Dear Jose,

as regards laws I'd like to play on your chess analogy. The termination rule of chess (checkmate) says that the game is over when the king can make no legal move. I found some numbers saying that there are some 1e43 potential configurations of pieces of which 1e34 are checkmate configurations. Let me for the purpose of discussion call this number infinite. Now, while the termination rule is an entirely unanschaulich prohibition (negation) in itself, it allows the observation of an infinity of actual checkmate configurations - when they occur! That is, only the negation of the negation 'produces' the actual case. So, I think there is a way from finiteness to infinity.

Heinrich

    Dear Heinrich,

    In my opinion, the only way from finite to infinity is attaching a 'clause' for infinity. For example, 'go an adding finite numbers infinitely' takes us to infinity. In the case of chess, the number of possible configurations is a very large finite number as you have pointed out. You add the clause 'let us take this finite number as infinite', and a way from finite to infinite seems possible. Without such a clause, finite things always remains finite. It is just a logical argument; based on it, I will argue that there exists a finite number of finite universes in infinite space. If actually infinite number of universes exist, my inference is wrong. However, it is impossible for us to know that, and so I just depend on logic.

    Jose P Koshy

    Dear Stefan,

    The choice is always there. It only implies that there are more than one possibility, and depending on the environment one of the possibilities happen. When a freewill is applied, a slight change happens in the environment favoring one possibility, which sometimes may be the least possible one to happen naturally. That is, freewill does not create any additional possibility. Number of possibilities is deterministic and so the 'choice' is deterministic, whether freewill is involved in it or not.

    This choice, a deterministic event, can be traced back to the fundamentals. However the 'choice' itself is not a causal factor, it is an event caused by other causal factors present at that time. It is interesting to note that you expect the possibility of a dualism existing at the fundamental level. In the model of nature, I visualize, motion is a property of matter, and force is reaction to motion. That creates two opposite causal factors, motion trying to move bodies away from each other, and force trying to bring them closer. This can be regarded as a dualism present in nature, an acting causal factor and a controlling causal factor, both being real. Without this dualism, the number of possibilities is just one; if motion alone is there, everything moves away from each other and if force alone exists, everything binds together into a single lump. So it is the dualism present at the fundamental level that creates 'choice' or 'multiple possibilities'.

    An observer, conscious or otherwise, does not contribute any fundamental causal factor. The power to observe is an emergent property. So also is the power to control. The power to control exists independent of the power to observe. A conscious observer just utilizes these two to suit his requirements. So in my opinion, there is no dualism like 'observer related causal factors' and 'physical causal factors'. We and our creations do not represent the end of events; events continue uninterrupted. In my opinion, we are just a part of events that happens in cycles, each cycle taking only finite time.

    Jose P Koshy

    Dear Stephen I Ternyik,

    Thank you for going through my essay and for the comments.

    Jose P Koshy

    Dear Jose P. Koshy,

    You wrote in the Abstract: "Fundamentalism, the belief that there exists some irreducible basic truths in anything connected with nature, has existed for a very long time."

    Nature produced one single unified VISIBLE infinite surface occurring eternally in one single dimension that am always illuminated by mostly finite non-surface light millions of years before humanly contrived finite mathematical information ever became evident on earth.

    Joe Fisher, Realist.

    Hi Jose, thanks for your reply. Albeit i agree that choices are limited by the past and by the conditions of the environment, i have huge trouble to decipher what you really mean by 'choices'.

    You wrote

    "When a freewill is applied, a slight change happens in the environment favoring one possibility, which sometimes may be the least possible one to happen naturally"

    Could you explain what this slight change is, what you physically mean by such a change and how it comes about?

    Thanks!

    Hi John,

    It seems to me that both of us have started off at different points to arrive at a somewhat similar destination. Your analysis was crisp and fun to read; certainly among the best ones.

    How do you, however, propose to deal with the block put up by Gödel's incompleteness theorem? In this context, unless I have misunderstood, it seems to imply that no respectable system can be reduced to a set of fundamentals. (In fact, it is this apparent roadblock that made me take a different path to this conclusion.)

    Regards,

    Aditya

      Dear Stefan,

      I will just give some simple examples. Flipping coin and throwing dice provide deterministic, not chaotic, environment (because the possibilities are definite). In the former, choice available is two, and in the latter, choice is six. Because of the deterministic nature, we can calculate the probability of getting a certain result in both cases. Suppose we tamper with the symmetry of the dice to get a certain result nearly always, we are using freewill. Here, the game has not changed, all factors that affect it has not changed, but an asymmetry has been introduced as an additional factor to affect the result.

      Similarly, water flows downhill normally along an existing path. We can create a canal and change the path. Here by invoking freewill, we are not changing the law of gravity, but just utilizing a possibility offered by gravity, a possibility that always existed.

      I think my viewpoint (whether right or wrong) is clear to you.

      Jose P Koshy

      Dear Jose,

      I think FQXi.org might be trying to find out if there could be a Natural fundamental. I am surprised that so many of the contest's entrants do not appear to know what am fundamental to science, or mathematics, or quantum histrionics.

      Joe Fisher, Realist

        Hi Jose, thanks. Now i have a clearer picture of the usage of your terms. Choice is then everything that is not forbidden by the laws of physics, but choice is not identical (synonymous) with freewill, notwithstanding that 'freewill' itself is - if one believes in it - not forbidden by the laws of physics.

        Still I struggle with determinism in your framework. Do you adopt the quantum mechanical interpretation of the multiverse to make 'freewill' coherent with 'choice'? I think this must be the case, but I am really not sure, please pardon me. I only can precisely determine how you use your terms and what they mean to you by knowing what's the 'real' difference between 'choice' and 'freewill', since a river and parts of its environment may have 'decided' to take one specific path out of a certain range of other possible ones.

        Dear Aditya,

        What I propose is theoretical model-building based on 'fundamentals' and laws of mathematics. The fundamentals are either arbitrary or self-explanatory. That means these cannot be explained within the model built up from the fundamentals. As such we can say the model is incomplete in itself because it contains statements that cannot be proved from the model.

        The model-building is intended for acquiring knowledge. The model thus obtained is a system that follows laws. Here the terms fundamentals, knowledge, system, laws and completeness are well defined. Fundamentals are the primary-causes, knowledge is understanding the causal factors and laws, laws are mathematical statements, and a system is something that is finite, dynamic, deterministic and made up of quantized entities. The model is complete if the formation of the system (starting from from the fundamentals) can be explained using relevant laws of mathematics. Our knowledge in that field is complete if we can identify the primary causes, all emergent causal factors, and the mathematical laws applicable at all levels.

        So what we have is a 'defined completeness'. Complete knowledge does not mean complete predictability; we need not know all paths leading from 'the fundamentals' to 'the system', we need know just the main route. We need not know from where the fundamentals came or why they came. These are either 'not much relevant' or 'just impossible'.

        Jose P Koshy

        Dear Stefan,

        There are no separate laws for physics, economics, politics, etc. The laws applicable in any domain are laws of mathematics. Each domain has certain properties which may be fundamental or emergent; it is these properties that act as causal factors. Free will arises from the properties of matter. So in my opinion, the most appropriate statement should be 'freewill is not forbidden by the system (universe).

        When there are multiple possibilities, one of the possibilities happen. We can say that a choice has occurred. But prima-facia, we cannot say whether there has been any freewill action behind that choice. Only on continued observation can we come to an inference. If something contrary to the natural choice (which has the highest probability) happens in a statistically-relevant number of times, we can infer that freewill lies behind the choice. That is, freewill is also a choice, but an unnatural choice.

        Jose P Koshy

        Dear Jose, thanks for your more precise description of your lines of reasoning.

        I have some more questions and annotations to make for fully understanding whether or not nature exhibits unnatural choices.

        I consider a Boing 747. In our world, it is very unlikely that the natural path is such that the probability that nature facilitates this Boing 747 must be considered very low.

        According to some quantum mechanical 'fluctuations', it nonetheless isn't forbidden by nature that a Boing 747 is facilitated without the help of any human being. Of course, this 'unnatural' possibility is just of theortical interest, because the assigned probabilities are too low to ever witness such an event.

        If I define 'freewill' in the sense that human beings have the limited freedom to choose between two - or more - alternatives by some causa finalis which stands outside any formal system, does your framework then say that nature indeed exhibits 'unnatural' choices? Since human beings can built a Boing 747 by making some choices, I am forced to conclude that the finished Boing 747 is a totally unnatural event.

        Surely, due to your lines of reasoning, there is no way to empirically decide whether or not some true freewill was engaged in the building of that Boing 747, since we have not a multitude of identical earths at hand with the same initial conditions that would lead - or not lead - to the same Boing 747 at the exact same time in all histories for all earths.

        But now I read in a comment from you to Heinrich Luediger that

        "based on it, I will argue that there exists a finite number of finite universes in infinite space."

        If I take the existence of a finite number of finite universes in infinite space for guaranteed, does this premise allow you to - logically - decide whether or not nature (whatever it is in its completeness) does exclusively only follow the first three causes Aristotle once defined, or whether it also allows freewill in the sense that not only some choices aren't predetermined in nature, but follow a teleological reason, a causa finalis that cannot be captured by any formal system only?

        I think this is an important question regarding the search for some 'fundamentals', albeit the answer to these questions regularily do not make any practical difference for the life of the person who answers them.

          Dear Jose,

          thank you for your essay, that's interesting for sure and I will rate it well.

          I've not fully understood something about your "Fundamentalism" proposal. You write that it implies cause-effect, but in a certain sense it seems to presume it in its very definition (Any field of knowledge has some fundamentals, based on which everything in that field can be logically explained, and so by identifying the fundamentals, we can arrive at the truth). Moreover, how your approach manage the Hume's argument against causation?

          bests,

          Francesco

            Dear Jose;

            Reading your essay was like swimming in a pool. It is full of statements without logical or factual explanations to sustain them. Your whole discourse indicates that you have what I consider a naïve conception of causality. Linear temporal causality has been shown to be inadequate to explain fundamental phenomena.

            The most valuable idea you expressed in your essay (which you really explained logically), is that if there were only one fundamental (there should be either one fundamental entity having more than one property or more than one fundamental entity having different properties) there will be nothing to be explained.

            In the end you left me disappointed, I was expecting that you would establish the basis for determining what's fundamental from your postulates.

            Truly yours;

            Diogenes

              Dear Diogenes,

              Thank you for your comments. I disagree with the statement, 'Linear temporal causality has been shown to be inadequate to explain fundamental phenomena'. It is argued, it is claimed, but not shown.

              Causality is a very simple concept. Why make it appear to be something very complex. However, simple causal factors lead to complex situations; that does not make the concept of causality complex.

              The basis for determining the fundamentals is to identify the causal factors, and finally arriving at the primary causes, which we can call fundamentals. Identifying the causal factors is not theoretical, it depends on observations.

              Jose P Koshy

              Dear Joe Fisher,

              FQXi has not asked us to identify the Natural fundamental. We are asked to explain what fundamental is, whether there is any need for something fundamental. None of us knows what is fundamental to science or mathematics. We can only try to do so.

              Jose P Koshy

              Dear Fransesco,

              I do not agree with Humes regarding causation. Hume, I think, consider that the regularity or pattern that is observed in nature is just our belief, and so causation is just our belief. Our technology works just because this regularity or pattern is factual and dependable, and not a mere belief. The belief may deceive us, but facts do not deceive. The technologies are developed based on causality. Then how can we deny causality.

              Jose P Koshy

              Dear Stefan,

              I agree with you that a finished Boeing 747 is a totally unnatural event. This unnaturalness comes from the fact that some free will action has taken place. I will take this as a proof for the existence of free will.

              Because of this unnaturalness, the event need not be repeated in any other Earth in our universe or other universes. However, if it repeats anywhere, the conditions would be identical to that of Earth (In my model of the universes, structures having freewill emerges during the middle period of expansion, and so any Boeing will emerge more or less at the same period of history of that universe.)

              So in my opinion, the emergence of humans or human like structures having free will is predetermined in any universe (assuming that all universes are identical and made up of the same fundamental entities). But, our creations like the Boeing are not predetermined. It is a teleological event caused by our purposeful action. Nature allows such actions; we can say that such possibilities exist in nature.

              Jose P Koshy

              Dear Jose,

              You are right, casuality works very well, but since it depends on its repetition over time, how can we consider it fundamental? it's not logically impossible that casuality stops working even tomorrow, since the only thing that we can say about it, is that it always works - till now. How about a casuality without time? Is then time more fundamental?

              Bests, thank you for answering!

              Francesco