The volume collects classics of Marxist historiography of science, including a new translation of Boris Hessen's “The Social and Economic Roots of Newton's ...

Our article is an overview of a selection of findings in physics relating to the issue of time—we do not present in it any “time theory” of our own. After making some general remarks on the issue of time, we present historical outline and a brief description of the current state of time interval measurements. Subsequently, we go on to discuss certain consequences of both theories of relativity: special and general. Here, time is a geometrical component of space-time continuum. Following (...) section is dedicated to time in the so-called Hamiltonian formulations of the theory of particles, where it appears as a parameter of evolution. The last section contains remarks referring to certain attempts of going beyond the recognized physical theories relating to the question of time. (shrink)

Historically, Ehrenfest’s theorem is the first one which shows that classical physics can emerge from quantum physics as a kind of approximation. We recall the theorem in its original form, and we highlight its generalizations to the relativistic Dirac particle and to a particle with spin and izospin. We argue that apparent classicality of the macroscopic world can probably be explained within the framework of standard quantum mechanics.

We give some information about new proofs of the incompleteness theorems, found in 1990s. Some of them do not require the diagonal lemma as a method of construction of an independent statement.

If $M \models PA (= Peano Arithmetic)$ , we set $A^M = \{N \subset_e M: N \models PA\}$ and study this family.

We give new proofs of both incompleteness theorems. We do not use the diagonalization lemma, but work with some quickly growing functions instead.

We transform the proof of the second incompleteness theorem given in [3] to a proof-theoretic version, avoiding the use of the arithmetized completeness theorem. We give also new proofs of old results: The Arithmetical Hierarchy Theorem and Tarski's Theorem on undefinability of truth; the proofs in which the construction of a sentence by means of diagonalization lemma is not needed.

We study cofinal extensions of models of arithmetic, in particular we show that some properties near to expandability are preserved under cofinal extensions.

Continuing the earlier research from [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001] we show that for the price of multiplying the number of parts by 3 we may construct partitions all of whose homogeneous sets are much smaller than in [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001]. We also show that the Paris–Harrington independent statement remains unprovable if the number of colors is (...) restricted to 2, in fact, the statement is unprovable in IΣb. Other results concern some lower bounds for partitions of pairs. (shrink)

For a primitive recursive consistent and strong enough theory T we construct an independent statement which has some clear metamathematical meaning.

We give a survey of automorphisms of countable recursively saturated models of Peano Arithmetic.

The article exposes the main theses of the ethical theory of Henryk Elzenberg, an eminent Polish philosopher and ethicist. The author outlines Elzenberg’s conception of ethics, the two types of values he differentiated, namely the „perfective” and the utilitarian, and the two ethical systems, the perfectionistic and the hedonistic, which characterises these two values. Finally, the author discusses the differentiation between goodness and beauty as the two perfective values as proposed by Elzenberg.

Let M be a countable recursively saturated model of Th(), and let GAut(M), considered as a topological group. We examine connections between initial segments of M and subgroups of G. In particular, for each of the following classes of subgroups HG, we give characterizations of the class of terms of the topological group structure of H as a subgroup of G. (a) for some (b) for some (c) for some (d) for some (Here, M(a) denotes the smallest M containing a, (...) , , and .). (shrink)

Archive Materials of Mieczysław Wallis are in the collection of Combined Libraries of Philosophy and Sociology Faculties of the University of Warsaw, the Institute of Philosophy and Sociology of the Polish Academy of Science and the Polish Philosophical Society. There are two files devoted to Henryk Elzenberg. They contain a rich historical material, not published before and not known to many people. It is a valuable source of knowledge in the field of the history of Polish philosophy. Wallis’s notes (...) provide a lot of unique informations both on Elzenberg’s private life and also his activity in the scientific community. Furthermore, they present his philosophical concepts, as well as his motions of life and adversities he had to cope with. M. Wallis’s memoirs are an unusual record of the friendship and scientific co-operation of the two scholars that lasted for a few decades. Wallis’s work creates also an intellectual testimony of the epoch, in which they both lived and worked. (shrink)

Henryk Skolimowski pays particular attention to the problem of ecological culture. He is convinced that only societies characterized by ecological culture are able to cope successfully with the most difficult problem of modernity which is the issue of the environment. The necessary condition for building man’s ecological culture, aside from equipping him with ecological knowledge as well as a system of values along with their normative equivalents, consists in shaping the pro-ecological attitude which manifests itself in particular actions. The (...) objective of the article is to present Skolimowski’s ideas on the essence of ecological culture and on the necessary actions to be undertaken to shape thinking, axiology, individual and social behavior in its light. (shrink)

This paper examines Tarskian semantics from the point of view of grammar. The author focuses on syntactic constructions available in languages used by Tarski, investigated by means borrowed from categorial grammar. He also tried to make the concept of truth, as defined by Tarski, closer to ordinary language.

Let M be a countable recursively saturated model of PA and H an open subgroup of G = Aut. We prove that I = sup {b ∈ M : ∀u < bfu = u and J = inf{b ∈ MH} may be invariant, i. e. fixed by all automorphisms of M.

We give some information about the action of Aut on M, where M is a countable arithmetically saturated model of Peano Arithmetic. We concentrate on analogues of moving gaps and covering gaps inside M.

We show that if M is a countable recursively saturated model of True Arithmetic, then G = Aut has nonmaximal open subgroups with unique extension to a maximal subgroup of Aut.