We consider modal epistemic and doxastic logics as intuitively inadequate logics of information, and we outline a modal system of the operator being informed that which avoids inconsistency with our intuitive concept of information. The system has modal structure of the normal modal logic K4, and is sound and complete on the class of all transitive frames. We compare this logic with Floridi’s KTB information logic, and we consider a possibility of extending our system to a dynamic logic.

The main aim of the present article is an outline of an intuitively adequate system of logic of the operator "being informed". Such a system should be different from the familiar systems of epistemic and doxastic logic. The principle of veracity occurring in epistemic logics does not describe adequately the information operator, since the information may be true as well as false. On the other hand, the principle of consistency of beliefs, occurring in doxastic logics, cannot be applied to information, (...) because the information can be inconsistent. Our logic of information, although it is based on Kripke's semantics, includes principles not occurring in the systems of epistemic and doxastic logics, such as the principle of incompleteness of information and the Brouwerian Axiom. We prove that this system is incomplete. We also suggest that it can be generalized to a dynamic logic in the sense of van Benthem. (shrink)

A consequence relation in the framework of preferential semantics based on the four-valued Belnap-Dunn logic is constructed which proves that the sorites paradoxes are unsound or invalid inferences .

The concept of inconsistency has become recently the subject of many studies focused on the principle ex contradictione sequitur quodlibet which is a hallmark of the classical inconsistency. Stanisław Jaśkowski was the first who took a non-classical standpoint toward this principle building a system of propositional logic which rejects this classical principle. Rejecting it implies important consequences for the concept of classical negation, and poses the question in which properties the op-eration of negation should be endowed. The intention of this (...) article is to define the concept of inconsistency as well as the concept of negation in a way satisfying the main intuitions natural language users connect with the two notions occurring in propositions containing vague concepts. The vagueness of natural language dis-course leads to the phenomenon of the seeming contradiction characteristic of natural language. A non-standard consequence relation for such a language has been defined in terms of preferential semantics making use of the concept of most classical model. This non-standard consequence relation is applied to the ethical discourse. The concepts introduced in this article have been used to an interpretation of the contradictories of Plato's Parmenides, as well as to the rejection of dialetheism. (shrink)

The paradoxes of vagueness are unsound or invalid reasoning on the ground of preferential semantics based on the four-valued Belnap-Dunn logic.

All empirical concepts belonging to natural language are vague. The vagueness of empirical discourse is a source of many semantical problems which have been known since ancient times. One of those problems concerns the so called sorites paradoxes. This article is an attempt to show that the paradoxes are either invalid or unsound inferences. Since classical logic is useless for semantical analysis of such inferences, the article makes use of the Belnap four-valued logic based on the bilattice FOUR. Belnap's logic (...) is the base logic for defining a nonmonotonic consequence relation which prefers models with classical valuations among all valuations of the four-valued logic whenever it is possible. The approach outlined in this article is intuitive, and has more advantages than the supervaluational approach. (shrink)

HERMENEUTIC INDICATORS OF PRESENTING THE HISTORY OF PHILOSOPHY The aim of the article is to discuss Hans-Georg Gadamer’s and Paul Ricoeur’s hermeneutic way of understanding the history of philosophy. I assume that hermeneutic reference to philosophical past appears as a unique dialogue with tradition, whereas their way of understanding the history of philosophy might be defined as “hermeneutic interpretation of tradition.” In order to show what its indicators are, I characterize the conception of hermeneutic experience (H.-G. Gadamer) as well as (...) the issue of the interpretation process (P. Ricoeur). Those thinkers are convinced that understanding of the history of philosophy involves the recognition of our own historicity. Keywords: HANS-GEORG GADAMER, PAUL RICOEUR, HISTORY OF PHILOSOPHY, HERMENEUTICS. (shrink)

In [4] the lattice of all subvarieties of the variety G n Ex defined by so called externally compatible identities of Abelian groups together with the identity x n ≈ y n , for any n ∈ N and n ≥ 1 was described. In that paper classes of models of the type (2,1) where considered. It appears that diagrams of lattices of subvariaties defined by externally compatible identities satisfied in a given equational theory depend on the language of the (...) considered class of algebras. A question was asked to what extent the diagram of the lattice of subvarieties of the variety defined by externally compatible identities of a given variety will depend on changing the type of algebras. In general case, the answer to this question seems to be very complicated. In this paper we describe the variety of Abelian groups of exponent p·q, where p,q are different primes of type (2,1,0). (shrink)

Against the background of a new Ten Commandments for the Polish business community a new course in business ethics is now being offered to students in the Faculty of Management and Economy of the Technical University of Gdańsk, ul. G. Narutowicza 11/12, 80‐952 Gdańsk, Poland. Dr Kinach‐Brzozowska, who introduced the course last year, describes its content and her students’needs and reactions.

Ambient assisted living technologies are increasingly presented and sold as essential smart additions to daily life and home environments that will radically transform the healthcare and wellness markets of the future. An ethical approach and a thorough understanding of all ethics in surveillance/monitoring architectures are therefore pressing. AAL poses many ethical challenges raising questions that will affect immediate acceptance and long-term usage. Furthermore, ethical issues emerge from social inequalities and their potential exacerbation by AAL, accentuating the existing access gap between (...) high-income countries and low and middle-income countries. Legal aspects mainly refer to the adherence to existing legal frameworks and cover issues related to product safety, data protection, cybersecurity, intellectual property, and access to data by public, private, and government bodies. Successful privacy-friendly AAL applications are needed, as the pressure to bring Internet of Things devices and ones equipped with artificial intelligence quickly to market cannot overlook the fact that the environments in which AAL will operate are mostly private. The social issues focus on the impact of AAL technologies before and after their adoption. Future AAL technologies need to consider all aspects of equality such as gender, race, age and social disadvantages and avoid increasing loneliness and isolation among, e.g. older and frail people. Finally, the current power asymmetries between the target and general populations should not be underestimated nor should the discrepant needs and motivations of the target group and those developing and deploying AAL systems. Whilst AAL technologies provide promising solutions for the health and social care challenges, they are not exempt from ethical, legal and social issues. A set of ELSI guidelines is needed to integrate these factors at the research and development stage. (shrink)

The lattices of varieties were studied in many works (see [4], [5], [11], [24], [31]). In this paper we describe the lattice of all subvarieties of the variety $G_{Ex}^n$ defined by so called externally compatible identities of Abelian groups and the identity xⁿ ≈ yxⁿ. The notation in this paper is the same as in [2].

We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minimal structures admit definable parameterizations by mild maps. We then use this parameterization to prove a result on the density of rational points on curves defined by restricted Pfaffian functions.

The Scottish Philosophy of Common Sense originated as a protest against the philosophy of the greatest Scottish philosopher. Hume's sceptical conclusions did not excite as much opposition as might have been expected. But in Scotland especially there was a good deal of spoken criticism which was never written; and some who would have liked to denounce Hume's doctrines in print were restrained by the salutary reflection that if they were challenged to give reasons for their criticism they would find it (...) uncommonly difficult to do so. Hume's scepticism was disliked, but it was difficult to see how it could be adequately met. At this point Thomas Reid stepped into the field. He was the only man of his time who really understood the genesis of Hume's scepticism and succeeded in locating its sources. At first sight it would seem that this discovery required no peculiar perspicuity. It would seem that nobody could help seeing that Hume's sceptical conclusions were based on Locke's premises, and that Hume could never be successfully opposed by any critic who accepted Locke's assumptions. But this is precisely one of those obvious things that is noticed by nobody. And in fact Reid was the first man to see it clearly. It thus became his duty to question the assumptions on which all his own early thought had been based. The result of this reflection was the conclusion that, since the "ideal theory" of Locke and Berkeley logically led to Hume's scepticism, and since scepticism was intolerable, that theory would have to be amended, or, if necessary, abandoned. This volume contains works by Thomas Reid, Adam Ferguson, James Beattie, and Dugald Stewart. (shrink)

A critically important ethical issue facing the AI research community is how AI research and AI products can be responsibly conceptualised and presented to the public. A good deal of fear and concern about uncontrollable AI is now being displayed in public discourse. Public understanding of AI is being shaped in a way that may ultimately impede AI research. The public discourse as well as discourse among AI researchers leads to at least two problems: a confusion about the notion of (...) ‘autonomy’ that induces people to attribute to machines something comparable to human autonomy, and a ‘sociotechnical blindness’ that hides the essential role played by humans at every stage of the design and deployment of an AI system. Here our purpose is to develop and use a language with the aim to reframe the discourse in AI and shed light on the real issues in the discipline. (shrink)

: Medical research is widely thought to have a fundamentally therapeutic orientation, in spite of the fact that clinical research is thought to be ethically distinct from medical care. We need an entirely new conception of clinical research ethics—one that looks to science instead of the doctor-patient relationship.

Floridi and Sanders, seminal work, “On the morality of artificial agents” has catalyzed attention around the moral status of computer systems that perform tasks for humans, effectively acting as “artificial agents.” Floridi and Sanders argue that the class of entities considered moral agents can be expanded to include computers if we adopt the appropriate level of abstraction. In this paper we argue that the move to distinguish levels of abstraction is far from decisive on this issue. We also argue that (...) adopting certain levels of abstraction out of context can be dangerous when the level of abstraction obscures the humans who constitute computer systems. We arrive at this critique of Floridi and Sanders by examining the debate over the moral status of computer systems using the notion of interpretive flexibility. We frame the debate as a struggle over the meaning and significance of computer systems that behave independently, and not as a debate about the ‘true’ status of autonomous systems. Our analysis leads to the conclusion that while levels of abstraction are useful for particular purposes, when it comes to agency and responsibility, computer systems should be conceptualized and identified in ways that keep them tethered to the humans who create and deploy them. (shrink)

Cognitive psychologists have recently identified alterations in perception and reasoning that contribute to the formation and maintenance of beliefs that happen to be delusional. Clinically significant delusions, however, are often deeply unusual. An account of their formation and maintenance must explain not merely how someone can come to hold false or uncommon beliefs, but also how someone can arrive at beliefs that seem profoundly improbable and even bizarre. This paper uses the philosophical concepts of the Bedrock and the Background to (...) provide an account of that foundational, nonrepresentational, non–rule-governed, dispositional structure of everyday understanding that underpins both our perception and our reasoning. The central claim is that the formation and maintenance of delusions becomes intelligible once they are seen to reflect disturbances to this foundational dispositional structure. Different dimensions of the Background are described along with the delusions that might follow from distortions to these dimensions. We challenge the assumption of much recent cognitive psychological theorizing that delusions can be understood as explanations of unusual experiences or as the product of hasty reasoning. Finally, the implications of the theory for the therapy of the delusional patient are briefly discussed. (shrink)

Most Gentzen systems arising in logic contain few axiom schemata and many rule schemata. Hilbert systems, on the other hand, usually contain few proper inference rules and possibly many axioms. Because of this, the two notions tend to serve different purposes. It is common for a logic to be specified in the first instance by means of a Gentzen calculus, whereupon a Hilbert-style presentation ‘for’ the logic may be sought—or vice versa. Where this has occurred, the word ‘for’ has taken (...) on several different meanings, partly because the Gentzen separator ⇒ can be interpreted intuitively in a number of ways. Here ⇒ will be denoted less evocatively by ⊲.In this paper we aim to discuss some of the useful ways in which Gentzen and Hilbert systems may correspond to each other. Actually, we shall be concerned with thededucibility relationsof the formal systems, as it is these that are susceptible to transformation in useful ways. To avoid potential confusion, we shall speak of Hilbert and Gentzenrelations. By aHilbert relationwe mean any substitution-invariant consequence relation onformulas—this comes to the same thing as the deducibility relation of a set of Hilbert-style axioms and rules. By aGentzen relationwe mean the fully fledged generalization of this notion in whichsequentstake the place of single formulas. In the literature, Hilbert relations are often referred to assentential logics. Gentzen relations as defined here are their exactsequentialcounterparts. (shrink)

Knowledge of mechanisms is critical for causal reasoning. We contrasted two possible organizations of causal knowledge—an interconnected causal network, where events are causally connected without any boundaries delineating discrete mechanisms; or a set of disparate mechanisms—causal islands—such that events in different mechanisms are not thought to be related even when they belong to the same causal chain. To distinguish these possibilities, we tested whether people make transitive judgments about causal chains by inferring, given A causes B and B causes C, (...) that A causes C. Specifically, causal chains schematized as one chunk or mechanism in semantic memory led to transitive causal judgments. On the other hand, chains schematized as multiple chunks led to intransitive judgments despite strong intermediate links. Normative accounts of causal intransitivity could not explain these intransitive judgments. (shrink)

It is shown that for every nonzero r.e. degree c there is a linear ordering of degree c which is not isomorphic to any recursive linear ordering. It follows that there is a linear ordering of low degree which is not isomorphic to any recursive linear ordering. It is shown further that there is a linear ordering L such that L is not isomorphic to any recursive linear ordering, and L together with its ‘infinitely far apart’ relation is of low (...) degree. Finally, an analogue of the recursion theorem for recursive linear orderings is refuted. (shrink)

The degree of doxastic revision required in response to evidence of disagreement is typically thought to be a function of our beliefs about (1) our interlocutor’s familiarity with the relevant evidence and arguments, and their intellectual capacities and virtues, relative to our own, or (2) the expected probability of our interlocutor being correct, conditional on our disagreeing. While these two factors are typically used interchangeably, I show that they have an inverse correlation in cases of disagreement about politically divisive propositions. (...) This presents us with a puzzle about the epistemic impact of disagreement in these cases. The most significant disagreements on (1) are the least significant disagreements on (2), and vice versa. I show that assessing the epistemic status of an interlocutor by reference to either (1) or (2) has uncomfortable consequences in these cases. I then argue that this puzzle cannot be escaped by claiming that we usually have dispute-independent reason to reject the significance of politically charged disagreement altogether. (shrink)

In this paper, we focus attention on the role of computer system complexity in ascribing responsibility. We begin by introducing the notion of technological moral action (TMA). TMA is carried out by the combination of a computer system user, a system designer (developers, programmers, and testers), and a computer system (hardware and software). We discuss three sometimes overlapping types of responsibility: causal responsibility, moral responsibility, and role responsibility. Our analysis is informed by the well-known accounts provided by Hart and Hart (...) and Honoré. While these accounts are helpful, they have misled philosophers and others by presupposing that responsibility can be ascribed in all cases of action simply by paying attention to the free and intended actions of human beings. Such accounts neglect the part played by technology in ascriptions of responsibility in cases of moral action with technology. For both moral and role responsibility, we argue that ascriptions of both causal and role responsibility depend on seeing action as complex in the sense described by TMA. We conclude by showing how our analysis enriches moral discourse about responsibility for TMA. (shrink)