Analogia entis as analogy universalized and formalized rigorously and mathematically in quantum mechanics as the shared base of nature and knowledge

Analogia entis as

Analogy universalized and formalized rigorously and mathematically in quantum mechanics as the shared

base of nature and knowledge

Vasil Penchev

• Bulgarian Academy of Sciences:Institute for the Study of Societies and Knowledge:Dept of Logical Systems and Models

• [email protected]

THE SECOND WORLD CONGRESS ON ANALOGY, POZNAŃ, MAY 24-26, 2017• (The Venue: Sala Lubrańskiego (Lubrański’s Hall at the Collegium Minus),

Adam Mickiewicz University, Address: ul. Wieniawskiego 1)• The presentation 24 May, 15:30

Introduction

The criticism of analogy• Analogy is often criticized for being unable to distinguish true

from false statements for both admit (and are admitted by) analogyo Analogy may be interpreted as metaphor and thus may be

both true and untrue• It admits more than one interpretationo Some interpretations of an analogy may be correct, and some

incorrect• Analogy seems to be relevant only to the first stage of

cognition or to the popular exhibition of science rather than to science by itself

The corresponding perfection of analogy

• This implies at least two directions for the perfection of analogyo Both refer to the relation of truth and analogy

• The first one starts from the truth as adequacy and tries to “repair” the analogy according to the criterion of adequacyo The second one, on the contrary, starts from the analogy as

such and search for a certain new kind of truth adequate to analogy as it is by itself

• Those two directions reflects the tension between analogy and scientific cognition

“Good analogy” vs “bad analogy” • The first one consists in the formally and disjunctively

separation of "good analogy“ from “bad analogy”o The former should generate only true statements unlike the

latter allowing of false propositions• However, repairing it in thus, it cannot be analogy properly:

o“Good analogy” is not an analogy• An analogy properly can be only “bad analogy”

o Any scientific notion or concept can be thought as a “good analogy” originated from some “bad analogy”

• However, scientific notion is not an analogy any more, after its perfection

The analogy mathematically formalized and rigorous

• The second pathway for perfecting analogy suggests it to be formalized as a way of modal, possible, and probable reasoningo That pathway correspons to analogy but does not to truth as

adequacy• Now, truth cannot be thought as the disjunctive alternative of

any statement falseo “True” (as well as “false”) is not quality from now on: hence, it is

quantity • Any statement turns out to be more or less true as well more or

less false

“Analogia entis”• Furthermore, one can add to the latter direction the ancient

and medieval, rather theological idea about the universality of analogy:

o Both things and statements share it as analogia entis• Then, analogia is the way of existing or being rather than

only a way of cognition or representing knowledgeo One should complement from the contemporary viewpoint

that all things are only probably existing just as all statements are only probably true

• The border between words (statements) and things is blurred once both have shared the model of probabilistic truth

Analogia entis: both probable reasoning and being

• This implies the intention for the probable reasoning in analogy to be unified with the probable existence of the things in realityo That approach is consistent to unifying both words (statements)

and things in analogia entis• Even more, the former probable reasoning/existence and the

latter ontological universality of analogy in analogy entis appear to be the same in a senseo Both probable and analogical seems to be both thing and word

(statement)

A few “side effects” of quantum mechanics• That fundamental problem was resolved in fact by quantum

mechanicso Indeed, its immediate and main task was how to describe

formally and mathematically the unification of continuous (smooth) motion in classical physics and the discrete motion

forced for the fundamental Planck constant• However afterwards, many borders in human cognition turn

out to be overcome for an impressive series of unificationso It includes both unification of things and words (statements)

and probabilistic unification of truth and untruth as a single unification in essence

Thesis:

Thesis (1)• The wave function of any quantum system can be

interpreted as its quantitative degree of analogy to any other quantum system• Therefore, it represents analogia entis in a rigorous, formal

and mathematical way in a scientific discipline such as quantum mechanics

• Any quantum state of any quantum system expressed by a wave function may be interpreted as the represented quantitatively analogy of that quantum system to all other quantum systems in the universe

• Quantum mechanics can be interpreted as a scientific doctrine of analogia entis

Thesis (2)• Furthermore, vice versa: a certain wave function can be

ascribed to any analogyoThus, it allows of its interpretation as the description of

some possible or existing quantum system• Indeed, the metaphysics of quantum mechanics involves

both cognition and reality as “complementary” and thus equivalent dimensionsoTherefor, both concepts of analogy and wave function may

be applied to both cognition and reality• As a result, a kind of mathematically described and universal

analogy as analogia entis can be introduced

Thesis (3)• The latter completes analogia entis formally and

mathematically for identifying any state "by itself" with some statement in analogy, i.e. with a proposition in our cognitiono Thus the fundamental intention of analogia entis turns out

to be realized in a quite unexpected way• That way consists in the meditation of a mathematical and

physical concept such as wave function for analogia entis to be grounded both theoretically and experimentally rather than only reasonably or in tradition

o As a result, quantum mechanics can be interpreted as a practical and scientific doctrine of analogia entis

Two main arguments for the thesis

Argument (1)• Any wave function can be interpreted as a series of qubits o A qubit is defined as usual as the normed superposition of two

orthogonal subspaces of the separable complex Hilbert space• That is way to be introduced it in quantum mechanics

o It may be considered equivalently as the generalization of the concept of a bit of classical information:

• If a bit is a choice between two equally probable alternatives, a qubit is the choice among an infinite set of alternativeso Thus a wave function being a quantity of quantum information is

able to describe mathematically the information of any infinite set or series

More about the Argument (1)• Then, each of those two orthogonal subspaces involved in the

definition of ‘qubit’ can be in turn interpreted as the quality of the same name in two independent (quantum) systemso Furthermore, the value of the qubit can be accepted as the

quantitative value of similarity (analogy) between the two system as to the quality at issue

• As: (1) any wave function is a value of quantum information inunits of qubits, and (2) any qubit means the degree ofsimilarity and analogy of the same quality in two different andcompared entities, the conclusion is:o (3) That wave function represents quantitatively similarity or

analogy of those two entities quality by quality

Argument (2)• Given any analogy decomposed as a “sum” of analogies of

the union of all qualities possessed by both systems as it was explained just before:

o The sense of the “sum” of analogies means that only the same quality can be analogical in both entities

• Furthermore, different qualities are represented by different qubits and thus independent of each other, or “orthogonal” mathematically saido Analogy turns out to be decomposed in a set of elementary and independent analogies, each of which correspond to the

same quality in both entities

More about the Argument (2)• Then, a value of qubit may be assigned to any particular sub-

analogy referring to a single qualityo A qubit as well as a bit is a unit of information

• This means that wave function is the quantity of information contained in an analogy of whether statements (words) or things, of whether cognition or reality

o As a result and particularly, cognition is grounded to be analogical to reality not less than a part of reality can be

analogical to another as well as a piece of cognition to another• The concept of wave function just as that of analogia entis is able

to underlie the fundamental possibility of cognition in a philosophical sense

A short comment of the thesis ant the arguments in its favor

The comment:• The thesis and arguments refer only to the interpretation of wave

function: they extend its meaning from the description of any quantum (and thus physical) system to the knowledge of the system by analogyo Quantum mechanics was the first scientific discipline crossed trough

the gap of cognition and reality• It was forced to do this for the a fundamental property distinguishing

it from all other sciences, which was articulated and postulated by Niels Bohr:o Quantum mechanics studies the system of measuring apparatus and

measured microscopic quantum entity only by the readings of the former

• Thus quantum mechanics includes cognition into reality inseparably

Identifying knowledge and reality• Thus the knowledge and reality of any system can be identified right in

the tradition of analogia entiso It links all to all by the tool of analogy: the unity of all underlies that

kind of universal and fundamental analogy• Thus, knowledge and reality are merged by and into analogyo Science created itself in modern age breaking the universal links of all

to all• It studies anything only analyzing and separating it from all others in

order to individuate a few essential causal reasons or interactions determining its behavior unambiguously

o Therefor, the fundamental condition is the initial distinction of knowledge and reality

The formalized holism borrowed from quantum mechanics

• Anyway, quantum mechanics manages to restore the holism of analogia entis in both mathematical and experimentally confirmable methodo Any item is described also as a state of the whole, or as the

description of its analogy to all other items in the universe• The cognition of the whole represented by a certain state of

the whole can be identified as reality as the existence of a determined part of the same whole

o A complicated symmetry appears: (cognition – whole –state) is equivalently transformable into

(existence – part – properties)

About analogia entis• Is that symmetry universal? Or the case of symmetry is only a

particular case?o Anyway, analogia entis seems to be the case of symmetry,

whether particular or universal• It is complementable by any nonzero difference of a state of the

whole and the corresponding part of the same whole in generalo However, that general case might be equivalent to the case of

analogia entis, alleged as particular• The concept of information unifying classical and quantum

information advocates in support of the equivalence of the “particular” case of analogia entis to the general one violating the symmetry

Conclusion

The world in analogy

• The world can be represented exhaustedly and quantitatively only by means of analogyo Analogy is equivalent to both difference and equivalence of

the corresponding part and state of the whole• Thus analogy is fundamentally holistic

o Quantum mechanics traces the pathway in which holism therefore analogy can be unified with science in both

consistent and mathematical way• That approach allows of restoring the doctrine of analogia

entis as the fundamental ontology, underlying quantum mechanics in particular

The self-referentability of analogia entis• Furthermore, the difference of a part and state of the whole can be

represented in turn as an analogy therefore implying the absolute universality of analogyo Analogy concentrates attention on the common or shared part of the

whole meant by it• That part does not exhaust the whole, but anyway it represents

relevantly a certain aspect of the latter and thus a state of ito Given the concept of quantum information as the information of

infinite series or sets, then:o The quantity of quantum information in the corresponding part and

state of the same whole can be equated to each other asa fundamental principle both philosophical and physical as well as

mathematical

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