Wonderful Knowledge. Aquinas on the Immutability and Eternity of God’s Knowledge The general concept of knowledge is a kind of concept closely akin to transcententals: its use is not restricted to a certain kind of being, and it does not itself designate a kind of entity. Such concepts may be applied to God not as metaphors: when we grasp (through the analysis of cases of finite knowledge) some general traits of knowledge as such, we can show that God has knowledge, (...) and his knowledge, as opposed to ours, is infinitely perfect. We have no insight into this realization of knowledge as opposed to ours, but as far as we know what general traits of knowledge are, it is important to know that God has infinitely perfect knowledge. To grasp the general traits of knowledge, I focus on the topic of mutability and immutability of knowledge analyzed systematically by Aquinas, and thus on the topic of identity criteria specific for knowledge in general: the question of when knowledge that p and knowledge that q are (in a certain knower) one and the same knowledge; the criteria of identity of knowledge vary according to natures of knowers. I think that the problem of the criteria of identity of knowledge is rather neglected in omniscience-immutability discussions. I analyze Aquinas’ arguments for the thesis that human knowledge is mutable, and God’s knowledge is absolutely immutable (they concern the role of tense). The analysis sheds light on some general traits of knowledge: it is always something formulated by the knower which manifests some truth to him, and in general the way it is formulated corresponds to (i) the way it manifests some truth, (ii) its identity criteria, (iii) the way it is propositional, (iv) the way it is related to tense, and finally (v) the nature of the knower. Focusing on the criteria of the identity of knowledge shows that God’s knowledge is absolutely immutable, and that time and change in its objects are nevertheless undoubtedly real. Keywords: God’s knowledge, knowledge, criteria of identity of knowledge, immutability; tense; transcendentals; omniscience-immutability arguments. (shrink)

In this paper we study the status of the arithmetical completeness of dynamic logic. We prove that for finitistic proof systems for dynamic logic results beyond arithmetical completeness are very unlikely. The role of the set of natural numbers is carefully analyzed.

A. Klimczuk, M. Skarzyński, Wnioski i rekomendacje, [in:] M. Juchnicka, Doradcze i edukacyjne aspekty reorientacji zawodowej i wsparcia zatrudnienia zwalnianych pracowników oświaty, Izba Rzemieślnicza i Przedsiȩbiorczości, Białystok 2015, pp. 289-306.

A. Klimczuk, M. Skarzyński, Modernizacja szkół zawodowych w oparciu o programy rozwojowe, [in:] M. Juchnicka, Formalnoprawne aspekty modernizacji szkolnictwa zawodowego, Izba Rzemieślnicza i Przedsiȩbiorczości, Białystok 2014, pp. 119-144.

A. Klimczuk, D. Borowski, M. Skarzyński, Wnioski i rekomendacje, [in:] M. Juchnicka, Formalnoprawne aspekty modernizacji szkolnictwa zawodowego, Izba Rzemieślnicza i Przedsiȩbiorczości, Białystok 2014, pp. 161-170.

The paper contains a comment on the criticism of the author's book Początek jest wszędzie (Prószynski i S-ka, 2002) by Marek Lagosz ("Przegląd Filozoficzny - Nowa Seria, 14, 2005, 121-133). The comment focuses on the following issues: (1) the conception of philosophy of physics; (2) some methodological questions, especially the role of models in physics; (3) some explanations concerning the model proposed by the present author and his coworkers. A few "ideological remarks" are also made.

Zaproponowano, by Quine’a kryterium istnienia (teoria zakłada istnienie zmiennych związanych) rozszerzyć na matematyczne struktury. W duchu tego kryterium każdą matematyczną strukturę można uważać za oddzielny świat, w którym istnieją tylko te byty, bez zakładania których struktura straciłaby sens. Niektóre matematyczne światy są używane przez fizyków do modelowania rzeczywistego świata. W takiej sytuacji ontologia danej struktury matematycznej przenosi się na fizyczny świat. Mówiąc bardziej prozaicznie, niektóre matematyczne struktury interpretuje się jako struktury fizycznego świata. Cud rozumienia świata sprowadza się do cudu tej (...) interpretacji. (shrink)

Noncommutative geometry is quickly developing branch of mathematics finding important application in physics, especially in the domain of the search for the fundamental physical theory. It comes as a surprise that noncommutative generalizations of probabilistic measure and dynamics are unified into the same mathematical structure, i.e., noncommutative von Neumann algebra with a distinguished linear form on it. The so-called free probability calculus and the Tomita-Takesaki theorem, on which this unification is based, are briefly presented. It is argued that the unitary (...) evolution, known from quantum mechanics, could be a trace of noncommutativity on a deeper level. Philosophical significance of these results is also discussed. (shrink)

In the previous paper (Filozofia Nauki No 3-4, 1994, pp. 7-17) we have shown how the initial and final singularities in the closed Friedman world model can be analysed in terms of the structured spaces in spite of the fact that these singularities constitute the single point in the b-boundary of space-time. In the present paper we generalize our approach by using methods of noncommutative geometry. We construct a noncommutative algebra in terms of which geometry of space-time with singularities can (...) be developed. This algebra admits a representation in the space of operators on a Hilbert space, and the initial and final singularities in the closed Friedman model are given by its two distinct representations. The striking feature of this approach is its analogy with the mathematical formalism of quantum mechanics. (shrink)

How to define space-time singularities is a serious problem in general relativity. Schmidt's b-boundary construction was commonly regarded as leading to the best (and very elegant) definition of singularities: space-time is said to be singular if it contains at least one b-incomplete curve. Unfortunately, Bosshard (1976) and Johnson (1977) demonstrated that the b-boundary of the closed Friedman universe consists of the single point. This means that the initial and final singularieties (i.e., the beginning and the end of the Friedman world) (...) coincide. So far no remedy to cure this disaster was known. In the present paper, the author reviews the results obtained by himself and W. Sasin (1994) which clarify the problem. The closed Friedman space-time together with its singularities is not smooth manifold but it turns out to be a structured space which is a strong generalization of the manifold concept. Consequently, if the problem is considered within the correct category, i.e. the category of structured spaces, the patologies dissapear. If one remains within the space-time everything is all right. It is only if one attempts to „touch” the singularity (to extend the differential structure from the inside of space-time to the singularity) when the beginning and the end of the universe coalesce. From the perspective of the Demiurg creating the closed Friedman universe the cosmic history is but a single point. The methodological significance of this result is briefly discussed. (shrink)