Witold Marciszewski

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.

The first good message is to the effect that people possess reason as a source of intellectual insights, not available to the senses, as e.g. axioms of arithmetic. The awareness of this fact is called rationalism. Another good message is that reason can daringly quest for and gain new plausible insights. Those, if suitably checked and confirmed, can entail a revision of former results, also in mathematics, and - due to the greater efficiency of new ideas - accelerate science’s progress. The awareness that no insight is secured against revision, is called fallibilism. This modern fallibilistic rationalism, i.e. the belief in the attainability of inviolable truths of reason which would forever constitute the foundations of knowledge. Fallibilistic rationalism is based on the idea that any problem-solving consists in processing information. Its results vary with respect to informativeness and its reverse - certainty. It is up to science to look for highly informative solutions, in spite of their uncertainty, and then to make them more certain through testing against suitable evidence. To account for such cognitive processes, one resorts to the conceptual apparatus of logic, informatics, and cognitive science.