Jan Wolenski

The relevance of metamathematical researches for philosophy of math- ematics is an indubitable matter. In the paper I shall speak about impli- cations of metamathematics for general philosophy, especially for classical epistemological problems. Let us start with a historical observation con- cerning Hilbert's programme, the rst research programme in metamathe- matics as a separate study of formal systems. This programme was strongly in uence by epistemological considerations. In fact, Hilbert wanted to se- cure all classical mathematics against inconsistencies and this aim had be achieved with the help of nitary consistency proof. Hilbert's claim is like the Cartesian project of reduction of all concepts to clarae et distinctae ideae. The epistemological commitment of original Hilbert's programme may be treated as a prelim- inary heuristic motivation for looking for epistemological implications of metamathematical results. It seems reasonable to examine in this respect three so-called limitative theorems: the rst Godel's incompleteness theo- rem , the second Godel's incom- pleteness theorem consistency of S, cannot be proved in S, providing that S is consistent) and Tarski's undenability theorem ; \S" stands for formal system containing elementary number theory. From the above-mentioned theorems we obtain an important, from philosophical point of view, conclusion: semantics of S cannot be expressed in S. Now, I shall present three applications of limitative theorems to the analysis of classical epistemological problems

Traces of the coherence theory are to be found in rationalistic epistemological systems of Leibniz, Spinoza, Kant, Hegel and Fichte. However, the first fully advanced coherence theory was proposed by Bradley in XIX century. He was followed by Joachim, McTaggart, and particularly Blanshard and Ewing. The coherence theory later became popular among philosophers of the Vienna Circle, notably in Neurath and Hempel.2 Recently, Rescher tried to combine various proposals of coherentists into one fully unified view.

This paper outlines an approach to the principle of bivalence based on very general, but still elementary, semantic considerations. The principle of bivalence states that “every sentence is either true or false”. Clearly, some logics are bivalent while others are not. A more general formulation of uses the concept of designated and non-designated logical values and is captured by “every sentence is either designated or non-designated”. Yet this formulation seems trivial, because the concept of non-designated value is negative. In order to refine the analysis, the class of anti-designated values has been distinguished. The non-trivial version of the principle of bivalence is expressed by “every sentence is either designated or anti-designated”. The last part of the paper mentions some extralogical reasons for considering the principle of bivalence with truth being a designated value as intimately connected to human thinking and behavior

This paper critically discusses two points concerning some recent views about the concept of truth. Firstly, contrary to Davidson, it shows that meaning of sentences cannot be explicated by T-equivalences. In particular, “is true” is an extensional predicate, but “means that” an intensional one. Secondly, the minimalist account of truth does not provide a satisfactory analysis of the concept of falsity. In this respect, minimalism does not satisfy Russell’s claim that any adequate truth-theory must be a theory of falsity as well.

One can often encounter an opinion that Polish scientific philosophy deserves to be much better known than actually is. This book is thought as a response to such a claim. The papers collected in this volume are divided into two parts: Background and Influence and History and Systematics. However, there is no sharp borderline between themes which are touched in both parts. Generally speaking, all papers of the first part relate the Lvov-Warsaw School to some philosophical movements external to it whereas the papers collected in the second one focus on internal issues connected with the school . Since the Polish school of mathematical logic is much better known than the Polish analytic philosophy we decided to omit here any treatment of the former. Thus, this collection centers on purely philosophical matters. We projected this volume not as an exhaustive panorama of Polish analytic philosophy but rather as a series of essays on particular persons or topic. As a result one can find here papers on Twardowski. Ajdukiewicz, Kotarbinski, Tarski and Lukasiewicz as well as on ethics on science, nominalism, and the methodology of psychology. We hope that this book will contribute to a better knowledge and evaluation of Polish achievements in analytic philosophy. We would like to express our gratitude to Professor Leszek Nowak, the editor-in-chief of Poznan Studies in the Philosophy of the Sciences and the Humanities, who initiated the idea of the collection and helped in its preparation

This paper examines some problems concerning modalities as operators acting on sentential arguments. At first, formal dependencies between modalities are described. Then, the problem of translations of modalities as operators into modalities as predicates is discussed. The author shows that although some predicates satisfy laws of the logical square for modalities, they cannot be represented by sentences with modal operators in front. The explanation of this fact is proposed by using Czeżowski\'s idea of modi entis and the content of presentations