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1

Paradoksy

100%

Tworak Z.

Filozofia Publiczna i Edukacja Demokratyczna

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2012

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vol. 1

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issue 1

94-103

EN

An important part of philosophical thinking are paradoxes. Many of them raise serious problems and are associated with crises of thought and revolutionary advances in the science. This paper is devoted to the notion of paradox and presents a potpourri of paradoxes. I give a very broad interpretation of the term paradox, far broader than will appeal to many logical purists.

2

Modal Logic and Game Theory

100%

Tworak Z.

Filozofia Nauki

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2017

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vol. 25

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issue 2

5-28

PL

In this paper, I demonstrate the fruitfulness of looking at modal logic from the perspective of game theory. In particular, I show how games in strategic form can be transformed into Kripke’s models for a multi-modal logic that combines the concepts of strategy profile, preference, and knowledge. The logic is sufficiently general to express solution concepts such as the best response, Nash Equilibrium, and Iterated Deletion of Strictly Dominated Strategies. Moreover, the logic allows us to derive the conditions on which these concepts are based.

3

On the Notion of Truth in Mathematical Intuitionism

100%

Tworak Z.

Filozofia Nauki

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2010

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vol. 18

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issue 4

49-76

PL

The basic philosophical idea of intuitionism is that mathematical entities exist only as mental constructions and that the notion of truth of a proposition should be equated with its verification or the existence of proof. However different intuitionists explained the existence of a proof in fundamentally different ways. There seem to be two main alternatives: the actual and potential existence of a proof. The second pro-posal is also understood in two alternative ways: as knowledge of a method of con-struction of a proof or as knowledge-independent and tenseless existence of a proof. This paper is a presentation and analysis of these alternatives.

4

Logic of Conditional Beliefs

100%

Tworak Z.

Filozofia Nauki

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2014

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vol. 22

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issue 2

37-54

PL

In this paper I present a simple logic for conditional beliefs in a multi-agent doxastic context (CDL). Conditional beliefs Bi((/() encode beliefs in ( we would have if we were to learn new information (. The account of this notion is close to the classical theory of belief revision (AGM) and the standard conditional logic, as developed by Stalnaker and Lewis. I give both semantic and axiomatic characterization of conditional beliefs. They are interpreted in terms of plausibility or preference ordering on worlds. I also investigate the relation between notions of belief and knowledge. The logic may be used, for example, for epistemic analysis of some extensive form games.

5

Self-Reference and the Problem of Antinomies

100%

Tworak Z.

Filozofia Nauki

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2008

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vol. 16

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issue 2

43-58

PL

In this paper, I try to give an account of situations in which self-reference is likely to occur. Generally, self-reference or circularity is relation in which something refers to itself (directly or via another, intermediate, objects). Self-referential objects sometimes lead to antinomies (inconsistencies) and sometimes do not. We can distinguish between vicious and innocuous self-referential objects. There is controversy whether all antinomies essentially involve some form of self-reference (S. Yablo has given an ingenious liar-style antinomy that, he claims, avoids self-reference). I suggest that self-reference is necessarily involved in finite antinomies, but not in infinity ones.

6

The Knower Paradox

100%

Tworak Z.

Filozofia Nauki

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2011

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vol. 19

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issue 3

29-47

PL

The Knower Paradox is an element of the class of paradoxes of self-reference. It demonstrates that any theory Ó which (1) extends Robinson arithmetic Q, (2) includes a unary knowledge predicate K, and (3) contains certain elementary epistemic principles involving K is inconsistent. In this paper I present different versions of the Knower Paradox (both in the framework of the first-order arithmetic and in the modal logic). There are several solutions of the paradox. Some of them I discuss in detail, namely solution developed within modal logic, solution proposed by C. A. Anderson and solution proposed by P. Égré. The common defect of these proposals is that they developed a connection between the concepts of knowledge and provability. Finally, I suggest a solution using the basic ideas of the revision theory of definitions.

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Paradoksy

Modal Logic and Game Theory

On the Notion of Truth in Mathematical Intuitionism

Logic of Conditional Beliefs

Self-Reference and the Problem of Antinomies

The Knower Paradox