Formalization of functionally complete propositional calculus with the functor of implication as the only primitive term

The most difficult problem that Leniewski came across in constructing his system of the foundations of mathematics was the problem of defining definitions, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leniewski's method of terminological explanations for the purpose of formalizing ukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of implicational definitions, which enabled me to define any propositionforming functor for any finite number of propositional arguments.To the memory of Jerzy Supecki     

Categorical and algebraic aspects of Martin-Löf Type Theory

In the paper there are introduced and discussed the concepts of an indexed category with quantifications and a higher level indexed category to present an algebraic characterization of some version of Martin-Löf Type Theory. This characterization is given by specifying an additional equational structure of those indexed categories which are models of Martin-Löf Type Theory. One can consider the presented characterization as an essentially algebraic theory of categorical models of Martin-Löf Type Theory. The paper contains a construction of an indexed category with quantifications from terms and types of the language of Martin-Löf Type Theory given in the manner of Troelstra [11]. The paper contains also an inductive definition of a valuation of these terms and types in an indexed category with quantifications.     

The mutating preconscious archetype in present-day ecological conditions

Competition is an important force behind evolution in present-day ecological conditions, its intensity varying according to the organisms' expectations vis-à-vis resources available. On the other hand, the role of mutation in the evolutionary process can hardly be underestimated: Leading to the change of the preconsciously functioning archetype, mutation makes it impossible for the ego to realize its image. This is a consequence of the clash between the mutated, preconsciously functioning archetype and the system of ethical and moral norms functioning in the collective superego of a given population group. The type of mutation that results from the accelerated pace of evolution can be viewed as a continuity in the development of an organism's behavior. The preconsciously functioning archetype, resulting from these mutations, contains impulses and predispositions that differ markedly from the impulses and predispositions functioning in the genetically determined "pattern of behavior." In a situation where anxiety results from the inhibition of impulses and dispositions, hostility reactions are likely to occur. In its turn, reactive hostility can induce anxiety, thus creating a reaction cycle. Underlying this mechanism is the mutated, preconsciously functioning archetype, which itself is a result of the development of civilization in our contemporary world.     

Kripke semantics for knowledge representation logics

This article provides an overview of development of Kripke semantics for logics determined by information systems. The proposals are made to extend the standard Kripke structures to the structures based on information systems. The underlying logics are defined and problems of their axiomatization are discussed. Several open problems connected with the logics are formulated. Logical aspects of incompleteness of information provided by information systems are considered.     

Verisimilitude based on concept analysis

In the paper ordering relations for comparison of verisimilitude of theories are introduced and discussed. The relations refer to semantic analysis of the results of theories, in particular to analysis of concepts the theories deal with.     

Liberalism in Poland: What Is Left?

Studies in East European Thought -     

Book reviews

Science as Salvation: a Modern Myth and its Meaning, Mary Midgley, 1994. London, Routledge x +256pp., Hb 04 15062713, £35; Pb 04 15107733, £8.99

Philosophical Naturalism, David Papineau, 1993 Oxford, Basil Blackwell xii +219pp., Hb 0631189025, £40; Pb 0631189033, £14.99

F. H. Bradley, Writings on Logic and Metaphysics, James W. Allard & Guy Stock (Eds), 1994. Oxford, Clarendon Press xv+357pp, Hb 0–198–24445–2, £40.00; Pb 0–198–24438‐X, £14.95

Invariance and Heuristics: Essays in Honour of Heinz Post, Steven French & Harmke Kamminga (Eds), 1993 Boston Studies in the Philosophy of Science, Vol. 148 Kluwer Academic Publishers, Dordrecht

Beyond Reason: Essays on the Philosophy of Paul Feyerabend, GONZALO MUNÉVAR (Ed.), 1991. Dordrecht, Kluwer Academic Publishers xxi + 535pp., hb, ISBN 0–7923–1272–4, £104.20

World Changes: Thomas Kuhn and the Nature of Science, Paul Horwich (Ed.), 1993. Cambridge, MA, Bradford Books/MIT Press vi + 356pp., pb, ISBN 0262581388, £14.95

Realism Rescued: How Scientific Progress is Possible, Jerold L. Aronson, Rom Harré & Eileen Cornell Way, 1994 London, Duckworth vii +213pp., Hb 0715624768, £30.00

Scientific Nihilism: On the Loss and Recovery of Physical Explanation, Daniel Athearn, 1994. State University of New York Press, Albany ix + 387pp., Hb ISBN 0–7914–1807–3, £52

Theism, Atheism, and Big Bang Cosmology, William Lane Craig & Quentin Smith, 1993. Oxford, Clarendon Press x +342pp., Hb 0198263481, £35; Pb 019826383X, £13.95     

AN EXPERIENTIALLY DERIVED BASE-RATE ERROR IN HUMANS

Abstract— Two experiments tested college students in a delayed matching-to-sample procedure designed to explore how multiple competitive sources of control interact in determining choice behavior. The primary sources of potential control were the frequency with which each of two colors was correct (base rates) and the accuracy of a sample in predicting the correct choice (accuracy rate). In one experiment, subjects ignored the base rates, and therefore made nonoptimal choices. These results mimicked the well-known base-rate error found in verbal responses to questions. In a second experiment, manipulations to increase subjects' motivation did not alleviate the error significantly. Together, these results suggest that the base-rate error may represent a broad behavioral pattern not restricted to verbal arenas. The results are compared with previous attempts to reconcile behavioral and cognitive lines of experimentation.