Deep Incompleteness: What Laplace's Demon Doesn't Know by Dean Rickles

Respected Professor Dean Rickles,

Nice arguments please....Your words in Page 2 in foot note...........Ultimately, my claim is that the impossibility of a theory of everything is the purely epistemological problem of not knowing what the world is made of, as evidenced by our constant, often radically changing theories. It is the lack of direct access to the nature of things that forbids this, and this is a result of finding ourselves part of the system we aim to study......................

I say, The nature and Universe are having hidden secrets still and the man is yet to find out many. The more he finds the more will unwrap....

I feel some of your concepts are represented in my essay also. Just Have a look at "A properly deciding, Computing and Predicting new theory's Philosophy"

Best regards

=snp

Dear Dean,

once again, you present an intriguing and well-argued essay. The initial question you pose---about how far we can stretch Gödelian results---is something that sometimes raises some eyebrows, and in principle, with good reason: Gödel's theorems have a very precisely defined range of applicability, that of axiomatic systems with a certain expressive power. Hence, or so the reasoning often goes, their applicability to physics (or other domains) is ultimately a category mistake---physics might be done with mathematical tools, but does not reduce to pure math.

There's something both right and wrong about this. I think a better way of framing this debate is to recognize that Gödel's results are really one application of a deeper principle in the particular domain of axiomatic systems, that principle being exposed by Lawvere's fixed-point theorem. With this, one can legitimately speak about extending 'Gödelian' (or perhaps, 'Lawverian') reasoning to domains beyond axiomatic systems, and describe phenomena like undecidability, the uncountability of the real numbers, the paradoxes of Russell, Richard, Grelling-Nelson and others, even von Neumann's treatment of self-reproduction within the same framework (see the expository article by fellow FQXi-contestant Noson Yanofsky on this: https://arxiv.org/abs/math/0305282). (And well, by means of self-advertisement, maybe you'd like to take a look at my essay, where I aim to apply these notions to quantum mechanics.)

You don't explicitly make the connection, but I think (correct me if I'm wrong) your argument can be read as a reply to another common strategy to deny the importance of Gödelian reasoning to our quest of understanding the world. That strategy, in principle, consists in noting that while it may be impossible to derive all possible phenomena from a given theory, nothing prevents us from achieving knowledge of that theory---as an example, suppose we lived in a cellular automaton universe, such as the Game of Life. There would be phenomena which we never could predict, as the general question of whether certain configurations occur is undecidable; yet, we could know the 'theory of everything', the CA's updating rule.

Against this, or so I read you, you mount the pessimistic meta-induction: so long as we find new phenomena, the picture of the world we have is liable to change; since in the example above, we'll always find new phenomena, we'll never be able to settle on a stable picture of the world in that sense. (Or at least, we won't be able to do so and know it; we might be right by accident, I suppose.)

I also relate very deeply to your point that the very preconditions of our knowing anything imply our inability of knowing everything---the mere act of knowing, in introducing the split between knower and known, ensures that no knowledge can ever be exhaustive. I have come to some similar conclusions in another essay of mine (http://bit.ly/AIbuddhanature).

There are also some shades of Popper's argument that no system can engage in perfect self-prediction.

Finally, I also appreciate the pointer towards the origin of Laplacian determinism in Cicero---I was not aware of that connection.

Thus, thanks, again, for a very thought-provoking essay. Best of luck in the contest!

Cheers

Jochen

Dear Dr. Rickles,

Thank you for a well-written and thought-provoking essay. You clearly describe the problem of completely describing a universe, when its description requires a split between an observer and the rest of the universe. But what if this spit is not arbitrary, but is an essential feature of an objective but contextual physical reality?

In my essay, I outline the general postulates for the "orthodox" interpretation of physics (HCM in my essay). The key postulate for the orthodox interpretation is postulate 4, which can be interpreted to state that the universe has no ambient surroundings. When expressed this way, it is accepted as obvious and without question. However, in my essay, I recast the postulate as asserting that physical reality exists in complete and perfect isolation from its positive-temperature ambient background, and I further argue that even the universe itself has an ambient background defined by the 2.7 K cosmic microwave background. When expressed this way, postulate 4 is seen as an idealization that does not exist in reality. There is no perfect isolation, and there is no ambient background at absolute zero. I refer to this interpretation, where any physical system necessarily exists within the context of its ambient background, as the DDCM. Perfect and complete description of a system as it exists within the context of its actual ambient background is defined by perfect reversible observation and measurement by an ambient observer.

I would value your thoughts on the relevance of my analysis on your excellent essay.

Best regard,

Harrison

Dear Prof. Rickles,

thank you for a clear and well argued essay. It contains a number of unconventional elemens that are very interesting (I particularly liked how you related these problems to ancient Insian philosophy and Jung's work).

If you have time, I would appreciate if you can have a look at my essay as well.

All good wishes,

Flavio

Dear Dean,

Thank you for the interesting essay. I agree with you that science gives no direct access to truth. What we believe is right today can be refuted tomorrow and our current worldview can be replaced by another one. This is how any scientific revolution works.

I wish you good luck

Boris

Dear Dean,

You argue for "deep incompleteness" with respect to our knowledge of ontology, focused on the 'observer-system' split (or 'mind/world' split) as if these are fixed boundaries. I do not believe you have exhausted the possibilities and in fact present a perspective that I believe offers a solution you have not considered: Deciding on the nature of time and space.

I invite you to read my (updated) essay and welcome comments, pro or con.

Best regards,

Edwin Eugene Klingman

Hi Dean,

and thank you for this wonderfully philosophical essay! Our phenomenal finitude as part of the whole that sustains us is where I start, and from Everett's perspective we are just entangled subsystems of the wave function of the universe where as you point out so forcefully, "a subsystem cannot observe a totality of which it is part".

In order to know the totality of the whole, the daemon would have to interact with the whole and so enter into and become entangled with it. And if one might stand free omniscient outside the whole system, I have the feeling that there would be nothing to see there at all, entanglement being that which 'gives us' observers as something from nothing.

Thanks!

Malcolm

Je suis, nous sommes Wigner!

Hi Dean,

Thanks for a beautifully written essay. Framing the Godel's theorem connection to reflexivity was a great line of inquiry. As you point out, Laplace Demon must be something outside the system with access to an infinite amount of resources if it is going to look inwards to the universe as some deterministic machine.

It might be interesting to connect the notions of reflexivity (the split between world and I) with indeterministic theories such as statistical mechanics. Any I immersed in a world will read inputs/output back to that world. However since it doesn't have access to everything in its own self-contained hardware, it will also input/output some level of noise. In any case, you might find my essay noisy machines interesting.

Thanks,

Michael

I enjoyed this essay very much! Very logical and deep analysis. Its conclusion is the way I interpret the first two verses of [link:www.taoistic.com/taoteching-laotzu/taoteching-56.htm]Chapter 56 in Tao Te Ching[/link] (I linked to them to avoid giving direct spoilers in the comment). (By "those who" from these verses I don't necessarily understand persons, but rather states of experience corresponding to different coarse grainings, more details in this comment). Cheers, Cristi

Great essay Dean. It caused me to think of the various work that has been done over the years on building a minimal ontology of the world. I have muddled around with this myself over the years (I think we may have even discussed it at one point or another). The subject/object division is, of course, at the very heart of any such ontology (if it exists -- as George Ellis has suggested, there may not be a minimum or a maximum). The ancient Buddhist and Hindu writers had some very interesting things to say about this. The so-called "mind only" school of Buddhist thought is particularly interesting in this regard, though one could argue that it denies any objective truth or reality.

Dear Dean,

I enjoyed a lot to read your well written essay. I endorse deeply "deep incompleteness". But it is difficult to think away the metaphysical Laplace's demon: a demon that stands for the deep reality that cannot be known by things within that reality. But which stands as judge, whether our theories are truth or not, or knows that our knowledge is necessarily incomplete.

The metaphysical demon is not chased away by the pessimistic meta-induction. Nor is he by underdetermination of the theory by the data or by any epistemic limitation on our knowledge.

I like very much your quote from Quine on page 7. But leaving away this 'unconceptualized reality' leaves us in a circular vacuum. How can truth be defined? How can we get to an objective picture - for which we aim for in science?

Also I never really understood, why there is this (conceptual?) necessity of a split into the known and the knower.

In my essay I postulate the necessity for objects and systems to be separable from the rest in order to have well defined properties. Which in a way is only possible approximately, since to know then the object it is necessary to interact with it. Is this similar to the above split of the known and the knower? Also this is an approximation, because the knower has to interact in order to know the known. The split has to be breached.

From the being a part of world and the necessity of the split does not necessarily lead to an underdetermination. Classical information can be defined as being available redundantly in abundance. So that a disturbance in observation does not change my relation to the object in a relevant way. The knowledge of relative quantities in the presence of symmetries (for instance distances and relative velocities) might be enough to be able to predict the future, Classical physics is totally compatible with the possibility of a Laplace's demon.

It seems to me that quantum mechanics forces us to give up this possibility. But then the problem is on how to maintain some sort of objectivity? Some sort of truth? Exactly this problem is discussed in my essay, where I embrace deep incompleteness and try under which conditions objectivity is maintained.

Thanks for your essay and I hope you find the time to read mine.

Luca

Dear Dean,

It is interesting to hear from the humanities about these subjects. This essay has the framework of a top-notch history of Philosophy lecture. This was one of the few essays that left me wanting more.

You have changed my mind on Jung. What little I have read about Jung presented him more about ornamentation than enlightenment. Great for fiction writers, but of little use those wishing to find the nature of things.

My only small critique is that I agreed with everything right away, there was no "Donald Duck is God" statement that you had to go uphill into the wind and rain to defend.

Best of luck,

Jeff Schmitz