God, Logic, and Quantum Information

GOD, LOGIC, AND ...

QUANTUM INFORMATION

VASIL PENCHEV • Dept. Logical Systems and Models, Institute for the Study of Societies and Knowledge, Bulgarian Academy of Sciences vasildinev@gmail.com ________________________ • 1st World Congress “Logic and Religion” • João Pessoa, Paraíba, Brasilia • 1 – 5 April 2015

An extended version of the presentation at the Congress at: • http://issuu.com/vasil7penchev/docs/joaopes soa/0 • http://www.authorstream.com/Presentation/ vasil7penchev-2342255-god-logic-quantuminformation/ • https://www.scribd.com/doc/249632993/God -Logic-and-Quantum-Information • http://www.slideshare.net/vasil7penchev/joa o-pessoa-42517166

The thesis is: • The concept of quantum information introduced by quantum mechanics allows of an interpretation of the world as conscious • Then logic is the result of the action of that conscious medium • Common scientific sense understands the world as unconscious, inert, “dead”, and absolutely opposing to the human being having free will, consciousness, thought

The concept of quantum computer • As usual, quantum mechanics and the theory of quantum information call that interpretation “quantum computer” or “the universe (world) as a quantum computer” • In fact, that term is misleading because “computer” means a piece of that unconscious, inert, and “dead” matter, which makes something similar to human calculating actions only externally, only looking like them • Thus, a “quantum computer”, though “quantum”, is a “computer”, only a “tool”

The free will of quantum computer • However, one can show that this “quantum computer” possesses the capability of free choice and some kind of natural teleology • A random “free choice” turns out to be guaranteed to any item in the universe according to quantum mechanics, more exactly according to the so-called “free will” theorems (Conway, Kochen 2006; 2009) • That natural teleology tends to order the universe by the time course itself: • Then logic is a set of those orderings as the result of that tendency

Free choice and goal of a quantum computer • The link between the free choice and teleology generates one phenomenon, which can be investigated by science • Mathematics connects them as to any finite set and generalizes that connection to any infinite set by the axiom of choice equivalent to the well-ordering theorem (or principle) • Thus “choice” and “well-ordering” turn out to be equivalent, where “well-ordering” is the strongest and mathematical concept for “order”

God as the free will of the universe • It can be called the free will of the universe and interpreted as a scientific conception of God or as a hypostasis of Him studied by theology • Free will underlain by quantum mechanics in the ground of nature is a usual term for theology • Theology understands the Divine Free Will as generating the human free will • In final analysis, quantum mechanics interprets that Divine Free Will as the free will of nature, which is rather similar in essence

Logic by the free will of the universe • The same viewpoint includes all logics or the conception of universal logic in a natural way • All kinds of logic are generalized as order and orderings to that universal order of logic • Then universal logic is the universal order of logic, to which tends the universe (1) by itself or (2) by the free will of the universe as a single quantum computer, or (3) by the Divine free will • Those three are only different interpretations of one and the same fact

Logic as a partial ordering • Any “logic of anything” can be seen as a partial ordering and thus as a stage of the universal and single well-ordering of the universe going to the past and accomplished by the “universe as a quantum computer” • The course of time orders that “anything” partially and gradually to some order • Even more, that order is the necessary and sufficient condition for that “anything” to occupy its destined place in the single universal order of all things

Time and ordering • Thus, any that should be a partial result in the ordering in the course of time from future to past by the meditation of the present, and of the choices made in the present • The time itself, or more exactly the natural course of time, is what orders all • However that natural course of time according to quantum mechanics is opposite and inverse to the prejudice of common sense: • The orderings grow up from past to future only by means of conservation without needing any free will for that, according to common sense

Arguments for the thesis: • (I) The course of time as ordering by itself • (II) Universal logic in terms of order and orderings • (III) The ontological interpretation of universal logic

Time in terms of quantum mechanics • Course of time can be described in terms of quantum mechanics as follows: • The future by itself is a coherent state, in which all is “mixed” in an absolutely homogenous way (Neumann 1932; Kochen, Specker 1968): • It is a superposition of all possible states, which can be interpreted both as states of the universe (following after Gibbs) and as items (separated elements) within the universe (after Boltzmann)

From a coherent state to a well-ordering • The absolutely coherent state of future decoheres gradually into less and less entangled quantum systems by means of choices (or “measurements”) made in the present • The next stage is the present • However it is not more than a “thin line”, a phase transition between two primary and opposite media or “rudiments of time”: future and the past

From community to dividing • Thus, those entangled quantum systems are being transformed in mechanical systems absolutely separated to each other in and after the limit from the present to the past • The tool of that dividing is de-coherence in a physical sense, or choice in both ontological and mathematical sense • This is the essence of the being understood as all existing and absolutely concentrated in the present: • However that essence transcends the present being referred to both future and past and can be designated as “time”

Universal logic • Universal logic can be considered as the series of partial orderings of some universal class, e.g. that of all sets • Any subset (“B”) of that class of orderings is a different “logic” • That subset “B” can be defined in two ways: • By means of some subclass or subset of that universal class of all as all orderings of it or some part of them: i.e. as the logic of something • By some property featuring unambiguously all elements of that class of the subset “B”

Two ways for a logic to be defined • Then, any given logic will be exactly one member of that series and can be defined: • (1) by the set, to which the partial orderings refer as its logic, and • (2) by the rule, which can generate just the partial ordering, i.e. by the property, which describes the set of all well-orderings representing the partial ordering in question • (1) refers the essence of logic to the matter, and (2): to the structure

(1) Logic as the “logic of something” • The definition (1) determines the logic as the “logic of something” where that “something” is the set or the class, which has to be ordered and its “logic” means the way and degree of that ordering • This suggests that the something in question is separated and distinguished from all other items in advance • Thus the ordering refers only to the internal structure of it rather than to external links, which are granted implicitly in the concept of that thing

Any scientific theory as a logic of something • The definition (1) includes both: • (1.1) Any scientific theory as the logic of the object of the theory, and properly • (1.2) The “logics of something” where that “something” is some set more interesting by the rule (2), which can generate it rather than by itself • Physics is an example of 1.1, and the too uncertain and amorphous class of all propositions as an example for 1.2

Logic defined by an abstract set of well-orderings • The definition (2) includes both: • (2.1) the case of the explicit property generating (all) well-orderings on any set independently of the interpretation of its elements, and • (2.2) the “topological representation” of the logic as the description of all well-orderings one by one rather than a common property determining unambiguously all well-orderings as it is in the former case

Logic as calculus • The idea for thought to be substituted by logical calculus has inspired logic for centuries • This suggests involving some relevant algebraic structure, usually such as lattice, in order to be formalized thought as a set of statements • Any set of well-orderings admits always a lattice and thus the cherished logical calculus to be deduced from it • However this is not true as to the initial, “material” set, to the set of subsets of which the wellorderings in question refer

Logic of something vs. logic as calculus • Consequently, the logic of anything turns out to depends essentially of what is ordered: • For example, any theory as that logic is true only in relation to its subject, but not at all • On the contrary, any logical calculus relying on the abstract properties of some sets of well-orderings and corresponding lattice is absolute independent of what is ordered • Consequently, the reduction of logic to lattices and thus different logical calculi is too attractive and ... dogmatic: Logic needs to abandon calculus ...

The ontological interpretation of universal logic • (III) The collaboration of quantum mechanics by the conception of quantum information allows of a natural ontological interpretation of universal logic • The universe and any item in it are to be “logical” in order to be able to become “past”, i.e. going to the past • The absolute and universal law consisting in transforming the future into the past implies universal logic

Ordering at all: both logic and time • There is a natural process of ordering in the course of time independent of what is ordered • The concept of universal logic and thus of any logic reflect the emancipation of order and ordering from what is ordered as well as the degree of that emancipation • The same emancipation can be also expressed by the concept of time and that of the physical time in nature in particular • One can say that both time and logic are different hypostases of one and the same for both are orderings

What is ordered ...

• What is ordered can be e.g. the world, i.e. the universe as a whole, or any part of it, i.e. any quantum system • What is ordered cannot be absolutely separated from the way of ordering • The cognition of ordering, i.e. the structure is referred as usual to logic and mathematics, and what is ordered to physics, biology and all other sciences: • There is an ostensible gap between them in cognition: the gap between the so-called spirit and matter

Universal logic “versus” what is ordered • So, universal logic can be interpreted as the successive partial results in the process of ordering independent of what is ordered • However universal logic can be understood “a little” otherwise: as a way that fundamental gap in cognition to be gradually overcome • This is the gap between • Spirit, subject, structure, mathematics, logics, and correspondingly: • Matter, object, thing or set, physics and natural sciences

Order, ordering, and well-ordering • That ordering is a well-ordering and it originates from the course of time • Thus “ordering” is understood in a rigorous and mathematical way • Furthermore, it can be referred to the qualitative concept of order at all • Information is some relation of orders • The quantity of information refers to the relation of well-orderings • Thus information and the quantity of information is immediately linked to universal logic and any logic in particular

The course of time orders ....

• According to quantum mechanics, the general course of time can be described as a (well-) ordering in thus • Consequently information should be also referred to the course of time expressing the relation of two or more different “times” or “logics” as different ways of ordering • That information units the past, present, and future as a universal concept and as a quantity invariant and conserving in the course of time • Consequently, information is what “glues” both time and logic

The choice of the present

• The coherent state of future is being ordered into the single well-ordering of the past here and now by the meditation of the all choices in the present accomplishing the ordering • Information can be also understood as the quantity of those ordering choices: • A bit is an elementary choice between two equally probable alternatives • A quantum bit (qubit) is an elementary choice among the elements of an infinite set • The corresponding information in the latter case is quantum: quantum information

The ordering of the orderings • That universal well-ordering in turn orders well all partial results, each of which is some logic • Consequently, the concept of universal logic means not only (1) A single universal and even logical and mathematical order of all, but furthermore: (2) A derivative, single, and universal order of all logics as a consecutive series of stages to the single universal logic or order

Universal logic as the series of all logics • Consequently, the series of all logics turns out to be well-ordered if that is the conception of universal logic • Even more, the quantity of (quantum) information can serve as a measure between two logics • The space of logics can be ordered in the distance of quantum information • That space is Hilbert space underlying quantum mechanics and thus nature according to it • The space of all logics turns out to be identical and thus indistinguishable from the space of all things

The “distance” between two logics • The distance between any two logics can be measured by the quantity of (quantum) information • However any value of quantum information is a wave function: • That is a state of some quantum system corresponds to any two logics • Consequently, the state of anything in the sense of quantum mechanics is the distance of two orderings as logics of it

Information as the distance between two logics: • Any logic is unambiguously determined by both: • (1) the information distance from the coherent state (the “absolute future”), and • (1) the single well-ordering (the “absolute past”) • The orderings underlie the things for any two of the formers represent a single state of the latters • Logic(s) underlies the world in the sense revealed by universal logic

Conclusions: • The concept of quantum information allows the universe to be considered as having both free choice and goal: thus both free will and teleology • This can be interpreted as a scientific equivalent or hypostasis of God • Universal logic is the result of the ordering of the universe • Any logic is a set of orderings in the way to a single universal order

REFERENCES:

• Conway, John and Kochen, Simon (2006) "The Free Will Theorem," Foundations of Physics 36(10): 1441–1473 (arXiv:quant-ph/0604079) • Conway, John and Kochen, Simon (2009) “The Strong Free Will Theorem,” Notices of the AMS 56(2): 226-232 (arXiv:0807.3286) • Kochen, S., Specker, E. (1968) Journal of Mathematics and Mechanics 17(1): 59-87.

• Neumann, J. von (1932). Mathematische Grundlagen der Quantenmechanik, Berlin: Springer, pp. 167-173 (Chapter IV.2).

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