The general aim of this book is to provide an elementary exposition of some basic concepts in terms of which both classical and non-dassicallogirs may be studied and appraised. Although quantificational logic is dealt with briefly in the last chapter, the discussion is chiefly concemed with propo gjtional cakuli. Still, the subject, as it stands today, cannot br covered in one book of reasonable length. Rather than to try to include in the volume as much as possible, I have put (...) emphasis on some selected topics. Even these could not be roverrd completely, but for each topic I have attempted to present a detailed and precise t’Xposition of several basic results including some which are non-trivial. The roots of some of the central ideas in the volume go back to J. Luka siewicz’s seminar on mathematicallogi. (shrink)

The role of classical logic as the base of formalized scientific theories seems to be unshakable. Yet legitimate doubts about its universal applicability in science have resulted in the development of alternative systems, among which constructive and modal logic are discussed in syntactic and semantic terms.

11 original. Modifications which I introduced are radical and often far going. In my opinion the Polish text had two main drawbacks. It was overloaded with informal considerations and at the same time formal concepts included in some parts of the book were presented in a too complicated way. Of course one of the motives to revise it was also the fact that much time has passed since I finished writing the Polish version and obviously certain decisions and ideas contained (...) in the first edition seem not quite relevant now. So it is not only the desire to make the exposition clearer but also the reasons of substantial nature which motivated writing a revised version. I do not think it desirable to bother the reader with a detailed discussion of all changes to which the Polish version was subjected and that is why I will confine myself to pointing out only the most significant ones. Explanations concerning logical and set-theoretical notions applied in the book have been shortened as much as possible, in the Polish version one whole chapter was devoted to the discussion of them. (shrink)

The two main points of this contribution are the following: (1) Applied mathematical theories might complement physical theories in an essential way; some applied mathematical theories allow us to understand phenomena we are unable to explain by resorting to physical theories alone, (2) In the case of social sciences it might be necessary to account for examined phenomena by resorting to the idea of goal-oriented activity (the causal approach typical for natural science might be unsatisfactory). Weinberg's idea of grand reductionism (...) ignores the two above mentioned facts and hence overestimates the foundational role of physics and its methodology. (shrink)

In this note I am reflecting on interrelations between three concepts of truth: that employed by Hilbert arguing his formalist view on the nature of mathematics, Freges idea of truth supported by mathematical intuition, and known as Aristotelian correspondence idea of truth concerning any propositions not merely mathematical.

The central claim of this paper is the following. There are two different types of notions applied in science, and in fact in any discourse whatsoever. Some of the notions are veristic, i.e. they refer to some specific fairly well defined entities (individual objects, species, relations, systems, regularities, etc.). But there are also heuristic notions that serve the users to call attention to the fact that a specific situation can be accounted for, or even less - there is a chance (...) that it can be accounted for, in a certain way known already from some earlier application of similar ideas. On numerous occasions we argue by analogy. Now, to argue by analogy means to treat the situation accounted for as „similar” to some other already familiar situations. The similarity in question can amount to some fairly explicitly stated expectations, which go beyond the available evidence. The heuristic notions can be characterized as the notions in terms of which such expectations are stated. Since the right interpretation of those expectations should be defined anew any time when an argument by analogy is applied, also the concepts they involve share this characteristic. Thus while the veristic concepts have some fixed references, the reference of a heuristic concept should be defined anew every time when the concept is used. A theory which involves any heuristic notions is called heuristic. A theory is said to be veristic if all the descriptive notions it involves are veristic. The notion of truth can be in a straightforward way applied to veristic theories only. (shrink)

The author presents three formal concepts of language: syntactical, semantical and pragmatical one. They are used to provide an analysis of the problem of context in the language.

The title of this paper is a theorem, which I am going to state and prove. The theorem extends from prepositional to predicate languages the result I presented in [5].

Tarski’s papers, in which he examines the idea of a consequence operation Cn,divide into two groups. One of them is formed by the papers that offer an analysis of the general idea of the consequence operation. Resorting to fundamental ideas of logical semantics, Tarski explains what, in his view, it means to say that a formula a of a language L is a logical consequence Cn of a set of formulas X of that language. Under the definition he proposed Cn (...) is the strongest operation on sets of formulas of L that preserves truth under all possible interpretations of the language. In the papers belonging to the second group , the consequence operation Cn is treated as an object of abstract studies. More specifically, it is treated as an abstract unary operation defined on the power set of a set S such that the following familiar conditions are satisfied: T1.X⊆Cn)⊆Cnand T2.IfX⊂YthenCn⊂CnActually, Tarski imposed on Cn one more requirement which in more recent investigations is often omitted. It is as follows: T3.Ifα∈Cn,thenforafinitesubsetX′⊆X,α∈Cn is known as the finitaryness condition. (shrink)

An axiomatic theory of non-monotonic consequence relations patterned upon some finitistic ideas going back to Gentzen was suggested by Gabbay [1985]. 1 More recently, an infinitistic approach patterned upon Tarski’s theory of consequence operation was examined by Makinson [l98.]. We compare the two approaches and examine them vis-`a-vis some intuitive adequacy conditions. An enlarged version of this note will appear in Studia Logica , in particular the reader is referred to it for the proofs of the results stated here.

Ryszard Wójcicki's book „Ajdukiewicz. A Theory of Meaning” opens a series of publications Filozofia polska XX wieku [Polish Philosophy of XXth Century], created by Wójcicki. The main subject of the book is a theory of the meaning of linguistic expressions, which was formulated in the thirties and is known as a directival theory of meaning. The aim that the author has set for himself is not only to present and popularise that theory (these aims are implied by (...) the character of the series), but also the evaluation of its material adequacy and its significance for further investigations of language as a means of representation and transmission of knowledge. Adam Nowaczyk tries to show that Wójcicki's critique of Ajdukiewicz's conception is unjustified, for the fallacy allegedly committed in this conception is either only apparent or else easily remediable. Wójcicki disagrees with Nowaczyk's objection. (shrink)

As Chinese Studies in Philosophy enters its twenty-fifth year, we wish to thank the editor since its inception, Professor Cheng Chung-ying of the University of Hawaii, for his many years of service, and to welcome with this issue our new editor, Professor Michael Schoenhals of Stockholm University.

This paper was presented at the Annual Conference of the Australian Association for Logic, Melbourne, November, 1979. The present note being complementary to [1], I shall only brie y recall the key notions to be exploited here, and for more details the reader is advised to consult [1]. By a propositional logic we mean a couple , where L is a propo- sitional language and C a structural consequence de- ned on L. A couple W = is said to be (...) a referential matrix for the language L i there exists a non-empty set T such that the following two conditions are satised: i. A is an abstract algebra similar to L, whose all elements belong to f0; 1g T , i.e. they are mappings from T into the two-element set f0; 1g. ii. D = ffa 2 A : a = 1g : t 2 Tg. (shrink)