Witold Marciszewski

There is a lot of fuzziness about the concept of civilization, and this is why the paper starts from an attempt to clarify this concept. This consists in selecting one entity which is commonly acknowledged as a system of civilization, examining its main features, and then exemplifying how to define them operationally. These features are treated as if they were answers to certain questions. Now other systems can be addressed with the same questions; if a system is able to answer them, in this way or other, it proves to be a civilizational system. The answers expected are those to express attitudes toward science, democracy, free market, tolerance, etc. Islam, e.g. does not prove to be a unique civilizational system, since there are represented in it much varying attitudes in each point in question. On the other hand, the communist paradigm does so, since it offers an answer of its own in each of the listed issues. Its answers directly oppose those offered by liberal civilization, thus there are at least two paradigms of civilization, the liberal and the anti-liberal. In the second part, it is argued that though the West is the cradle of liberal civilization, there is no one-to-one correspondence between the trait of being Western and that of being liberal. Also the main totalitarian projects of civilization were bom in the West, while same seeds of liberal civilization (Christianity, science as stemming from mathematics, etc.) came from the East. Nowadays, significant contributions to liberal civilization are due to people from any race, culture and continent. The destiny of liberal civilization is to become universal, while the Western contribution to it, when seen in a great evolutionary perspective, is just a historical episode.

The paper is meant as a survey of issues in computational complexity from the standpoint of its relevance to social research. Moreover, the threads are hinted at that lead to computer science from mathematical logic and from philosophical questions about the limits and the power both of mathematics and the human mind. Especially, the paper addresses Turing's idea of oracle, considering its impact on computational (i.e., relying on simulations) economy, sociology etc. Oracle is meant as a device capable of finding the values of uncomputable functions. Such an idealized entity is exemplified by the human mind's procedure of recognizing the truth of the Gödelian sentence, of identifying uncomputable numbers through Turing's diagonal procedure, etc. Since such procedures are strictly defined and are as reliable as any calculations, they are worth to be called computation as well. From the computation in the strict sense, that defined as purely algorithmic (mechanical) process, one distinguishes them with the term "hipercomputation". Now the following questions arise. - Are there undecidable problems (ie. not decidable with appropriate algorithms) in social research as are (according to what is reported esp. By S. Wolfram) in natural sciences? The answer in the negative would impose limitations on computer simulations (as entirely relying on algorithms). - If there are, then we have the next question: can such problems be addressed with hipercomputational procedures? - How such hipercomputational procedures would be related to analog computation (coextensive, everlappiing, etc.)? Another set of issues is stated in terms of tractability of decidable problems, that is, the efficiency of algorithms needed for solutions. As inefficient are regarded those which require more resources (time, memory, etc.) than is available in a foreseeable future. In this context, one discusses methods of such an efficient organizing computational processes to overcome the scarcity of resources; thus parallel, distributive, interactive, etc. computing are used as remedies. The paper claims, hinting at F.Hayek's ideas, that in some social systems (e.g., stock exchange, and free market in general) such an efficient organization of their computational activities spontaneously evolves. And this is the main source of its advantages over the central economic planning (as defended by O. Lange). This noticing (in terms of complexity theory) of analogy between Hayek's point and the current discussion of efficiency of algorithms is what may count as an original contribution of the present paper

When discussing Kazimierz Ajdukiewicz's role in philosophy, it is worthwhile recalling his participation in scholarly controversies. It was characteristic of his open mind that his taking part in debates was motivated by a vivid interest in various ways of thinking. Ajdukiewicz's intellectual power consisted, so to speak, in his ability of not to understand. This ability has brought him success in some important debates, concerning i.a. the classical logical concept of contradiction and the debate on universals raised in modern Poland with the nominalistic program of Stanislaw Lesniewski and Tadeusz Kotarbiński. In this latter debate Ajdukiewicz shows that when one says that individuals exist, the word „exist" refers to something different that in the statement that universals exist. In other words, the functor „is" has a different category in the definition of an individual from that appearing in the definition of a universal; hence there must be two different senses of the word „exist"

1. STRUCTURE AND REFERENCES 1.1. The main part of the dictionary consists of alphabetically arranged articles concerned with basic logical theories and some other selected topics. Within each article a set of concepts is defined in their mutual relations. This way of defining concepts in the context of a theory provides better understand ing of ideas than that provided by isolated short defmitions. A disadvantage of this method is that it takes more time to look something up inside an extensive article. To reduce this disadvantage the following measures have been adopted. Each article is divided into numbered sections, the numbers, in boldface type, being addresses to which we refer. Those sections of larger articles which are divided at the first level, i.e. numbered with single numerals, have titles. Main sections are further subdivided, the subsections being numbered by numerals added to the main section number, e.g. I, 1.1, 1.2,..., 1.1.1, 1.1.2, and so on. A comprehensive subject index is supplied together with a glossary. The aim of the latter is to provide, if possible, short defmitions which sometimes may prove sufficient. As to the use of the glossary, see the comment preceding it.

This paper represents such an amateur approach; hence any comments backed up by professional erudition will be highly appreciated. Let me start from an attempt to sketch a relationship between professionals’ and amateurs’ contributions. The latter may be compared with the letters to the Editor of a journal, written by perceptive readers, while professionals contribute to the very content of the journal in question. Owing to such letters, the Editor and his professional staff can become more aware of the responses of educated public to the journal’s output

There seems to be something mysterious about applications of for- mal systems, including those of logic, to empirical reality 1 . If logic is to be applied to empirical situations, like those described in an ordinary lan- guage, then { it seems to some people { its statements cannot be necessary, or analytic, propositions. However, they are both applicable and necessary. This supposed puzzle constitutes a signicant part of the problem of philo- sophical foundations of logic 2 . To this mind of the present writer, there is no mystery of applications, since any empirical, or even ostensive, predicate can be involved in cer- tain meaning postulates, e.g. \No red is green", which are both empirical and necessary propositions; empirical as they involve ostensibly dened predicated; necessary, as it is enough to know their meaning to state, their validity. The case of logical theorems can be considered at the same footing, logical constants being treated as dened ostensively. Nevertheless, not an individual state of mind but the actual state of scholarly discussions makes something a problem; in the present state of foundational discussions on logic, the \mystery of applications" preserves its vitality, hence any new way of dealing with it proves welcome

Intelligent problem-solving depends on consciously applied methods of thinking as well as inborn or trained skills. The latter are like resident programs which control processes of the kind called (in Unix) daemons. Such a computational process is a fitting reaction to situations (defined in the program in question) which is executed without any command of a computer user (or without any intention of the conscious subject). The study of intelligence should involve methods of recognizing those beliefs whose existence is due to daemons. Once having been aware of so produced belief, one can assess it critically and, if possible and necessary, make it more rational. Eg, beliefs concerning properties of time are produced by a daemon-like intuition, likewise the Euclidean properties of space. The merit of getting aware of such daemon's activities, and so transforming implicit beliefs into explicit ones, lies mainly in the axiomatic characterization of the properties involved. That makes possible to improve a daemon-like conceptual equipment (producing beliefs) by suitable modifications of the axioms, or postulates. Such postulate sets can also define artificial daemons to either emulate or improve natural intelligence.