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On the precise definition of inconsistence

Dear Diego

You mix up too many layers in this discussion. I can separate at least four:

- What quantic objects really do and to what extent we can understand them.
- What says one or another mathematical theory.
- How we can interpret their predictions.
- The foundation problem for these theories, from the point of view of mathematical logic.

Those layers are almost disjoint problems. There are entire worlds lying in between.

As a logician I want to speak only about the last question.

As in the proof of the Schrödinger equation, one uses together relativist arguments and classical arguments, one cannot answer the following ""easy"" question: does an electron live in a three dimendional euclidian space with extra time or does it live in a four dimensional Minkowski space time? Whatever answer you give, a part of the proof used for the equation will be contradicted.

As the theory does not give an unambigous answer to this question, I must agree with Akira Kanda. At least this part of the theory is deeply inconsistent from the point of view of  mathematical logic. 

This remark has nothing to do with the other questions put above, or in your correspondence. It has also nothing to do with the problem if some of us do understand or not QM, whatever does it mean (which layer do we understand better...) 

Please don't panic, QM is not the only one segment of physics which lacks a consistent foundation, as requested by the mathematical logic. At least 99 % of physics is in this state, maybe already 100 %. And, as I must admit, we do not have any fast solution to this question.


Mihai Prunescu


Dear Chandra,

Perhaps this mail will not reach you as removed from this list. Otherwise, have a good trip and a safe return home to India.

I cannot agree more with your qualification of the discussion of " inconsistence" of quantum mechanics as "ridiculous" on the basis of the dual logic as THE ontology. 

But one does not even go eastbound to find that inconsistence is not unsurmountable; the doctrine of dialetheia by Priest and the relation with paraconsistence logic is established (in the West).

As shown by Peter Kingsley the presocratic ontology basic to Greek science is non-dualist; the hegemony of Athens in the Greek Confederation required its condemnation. Western civilization was and is based on the imposition of dual logic and further promoted as the paramount sense of reality. 

The hegemonics of dualism is such that recently I came to learn from a scholar that Daoist doctrine is dualist, to further use it as a basis for "waveparticle complementarity".  With this ontology, then the nodal sets of waves (the zero set of waves, which stand for particles!!) should be called as "complementary" to the waves themselves. I find this ridiculous. They are crucial to and inseparable from the waves of pattern formation and recognition, as already appears in cymatics. (in the case of four dimensional linear wave equation they yield quaternionic solutions related to RxS, S the Hopf fibration, as per my work, highly non-pointlike). 

Actually, would we neglect these zero sets geometries them there is no harmonics, as already Lord Rayleigh showed in 1877 with his chapter  on cymatics in his Theory of Sound !!.

They are not a mode of knowledge about "something else".

But then, returning to the claimed dualism of Dao, what about the "small jin (yang)" in Taijitu? Very much seems that the hegemonics of dualism produces their obliteration.

Would  dualism be the case of Daoism  all the theoretical conceptualization and therapeutics of Traditional Chinese Medicine (accupuncture, moxibustion, etc) would collapse.

Thank you for your comments on Advayta and on the need of rewriting calculus -and abandoning the Bourbakist frenzy of formalism in mathematics!

Well, Chandra, hope that sometime, my friend, we shall meet again.


2017-03-01 3:10 GMT-03:00 C. K. Raju <>:

Dear Diego and others,

I find this discussion ridiculous.

First, what is "deep" inconsistency? On conventional formalism, inconsistency trivializes the theory since EVERY proposition is both true and false. It surely can't get any "deeper"!

Second, what is the value of consistency? On 2-valued logic "A and not-A" is inconsistent. But that is not the case in quasi truth-functional logic or Buddhist catuskoti (or Jain syadavada).1 So, why should the world obey 2-valued logic? Because church theology said2 that God is bound by 2-valued logic? Or because Western philosophers like Kant and even Russell (when he wrote his Principia) were ignorant and unaware of other systems of logic? Because formalist choose to do math with it?

Obviously, irrespective of Western myths and social opinion, the only serious way to decide which logic applies to the real world, is to decide it empirically. That tells us that 2-valued logic is only approximate. (See my book Time: Towards a Consistent Theory,3 for a formal proof(!) that a quasi truth-functional logic is a quantum logic.)

Of course, physicists don't really understand math at that level, which is why the mathematician (Field medallist, Abel laureate) Atiyah thought he could grab credit for my thesis on quantum mechanics and get away with it.4 That is the stock way by which the West concocts history, by stealing and then claiming "independent rediscovery": what I have called "revolution by rediscovery" in the cases of Copernicus and Newton.5

What further complicates matters is that time relates to logic (e.g. the temporal logic corresponding to a non-trivial structure of time is a quasi truth-functional logic) and, on the formalist misunderstanding of calculus one can't even write down the differential equations of physics without assuming that time is like the formal real line.

Clearly we need to abandon formalism as a dead philosophy of math, and switch to zeroism (and do calculus with non-Archimedean arithmetic), to be able to do the math needed for everything from computers to qm to down-to-earth geometry. (For an account of zeroism, see the article in the Springer encyclopedia,6 or the video of my conversation with the Dalai Lama.7)

As for your question about Buddhism and Advait Vedant, Diego (which precipitated this response), it is true that the adi Shankar was influenced by Buddhism, and Sriharsa, in his Khandanakhandakhadya uses Nagarjuna's arguments to demolish Nyaya beliefs, particularly on the question of time, etc. But there are many differences. In the first place Buddhists are not only atheists and God-disbelievers, they are nastiks in that they reject the belief in the authority of the Veda-s as a means of proof (pramana). Because they accept only empirical proof (pratyaksa) and inference (anumana) they reject also the belief in atman. But that is central to Advait Vedanta: recall that the adi Shankar compiled a list of sixteen principal Upanishads which concern atman. One cannot assert the non-dualism of atman=Brahman without it. Buddhists do not, however, reject the belief in quasi-cyclic time and previous lives which is the physical basis of the notion of atman, as explained in my Eleven Pictures of Time, or this article.8

A request: please remove me from this list, and I won't respond to any private reactions for the rest of March, being busy travelling to Malaysia, Germany, and Holland.


C. K. Raju

1 CKR, "Logic" Encyclopedia of Non-Western Science, Technology, and Medicine, ed. Healine Selin, Springer, Dordrecht, 2008, 2016, pp. 2564-70.

2 CKR, "The Religious Roots of Mathematics", Theory, Culture & Society 23 (Jan-March) 2006, Special Issue ed. Mike Featherstone, Couze Venn, Ryan Bishop, and John Phillips, pp. 95–97.

3 CKR, Time: Towards a Consistent Theory, Kluwer Academic, Dordrecht, 1994, chp. 6B, Quantum mechanical time, appendix.

4 "Retarded Differential Equations and Quantum Mechanics", Letter by M. Walker in Notices of the American Mathematical Society, 54 (4) (2007) p. 472 belatedly acknowledging my prior published work, on behalf of Atiyah, but hiding the fact that Atiyah was personally informed about it after the first time he tried. See

5 CKR, Is Science Western in Origin? Multiversity Penang, 2009, Daanish books, Delhi, 2009, reprint Other India Bookstore, Goa, 2014, etc., back cover,

6 CKR, "Zeroism", Encyclopedia of Non-Western Science, Technology, and Medicine, ed. Healine Selin, Springer, Dordrecht, 2016, pp. 4604-4610.

7 Conversation with the Dalai Lama on "Buddhism and science",

8 "Atman, Quasi-Recurrence and paticca samuppada, in Self, Science and Society, Theoretical and Historical Perspectives, ed. D. P. Chattopadhyaya, and A. K. Sengupta, PHISPC, New Delhi, 2005, pp. 196–206.

From: <> on behalf of Stuckey, Mark <>
Sent: Tuesday, February 28, 2017 3:41 PM
Subject: RE: [Sadhu Sanga] QM is deeply inconsistent and completely waste of time

Thnx Menas, I had intended to offer such a reply, but obviously I hadn't gotten around to it.


The original poster also mentioned the non-relativistic nature of the Schrodinger eqn as a reason for doubting its validity. One could say the same of Newtonian mechanics, but of course we use Newtonian mechanics to do virtually all of our mechanical engineering (a noted exception would be particle beam colliders). We understand Newtonian mechanics to follow from small v/c in special relativity, so it is on sound theoretical ground. Likewise, the Schrodinger eqn follows from the relativistic Klein-Gordon equation in the non-relativistic limit. See p 172 of Zee, A.: Quantum Field Theory in a Nutshell. Princeton UP, Princeton (2003). So, it too works very well for a wide range of phenomena and is on sound theoretical ground.


It is true that foundations of physics has not reached agreement on an interpretation of quantum physics (most notably concerning quantum entanglement), but practicing physicists have very effective models if not ontologies for doing calculations and conducting experiments. As a practicing physicist in foundations of physics I'm certainly biased, but I agree with Menas that anyone who believes QM is inconsistent and a complete waste of time has very likely not actually DONE any QM theory or experiment. Once you actually analyze the experimental results using quantum physics, you will see that it is all very consistent. Whether it is a waste of time is a value judgement. If you're not interested in the tremendous technological contributions or scholarly discourse that has resulted from quantum physics, then you might well consider it a waste of time.


Mark Stuckey


W.M. Stuckey, PhD

Professor of Physics

Elizabethtown College

(717) 361-1436




From: [] On Behalf Of Menas Kafatos
Sent: Monday, February 27, 2017 8:26 AM
Subject: Re: [Sadhu Sanga] QM is deeply inconsistent and completely waste of time


For anyone to think that QM is deeply inconsistent and completely waste of time displays lack of some basic knowledge: That QM is responsible for an estimated 50% or more of the world's GNP. That widely used devices such as the smart phone, nuclear reactors, integrated circuit etc. would not even exist. That basic biological processes like photosynthesis are quantum and probably brain processes as well. That the sun powers itself because of nuclear reactions, which are quantum. That chemistry is quantum. That the world is quantum, not classical. etc. etc.


And last but not least, the quantum worldview opened the door to conscious participation of the observer.


As we explain with Deepak Chopra in the recently released bestselling book "You Are the Universe", we start from the quantum and build on it. Not reject it. 


With respect,




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