This note discusses some problems concerning intended, standard, and nonstandard models of mathematical theories. We pay attention to the role of extremal axioms in attempts at a unique characterization of the intended models. We recall also Jan Woleński’s views on these issues.

We review the four recent monographs by Roman Murawski.

The article juxtaposes modern skepticism stating lack of the criterion of true beliefs about transcendent reality with respect to their contents, but accepting the assumption about existence and cognoscibility of those contents on the one hand, and — after M. F. Burnyeat — ancient skepticism understood as one that questions this assumption on the other. The doubt as to existence of beliefs — resp. propositions as contents of beliefs — is a link joining ancient skeptics with Wittgenstein. Their skepticism is (...) not - as modern skepticism - an epistemological position, but an ontological one — nominalism — questioning existence of universals that are the conditions of meaning and hence the conditions of truth of propositions. This is why the ancient dispute concerning the truth was in fact a dispute over the problem of universals, i.e. over existence of constant rules deciding which ways of connecting the subject and the predicate in a proposition are right and which are not. Realists referred to such rules, sophists denied their existence, and skeptics stated that without having such a rule at their disposal they do not ha-.: a basis for deciding the dispute between realists and sophists. This does not have much to do either with so-called correspondence concept of the truth or with the modern understanding of conceptual realism talking about \"ideal paradigms\" or \"common properties\" of things. Today\'s typologies of philosophical positions do not fit antiquity. Ch. S. Peirce\'s and D. Armstrong\'s arguments lead to the conclusion that Plato was a... nominalist in the modern meaning of the world. P. T. Geach\'s and N. Wolterstorff s analyses allow stating the same about St Thomas Aquinas. This places under the question mark the statement that the latter could be an advocate of the generally ascribed to him correspondence theory of truth, which also cannot be derived from Aristotle\'s philosophy without any doubts. (shrink)

The article is an analysis of various versions of the correspondence theory of truth and shows that this theory - in all of its versions - rests on two irreconcilable assumptions. First, according to the theory, the relation between the truth bearer and the truth maker - i.e. the portion of reality which makes the bearer true - is a grounded relation, which means that it holds whenever the elements grounding the relation exist, and that each of the elements may (...) exist independently of the other. Secondly, the correspondence theory of truth explicitly or implicitly presupposes that the truth maker always - i.e. necessarily - makes the truth bearer true. The first assumption implies that truth as a feature of convictions, assertions, judgments, etc. is either impossible or by nature unrecognizable. The second assumption is fulfilled only when the alleged "grounded" relation is replaced by an internal relation of identity between the truth bearer and its truth maker. The thesis that the so-called relation of correspondence between thought and reality is essentially their identity follows - contrary to what is commonly believed - from every version of the correspondence theory of truth that does not lead to either nihilism or scepticism. The author illustrates this fact by means of an analysis of the theories of G. E. Moore, B. Russell, H. Field, B. Smith and A. Newman. All of this paves the way for the identity theory of truth, which nevertheless faces its own difficulties in providing a satisfactory explanation of the existence of falsity. (shrink)

The concepts of measurement and measurable quantity are discussed. A probabilistic interpretation independent of the arrow of time is recommended and a definition of quantizable physical systems is given. The space of states of information about the physical system is Schwarz space rather than Hilbert space.

It is shown explicitly that the linearized theory does not constitute any approximation to the exact solutions in the case of free fields. The only regular solution satisfying, as boundary condition, the requirement of a sufficiently rapid decrease at infinity is a flat space. The problem of conservation laws is discussed anew. The continuity equation satisfied by Einstein's pseudotensor does not guarantee the existence of global conservation laws. Solutions violating the energy conservation are interpretable as representing gravitational radiation absorbed or (...) emitted by sources at infinity. (shrink)

Chciałem Go pożegnać. Kilkakrotnie próbowałem napisać choć parę słów. O Nim samym. Okazało się, że nie potrafię. Udało mi się tylko przedstawić Jego poglądy na reizm Tadeusza Kotarbińskiego, ale uczyniłem to gdzie indziej. Muszę tu poprzestać na ofiarowaniu Mu tego, co napisałem na Jego dziewięćdziesiąte urodziny, w osiemdziesięciolecie naszej przyjaźni.