Anyone opening an entry page in this dictionary for the first time sees several things at once: a quotation giving the definition, with its source (on the English pages, a translation of the quotation from Mazur's Polish text), sometimes the number of the definition, a list of the concepts used in the definition, and a list of the entries that make use of it. This essay explains where these come from, that is, how Mazur builds his theories: how he forms definitions, where he starts and how he derives theorems from definitions. The entry pages for emotion, message and a few other entries will serve as examples.
One caveat to begin with. The word aksjomat (Polish for ‘axiom’) does not occur in any of the five books by Mazur discussed on this site, and there is no question of axiomatics here: in the view of the author of this project, Mazur did not formalise his theories axiomatically. He bases his argument on two things that he himself describes explicitly: agreements about names, and concepts that he uses without definition. That is where we must start.
Phenomenon first, then the name
Mazur starts from a question which, in his view, is pointless in science: ‘what is X?’. To answer it, one would have to understand what the questioner is asking, and it is precisely X that is not understood. Mazur shows this with the invented word ‘quax’: anyone asked what it means can only reply with the same question (Cybernetyka i charakter (‘Cybernetics and Character’, 1976), p. 26).
Scientists proceed the other way round. They describe the phenomenon they are studying, and since the description can be long and would have to be repeated every time the phenomenon is referred to, they agree with their readers to replace it with a short term. Mazur calls such an agreement a terminological convention (p. 27). Physics gives the model: instead of speaking each time of the ratio of energy to time, one speaks of power (p. 27). Hence an important conclusion: a convention cannot be wrong. At most a term can be inconvenient, and in a dispute one changes the name and keeps the description, because it is the description that shows which concept is needed (Jakościowa teoria informacji (‘A Qualitative Theory of Information’, 1970), p. 14).
Mazur applies this principle to himself. When he calls the action of the correlator on the homeostat emotion, he is not explaining an everyday word, but giving a short name to a phenomenon that interests him; he could have chosen another word, and he chose the one that readers would find easiest to take in (Cybernetyka i charakter, p. 30). He sums up the principle in the slogan ‘phenomena first, then terminology’ (p. 30). He approaches everyday words with caution, because they arose without definitions: one hears them many times in similar situations and falls into the habit of using them (p. 29). This is shown by the anecdote about the chess player Makarczyk, who took a German expression wishing someone an enjoyable meal for a fellow diner's surname and responded with his own surname (p. 29).
Mazur had described the same matters earlier, from the practical side, in Terminologia techniczna (‘Technical Terminology’, 1961). A term there is a name that cannot be understood without a definition, even if one knows all of its words: a termometr rtęciowy (‘mercury thermometer’) is not a thermometer made of mercury (p. 10). The principle of systematicity also yields a way of defining: it is enough to indicate the immediately superordinate concept and what distinguishes the given concept from it, as with an electric induction furnace, which is an electric furnace heating metal by means of a current induced in it (ibid., p. 30).
Two forms of definition on the entry pages
The dictionary has 309 entries and 313 definitions, because four entries have two each. The definitions come from three books and take two forms.
Jakościowa teoria informacji (1970) is an exposition with numbered definitions. Each has the same structure: first the term, then jest to (‘is’, the defining copula in Mazur's Polish) and the description. The number is made up of the chapter number and a sequential number within the chapter: Definition 3.3 introduces the message, Definition 6.2 introduces information, and Definition 7.1 introduces informing. In nine cases the term stands in the definition in its full, longer form, such as transformacja odwrotna do transformacji… (‘inverse transformation of the transformation…’), and the entry page gives it in shortened form. This book is the source of 141 of the dictionary's definitions; their order is shown in the definitions in order view.
Cybernetyczna teoria układów samodzielnych (‘A Cybernetic Theory of Autonomous Systems’, 1966) and Cybernetyka i charakter (1976) do not number their definitions. A concept appears in the course of the argument: Mazur singles out some part of a phenomenon and announces what he will call it. In the 1966 book this is usually done with a phrase built on będziemy (‘we shall’, as in ‘we shall call’; 26 of 48 definitions), in the 1976 book most often with the word czyli (‘that is’; 47 of 124). This is how, for example, rigid properties and character classes are introduced. These two books are the source of 172 definitions, taken word for word from sentences of the text (on the English pages, in translation); the page then notes that the definition is not numbered and shows the sentence in which it stands, in translation, with the Polish original below it. Both forms, however, have the same structure: on one side a name, on the other a description made up of other concepts.
The chain of concepts and its end
Every description consists of words that may themselves require an agreement. Mazur observes that such a chain of definitions could be continued without end, but in practice it breaks off at words that no longer give rise to misunderstandings (Cybernetyka i charakter, pp. 28–29). On the entry page, the first step of this chain is shown by the list of concepts used in the definition; the following ones become visible as you move from one entry page to the next. From emotion this leads through the homeostat, the accumulator and the alimentators to the autonomous system, whose definition refers to the ability to control and the ability to counteract its loss; neither of these two concepts has an entry of its own.
The chain thus breaks off in two kinds of places. The first are concepts adopted without definition. The dictionary distinguishes three of them: set, relation and elementary object, but only the set occurs in definitions, in 35 entries, and Mazur uses it in his text without defining it. This is the point at which the text stops defining, not a base from which the rest of the theory could be derived. The second are the fourteen concepts that occur in definitions but have no entries of their own, although Mazur specifies most of them elsewhere in his books; the concept graph shows them as a separate kind of node, and the guides to the domains list them in their ‘Open questions in the dictionary and the theory’ sections.
From definitions to theorems
Definitions are half of the method. The other half is theorems, that is, what follows from the definitions. Jakościowa teoria informacji has 33 of them, each with a proof; Mazur announces that they can be followed without a knowledge of mathematical logic (p. 12). The first theorems concern transformation itself, for example the fact that a transformation combined with its inverse transformation changes nothing (Theorem 4.3), and then they return in the same form for codes and for information. How the whole classification of transmissions follows from a single theorem is described in the essay ‘Information according to Mazur’.
In Cybernetyka i charakter the consequences take another form. From the definition of the character parameters follows the theorem that character cannot be remade. Mazur distinguishes two sides here: the theoretical truth of the theorem is of the same kind as the truth that a triangle has three angles, while its practical significance comes from the fact that such properties really occur (p. 274). From the theorem on character dynamism he derives 35 particular theorems, which the essay ‘Character as control’ discusses.
Theory and experience
Mazur distinguishes theory from empirical knowledge by what each tells us. Empirical knowledge tells us that one fact usually follows another; theory tells us how one fact turns into the other. He illustrates this with artillery fire: someone working empirically knows that after a shot the shells land, while a theorist calculates the point of impact from the point of firing and the path of the shell (p. 38). Every step of one procedure has its counterpart in the other: the sample corresponds to the model, measurement to calculation (pp. 39–40). A doubtful result is checked against a less doubtful one, so a weak theory is verified by strong empirical evidence, and weak empirical evidence by a strong theory (p. 40).
Hence the way in which Mazur treats agreement with experience. He derived the manifestations of exodynamism from an analysis of the correlator, not from observing children; when he compares them with what is known about children and finds agreement, he writes that it is the empirical evidence that agrees with the theory, not the other way round — just as a shaft turned on a lathe conforms to the geometrical model of a cylinder (p. 350).
How to read an entry page
All this suggests a simple way of reading. On an entry page it is worth checking the source first: whether the definition has a number or was taken from a sentence of the text. Then the concepts used in the definition, because its meaning depends on them, and the entries that make use of the given concept. Those who prefer to go step by step will find ready-made sequences of entry pages in the reading trails; the trail ‘From control to the autonomous system’ leads in fourteen steps from the first concept of cybernetics to the homeostat.