Dear Gennaro,
Would it be too naive to to view QM as a member of the ur-category, i.e.,
the system of a commutative triangle (of arrows) as shown below ?
f g
Feature ----------> Event ----------> Theory
(Firstness) (Secondness) (Thirdness)
[Object] [Sign] [Interpretant]
| ^
| |
|______________________________________|
h
Figure 1. Quantum mechanics, Peircean metaphysics and semiotics as members
of the ur-category, a commutative triangle. f = natural process; g =
mental process; h = information flow, grounding, correspondence, etc.
If this scheme is true, there may exist a deep connection among QM,
metaphysics and semiotics that may not have been discussed widely among
quantum physicists, philosophers and semioticians.
Let me know what you think of this 'wild' speculation.
Sung
> Dear Sung,
>
> Thank you for your kind interest and comments. My main problem by now is
> how to translate in category theory the scheme that you find in the paper
> and that I attach here for your commodity. My problem is how to deal with
> the fact that we have no representation of the uninterpreted ontology and
> therefore we cannot establish an ordinary morphism between the categories
> State, observable and property and the elements of that uninterpreted
> ontology. However, we can establish an analogy at the level of operations,
> that is, we have reasons to think that preparation, pre measurement and
> measurement have their analogue in the context of an uninterpreted
> ontology.
> Regards,
> Gennaro
>
>
>
>
> On 18/dic/2014, at 22:30, Sungchul Ji <[email protected]> wrote:
>
>> Stan,
>>
>> I am afraid you may be mis-reading Figure 1 and Auletta's interpreation
>> of
>> QM. Sure a social construction is involved as indicated by mapping g,
>> but
>> the fundamental reality inferred by the human mind is not only the
>> result
>> of g alone but also of f (which occurs even without any human
>> intervention) and h (which involves both the human mind and the reality
>> itself through empirical testing of mental models). If this analysis
>> is
>> correct, you may be focusing on about 1/3 of the reality when you assert
>> that Figure 1 is "almost a social construction".
>>
>> With all the best.
>>
>> Sung
>>
>>
>>> Sung, all -- I note that the Auletta proposal in the abstract is almost
>>> a
>>> social constructivist argument! Features and events are constructed by
>>> observers. In fact, all of QM begins as a material construction by
>>> observers.
>>>
>>> STAN
>>>
>>> On Wed, Dec 17, 2014 at 9:09 PM, Sungchul Ji <[email protected]>
>>> wrote:
>>>>
>>>> (For undistorted figures, see the attached.)
>>>>
>>>> Howard wrote:
>>>>
>>>> That's what Hertz said:
>>>>
>>>> "We do not know, nor have we any way of knowing if (7660-1)
>>>> the theory corresponds to reality other than how well
>>>> it predicts events."
>>>>
>>>> Statement (7660-1) of Hertz (for a more detailed version, see [1],
>>>> attached) seems consistent with the new interpretation of quantum
>>>> mechanics (called âa moderate, non-naive realistic attitudeâ)
>>>> recently
>>>> proposed by Auletta and his coworkers [2], whose abstract reads:
>>>>
>>>> âAbstract: The terms wave and particle are of classical origin
>>>> (7660-2)
>>>> and are inadequate in dealing with the novelties of quantum
>>>> mechanics with respect to classical physics. In this paper we
>>>> propose to substitute the wave-particle terminology with that of
>>>> features-event complementarity. This approach aims at solving
>>>> some of the problems affecting quantum-mechanics since its birth.
>>>> In our terminology, features are what is responsible for one of
>>>> the most characterizing aspects of quantum mechanics: quantum
>>>> correlations. We suggest that an (uninterpreted) basic ontology
>>>> for quantum mechanics should be thought of as constituted by
>>>> events, features and their dynamical interplay, and that its
>>>> (interpreted) theoretical ontology (made up by three classes of
>>>> theoretical entities: states, observables and properties) does
>>>> not isomorphically correspond to the uninterpreted ontology.
>>>> Operations, i.e. concrete interventions within the physical world,
>>>> like preparation, premeasurement and measurement, together with
>>>> reliable inferences, assure the bridge between interpreted and
>>>> uninterpreted ontology.â
>>>>
>>>> I also noticed that the Auletta et al. interpretation of QM seems
>>>> compatible with both the RPM category theory of reality (Figure 1) and
>>>> the
>>>> PPP category theory of science (Figure 2), both of which having been
>>>> discussed on these lists earlier this year (if requested, I would be
>>>> happy
>>>> to provide the relevant posts and publications [3, 4]):
>>>>
>>>> f g
>>>> Reality -------> Phenomenon --------> Model
>>>> | ^
>>>> | |
>>>> |______________________________________|
>>>> h
>>>>
>>>> Figure 1. The RPM category theory of reality.
>>>> The commutative condition, f x g = h, is satisfied; f = natural
>>>> process;
>>>> g
>>>> = mental process; h = correspondence or correlation.
>>>>
>>>>
>>>>
>>>> f g
>>>> Possibility -------> Probability ---------> Pattern
>>>> | ^
>>>> | |
>>>> |_____________________________________________|
>>>> h
>>>>
>>>> Figure 2. The PPP category theory of sciences, including quantum
>>>> mechanics.
>>>> f = natural process; g = mental process; h = correspondence or
>>>> correlation; the commutative condition is satisfied, i.e., f x g = h.
>>>>
>>>>
>>>> I have just begun reading the papers kindly sent to me by Auletta
>>>> (whom
>>>> I
>>>> met at an interdisciplinary conference held in Graz last month), but
>>>> I
>>>> can already see how his new interpretation of QM may be represented
>>>> visually using the category-theoretical diagrams:
>>>>
>>>>
>>>> f g
>>>> Features ---------> Events ---------> Theories
>>>> (Object) (Sign) (Intepretant)
>>>> | ^
>>>> | |
>>>> |________________________________________|
>>>> h
>>>>
>>>> Figure 3. Quantum mechanics as a mathematical category.
>>>> f = natural process (or sign production); h = mental process (sign
>>>> interpretation); h = correspondence or correlation (correspondence,
>>>> correlation, or information flow); The commutativity condition, f x g
>>>> =
>>>> h,
>>>> is satisfied; i.e., the mappings f, g and h can be so defined as to
>>>> satisfy the commutativity condition.
>>>>
>>>> If Figure 3 adequately represents Auletta et alâs interpretation of
>>>> QM
>>>> [2], and since Peircean sign can be similarly represented as a
>>>> category
>>>> (as shown in the parentheses), it may be logical to conclude that QM
>>>> can
>>>> be viewed as a Peircean sign and the quantum mechanical process as a
>>>> semiosis.
>>>>
>>>> With all the best.
>>>>
>>>> Sung
>>>> ___________________________________________________
>>>> Sungchul Ji, Ph.D.
>>>> Associate Professor of Pharmacology and Toxicology
>>>> Department of Pharmacology and Toxicology
>>>> Ernest Mario School of Pharmacy
>>>> Rutgers University
>>>> Piscataway, N.J. 08855
>>>> 732-445-4701
>>>>
>>>> www.conformon.net
>>>>
>>>>
>>>>
>>>> References:
>>>> [1] Pattee, H. (2013 ?) . A diagram depicting the Hertzian
>>>> epistemology. Attached.
>>>> [2] Auletta, G. and Torcal, L. (2011). From Wave-Particle to
>>>> Features-Event Complementarity.
>>>> Int. J. Theor. Phys. 50:3654â3668 DOI 10.1007/s10773-011-0833-8.
>>>> [3] Ji, S. (2014). Planckian Distributions in Molecular Machines and
>>>> Living Cells: Evidence for Free Energy Quatnization in Biology.
>>>> [4] Ji, S. (2014). Gaussian and Planckian Distributions in Brain
>>>> Processes underlying Decision Making and Mind-Body Coupling. The
>>>> Structure of Credition: Valuation, Association and Decision Making.
>>>> University of Graz, 11/26-29/2014. The lecture is uploaded to Youtube.
>>>>
>>>>
>>>>
>>>>
>>>>> At 08:43 AM 12/1/2014, Frederik Stjernfelt wrote:
>>>>>
>>>>>> Howard often refers to what "physicists" mean about this and that.
>>>>>> This is highly relevant as concerns physics but maybe less so as
>>>>>> concerns epistemology and ontology.
>>>>>
>>>>> HP: I agree that most "this and thats" of physics are not highly
>>>>> relevant to philosophers' concerns. On the other hand, can you name
>>>>> any prominent philosophers who regard as irrelevant what physicists
>>>>> have learned about epistemology and ontology in the last century?
>>>>>
>>>>>> FS: In my experience there are different views about the relevance
>>>>>> and character of these issues among physicists. Many physicists seem
>>>>>> concerned with which things must exist if their models are true -
>>>>>> and ontology is nothing more than that. But even if physicists did
>>>>>> unanimously agree, we should not expect a vote among phycisists (nor
>>>>>> any other select group) to be able to settle these issues.
>>>>>
>>>>> HP: I agree. There are certainly different views because there are
>>>>> still great mysteries. Actually, a vote was taken 17 years ago over
>>>>> the <http://arxiv.org/pdf/1301.1069v1.pdf>interpretations of QM. This
>>>>> lack of consensus over interpretations remains just as great as ever.
>>>>>
>>>>> I conclude from this lack of consensus on interpretation, but
>>>>> agreement on the predictive efficacy of QM formalism, that a theory
>>>>> does not need or even have a "true interpretation." That's what Hertz
>>>>> said: We do not know, nor have we any way of knowing if the theory
>>>>> corresponds to reality other than how well it predicts events.
>>>>>
>>>>> Howard
>>>>>
>>>>>
>>>>
>>>>
>>>>
>>>
>>
>>
>
>
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