Václav Polák:

Mathematized Humanities via Humanized Mathematics

DAVAY Brno, 1992. Czech Republic, EU.




ln this book, operation logic is presented and on its base paramathematics is developed.

Operation logic (denoted also as ols-logic or simply OLS which means the abbreviation of operation logic system) is a formal logic, which is nonmonotonic, paraconsistent, multiagent and dynamic logic, which has local and limited reasoning, which has selfreflection and knowledge integration and which has living-through semantics.


Paramathematics is a part of mathematics. It represents the new mathematical methodology. Classical mathematical methodology works on the basis definition-theorem—proof. Every definition must be precise. Every theorem must be valid without exceptions and is valid for ever. Proof is the lecturing about the rule-based deductive reasoning. Mathematical theory is logically omniscient and does not contain contradictions. Paramathematical methodology on the other hand works on the basis declaration-assertion—justification. Declarations define notions either by mathematical definitions or by examples, case studies, analogies, metaphors and declarative definitions. Assertions are either mathematical theorems or general statements with exceptions, which may be invalidated (so assertions are valid not for ever). Justifications are either mathematical proofs or represent other types of reasoning (case-based. qualitative-based, ideological-based and knowledge-interpretation-based). Paramathematical theories may contain contradictions.

Classical mathematics is based on first—order predicate logic (fol—logic),  so classical mathematics is fol—mathematics.

Paramathematics is based on ols-logic, so paramathematics is ols—mathematics. lt uses ols—well-defined-formulas, which are semantic-language-clauses. These formulas are close to natural language sentences, but they work with notions (not with words) and they contain no grammatical rules. The semantic language is defined by ols—phrasal—lexicon, in which there are stored all used semantic—language—clauses_ all used semantic—language-nouns, all synonyms, metaphors, analogies, case studies, semantic features, declarative definitions, metaphoric definitions and images of prototypes.

Social sciences uses natural—Ianguage-based common—sense reasoning in their theories. Paramathematics represents the formalization of this process. So every human science theory can be translated into paramathematical theory without a loss of information and without semantical deformations. So presented  paramathematics is a humanized mathematics and paramathematical theories represent mathematized humanities. So paramathematics is a tool for transforming social sciences into exact sciences.


This book consists of these three mutually independent (but supporting each other) parts:

(A) Operation logic — a base for paramathematics [1992)

(B) Paramathematics for social science theories (1991)

(C) Language, consciousness and algorithmic personality (1990)


The part A contains the basic information about operation logic and paramathematics, and compares OLS with other logics. The part B presents OLS as the set of algorithms navigating along certain evaluated oriented multigraphs and creating these multigraphs. By this implementation aspects of OLS as artificial intelligence system is studied, too. Also as example ols-living-through of a small part of one ols—story is exhibited here. Also as example the small part of paramathematical theory of types of forest ecosystems (representing qualitative ecology) is shown here. The part C presents OLS as the theory of special nested sequences starting from basic sequence called basic-pattern-of-consciousness, Then ols—paradigm of language is exhibited and ols-personality processing is defined (speech-acts processing, multicriterial decision—making, reasoning, knowledge—integration hierarchy (with meta—knowledge of philosophical categories and ethical attitudes), knowledge—interpretation processing, mimics and emotionality processing, program—synthetizing as a part of from—experience—learning). Then as example one paramathematical theory of anthropogenesis is developed. Then steam engine innovations are presented as example of creativity processing. Also humor processing and a meta—knowledge for analysing stories are done. Also a methodology of ols—analyses (i.e. linguistic, semantic and system ols—analyses) are described. At last the simplified model of procaryotic cell is done, exhibiting basic-pattern—of—life, which is an analogon to the basic—pattern—of-consciousness.


The presented book addresses many types of scientists. All these scientists must first read Al., A2., A2.1. — A2.3., A2.6., A2.7., and then (according to headlines in contents) they can read any other presented topics which they are interested in. Namely this book can read mathematicians, logicians, computer scientists (working in artificial intelligence), psychologists, linguists, sociologists, scientists working in evolution theory  (fylogenesis, anthropogenesis. sociogenesis, technogenesis and ontogenesis), philosophers studying knowledge integration, art scientists and application scientists studying multicriterial decision-making (urban planning. land—use planning. Political decisions, decisions in entrepreneurial strategies and medical decisions).


This book is sponsored partly by Masaryk University within scientific duties of the author, and partly by Avenira Foundation within the grant “Usage of Smidak principles in applications of operation logic". If one uses Smidak principles (see Smidak E.F., Smidak Prinzipien (Avenira, Luzern 1991)) in OLS, one obtains very powerful tool for knowledge-integration applications.


I thank to PHDr.h.c. E.F. Smidak, president of Avenira Foundation, for interest, very valuable support and inspiring discussions about applications of Smidak principles in human society.


Brno, May 3. 1992. Doc. RNDr, V, Polak CSc,

Department of Appl. Math., Faculty of Sci., Masaryk University -

Janackovo nam. 2a. CSFR-66295 Brno, Czechoslovakia


Dr. Vaclav Polak