Philosophical issues of pragmatic theories: genesis and architectonics, I / Философские проблемы прагматических теорий: генезис и архитектоника, 1

Жолков Сергей Юрьевич кандидат физико-математических наук профессор, Российский государственный университет нефти и газа (НИУ) им. И.М. Губкина 119991, Россия, г. Москва, Ленинский проспект, 65 Zholkov Sergey PhD in Physics and Mathematics Professor, the Department of Applied Mathematics, Gubkin Russian State University of Oil and Gas (National Research University) 119991, Russia, Moscow, Leninsky Prospekt 65 sergei_jolkov@mail.ru Другие публикации этого автора

Philosophic Problems of Pragmatic Theories: Genesis and Architectonics

Sergei Yu. Zholkov (Jolkov)

Gubkin Russian State University of Oil and Gas, 119991, Moscow, Leninsky prospect, b. 65

Part I

1 Introduction

Human activity in its individual and particular social forms, its motives, goals and means, plans and actions are an essential subject of scientific research. Dedicated activity of individuals, human associations (economic, sociopolitical, religious, cultural, professional, ethnic), states and state formations — its subjects, in accordance with their objective interests and subjective errors in context of solving technical, military-political and social problems of society we shall refer to as real pragmatics (Greek πράγματος — course of action).

However, goals and actions of humans are based on their thoughts — “everything which sets men in motion must go through their minds” (Engels & Marx,1886)— the pragmatic theories formed in their minds that describe real pragmatics, its primary driving forces, relevant solutions and stratagems, shall be the cornerstone of future success or failure. Therefore, the definition of universally valid principles and requirements for veritable analysis and architectonics of pragmatic theories capable of supporting trustworthy conclusions, effective strategies and valid solutions in concreto is a natural and significant problem of information theory philosophy, system analysis and management. The veritability of a pragmatic theory and foundation of its conclusions is a necessary condition of correct decision and successful activity.

It should be noted that the Greek word πράγματος is used in philosophy in different conceptual formations. Introduced by C. Peirce in letters to Lady Welby, it served as a name to an entire school of thought. According to Peirce himself, pragmatism (pragmaticism in C. Peirce’ terms) is built on the methodological principle of testing the verity of basic foundations (“primary verity”) through verifying (“future serviceableness for our ends”) conclusions of a theory built on them. The very principle (technique) is not innovative — it was explicitly used by Aristotle as the second method of testing axioms (“Posterior Analytics”) — however, when highlighted by Peirce, it was subjected to heated discussions and branching development in works of J. Dewey, G. Mead, F. Schiller, S. Hook, W. Quine, D. Davidson, R. Rorty etc. It should also be noted that the term “pragmatic law” was introduced by I. Kant in “Critique of Pure Reason”, Section 1 of Canon of Pure Reason. Nevertheless, despite the use of the same Greek term (πράγματος), analyzing architectonics of pragmatic theories as theories of real pragmatics and human pragmatic activity built on those theories has little to do pragmatism and its problematics.

The natural interdisciplinarity of pragmatic problems and theories will be regarded in context of finding the required conditions of reliable, substantiated and effective solutions to practical problems of real pragmatics and not a “pragmatic turn” in general theory social sciences along the lines of “theory of practices”(Volkov&Harhordin, 2008). Neither “language games in the entirety of practices”, nor literature and methods of reading and interpretation based on authority of scientific communities, nor “doings and sayings”, nor the faith in reality due to loyalty to a certain way of life and thought, nor general theory concepts of historical sociology of science or, moreover, literary theory (Volkov&Harhordin 2008, 13–16,33,101) are considered. On the opposite, solution-related problems and methods are as objectivized as possible, and essential requirements are formed: to information as a source of future theory, to theory strictness during the process quantitative, logical and stochastic analysis, to substantiation of solutions’ and actions’ conclusions and constructivity.

The practical approach implies real problems of analyzing and managing large systems including technological, political, economic and social components (the last three being generally relegated to human sciences) as natural examples of pragmatic problems. We make decisions based on synthesized analysis of a system. However, the reality is that natural-science (technological) and human theories we must rely on have a drastic disparity in their degree of reliability. This stems from the difference in the level of requirements presented to technological and human knowledge accordingly. All this unavoidably reflects on reliability of a theory as a whole and subsequent prognoses and recommendations — and leads to woeful consequences.

System analysis of pragmatic problems in natural synergy of natural-science and socio-humanitarian components is a real necessity. But, as it’s commonly known, according to some highly influential point of view (tracing its roots to Windelband, Dilthey and Rickert) researching human-science components through precise and strict methods is impossible due to its “uniqueness”. Of course, the specificity of socio-humanitarian information, problematics and analysis methods is undisputable. But are they truly as “idiographic” and impervious to system analysis? It would be more fruitful to state which part of human-science activity can be subjected to strict fundamental andevidence-basedanalysis without denying the possibility a priori. This approach is consistent with the modern scientific cognition’s(post-non-classic scientific rationality by Stepin’s (2000, 2015) classification) multifactoriality of goals and interdisciplinarity of research.

This approach, proven to be necessary by specialists in mathematics, theory of management and system analysis (ex. (Kuznetsov 1999, 2001; Optner 1960; Moiseev 1982)), is also backed up by the philosophic stance formulated by (Stepin 2015, pp.102,100):

modern day natural science is marked by an increasing role of researching complex developing systems featuring “synergetic characteristics” and including humans and their activity as their components. The methodology of researching such objects brings together natural-science and human-science cognition, erasing the rigid barriers between them… however, it is necessary to recognize that cognition in socio-humanitarian sciences and natural sciences has common traits exactly because it’s scientific cognition. Their difference takes root in the specifics of application subject… Nevertheless, as complex as the subject of socio-humanitarian sciences is, a firm stance on its objective study and identification of laws is an essential characteristic of the scientific approach.

The aforementioned common argument of “scientific approach” in substantiation of synthesis of scientific research methods in “sciences of nature” and “sciences of spirit” and the fruitfulness of applying strict research methods of natural science for the human-science component of pragmatic theories will receive significant support in the end of the article, presented in new results. The acquisition of these results became possible through applying such synthesized research methods. Their expounding and comparative analysis with the paradigm of (post-non-classic) “theoretical knowledge” of V.S. Stepin is the main goal of this article.

It is essential to identify: the role of critical analysis of information for building an information base; classification of its objects; determining and studying the basis of a theory and structuring of its components; formulating common laws and requirements to architectonics of veritable and contensive pragmatic theories’components; confirming the fruitfulness of presented methods with new subject-applied results acquired through their use.

2 Critical analysis of information. Information base

Information on researched objects, processes and research subject as a whole, recorded via objective means of observation (monitoring), recordable, reproducible and verifiable (subject to free verification) — i.e. only objectivized as much as possible, can become the foundation of a veritable pragmatic theory. Its (information’s) merits or flaws will largely define the depth and adequacy of the theory itself.

The fundamental property of elements and systems in material world is the capability to be observed and recorded both by [scientific] tools and subjects (humans). Our notions depend on perception tools, both technical (i.e. microbiology could only emerge after the appearance of microscopes, etc.) and human-biological. Initial knowledge is always a result of experience, empirical or intellectual (study and analysis of texts: “extracted not from practice but taken from previously established systems of knowledge” (Stepin 2015, p.22)). “The cognizing subject always receives the subject of research… in form of practice, as it has no other way of perceiving reality other than through the prism of this practice” (Stepin 2015, p.84). Natural events always allow multiplication (repetition of direct observation and experiment through experience). Consequently, the majority of information in nature allows free multiplication — the possibility of repeating the experiment by any researcher (intersubjectivity), through which natural-science information can be verified and recognized by one. This allows singling out the meaningful factors, filtering the subjective component and then formalizing idealized speculative experiments, forming initial hypotheses and verifying them.

Most of pragmatic information on human activity (as opposed to objective information on physical world) is subjective and essentially is narratives of people as subjects of pragmatics. Personal experience of the absolute majority of people is limited — they are mostly focused on personal problems rather than the requirements of accuracy and completeness of reality perception, so the possibility of distortion is significant. Moreover, through inherited “thinking patterns” and “learned forms (Lorenz 1998, pp.341,345,371,389),established conventions and haste and unsubstantiated conclusions different people describe and evaluate the same events differently. Specifics of pragmatic information interaction also feature: heterogeneity of components; insufficiency and uncertainty of information; subjectivity of legislations and social mechanisms; subjectivity of actions and regulating institutions.

Objective perception of objects and events in real pragmatics isn’t any less (perhaps even more) important than it is for natural-science theories. Objective research of real pragmatics, independent of “internal conditions of our Self” (Lorenz 1998, 246), requires independent means of observation, measurement and statistical analysis suppliable by modern technologies. In presence of all modern observation means there is no reason to consider the socio-humanitarian realm less informative than the physical one and prohibitive of objectivizing (Lorenz 1998, pp. 246–47, 253–55, 258; Zholkov 2015) information. The subjective component in human-science realm is immensely more significant — however, that is a separate issue (more on human-science information: (Zholkov 2015)).

Pragmatic information necessary (and sufficient, accordingly) to derive all the assertions of a given theory is called a necessary (and sufficient, accordingly) information base. The aspiration of natural-science theories to minimize the necessary information base (“But to derive two or three general Principles of Motion from Phaenomena, and afterwards to tell us how the Properties and Actions of all corporeal Things follow from those manifest Principles”: Newton, Opticks, Query 31) is natural and justified. This should also be a guideline for pragmatic theories.

A necessary predecession of any theory is critical analysis of information, a meta-theoretical stage of research. An information base is empirics serving as a base for creating a theory’s empirical basis. Due to specifics of Russian language the word “base” is ambiguous. It’s both causes behind our statements and fundaments we build on. We shall define “bases” as causes (i.e. why, where from) and systems of fundamental principles — primary statements as theory basis (from what, on what), not base of theory. The information base of any scientific theory (including pragmatic) has a necessary requirement of adequacy — matching cognition with its subject.

The process of translating pragmatic information into a pragmatic theory’s information base must include correct structuring of information, verification of adequacy (reliability) and completeness, removal of contradictions. Critical analysis must identify facts – reliable results of observation and measurement to include into a theory’s information base. To become scientific information, facts picked from “pure stream of sense experience” (Quine 1979, p.2) must be structured, linked and arranged through critical analysis in context of future theory. “Experience itself provides no verity… The building of science requires not just material, but plan, harmony” (D.Mendeleev, cited from Smirnov 1974, p.91).

“No inquiry [is] possible without some conceptual scheme”, Quine states (1979, p.4); information laid into a theory’s foundation becomes scientific knowledge, not just “pure stream of consciousness” or reference — “traces not of past sensation but of past conceptualization” (Quine 1979, 10). Pragmatic information to be put into a theory’s foundation is not just a random set of facts, but a system of facts — structured, linked and built through critical analysis in context of future theory. Kant (1929) wrote, “In so far as the manifold representations of intuition are given to us, they are subject to the former of these two principles; in so far as they must allow of being combined in one consciousness, they are subject to the latter. For without such combination nothing can be thought or known, since the given representations would not have in common the act of the apperception ‘I think’, and so could not be apprehended together in one self-consciousness” (p. 156).

The “conceptual scheme” should only have veritable information synthesized into it, the facts. A veritable information base is the first step pointing us to the “sure path of science”, when reason “has to deal not with itself alone but also with objects” (Kant 1929, 18) — and as such, the problem of veritability remains one of utmost importance. Veritability depends, first and foremost, on accuracy and completeness of observations and measurements as well as safekeeping and availability of information.

3 Objects and expressive tools of pragmatic theories

The capability of being observed and measured by (scientific) equipment as well as human subjects is a fundamental property of several phenomena (substances, processes, events) in the outside world. This property is also shared by phenomena of substantive experiments conducted by a researcher, comprising an important (operational) part of modern research, differentiating them from speculative natural philosophy.

Elements of observable reality in our perception (and sensual contemplation) we refer to as entities. A significant part of empirical experience allows free multiplication. As discussed above, its constancy allows us to create the sufficiently reliable part of empirical information. Images of entities, linked in our consciousness in context of research and creation of theory (conception) we refer to as objects (in full accordance to (Kant 1929, p.441). These objects have an entity-based prototype (reference) – we shall refer to them as real and classify them as phenomenal objects.

Empirical experience also provides us hypothetical entities of evolutionary theories (based on archeological excavations) we assume to be pre-existing, but at the same time we have no real results of observing or measuring them. They become prototypes (references) of objects we can call hypothetical and also classify as phenomenal.

It must be noted that phenomenal objects are not just entities, but idealized entities and processes: material point with mass, its trajectory (sans width), ideal gas, surface without friction or a system impervious to outside influence etc. Quine (1979) calls them «deliberate [and] useful myths» and stresses that their non-existence in reality does not falsify mechanics; in a somewhat extreme expression, he calls them pointlessly true due to absence of counter-examples (p.250).

Objects of pragmatic theories matching observed entities and subject of socio-humanitarian activity with all the specifics of human-science information are also phenomenal.

Of course, real world entities and theory objects are not the same (horse ≠ “idea of horse”); Stepin (2015) suggests calling objects operated by a researcher inside theoretical scheme operational objects, researched entities – entities of research (p.58). Conjectures posed by objects in theory can extend beyond empirics just as assumptions can disregard meaningless properties of entities.

In (Stepin 2000) all subjects of a scientific theory are suggested to be called abstract and “ideal”, identifying two primary types of objects: empirical and theoretical.

Empirical objects are abstractions describing properties of real entities of experience. They are determined schematizations of real world’s fragments… Theoretical objects, unlike empirical, are idealized, “logical reconstructions of reality”. They can bear not just the corresponding properties and relations of real objects, but also properties not such object possesses. Theoretical objects form the essence of terms such as “point”, “ideal gas”, “black body” etc. In logic methodology research theoretical objects are sometimes called theoretical constructs as well as abstract objects… Expressions of theoretical language are built around abstract objects, links and relations of which form the immediate meaning of such expressions… as a replacement of certain real properties and real connections determined by practice… Such metamorphosis of entity properties into a separate object can be only conducted in abstract (Stepin 2000, 104–105).

However, in discussion of empirical objects it would be natural to focus not on abstraction (abstractio in Latin, interpreted as estrangement) but matching the object of theory with its prototype (reference) entity and separate objects of theory and their real referents as objects and entities. But — and that is a matter of fundamentals — objects of actual natural-science theories (let alone pragmatic) can have fundamental differences, so the object model proposed by Stepin (2000) must be clarified, supplemented and developed.

Let us start by classifying objects. Phenomenal objects do not and cannot fully describe a pragmatic or even a natural-science theory. The most important and prominent examples of super-phenomenal objects are real numbers and continuous functions (without which physical science would not exist). A real number is an infinite object that cannot be represented on any physical medium or verified by real equipment: an infinite non-periodic fraction cannot be recorded on a finite material medium since the area is finite (an infinite amount of numbers with a size limited from below takes up an infinite area), nor reproduced in reality in finite amount of time (as a finite amount of time can only contain a finite amount of real actions). Note that these are not even conceptual, but noumenal objects. However, without real numbers, continuous functions and derivatives it is impossible to define continuous movement and create models with continuous time and natural sciences as a whole. Essential elements of scientific theories span far beyond empirics.

The objects known to all since school: segments, triangles, polygons, circumference, disks… in geometry as a strict theory are also super-phenomenal objects containing an infinite amount of points. As indicated by the axiom of continuity (completeness) (Alexandrov1987,p.30).Moreover, any segment has the cardinality of continuum — strictly greater than the cardinality of a countable set — this fact is proven in any decent university course of mathematical analysis. All aforementioned geometrical figures have a cardinality of continuum — that is somewhat harder to prove.

In general, all objects defined through infinite procedure or possessing infinite properties would be super-phenomenal.

The separation of objects into phenomenal and super-phenomenal stems from the specifics of objects inside the theory itself. The specifics of our perception of reality induces a different separation of a theory’s objects: real and ideal. Real objects of a theory (realities) are marked by their entity prototypes’ affiliation with observable and measurable (and thus finite) empirical realm. Ideal objects of a theory (ideals) are a product of our minds. Of course, all ideal objects (ideals) would be super-phenomenal. All super-phenomenal and more so objects are products of rationalistic experience or, put differently, intellectual contemplation.

So, real objects of a theory can be phenomenal (for example, any natural or rational number, massive material bodies…), super-phenomenal (real number (reference – a point on a number line), continuous function (reference — a drawn plot)…). Ideal objects: a line; a plane; multidimensional space and its subsets; different complex objects of topology; infinite cardinal numbers determining the cardinality of any infinite set (transfinite number of its elements); infinite ordinals quantifying ordinal types of infinite ordered sets; molecules; objects of nuclear physics that cannot be directly observed or measured… The base of separating ideas into realities and ideals is formed by the ideas of D. Hilbert describing the notion of separating objects and judgments of mathematics into real and ideal in his 1926–28 works (details in (Kolmogorov &Dragalin 2004; Zholkov 2004).

It would be beneficial to definitively separate idealization and introduction to theory of ideals (ideal objects). Idealization implies assumptions that modify certain quantitative characteristics of real objects (not ideals) without changing the essence of entities or problems. The necessary elaborations would be appropriately considered along with the stance described in (Gaidenko 1993). Any phenomena (entities and processes) of empirical experience put together by our consciousness in theory fragments would “belong to the sphere of thought” (Gaidenko 1993, 181–82). In a sense they would become idealized, as in theory we distance ourselves from negligible differences of real entities (always present) we theoretically equate to the same object. However, a view on the most basic objects of finite mathematics, natural numbers, as “ideal formations” as described by A.Szabo and P.P.Gaidenko (in Gaidenko 1993, p.181–82) in the discussion of ancient Greek “mathematical program” seems to be a controversial concept (even if dating back to Plato).

All objects of a theory are “theoretical” (different from real entities), so the division offered in (Stepin 2000, p.104) or (Stepin 2015, p.29) seems less clear:

Among ideal objects… it is customary to identify at least two basic varieties – empirical and theoretical objects. Empirical objects are abstractions capturing the properties of real entities of experience… Properties carried by empirical objects can be found in corresponding real entities… Theoretical objects, unlike empirical, are idealizations… Only some of theoretical objects can be defined strictly inside the theory… This fact is often in scientific logic as a statement that not all, but only some terms of a theoretical system must have an operational meaning.

A.I. Lipkin also proposes classifying all objects of physical theories as “ideal” (Lipkin 2015, p.199).

Of course, it is impossible to observe or verify dogmatic notions of religions and ethical norms (as such they exist in plural). They go beyond the limits of both empeirea and ratio as they are based on dogmatic postulates of faith, not reason.

Means of expression are means of describing objects of research and their properties, relations between them (interconnections), making judgments and formulating problems; in short — means of description and research.

In process of cognition and interaction humans use various means of expression: musical; plastic: (gestures, dance, ballet); visual (graphic arts, including digital, ideograms, visual imagery) — a visual plot can tell a mathematician just as much as words and symbols; it would be appropriate to mention a certain Zen practice, koan; and, of course, the most profound one — language. But the complications emerging in process of constructing scientific theories: forming up basic principles, critical analysis of information or semantic knowledge, conclusiveness of the findings, their interpretations go beyond purely linguistic problems. Technological problems of theories (activities) are not problems of language, their solutions are problems of technology — not linguistics, new technologies are not reducible to linguistic innovation.

Words in natural speech (as combinations of letters/sounds or ideograms) indicate objects of knowledge. Phrases express actions, properties and connections, and develop into texts — moreover, any formalized theory uses phrases of natural speech. Then our consciousness qualifies phrases as true or false — consistent or inconsistent with our experience and knowledge.

In pragmatic theories a special language would be appropriate to use in mathematical models for qualitative or quantitative analysis in presence of sufficient numerical statistics or as a formalized apparatus of conceptual models. Special language of a theory in construction has universal structure regardless of substantive content. Theories start with introduction of concepts — primary terms: a minimal list of undefinable terms, determined as undefinable as any attempt to descriptively define them would lead to creation of new terms, invalidating the attempt. To the ends of depicting objects, symbols are introduced (strictly speaking, letters or ideograms of natural language are also symbols): for constants — symbols of individuals and object variables expressing basic terms. It is possible that variables have a different nature or even different origin — then they are sorted and discussed as individuals or variables of a given sort.

Noted, the term “concept” was used back in the days of Abélard in XII century, but differently — as a universalia connecting an entity and expression of an entity, as a universal bond between entity and name — which, unlike a “term”, is inextricably linked to communication (Abelard 1995; Neretina 1994).

For naming entity prototypes (references) it seems appropriate to use V.S. Stepin’s term of “construct” (Stepin 2000, 2015).

But if concepts are not defined, how are they introduced (determined)? — Through relations (defining connections), operations (defining actions performed with objects), properties defined in basic principles (see next chapter). This is the model proposed by Aristotle; in Prior Analytics he speaks of an indirect identification of an object’s essence by properties as its “characteristics”. A universal and commonly known example would be Euclidian geometry, as it is described and analyzed in (Zholkov 2013). Subsequently, the understanding of concepts’ nature and the single possible way of their introduction provided by Aristotle was lost, and descriptions shifted to being started with verbose definitions.

Functional symbols that define operations with appropriate variable, propositional variables and predicate symbols for formulating statements and logical inference are also considered defined. Then by inductional rules (from simple to complex) phrases and texts of a theory are formed. All this shapes the language of a theory — and does it inductionally, from simple to complex (not inductively, from particulars to generals); mathematical theories are also structured inductionally (Kolmogorov &Dragalin 2004; Zholkov 2004); inductional structure of science is also demonstrated in (Stepin 2015, 24).

All objects of a theory are described via symbols and other means of language. Some of them are concepts, others are derivative objects (terms) defined through concepts and axioms through logical and functional constructions. All this is discussed below.

To be continued (Part 2)