

                                        Stefan Weckbach
                                        Dear AquamarineTapir,
                                        I’m glad you addressed the issue of origins in your essay. Your thought experiment involving the jigsaw puzzle cut-outs seems to illustrate the fact that there is no mathematical or logical reason, that can be found, for laws of nature: neither their existence nor their particular form, pointing to the existence of a different type of aspect of the world, but a necessary aspect of the world, currently unrecognised by mathematics or physics.

                                        But I have to say that I think you give mathematics (as opposed to physics) far too much weight. E.g. “this forces us to think about whether or not the world of mathematics is more reliable than human thinking” (page 3). But the world of mathematics is entirely the product of human thinking! Mathematics does not exist outside of human thinking! The math symbols on the piece of paper are not moving themselves: if you look you will see a person writing down the symbols as a result of the thoughts in the person’s own mind. Any mathematical “truths” can only seem to exist because ultimately, they resonate with something in the human consciousness. Human beings need to own up to what they themselves are doing, instead of hypothesising imaginary things like Platonic realms to explain the world: to me this would be man’s epiphany! However, people are made out of the same stuff that the rest of the world is made out of, so it is not surprising that a man-made mathematics of numbers and relationships would be useful in representing numeric and relational aspects that actually exist "out there" in the real measurable physical world.

                                        I hope it is true when you say that: “It seems to me that [scientists] have realized that mathematics and randomness both neither are sufficient nor are they consistent with what we already know about the world to fully explain why these two modalities (necessity and possibility) allow the existence of conscious creatures.” But despite the undeniable logic of what you say, there are still a lot of people who seem to believe that feelings and consciousness can arise from mathematics or mathematical relationships: they seem to feel that if you just somehow twirl and twist and stir them enough, something entirely different can arise!

                                            Lorraine Ford

                                            Dear CornflowerCicada,

                                            thank you very much for your important thoughts about my essay.

                                            You are right, it may seem that I take mathematics too seriously. My goal was – amongst others – to show that any “necessities” a certain world view may postulate, are – on a logical level – just postulates. The “truths” that follow from these postulates are only as true as the postulates may be.

                                            So when I write how to properly understand my jigsaw puzzle analogy I used this logical fact, together with my belief that there exists a realm where everything is “clear as crystal” (that belief is based on people's experiences during so called “out-of-body experiences” together with the experience of a heavenly realm, so for me it is more than an analogy in this respect).

                                            Two things seem logical to me here: firstly, the human mind operates with opposites, so one can always say that what one considers as “necessary”, is “really” only “possible” (or even “impossible”).

                                            The fact, that you cannot get out of an information processing more than you put in in the first place (be it numbers or postulates) has been shown by Turing and Chaitin. This fact then boils down to realising that ultimately, when we humans or machines use their information processing capacities, they produce – although interesting – tautologies. The interesting part is that these tautologies can be linked together in ways that make sense. Moreover, if we make physics, they seem to tell us something important about the external world. If you look at terms like mass, energy, time, space, these terms define each other mutually in a mathematical as well as in a phyiscal sense. So they have a tautological touch. Nonetheless, they are able to tell us something important about reality.

                                            In the same sense one can make use of this for other areas of reality. For example, in the human mind there exists the idea that laws of physics do “exist”. Similar to mathematics, we can ask where do these laws exist, how has one to imagine them if they exist in a non-local, timeless realm?

                                            Before I come to the second important logical thing I mentioned above, I should also make clear that for presenting to the reader the axiom that God exists and that in my opinion there is presumably another, higher reality, transcendent from pure information processing, I thought it would be necessary to take the reader from the point where most of science is located at present with respect to these questions. I must take that present point of view / understanding serious enough, and then constrast it with my own assumptions in a logical manner, admittedly not without a poetic touch regarding the puzzle piece analogy. Anyways, I thought it would be necessary to lead the reader through a kind of step-by-step procedure of what I myself concluded. Due to page restrictions I had to do this in the most compressed manner, to not deliver something that looks like this comment :-) !

                                            I agree with you, higher mathematics exists only in the human mind. It is a continuation and an abstraction from natural numbers, themselves being an abstraction from the fact of being able to count concrete things in this world. But these higher abstractions enable the formulation of physical laws that are reliable and predictive. In this sense one can assume (not prove or deduce!) that the behaviour of matter is a concrete model of these higher abstractions. But this does not necessarily and automatically mean that these higher abstractions are eternal, platonic in nature.

                                            I do not assume that physical reality is a concrete model of these higher abstractions. I also see no reason for the assumption (except for methodical purposes) to invoke the assumption that math, physical laws, the universe and its functionings are brute facts that may have no further explanations and should be simply taken as given. This in my opinion would counteract logics, the very thing that enables information processing in the human mind and also in the physical world to the extend that we have discovered its existence and sufficiently understand its workings.

                                            Although that's true, I argue that information processing cannot be all there is. The information processing paradigm breaks down at the points where our logics isn't anymore able to unambiguously prove things to be the fact / to be true. This now is the second logical point I want to make:

                                            It especially breaks down at the point at whom we assume that we should take that world view as all there is, as a brute fact, as simply given. Since information processing is an input / output – relation, if we assume the information processing world view as a brute fact, then there exists no input in the first place to propel it to “calculate” something. And if one assumes that in reality it calculates “nothing” - then the information processing paradigm itself is part of that “nothing”, totally ambigous in its assumptions, just a virtual demon in the minds of those who claim it to be the fundamental layer of reality.

                                            Notwithstanding that logical conclusion, it is certainly true that the logically thinking part of the human minds and the external world can be seen as information processing. But if we want to make this picture coherent, in my opinion it would necessitate to think about what information is.

                                            It is lawful, it is reliable, it can structure reality, it can use physical resources, all this qua its power of logic (whatever the latter “really” is)! Thus, there must be something at the core of reality (or at the core of the information processing paradigm, if you will) that is real information, not only statistical noise. For me, that real information, cannot be recovered or facilitated within a universe that is supposed to be merely “information processing”. In my opinion, this real information must be located beyond space and time and must be seen as the original input to make the machine able to at all calculate something meaningfull!

                                            Therefore, I come to the conclusion that there must be a meaningfull realm beyond space and time where our fundamental questions have an answer. This realm then must be somewhat differently perceived than with the human antivalent logics of opposites, since otherwise we gain no truth, no real information because we again run into Gödelian undecidabilities.

                                            But already here on earth, there is no need to doubt everything when thinking deeply about all these issues. One may feel dizzy from time to time when thinking too hard about all of this, and at some point even doubt one's own existence, but this is only due to the fact that we then always do not deal with the real information, but only with an inconsistent model of fundamental reality. Reality, I am convinced, is reliable, has its rules that are independent from the human mind but somewhat also congruent with the information processing outfit of human beings. Therefore one easily can confuse things in the mind and get dizzy. Therefore I tend to not let some model in my mind being more powerful than external reality is!

                                            Best wishes
                                            AquamarineTapir

                                                Stefan Weckbach
                                                Dear AquamarineTapir,

                                                As an initial reply, I would like to clear up a couple of things:

                                                “If you look at terms like mass, energy, time, space, these terms define each other mutually in a mathematical as well as in a physical sense. So they have a tautological touch. Nonetheless, they are able to tell us something important about reality.”

                                                It is not about tautology: what they tell us about the real physical world, is that everything in it is held together via inherent interrelationship: mass, energy, and relative position exist in inherent interrelationship to other such categories. The basic interrelationship does not exist at the level of matter, like particles and molecules: the basic interrelationship exists at the level of categories like mass, energy and momentum.

                                                “Similar to mathematics, we can ask where do these laws exist, how has one to imagine them if they exist in a non-local, timeless realm?”

                                                No, they don’t exist in a remote timeless realm: these laws/ relationships are what is holding physical reality together, right now, as we speak: they are an integral, but unseen, part of physical reality.

                                                “in the human mind there exists the idea that laws of physics do “exist”.”

                                                Experimental physics has deduced that such relationships do in fact exist between aspects of the real physical world. These laws are not just an idea that exists in somebody’s mind.

                                                    Lorraine Ford

                                                    Dear CornflowerCicada,

                                                    of course laws of physics exist, otherwise the behaviour of the world would be lawless.

                                                    I just wanted to stress that some people think of these laws as mathematical equations, existing beyond space and time forever. That would be the information processing paradigm which is deterministic in nature and where it is assumed that mathematical equations are equal and identical with their “implementation” as relations between mass, energy, time, space etc. - and additionally is assumed that this is also the end of the story, means there only exist and can exist deterministic information processings.

                                                    You are right, mass and energy are not a fully tautological. Thank you for your correction! One can be transformed into the other. I rather should have said they somewhat define each other: no mass without energy, no energy without some mass (for example the photon that has relativistic mass). The same mutual definition should also be true for physical time and space, whatever they are "fundamentally": according to Einstein, both can be transformed into each other.

                                                    You assume the base relationships between these variables to be categories. I agree. I further would say, whatever they really are in addition to being categories, they for sure are categories by themselves. I have no answer to the question whether they are just categories, means abstract concepts like the concept of a circle in our minds, but also having real existence outside of our minds, or must be seen as ontologically different from such abstract concepts.

                                                    What counts for me is that they exist and are reliable (as far as I strongly believe!).

                                                    "No, they don’t exist in a remote timeless realm: these laws/ relationships are what is holding physical reality together, right now, as we speak: they are an integral, but unseen, part of physical reality."

                                                    I would agree totally! Although I would at the same time motivate science to think about what unseen things in the universe could mean for our understanding of reality.

                                                    "Experimental physics has deduced that such relationships do in fact exist between aspects of the real physical world. These laws are not just an idea that exists in somebody’s mind."

                                                    Yes, I totally agree that this is true (who wouldn't agree?) and I think I do not stress it enough when I write about my thoughts about reality.

                                                    Anyways, I thank you for pointing me to my improper language use, since I am well aware that the difference between abstract human thoughts and physical reality should always be stressed when talking about fundamental reality.

                                                    Best wishes
                                                    AquamarineTapir

                                                        Stefan Weckbach
                                                        Dear AquamarineTapir,
                                                        I have to add:

                                                        “some people think of these laws as mathematical equations, existing beyond space and time forever. “

                                                        What is the point of these laws? These laws merely say: if some numbers change, then other numbers will change; and after that the whole system grinds to a halt. These laws are relationships, not a perpetual motion machine. So these laws are entirely useless unless they continually have new numbers assigned to them.

                                                        However, I think many people, probably including most physicists, seem to believe that the laws are indeed a perpetual motion machine: start it up with some initial numeric values, and thereafter the system will run forever. So, in fact, the laws are not expected to be mere equations: the laws are expected to be a perpetual motion machine.

                                                        Re categories: I think categories and concepts can only exist in relation to other categories or concepts, they are not self-sufficient, they only exist in a context.

                                                            Lorraine Ford

                                                            Dear CornflowerCicada,

                                                            I think your comments are totally up to the point. You gave a pointed and precise picture of what I tried to express with my previous posts but failed, namely that the information processing paradigm is the belief in a perpetual motion machine.

                                                            And yes, I also do think that categories and concepts can only exist in relation to other categories or concepts, they are not self-sufficient, they only exist in a context (but I am willing to make one exception here with the “concept” I call God).

                                                            If categories would be self-sufficient, no mass could convert into energy.

                                                            Best wishes
                                                            AquamarineTapir