Let I be an ideal of subsets of a Polish space X, containing all singletons and possessing a Borel basis. Assuming that I does not satisfy ccc, we consider the following conditions (B), (M) and (D). Condition (B) states that there is a disjoint family F $\subseteq$ P(X) of size c, consisting of Borel sets which are not in I. Condition (M) states that there is a Borel function f: X → X with $f^{-1}[\{x\}] \not\in$ I for each x ∈ (...) X. Provided that X is a group and I is invariant, condition (D) states that there exist a Borel set B $\not\in$ I and a perfect set P $\subseteq$ X for which the family $\{B + x: x \in P\}$ is disjoint. The aim of the paper is to study whether the reverse implications in the chain (D) $\Rightarrow$ (M) $\Rightarrow$ (B) $\Rightarrow$ not-ccc can hold. We build a σ-ideal on the Cantor group witnessing (M) & ¬ (D) (Section 2). A modified version of that σ-ideal contains the whole space (Section 3). Some consistency results on deriving (M) from (B) for "nicely" defined ideals are established (Sections 4 and 5). We show that both ccc and (M) can fail (Theorems 1.3 and 5.6). Finally, some sharp versions of (M) for invariant ideals on Polish groups are investigated (Section 6). (shrink)
We address ZFC inequalities between some cardinal invariants of the continuum, which turned out to be true in spite of strong expectations given by [11].
This paper is concerned with n-localization property introduced by Newelski and Rosłanowski in [10] and getting it for CS iterations of forcing notions.
This paper commemorates thepresentation of the honorary doctorate, in May2001 by the University of ód, toProfessor Andrzej Walicki. On this occasion,the Honorary Graduate delivered a lecturedevoted to his first philosophy teacher –Sergej Iosifovich Hessen, a prominent RussianNeo-Kantian philosopher and a liberal inmatters social and political. I try to analyzethe main features of Hessen''s philosophicalneo-Kantianism, in particular the inevitabilityof a choice between the absolute and therelative both in epistemology and in ethics inthe context of contemporary philosophy.
We study the cardinal invariants of measure and category after adding one random real. In particular, we show that the number of measure zero subsets of the plane which are necessary to cover graphs of all continuous functions may be large while the covering for measure is small.
We continue investigations of reasonable ultrafilters on uncountable cardinals defined in previous work by Shelah. We introduce stronger properties of ultrafilters and we show that those properties may be handled in λ-support iterations of reasonably bounding forcing notions. We use this to show that consistently there are reasonable ultrafilters on an inaccessible cardinal λ with generating systems of size less than $2^\lambda$ . We also show how ultrafilters generated by small systems can be killed by forcing notions which have enough (...) reasonable completeness to be iterated with λ-supports. (shrink)
The ancient Greeks used the term catharsis for the cleansing of both the body by medicine and the soul by art. In this inspiring book, internationally renowned cardiologist Andrzej Szczeklik draws deeply on our humanistic heritage to describe the artistry and the mystery of being a doctor. Moving between examples ancient and contemporary, mythological and scientific, Catharsis explores how medicine and art share common roots and pose common challenges. The process of diagnosis, for instance, belongs to a world of (...) magic and metaphor; the physician must embrace it like a poem or painting, with particular alertness and keen receptivity. Speculation on ways to slow aging through genetics, meanwhile, draws directly on the dream of immortality that artists and poets have nourished through the ages. And the concept of catharsis itself has made its way from the writings of Aristotle to today's growing interest in the benefits of music to health, especially in newborns. As Szczeklik explores such subjects as the mysteries of the heart rhythm, the secret history of pain relief, the enigmatic logic of epidemics, near-death or out-of-body experiences, and many more, he skillfully weaves together classical literature, the history of medicine, and moving anecdotes from his own clinical experiences. The result is a life-affirming book that will enrich the healing work of patients and doctors alike and make an invaluable contribution to our still-expanding vision of the art of medicine. (shrink)
On the basis of arguments put forth by (Kripke, 1977a) and (Kripke, 1980), it is widely held that one can sometimes rationally accept propositions of the form "P and not-P" and also that there are necessary a posteriori truths. We will find that Kripke's arguments for these views appear probative only so long as one fails to distinguish between semantics and presemantics—between the literal meanings of sentences, on the one hand, and the information on the basis of which one identifies (...) those literal meanings, on the other. This same failure, it will be argued, underlies the popular thesis that intersubstituting co-referring terms sometimes turns true sentences into false ones and vice versa. Though seemingly plausible, this thesis has a number of counterintuitive consequences, among them that the occurrence of “snow” in “it is true that snow is white” doesn’t refer to snow. An understanding of the distinction between semantics and presemantics suggests a way to develop a semantic system that doesn’t have these consequences and that, moreover, reconciles our intuitions concerning cognitive content with some powerfully argued theses of contemporary philosophy of language. Some of this paper's main contentions are anticipated by Andrzej Boguslawski in his 1994 paper “Sentential Complementation and Truth.”. (shrink)
In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an (...) appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas. (shrink)
The paper is a brief survey of the most important semantic constructions founded on the concept of possible world. It is impossible to capture in one short paper the whole variety of the problems connected with manifold applications of possible worlds. Hence, after a brief explanation of some philosophical matters I take a look at possible worlds from rather technical standpoint of logic and focus on the applications in formal semantics. In particular, I would like to focus on the fruitful (...) marriage of possible world semantics and algebra and its evolution leading to very general construction of Wójcicki called referential semantics and some of its refinements. The presentation is informal and sketchy; the main purpose is to put in one place a short, and readable I hope, description of the most important constructions and to point out the main sources of these solutions. (shrink)
The article presents a formalization of Anselm's so-called Ontological Arguments from Proslogion . The main idea of our research is to stay to the original text as close as is possible. We show, against some common opinions, that (i) the logic necessary for the formalization must be neither a purely sentential modal calculus, nor just non-modal first-order logic, but a modal first-order theory; (ii) such logic cannot contain logical axiom ⌜ A → ⋄ A ⌝; (iii) none of Anselm's reasonings (...) requires the assumptions that God is a consistent object or that existence of God is possible (in symbols "⋄Eg"); (iv) no such thing as the so-called Anselm's Principle (in symbols "□(Eg → □Eg)") is involved in any of the proofs; (v) Anselm's claims (that God exists in reality and that God necessarily exists in reality) can be obtained independently, hence there is no need for presenting them in an opposite order than Anselm did. Moreover we show a single line of reasoning underlying the whole Proslogion and allowing Anselm to deduce many theorems concerning God's nature. Last but not least we study the possibility of proving the uniqueness of God within the outlined theory. (shrink)
Machine generated contents note: List of contributors; Acknowledgments; Introduction: the humanist tradition in Russian philosophy G. M. Hamburg and Randall A. Poole; Part I. The Nineteenth Century: 1. Slavophiles, Westernizers, and the birth of Russian philosophical humanism Sergey Horujy; 2. Alexander Herzen Derek Offord; 3. Materialism and the radical intelligentsia: the 1860s Victoria S. Frede; 4. Russian ethical humanism: from populism to neo-idealism Thomas Nemeth; Part II. Russian Metaphysical Idealism in Defense of Human Dignity: 5. Boris Chicherin and human dignity (...) in history G. M. Hamburg; 6. Vladimir Solov'iev's philosophical anthropology: autonomy, dignity, perfectibility Randall A. Poole; 7. Russian panpsychism: Kozlov, Lopatin, Losskii James P. Scanlan; Part III. Humanity and Divinity in Russian Religious Philosophy after Solov'iev: 8. A Russian cosmodicy: Sergei Bulgakov's religious philosophy Paul Valliere; 9. Pavel Florenskii's trinitarian humanism Steven Cassedy; 10. Semën Frank's expressivist humanism Philip J. Swoboda; Part IV. Freedom and Human Perfectibility in the Silver Age: 11. Religious humanism in the Russian silver age Bernice Glatzer Rosenthal; 12. Russian liberalism and the philosophy of law Frances Nethercott; 13. Imagination and ideology in the new religious consciousness Robert Bird; 14. Eschatology and hope in silver age thought Judith Deutsch Kornblatt; Part V. Russian Philosophy in Revolution and Exile: 15. Russian Marxism Andrzej Walicki; 16. Adventures in dialectic and intuition: Shpet, Il'in, Losev Philip T. Grier; 17. Nikolai Berdiaev and the philosophical tasks of the emigration Stuart Finkel; 18. Eurasianism: affirming the person in an 'Era of Faith' Martin Beisswenger; Afterword: on persons as open-ended ends-in-themselves (the view from two novelists and two critics) Caryl Emerson; Bibliography. (shrink)
In this paper we examine Prior’s reconstruction of Master Argument [4] in some modal-tense logic. This logic consists of a purely tense part and Diodorean definitions of modal alethic operators. Next we study this tense logic in the pure tense language. It is the logic K t 4 plus a new axiom ( P ): ‘ p Λ G p ⊃ P G p ’. This formula was used by Prior in his original analysis of Master Argument. ( P ) (...) is usually added as an extra axiom to an axiomatization of the logic of linear time. In that case the set of moments is a total order and must be left-discrete without the least moment. However, the logic of Master Argument does not require linear time. We show what properties of the set of moments are exactly forced by ( P ) in the reconstruction of Prior. We make also some philosophical remarks on the analyzed reconstruction. (shrink)
The formalist point of view maintains that formal derivations underlying proofs, although usually not carried out in practice, contribute to the confidence in mathematical theorems. Opposing this opinion, the main claim of the present paper is that such a gain of confidence obtained from any link between proofs and formal derivations is, even in principle, impossible in the present state of knowledge. Our argument is based on considerations concerning length of formal derivations. Thanks to Jody Azzouni for enlightening discussions concerning (...) the subject of this paper and to anonymous referees whose important remarks permitted us to correct the arguments and improve presentation. The remaining flaws remain, of course, solely the responsibility of the author. This research was partially supported by NSERC discovery grant and by the Research Chair in Distributed Computing at the Université du Québec en Outaouais. CiteULike Connotea Del.icio.us What's this? (shrink)
Mathematical theory of voting and social choice has attracted much attention. In the general setting one can view social choice as a method of aggregating individual, often conflicting preferences and making a choice that is the best compromise. How preferences are expressed and what is the “best compromise” varies and heavily depends on a particular situation. The method we propose in this paper depends on expressing individual preferences of voters and specifying properties of the resulting ranking by means of first-order (...) formulas. Then, as a technical tool, we use methods of second-order quantifier elimination to analyze and compute results of voting. We show how to specify voting, how to compute resulting rankings and how to verify voting protocols. (shrink)
It is well known that Husserl clearly recognized the importance of the introduction of idealization in physics and its contribution to the further advancement in natural sciences. The history of the successful applications of idealization in natural sciences encouraged attempts to extend the use of this sophisticated instrument of theoretical investigation and theory construction to other domains of science. Since Husserl designed his phenomenology as the rigorous science of consciousness we have to find out why he did not use the (...) method he understood so well to study experiences, the objects located by him in the domain of consciousness. The paper offers an answer to this question. It explains why Husserl conceived of the method of idealization as a tool of objectivization of previously subjective knowledge. Since idealization is used to objectify knowledge its application to experiences, conscious acts would produce objective knowledge of consciousness. This, however, would contradict phenomenological assertion that subjectivity is an essential component of experience and that the reliable knowledge about conscious acts could not be objectified. It is the core of Husserl's argumentation that there is no place for idealization in the research on consciousness. (shrink)
The issue of adequacy of the Turing Test (TT) is addressed. The concept of Turing Interrogative Game (TIG) is introduced. We show that if some conditions hold, then each machine, even a thinking one, loses a certain TIG and thus an instance of TT. If, however, the conditions do not hold, the success of a machine need not constitute a convincing argument for the claim that the machine thinks.
The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.
Second-order quantifier elimination in the context of classical logic emerged as a powerful technique in many applications, including the correspondence theory, relational databases, deductive and knowledge databases, knowledge representation, commonsense reasoning and approximate reasoning. In the current paper we first generalize the result of Nonnengart and Szałas [17] by allowing second-order variables to appear within higher-order contexts. Then we focus on a semantical analysis of conditionals, using the introduced technique and Gabbay’s semantics provided in [10] and substantially using a third-order (...) accessibility relation. The analysis is done via finding correspondences between axioms involving conditionals and properties of the underlying third-order relation. (shrink)
This paper argues for the idea that the logic of questions should focus its attention on the analysis of arguments in which questions play the role of conclusions. The relevant concepts of validity are discussed and the concept of the logic of questions of a semantically interpreted formalized language is introduced.
The concept of search scenario is explicated in terms of erotetic logic, i.e., the logic of questions. Different kinds of erotetic search scenarios are characterized. The basic logical properties of erotetic search scenarios are analyzed.
The main theorem says that a consequence operator is an effective part of the consequence operator for the classical prepositional calculus iff it is a consequence operator for a logic satisfying the compactness theorem, and in which every finitely axiomatizable theory is decidable.
In this paper we give probably an exhaustive analysis of the geometry of solids which was sketched by Tarski in his short paper [20, 21]. We show that in order to prove theorems stated in [20, 21] one must enrich Tarski's theory with a new postulate asserting that the universe of discourse of the geometry of solids coincides with arbitrary mereological sums of balls, i.e., with solids. We show that once having adopted such a solution Tarski's Postulate 4 can be (...) omitted, together with its versions 4' and 4". We also prove that the equivalence of postulates 4, 4' and 4" is not provable in any theory whose domain contains objects other than solids. Moreover, we show that the concentricity relation as defined by Tarski must be transitive in the largest class of structures satisfying Tarski's axioms. We build a model (in three-dimensional Euclidean space) of the theory of so called T*-structures and present the proof of the fact that this is the only (up to isomorphism) model of this theory. Moreover, we propose different categorical axiomatizations of the geometry of solids. In the final part of the paper we answer the question concerning the logical status (within the theory of T*-structures) of the definition of the concentricity relation given by Tarski. (shrink)
In earlier publicationss of the first author it was shown that intentional explanation of actions, functional explanation of biological traits and causal explanation of abnormal events share a common structure. They are called explanation by specification (of a goal, a biological function, an abnormal causal factor, respectively) as opposed to explanation by specification under a law. Explanation by specification is guided by a schematic train of thought, of which the argumentative steps not concerning questions were already shown to be logically (...) valid (elementary) arguments. Independently, the second author developed a new, inferential approach to erotetic logic, the logic of questions. In this approach arguments resulting in questions, with declarative sentences and/or other questions as premises, are analyzed, and validity of such arguments is defined. In the prcsent paper it is shown that all four kinds of erotetic argumentative steps occurring in the train of thought of explanation by specification are valid arguments in the sense of inferential erotetic logic. Hence, in view of the fact thal tl~eo ther argumentative steps were already shown to be valid, it may be concluded that the logical structure of explanation by specification can be as well-established as that of explanation by nomological subsumption. Moreover, explanation by specification provides some illustrations of the applicability of erotetic logic in everyday life and some empirical sciences. (shrink)
Milestones was a manifesto of rightwing, anti-revolutionary liberalism, according to which the political events of 1905 should have officially concluded the intelligentsia’s battle against autocracy and inaugurated the intelligentsia’s cooperation with Russia’s “historical rulers” to turn the country into an economically and culturally strong “state of law.” All the Milestones ’ authors agreed that Russia’s intellectual history was not identical with the traditions of the radical intelligentsia, and that there was need for a new intellectual canon focused on religious thought (...) and efforts to define the Russian national identity. (shrink)
Three semantic relations are analyzed: the relation of implication of a question by a question and a set of declarative sentences, the relation of implication of a question by a question, and the relation of strong implication of a question by a question and a set of declarative sentences. The connections between these concepts and the concepts of relative soundness, partial answerhood and presupposition are examined. The principal results are theorems about, to speak generally, epistemic reducibility of well-posed questions to (...) sequences of implied yes-no questions. (shrink)
Our aim is to express in exact terms the old idea of solving problems by pure questioning. We consider the problem of derivability: Is A derivable from by classical propositional logic?. We develop a calculus of questions E *; a proof (called a Socratic proof) is a sequence of questions ending with a question whose affirmative answer is, in a sense, evident. The calculus is sound and complete with respect to classical propositional logic. A Socratic proof in E * can (...) be transformed into a Gentzen-style proof in some sequent calculi. Next we develop a calculus of questions E **; Socratic proofs in E ** can be transformed into analytic tableaux. We show that Socratic proofs can be grounded in Inferential Erotetic Logic. After a slight modification, the analyzed systems can also be viewed as hypersequent calculi. (shrink)
First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given.
This book provides a much needed insight not only into the importance of Hegel and the importance of Derrida's work on Hegel, but also the very foundations of postmodern and deconstructionist thought. Eleven essays by key contributors in the field present a comprehensive picture of Hegel's place in deconstruction today. Contributors: Stuart Barnett, Robert Bernasconi, Simon Critchley, Suzanne Gearhart, Werner Hamacher, Heinz Kimmerle, Jean-Luc Nancy, John H. Smith, Kevin Thompson, Andrzej Warminski.
Piotr Buczkowski/Poznari THE LEVELS OF CONSCIOUSNESS Some remarks on sociology of knowledge /. Introduction Sociology of knowledge is a subbranch of social ...
We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof- theoretic and model-theoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and logic translation, can be recovered by their abstract (...) properties and are preserved and reflected by translations under suitable conditions. (shrink)
Some people approve of certain general rules of behavior, or some concrete cases. The others disapprove of or are indifferent to them. In this paper I suggest an axiom system which formalizes the use of these utterances. It may be considered as a special (individualistic) approach to deontic logic.
We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order (...) to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely. (shrink)
In earlier publications of the first author it was shown that intentional explanation of actions, functional explanation of biological traits and causal explanation of abnormal events share a common structure. They are called explanation by specification (of a goal, a biological function, an abnormal causal factor, respectively) as opposed to explanation by subsumption under a law. Explanation by specification is guided by a schematic train of thought, of which the argumentative steps not concerning questions were already shown to be logically (...) valid (elementary) arguments.Independently, the second author developed a new, inferential approach to erotetic logic, the logic of questions. In this approach arguments resulting in questions, with declarative sentences and/or other questions as premises, are analyzed, and validity of such arguments is defined. (shrink)
The technological advances of the 20th century resulted in the creation of the Internet and its introduction into everyday life on a global scale. The Internet provides access to information and the sale and purchase of goods. Medications are also subject to trade. Their sale is conducted by online pharmacies and their global turnover amounts to hundreds of billions of dollars. Medications ordered over the Internet are sent by mail all over the world. Considering the events of recent years, (...) we cannot exclude the risk of a terrorist attack through online pharmacies. Terrorists can establish such companies, legally or illegally, or acquire ones already existing. Parcels, which are highly trusted by the customers of online pharmacies, can, for example, be contaminated with dangerous materials. The sale of online medications in the international system is potentially dangerous and requires international regulation. (shrink)
This paper develops a new proof method for two propositional paraconsistent logics: the propositional part of Batens' weak paraconsistent logic CLuN and Schütte's maximally paraconsistent logic Φv. Proofs are de.ned as certain sequences of questions. The method is grounded in Inferential Erotetic Logic.
It is claimed that Kuipers' approach to explanation opens the possibility for a further refinement of his own refined HD method for the evaluation of theories. One severe problem for the HD method, refined or not, is theory-ladeness. Given that experimental results are theory-laden, the comparative evaluation of alternative hypotheses is always relative to background knowledge. This difficulty can be avoided by supplementing HD considerations with the principle of inference to the best explanation. The authors sketch a program for doing (...) this. The general idea plays on some similarities between Kuipers' account of explanation and Lipton's. The former, however, is considered more flexible than the latter, which makes it even more attractive for the purpose under consideration. (shrink)
The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity representation is rather (...) independent of the underlying proof method, provided that some form of (analytic) cut is admissible. We will also discuss some generalisations of the system and compare it with other formalizations of linearity. (shrink)
We consider structures of the form (Φ, Ψ, R ), where Φ and Ψ are non-empty sets and is a relation whose domain is Ψ. In particular, by using a special kind of a diagonal argument, we prove that if Φ is a denumerable recursive set, Ψ is a denumerable r.e. set, and R is an r.e. relation, then there exists an infinite family of infinite recursive subsets of Φ which are not R -images of elements of Ψ. The (...) proof is a very elementary one, without any reference even to e.g. the -theorem. Some consequences of the main result are also discussed. (shrink)
The equivalence connective in ukasiewicz logic has its algebraic counterpart which is the distance function d(x,y) =|x–y| of a positive cone of a commutative -group. We make some observations on logically motivated algebraic structures involving the distance function.
For a complete Heyting lattice , we define a category Etale (). We show that the category Etale () is equivalent to the category of the sheaves over , Sh(), hence also with -valued sets, see [2], [1]. The category Etale() is a generalization of the category Etale (X), see [1], where X is a topological space.
Several context-specific social and political factors in Eastern and Central Europe are described — factors that must be considered while developing strategies to introduce Computer Ethics. Poland is used as a primary example. GNP per capita, the cost of hardware and software, uneven and scant distribution of computing resources, and attitudes toward work and authority are discussed. Such “geographical factors” must be taken into account as the new field of Computer Ethics develops.
