This book is a study in the logic of questions (sometimes called erotetic logic). The central topics in erotetic logic have been the structure of questions and the question-answer relationship. This book doesn't neglect these problems, but much of it is focussed on other issues. The main subject is the logical analysis of certain relations between questions and the contexts of their appearance. And our aim is to elaborate the conceptual apparatus of the inferential approach to the logic of questions. (...) Questions are asked for many reasons and for different purposes. Yet, before a question is asked or posed, a questioner must arrive at it. In many cases arriving at a question resembles coming to a conclusion: there are some premises involved and some inferential thought processes take place. If we agree that a conclusion need not be "conclusive", we may say that sometimes questions can play the role of conclusions. But questions can also perform the role of premises: we often pass from some "initial" question to another question. In other words, there are inferential thought processes - we shall call them erotetic inferences - in which questions play the roles of conclusions or conclusions and premises. The inferential approach to the logic of questions focusses its attention on the analysis of erotetic inferences. This book consists of eight chapters. (shrink)

"The importance of questions is beyond doubt. But the degree of attention paid to them in logic and linguistics is still less than they deserve." What is a question? How to represent questions in formal languages? How to model reasoning in which questions are involved? Can we prove anything by means of pure questioning? How to model goal-directed problem solving? These are the main issues of Andrzej Wi niewski's "Questions, Inferences, and Scenarios." This book offers a state-of-the-art exposition of (...) Inferential Erotetic Logic, that is, an approach to the logic of questions focused on inferences which lead to questions as conclusions. Wi niewski characterizes semantic relations which determine validity of these inferences within the framework of Minimal Erotetic Semantics, applicable to a wide range of formal languages. He elaborates in detail the concept of erotetic search scenario, a tool for modelling problem solving. Moreover, the author presents some applications of Inferential Erotetic Logic in proof theory. Andrzej Wi niewski is one of the most prominent contemporary researchers in the logic of questions. Currently, he is a full professor at the Department of Logic and Cognitive Science, Institute of Psychology, Adam Mickiewicz University in Pozna, Poland. (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.

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 Δ 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)

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)

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)

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.

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.

Inferential erotetic logic and inquisitive semantics give accounts of questions and model various aspects of questioning. In this paper we concentrate upon connections between inquisitiveness, being the core concept of INQ, and question raising, characterized in IEL by means of the concepts of question evocation and erotetic implication. We consider the basic system InqB of INQ, remain at the propositional level and show, inter alia, that: a disjunction of all the direct answers to an evoked question is always inquisitive; a (...) formula is inquisitive if, and only if it evokes a yes–no question whose affirmative answer expresses a possibility for the formula; inquisitive formulas evoke questions whose direct answers express all the possibilities for the formulas, and each question erotetically implies a question whose direct answers express the possibilities for the direct answers to the implying question. (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.

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.

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.

The concepts of question evocation and erotetic implication play central role in Inferential Erotetic Logic. In this paper, deduction theorems for question evocation and erotetic implication are proven. Moreover, it is shown how question evocation by a finite non-empty set of declaratives can be reduced to question evocation by the empty set, and how erotetic implication based on a finite non-empty set of declaratives can be reduced to a relation between questions only.

There are inferences from a sentence or a set of sentences to a question. The relation between the premises and conclusions of such inferences is sometimes called arising.

A relativized concept of a possiblecorrect answer to a why-question is introduced. Acertain procedure of looking for acceptable answers towhy-questions is analyzed in terms of erotetic logic,i.e., the logic of questions.

The concepta question is reducible to a non-empty set of questions is defined and examined. The basic results are: (1) each question which is sound relative to some of its presuppositions is reducible to some set of binary (i.e. having exactly two direct answers) questions; (b) each question which has a finite number of direct answers is reducible to some finite set of binary questions; (c) if entailment is compact, then each normal question (i.e. sound relative to its presuppositions) is (...) reducible to some finite set of binary questions. (shrink)

entailment; families of sets; logic of questions.

An alternative conceptual setting of the basic system of inquisitive semantics is presented. A situational interpretation of the proposed formalism is discussed.

By and large, Inferential Erotetic Logic (IEL, for short) is an approach to the logic of questions which puts in the centre of attention inferential aspects of questioning. IEL is not an enterprise of the last few years only. The idea originates from the late 1980s. It evolved through time. Initially, the stress was put on the phenomenon of question raising. This changed gradually, as some forms of reasoning that involve questions have appeared to be analyzable by means of the (...) conceptual apparatus developed. In this essay I present the basics of IEL and comment on them. Most, though not all, of the ideas discussed here have been scattered across my earlier publications. The invitation from the organizers of the Asking and Answering workshop (Greifswald, September 2020) resulted in an attempt of presenting the themes of IEL in a concise but, as I hope, also comprehensible way. (shrink)

We consider structures of the form, 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 issue of reduction of propositions to sets of possible worlds is addressed. It is shown that, under some natural assumptions, there always exist recursive propositions, i.e. decidable sets of possible worlds, which are not assigned to any sentence of a language. Some consequences of this result are discussed.

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 method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. (...) Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction. (shrink)

This paper is my last word, in the present journal, in the debate I have been having with Walter Block on the subject of evictionism as an alleged libertarian “third way,” capable of transcending the familiar “pro-life” and “pro-choice” dichotomy. In this debate, I myself defended what might be regarded as a qualified “pro-life” position, while Block consistently argued that the mother is morally allowed to expel the fetus from her womb provided that no non-lethal methods of its eviction are (...) available. While my position articulated in this paper contains an element of what Block might consider a concession on my part—i.e., an explicit declaration that abstaining from lethal evictions of fetuses conceived as a result of rape is a libertarian duty, but only an imperfect one—I continue to regard the unqualified support of evictionism as indefensible on libertarian grounds. (shrink)

This paper is concerned with n-localization property introduced by Newelski and Rosłanowski in [10] and getting it for CS iterations of forcing notions.

In this paper, we want to present the genesis of Stanisław Leśniewski’s mereology. Although ‘mereology’ comes from theword ‘part’, mereology arose as a theory of collective classes. That is why we present the differences between the concepts of being a distributive class and being a collective class. Next, we present Leśniewski’s original mereology from 1927, but with a modern approach. Leśniewski was inspired to create his concept of classes and their elements by Russell’s antinomy. To face it, Leśniewski had to (...) define the concept of being an element of based on the concept of being part of. Leśniewski showed that in his theory, there is no equivalent to Russell’s antinomy. We will show that his solution has nothing to do with the original approach because, in both cases, we are talking about objects of a different kind. Russell’s original antinomy concerned distributive classes, and Leśsniewski’s considerations concerned collective classes. (shrink)

The objective of the paper is a presentation and an interpretation of Władysław Stróżewski’s views on aesthetics. Built upon the foundation provided by classical metaphysics, Stróżewski’s aesthetics is simultaneously a continuation of the tradition of phenomenological interpretation of art. Stróżewski extends Roman Ingarden’s aesthetic theory by including the idea of numinous concretion, largely inspired by the works of Rudolf Otto. As a result, this new phenomenological perspective transcends the narrowly understood ‘aesthetics’ of the work of art towards the inherent dimension (...) of the sacred. Moreover, Stróżewski’s scrutiny of the aspect of art that goes beyond the aesthetic reveals an important relationship obtaining between his insights and the theological aesthetics of Hans Urs von Balthasar. Thus Stróżewski’s ideas turn out to be of significance to contemporary aesthetic and theological debates. In particular, he shows the movement of beauty from aesthetic to transcendental, and ultimately towards the sacred, where numinosum is manifested as Mystery. (shrink)

The paper consists of two parts, outlined in the title.I. In the historical science time appears as an element of the historian’s workshop. The historian collects source information, evaluates them and assigns respective dates. Only on the ground of thus “processed” sources may he reproduce the past: events and longer development processes, setting them in time. This dated time is understood colloquially as something objective, which runs one way and may be measured.II. A historian who studies the past reality depends (...) on the extent to which those sources are preserved. As a result of their interpretation, with the use of increasingly excellent research methods, he reproduces that reality. He must carry out an ongoing selection of historical facts found. This exposes him to temptations of such selection of those facts so as to adjust the historical knowledge to serve well the national interests, his own political opinions, etc. In this way the historian exerts influence on social awareness, which may consists of various myths and stereotypes, which sometimes lead to negative social behaviors: aggression, chauvinism, etc. Therefore, for researcher honesty’s sake and in the sense of moral responsibility, he must be careful to be as impartial as possible in his work. (shrink)

Natural Deduction Natural Deduction is a common name for the class of proof systems composed of simple and self-evident inference rules based upon methods of proof and traditional ways of reasoning that have been applied since antiquity in deductive practice. The first formal ND systems were independently constructed in the 1930s by G. Gentzen and S. Jaśkowski and … Continue reading Natural Deduction →.

The aim of the paper is to examine the nature of moral and legal norms in a broader context: first, taking into account logical and methodological assumptions, second, in the perspective of psychology of emotions and legal policy. The basic subject of the research carried out by Leon Petrażycki was represented by law. Originally, it had a psychological character, not an objective, eternal, and unchanging one. To fully understand the genesis and nature of morality and law, Petrażycki addressed the study (...) of mental phenomena, especially emotional experiences. First, however, he developed appropriate rules of logic and scientific methodology. Then he developed a new classification of mental phenomena, among which the fundamental role is played by bilateral emotions. At some stage, emotions begin to cooperate with cognitive processes, first of all with imaginations. Imaginations of acts, such as theft, betrayal, murder, can cause repulsive emotions, and type imaginations, such as truthfulness, charity, justice can evoke apulsive emotions. On the basis of such associations, judgments are created over time, the content of which becomes a basis for fundamental rules of conduct, that is, for norms. There are two fundamentally different types of norms: moral norms and legal norms. The norms of the first type are imperative and represent the nature of validity, while the norms of the second type are imperative-attributive and they also always entitle someone to something, i.e. they give someone a right. This division determines a fundamental difference between morality and law. (shrink)