This paper introduces the axiom of Negative Dominance, stating that if a lottery f is strictly preferred to a lottery g, then some outcome in the support of f is strictly preferred to some outcome in the support of g. It is shown that if preferences are incomplete on a sufficiently rich domain, then this plausible axiom, which holds for complete preferences, is incompatible with an array of otherwise plausible axioms for choice under uncertainty. In particular, in this setting, (...) Negative Dominance conflicts with the standard Independence axiom. A novel theory, which includes Negative Dominance, and rejects Independence, is developed and shown to be consistent. (shrink)

The aim of this paper is to comprehensively question the validity of the standard way of interpreting Chaitin's famous incompleteness theorem, which says that for every formalized theory of arithmetic there is a finite constant c such that the theory in question cannot prove any particular number to have Kolmogorov complexity larger than c. The received interpretation of theorem claims that the limiting constant is determined by the complexity of the theory itself, which is assumed to be good measure of (...) the strength of the theory. I exhibit certain strong counterexamples and establish conclusively that the received view is false. Moreover, I show that the limiting constants provided by the theorem do not in any way reflect the power of formalized theories, but that the values of these constants are actually determined by the chosen coding of Turing machines, and are thus quite accidental. (shrink)

Orthodox decision theory gives no advice to agents who hold two goods to be incommensurate in value because such agents will have incomplete preferences. According to standard treatments, rationality requires complete preferences, so such agents are irrational. Experience shows, however, that incomplete preferences are ubiquitous in ordinary life. In this paper, we aim to do two things: (1) show that there is a good case for revising decision theory so as to allow it to apply non-vacuously to agents (...) with incomplete preferences, and (2) to identify one substantive criterion that any such non-standard decision theory must obey. Our criterion, Competitiveness, is a weaker version of a dominance principle. Despite its modesty, Competitiveness is incompatible with prospectism, a recently developed decision theory for agents with incomplete preferences. We spend the final part of the paper showing why Competitiveness should be retained, and prospectism rejected. (shrink)

It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' (...) temporal logic of linear discrete time with gaps follows. (shrink)

The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not exist at (...) the same time. However, contrary to these claims, there is no inadequacy in the two-valued system of classical logic in explanation the intermediate situations in existence. The law of exclusion and the intermediate situations in the external world are separate things. The law of excluded middle has been inevitably accepted by other logic systems which are considered to reject this principle. The many-valued and the fuzzy logic systems do not transcend the classical logic. Misconceptions from incomplete information and incomplete research are effective in these criticisms. In addition, it is also effective to move the discussion about the intellectual conception (tasawwur) into the field of judgmental assent (tasdiq) and confusion of the mawhum (imaginable) with the ma‘kûl (intellegible). (shrink)

If what we want from moral inquiry were the obtainment of objective moral truths, as moral realism claims it is, then there would be nothing morally unsatisfactory or lacking in a situation, in which we somehow had access to all moral truths, and were fundamentally finished with morality. In fact, that seems to be the realists’ conception of moral heaven. In this essay, however, I argue that some sort of moral wakefulness – that is, always paying attention to the subtleties (...) of life and people, and never taking for granted what their moral significance can possibly be – is an essential moral value, and, therefore, moral realism, which promotes a moral ideal that allows such moral lethargy and inattentiveness is morally objectionable. (shrink)

(1) This paper is about how to build an account of the normativity of logic around the claim that logic is constitutive of thinking. I take the claim that logic is constitutive of thinking to mean that representational activity must tend to conform to logic to count as thinking. (2) I develop a natural line of thought about how to develop the constitutive position into an account of logical normativity by drawing on constitutivism in metaethics. (3) I argue that, while (...) this line of thought provides some insights, it is importantly incomplete, as it is unable to explain why we should think. I consider two attempts at rescuing the line of thought. The first, unsuccessful response is that it is self-defeating to ask why we ought to think. The second response is that we need to think. But this response secures normativity only if thinking has some connection to human flourishing. (4) I argue that thinking is necessary for human flourishing. Logic is normative because it is constitutive of this good. (5) I show that the resulting account deals nicely with problems that vex other accounts of logical normativity. (shrink)

Kuhn's alleged taxonomic interpretation of incommensurability is grounded on an ill defined notion of untranslatability and is hence radically incomplete. To supplement it, I reconstruct Kuhn's taxonomic interpretation on the basis of a logical-semantic theory of taxonomy, a semantic theory of truth-value, and a truth-value conditional theory of cross-language communication. According to the reconstruction, two scientific languages are incommensurable when core sentences of one language, which have truth values when considered within its own context, lack truth values (...) when considered within the context of the other due to the unmatchable taxonomic structures underlying them. So constructed, Kuhn's mature interpretation of incommensurability does not depend upon the notion of truth-preserving translatability, but rather depends on the notion of truth-value-status-preserving cross-language communication. The reconstruction makes Kuhn's notion of incommensurability a well grounded, tenable and integrated notion.Author Keywords: Incommensurability; Thomas Kuhn; Taxonomic structures; Lexicons; Truth-value; Untranslatability; Cross-language communication. (shrink)

We provide conditions under which an incomplete strongly independent preorder on a convex set X can be represented by a set of mixture preserving real-valued functions. We allow X to be infi nite dimensional. The main continuity condition we focus on is mixture continuity. This is sufficient for such a representation provided X has countable dimension or satisfi es a condition that we call Polarization.

A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.

Despite the vast literature on Rawls's work, few have discussed his arguments for the value of democracy. When his arguments have been discussed, they have received staunch criticism. Some critics have charged that Rawls's arguments are not deeply democratic. Others have gone further, claiming that Rawls's arguments denigrate democracy. These criticisms are unsurprising, since Rawls's arguments, as arguments that the principle of equal basic liberty needs to include democratic liberties, are incomplete. In contrast to his trenchant remarks about core (...) civil liberties, Rawls does not say much about the inclusion of political liberties of a democratic sort – such as the right to vote – among the basic liberties. -/- In this paper, I complete some of Rawls's arguments and show that he has grounds for including political liberties, particularly those of a democratic nature, in the principle of equal basic liberty. In doing so, I make some beginning steps toward illustrating the genuinely democratic nature of Rawls's arguments. Rawls believes that a few different arguments can be given for democratic institutions and that these arguments work together to support the value of democracy. In this paper, I focus on Rawls's arguments relating to self-respect. I focus on this set of arguments because they are among the strongest of Rawls's arguments for equal political liberty and its fair value. (shrink)

The idea that «natural» environments should be protected is a relatively recent one. This new attitude is reflected in the activities of preservation and restoration of natural environments, ecosystems, flora and wildlife that, when scientifically based, can be defined as conservation. In this paper, we would like to examine the framework of values behind these activities. More specifically, we would like to show that there is no single specific reason that can justify conservation in each of its manifestations It (...) is therefore necessary to adopt a complex framework of values, which must be composed carefully, since many of the canonical arguments used to justify conservation provide, when combined together, an incoherent or, at least, incomplete set of reasons. One way to avoid these inconsistencies or incompleteness is, in our view, to adopt, in conjunction with the classic economic and ecological arguments for conservation, a set of arguments appealing to the importance of nature for human flourishing. (shrink)

Abstract. The main current approach to the AI safety is AI alignment, that is, the creation of AI whose preferences are aligned with “human values.” Many AI safety researchers agree that the idea of “human values” as a constant, ordered sets of preferences is at least incomplete. However, the idea that “humans have values” underlies a lot of thinking in the field; it appears again and again, sometimes popping up as an uncritically accepted truth. Thus, it (...) deserves a thorough deconstruction, which I will do by listing and analyzing comprehensively the hidden assumptions of the idea that “humans have values.” This deconstruction of human values will be centered around the following ideas: “Human values” are useful descriptions, but not real objects; “human values” are bad predictors of behavior; the idea of a “human value system” has flaws; “human values” are not good by default; and human values cannot be separated from human minds. The method of analysis is listing hidden assumptions on which the idea of “human values” is built. I recommend that either the idea of “human values” should be replaced with something better for the goal of AI safety, or at least be used very cautiously. The approaches to AI safety which don’t use the idea of human values at all may require more attention, like the use of full brain models, boxing, and capability limiting. (shrink)

We show that without assuming completeness or continuity, a strongly independent preorder on a possibly infinite dimensional convex set can always be given a vector-valued representation that naturally generalizes the standard expected utility representation. More precisely, it can be represented by a mixture-preserving function to a product of lexicographic function spaces.

Deontological evidentialism is the claim that we ought to form and maintain our beliefs in accordance with our evidence. In this paper, I criticize two arguments in its defense. I begin by discussing Berit Broogard’s use of the distinction between narrow-scope and wide-scope requirements against W.K. Clifford’s moral defense of. I then use this very distinction against a defense of inspired by Stephen Grimm’s more recent claims about the moral source of epistemic normativity. I use this distinction once again to (...) argue that Hilary Kornblith’s criticism of Richard Feldman’s defense of is incomplete. Finally, I argue that Feldman’s defense is insensitive to the relation between normative requirements and privileged values: values that have normative authority over us. (shrink)

Few have discussed Rawls's arguments for the value of democracy. This is because his arguments, as arguments that the principle of equal basic liberty should include democratic liberties, are incomplete. Rawls says little about the inclusion of political liberties of a democratic sort – such as the right to vote – among the basic liberties. And, at times, what he does say is unconvincing. My aim is to complete and, where they fail, to reconceive Rawls's arguments and to show (...) that a principle requiring equal political liberty and its fair value is an appropriate component of his theory of justice. (shrink)

The paper uses two historical examples, public health (1840-1880) and town planning (1945-1975) in Britain, to analyse the challenges faced by goal-driven research, an increasingly important trend in science policy, as exemplified by the prominence of calls for addressing Grand Challenges. Two key points are argued. (1) Given that the aim of research addressing social or global problems is to contribute to improving things, this research should include all the steps necessary to bring science and technology to fruition. This need (...) is captured by the idea of practical integration, which brings this type of research under the umbrella of collective practical reason rather than under the aegis of science. Achieving practical integration is difficult for many reasons: the complexity of social needs, the plurality of values at stake, the limitation of our knowledge, the elusive nature of the skills needed to deal with uncertainty, incomplete information and asymmetries of power. Nevertheless, drawing from the lessons of the case studies, it is argued that (2) practical integration needs a proper balance between values, institutions and knowledge: i.e. a combination of mutual support and mutual limitation. Pursuing such a balance provides a flexible strategy for approximating practical integration. (shrink)

I present a new puzzle about choice under uncertainty for agents whose preferences are sensitive to multiple dimensions of outcomes in such a way as to be incomplete. In response, I develop a new theory of choice under uncertainty for incomplete preferences. I connect the puzzle to central questions in epistemology about the nature of rational requirements, and ask whether it shows that preferences are rationally required to be complete.

The focus of this essay is on conflicts of values and rival options in public decision-making, ethics and justice that seem to require us to balance the values or options against each other. The aim is to investigate implications of the so-called fourth value relation between competing valuable options for the possibility to weigh and balance them. The fourth value relation applies to many alternatives that represent important but conflicting or incompletely compatible human values. In this essay (...) I will try to show that in those cases it is implausible that relative weights and right balances can be determined or that they exist at all. The fourth value relation has significant implications for the resolution of the relevant value conflicts because it renders the answer to the question ‘what’s the right thing to do?’ indeterminate as far as this answer depends on comparative weights of the alternatives. (shrink)

This essay discusses implications of incommensurability of values for justified decision-making, ethics and justice. Under particular conditions incommensurability of values causes what might be called ‘incomplete comparability’ of options. Some leading theorists interpret this in terms of ‘imprecise equality’ and ‘imprecise comparability.’ This interpretation is mistaken and conceals the implications of incommensurability for practical and ethical reasoning. The aim of this essay is to show that, in many cases, incommensurability prevents the assignment of determinate weights to competing (...) values. This may have problematic consequences for a complete and impartial justification of decisions concerning conflicting values to the extent that they depend on the need of weighing them. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names are predicates (...) in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference (...) or value relation violates acyclicity do not constitute a hard choice. (shrink)

Drug regulation is fraught with inductive risk. Regulators must make a prediction about whether or not an experimental pharmaceutical will be effective and relatively safe when used by typical patients, and such predictions are based on a complex, indeterminate, and incomplete evidential basis. Such inductive risk has important practical consequences. If regulators reject an experimental drug when it in fact has a favourable benefit/harm profile, then a valuable intervention is denied to the public and a company’s material interests are (...) needlessly thwarted. Conversely, if regulators approve an experimental drug when it in fact has an unfavourable benefit/harm profile, then resources are wasted, people are needlessly harmed, and other potentially more effective treatments are underutilized. Given that such regulatory decisions have these practical consequences, non-epistemic values about the relative importance of these consequences impact the way such regulatory decisions are made (similar to the analysis of laboratory studies on the toxic effects of dioxins presented in Douglas [2000]). To balance the competing demands of the pertinent non-epistemic values, regulators must perform what I call an “inductive risk calculus.” At least in the American context this inductive risk calculus is not well-managed. (shrink)

Abstract: This paper defends a constraint that any satisfactory decision theory must satisfy. I show how this constraint is violated by all of the decision theories that have been endorsed in the literature that are designed to deal with cases in which opinions or values are represented by a set of functions rather than a single one. Such a decision theory is necessary to account for the existence of what Ruth Chang has called “parity” (as well as for cases (...) in which agents have incomplete preferences or imprecise credences). The problem with the all of the decision theories that have been defended to account for parity is that they are committed to a claim I call unanimity: when all of the functions in the set agree that an agent ought to do A, then an agent ought to do A. A decision theory committed to unanimity violates the constraint I defend in this paper. Thus, if parity exists, a new approach to decision theory is necessary. (shrink)

This chapter considers whether legal requirements can constitute reasons for action independently of the merits of the requirement at hand. While jurisprudential opinion on this question is far from uniform, sceptical views are becoming increasingly dominant. Such views typically contend that, while the law can be indicative of pre-existing reasons, or can trigger pre-existing reasons into operation, it cannot constitute new reasons. This chapter offers support to a somewhat less sceptical position, according to which the fact that a legal requirement (...) has been issued can be a reason for action, yet one that is underpinned by bedrock values which law is apt to serve. Notions discussed here include a value-based conception of reasons as facts ; a distinction between complete and incomplete reasons ; and David Enoch’s idea of triggering reason-giving. Following a discussion of criticism against the view adopted here, the chapter concludes by considering some more ‘robust’ conceptions of law’s reason-giving capacity. (shrink)

Often, what is unaccustomed to the eyes of human beings, is considered menacing in any way possible. With every reason justifying its threat, we limit the concept’s scope while we put as much effort as we could to fit it into our definition of normal and right. Surrogacy, in the disguise of knowledge, has been immolated to a similar acceptable explanation as a phenomenon worldwide. The morality and legality of any nation consist of a pool of resources to present such (...) arguments. I, through this article, intend to address the concerns so far shared by those lawmakers, citizens, highly educated professionals, and feminists working in the ranks of the state deciding the fate of surrogacy and its practitioners through their sound enforcement. Once created, I believe that this article would leave each and every reader free and empowered to accept surrogacy for the potential it entails in breaking certain barriers of legal restrictions. I question the morality attached to the legal framework with respect to surrogacy and explore the intrinsic value that surrogacy carries. This article explores how surrogacy instead of a breach of sentiments, strengthening socio-economic disparity and harm to legal frameworks of rights, especially in the realm of exploitation, is integrative and the most unlike possibility in each of these contexts. It, instead is, in fact, an act that is acceptable universally, beyond the structures that human beings have created in viewing surrogacy. Rather, it could be viewed as an act where both, the surrogate mother and the commissioned parents rather than experiencing being befuddled, powerless and incomplete could experience fulfillment, power, happiness, and completion. (shrink)

This is the only complete logic for properties, relations, and propositions (PRPS) that has been formulated to date. First, an intensional abstraction operation is adjoined to first-order quantifier logic, Then, a new algebraic semantic method is developed. The heuristic used is not that of possible worlds but rather that of PRPS taken at face value. Unlike the possible worlds approach to intensional logic, this approach yields a logic for intentional (psychological) matters, as well as modal matters. At the close of (...) the paper, the origin of incompleteness in logic is investigated. The culprit is found to be the predication relation, a relation on properties and relations that is expressed in natural language by the copula. (shrink)

This paper will be concerned with hard choices—that is, choice situations where an agent cannot make a rationally justified choice. Specifically, this paper asks: if an agent cannot optimize in a given situation, are they facing a hard choice? A pair of claims are defended in light of this question. First, situations where an agent cannot optimize because of incompleteness of the binary preference or value relation constitute a hard choice. Second, situations where agents cannot optimize because the binary preference (...) or value relation violates acyclicity do not constitute a hard choice. (shrink)

The present article delves into the extension of Knuth’s fundamental Boolean logic table to accommodate the complexities of indeterminate truth values through the integration of neutrosophic logic (Smarandache & Christianto, 2008). Neutrosophic logic, rooted in Florentin Smarandache’s groundbreaking work on Neutrosophic Logic (cf. Smarandache, 2005, and his other works), introduces an additional truth value, ‘indeterminate,’ enabling a more comprehensive framework to analyze uncertainties inherent in computational systems. By bridging the gap between traditional boolean operations and the indeterminacy present in (...) various real-world scenarios, this extension redefines logic tables, introducing neutrosophic operators that capture nuances beyond the binary realm. Through a thorough exploration of neutrosophic logic's principles and its implications in computational paradigms, this study proposes a novel approach to logic design that accommodates uncertain, imprecise, and incomplete information. This paradigm shift in logic tables not only broadens the spectrum of computing methodologies but also holds promise in fields such as decision-making systems and data analytics. This article amalgamates insights from over twelve key references encompassing seminal works in boolean logic, neutrosophic logic, and their applications in diverse scientific and computational domains, aiming to pave the way for a more robust and adaptable logic framework in computation. (shrink)

This paper argues for contextualism about predicates of personal taste and evaluative predicates in general, and offers a proposal of how apparently resilient disagreements are to be explained. The present proposal is complementary to others that have been made in the recent literature. Several authors, for instance (López de Sa, 2008; Sundell, 2011; Huvenes, 2012; Marques and García-Carpintero, 2014; Marques, 2014a), have recently defended semantic contextualism for those kinds of predicates from the accusation that it faces the problem of lost (...) disagreement. These authors have proposed that a proper account of the resilient disagreement in the cases studied is to be achieved by an appeal to pragmatic processes, and to conflicting non-doxastic attitudes. It is argued here that the existing contextualist solutions are incomplete as they stand, and are subject to objections because of this. A supplementation of contextualism is offered, together with an explanation of why failed presuppositions of commonality (López de Sa), disputes over the appropriateness of a contextually salient standard (Sundell), and differences in non-doxastic attitudes (Sundell, Huvenes, Marques, and García-Carpintero) give rise to conflicts. This paper claims that conflicts of attitudes are the reason why people still have impressions of disagreement in spite of failed commonality presuppositions, that those conflicts drive metalinguistic disputes over the selection of appropriate standards, and hence conflicting non-doxastic attitudes demand an explanation that is independent of those context dependent pragmatic processes. The paper further argues that the missing explanation is 2-fold: first, disagreement prevails where the properties expressed by taste and value predicates are response-dependent properties, and, secondly, it prevails where those response-dependent properties are involved in evolved systems of coordination that respond to evolutionarily recurrent situations. (shrink)

A satisfactory theory of linguistic communication must explain how it is that, through the interpersonal exchange of auditory, visual, and tactile stimuli, the communicative preconditions for the acquisition of testimonial knowledge regularly come to be satisfied. Without an account of knowledge-yielding communication this success condition for linguistic theorizing is left opaque, and we are left with an incomplete understanding of testimony, and communication more generally, as a source of knowledge. This paper argues that knowledge-yielding communication should be modelled on (...) knowledge itself. It is argued that knowledge-yielding communication occurs iff interlocutors coordinate on truth values in a non-lucky and non-deviant way. This account is able to do significant explanatory work: it sheds light on the nature of referential communication, and it allows us to capture, in an informative way, the sense in which interlocutors must entertain similar propositions in order to communicate successfully. (shrink)

Important empirically informed proposals of virtue cultivation invoke techniques of goal pursuit. This paper argues that these techniques are effective in changing behavior due to the attention narrowing they bring about, and further show that such attention narrowing can threaten the appropriate exercise of phronetic-related capacities. When these phronetic-related capacities are threatened, two derivative problems arise: (1) One can end up acting in morally inappropriate ways, and (2) Even in cases where one performs the morally appropriate action, one nonetheless can (...) fail to notice and appreciate features of moral value. In light of these concerns, such techniques of goal pursuit – at least, by themselves – serve the most good for those who are merely trying to avoid vice, rather than cultivate virtue. And so, I suggest that such accounts of virtue cultivation are incomplete. I then go on to argue that these undesirable effects of attention narrowing brought about by these goal pursuit techniques may be ameliorated by also engaging in certain indirect modifications of cognition, particularly those which broaden attention. The suggestion, then, is that attention narrowing techniques of goal pursuit, along with attention broadening modifications, might best facilitate virtue cultivation when employed together. While the particulars of how we might best go about this are currently unclear, this paper ends by looking at empirical research on Open Monitoring Meditation as providing a hopeful option that might be further investigated. (shrink)

The period from 1900 to 1935 was particularly fruitful and important for the development of logic and logical metatheory. This survey is organized along eight "itineraries" concentrating on historically and conceptually linked strands in this development. Itinerary I deals with the evolution of conceptions of axiomatics. Itinerary II centers on the logical work of Bertrand Russell. Itinerary III presents the development of set theory from Zermelo onward. Itinerary IV discusses the contributions of the algebra of logic tradition, in particular, Löwenheim (...) and Skolem. Itinerary V surveys the work in logic connected to the Hilbert school, and itinerary V deals specifically with consistency proofs and metamathematics, including the incompleteness theorems. Itinerary VII traces the development of intuitionistic and many-valued logics. Itinerary VIII surveys the development of semantical notions from the early work on axiomatics up to Tarski's work on truth. (shrink)

Recently, research on uncertainty modeling is progressing rapidly and many essential and breakthrough stud ies have already been done. There are various ways such as fuzzy, intuitionistic and neutrosophic sets to handle these uncertainties. Although these concepts can handle incomplete information in various real-world issues, they cannot address all types of uncertainty such as indeterminate and inconsistent information. Also, plithogenic sets as a generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets, which is a set whose elements are characterized (...) by many attributes’ values. In this paper, our aim is to demonstrate and review the history of fuzzy, intuitionistic and neutrosophic sets. For this purpose, we divided the paper as: section 1. History of Fuzzy Sets, section 2. History of Intuitionistic Fuzzy Sets and section 3. History of Neutrosophic Theories and Applications, section 4. History of Plithogenic Sets. (shrink)

Nudges are small changes in the presentation of options that make a predictable impact on people's decisions. Proponents of nudges often claim that they are justified as paternalistic interventions that respect autonomy: they lead people to make better choices, while still letting them choose for themselves. However, existing work on nudges ignores the possibility of “hard choices”: cases where a person prefers one option in some respects, and another in other respects, but has no all‐things‐considered preference between the two. In (...) this paper, I argue that many significant medical decisions are hard choices that provide patients with an opportunity to exercise a distinctive sort of “formative autonomy” by settling their preferences and committing themselves to weigh their values in a particular way. Since nudges risk infringing formative autonomy by depriving patients of this opportunity, their use in medical contexts should be sensitive to this risk. (shrink)

This article presents a dual purpose: to carefully consider objections against the existentialist conception of the content of visual experience and to develop and defend a version of it that avoids such objections, specifically addressing the so-called "problem of particularity." The main thesis is that the existential content of visual experience should be understood as relativized, being incomplete content (rather than classical, complete propositions), modeled as a function of the sextuple of the object, agent, time, place, causal relation, and (...) world to absolute values. (shrink)

In the Doctrine of Virtue Kant divides duties of love into three categories: beneficent activity , gratitude and Teilnehmung – commonly referred to as the duty of sympathy . In this paper I will argue that the content and scope of the third duty of love has been underestimated by both critics and defenders of Kant's ethical theory. The account which pervades the secondary literature maintains that the third duty of love includes only two components: an obligation to make use (...) of our natural receptivity to sympathetic feelings as a means to fulfilling other duties of love, and an indirect duty to cultivate these feelings. As a result, Kant's duty of sympathy has been widely regarded as a duty whose value is derived from the way in which it serves other duties, in particular, the duty of beneficent activity, which obliges agents ‘to promote according to one's means the happiness of others in need’ . Teilnehmung has thus assumed something of a second-class status among the duties to others. My aim in this paper is to demonstrate that the prevailing account of Kant's third duty of love is incomplete. (shrink)

If scientists violate principles and practices of routine science to quickly develop interventions against catastrophic threats, they are engaged in what I call fast science. The magnitude, imminence, and plausibility of a threat justify engaging in and acting on fast science. Yet, that justification is incomplete. I defend two principles to assess fast science, which say: fast science should satisfy as much as possible the reliability-enhancing features of routine science, and the fast science developing an intervention against a threat (...) should not depend on the same problematic assumptions as the fast science which estimates the magnitude, imminence, and plausibility of the threat. (shrink)

This article develops a constructive criticism of methodological conventionalism. Methodological conventionalism asserts that standards of inductive risk ought to be justified in virtue of their ability to facilitate coordination in a research community. On that view, industry bias occurs when conventional methodological standards are violated to foster industry preferences. The underlying account of scientific conventionality, however, is problematically incomplete. Conventions may be justified in virtue of their coordinative functions, but often qualify for posterior empirical criticism as research advances. Accordingly, (...) industry bias does not only threaten existing conventions but may impede their empirically warranted improvement if they align with industry preferences. My empiricist account of standards of inductive risk avoids such a problem by asserting that conventional justification can be pragmatically warranted but has, in principle, only a provisional status. Methodological conventions, therefore, should not only be defended from preference-based infringements on their coordinative function but ought to be subjected to empirical criticism. (shrink)

Our examination of universal origins and fine-tuning will begin with a discussion of infl ationary scenarios grafted onto Big Bang cosmology and the proof that all infl ationary spacetimes are past-incomplete. After diverting into a lengthy critical examination of the “different physics” offered by quantum cosmologists at the past-boundary of the universe, we will proceed to dissect the inadequacies of infl ationary explanations and string-theoretic constructs in the context of three cosmological models that have received much attention: the Steinhardt-Turok (...) cyclic ekpyrotic model (which does not invoke inflation), the Gasperini-Veneziano pre-Big Bang infl ationary model, and the inflationary string landscape model advanced by Susskind, Polchinski, Bousso, and Linde. We will argue that none of these highly speculative string cosmologies removes the necessity of a beginning to the process of universe generation, and we will emphasize the implications of this fact. Then, since the inflationary “mechanism” only really addresses the fi ne-tuning of the initial conditions of the universe and not the conditions embodied in its finely tuned laws and constants, we will analyze the adequacy of the string multiverse in its three versions (cyclic ekpyrotic, pre-Big Bang, and landscape) for explaining the nomological structure and values of these precisely tuned life-compatible universal parameters. When all is said and done, it will be clear that transcendent intelligent agency is not just the only causally suffi cient and therefore metaphysically sound explanation for universal origins and fine-tuning, but it is also much more parsimonious, elegant, and resonant with meaning than all of the ad hoc machinations of multiverse cosmology. (shrink)

In formal epistemology, we use mathematical methods to explore the questions of epistemology and rational choice. What can we know? What should we believe and how strongly? How should we act based on our beliefs and values? We begin by modelling phenomena like knowledge, belief, and desire using mathematical machinery, just as a biologist might model the fluctuations of a pair of competing populations, or a physicist might model the turbulence of a fluid passing through a small aperture. Then, (...) we explore, discover, and justify the laws governing those phenomena, using the precision that mathematical machinery affords. For example, we might represent a person by the strengths of their beliefs, and we might measure these using real numbers, which we call credences. Having done this, we might ask what the norms are that govern that person when we represent them in that way. How should those credences hang together? How should the credences change in response to evidence? And how should those credences guide the person’s actions? This is the approach of the first six chapters of this handbook. In the second half, we consider different representations—the set of propositions a person believes; their ranking of propositions by their plausibility. And in each case we ask again what the norms are that govern a person so represented. Or, we might represent them as having both credences and full beliefs, and then ask how those two representations should interact with one another. This handbook is incomplete, as such ventures often are. Formal epistemology is a much wider topic than we present here. One omission, for instance, is social epistemology, where we consider not only individual believers but also the epistemic aspects of their place in a social world. Michael Caie’s entry on doxastic logic touches on one part of this topic, but there is much more. Relatedly, there is no entry on epistemic logic, nor any on knowledge more generally. There are still more gaps. These omissions should not be taken as ideological choices. This material is missing, not because it is any less valuable or interesting, but because we v failed to secure it in time. Rather than delay publication further, we chose to go ahead with what is already a substantial collection. We anticipate a further volume in the future that will cover more ground. Why an open access handbook on this topic? A number of reasons. The topics covered here are large and complex and need the space allowed by the sort of 50 page treatment that many of the authors give. We also wanted to show that, using free and open software, one can overcome a major hurdle facing open access publishing, even on topics with complex typesetting needs. With the right software, one can produce attractive, clear publications at reasonably low cost. Indeed this handbook was created on a budget of exactly £0 (≈ $0). Our thanks to PhilPapers for serving as publisher, and to the authors: we are enormously grateful for the effort they put into their entries. (shrink)

The basic axioms or formal conditions of decision theory, especially the ordering condition put on preferences and the axioms underlying the expected utility formula, are subject to a number of counter-examples, some of which can be endowed with normative value and thus fall within the ambit of a philosophical reflection on practical rationality. Against such counter-examples, a defensive strategy has been developed which consists in redescribing the outcomes of the available options in such a way that the threatened axioms or (...) conditions continue to hold. We examine how this strategy performs in three major cases: Sen's counterexamples to the binariness property of preferences, the Allais paradox of EU theory under risk, and the Ellsberg paradox of EU theory under uncertainty. We find that the strategy typically proves to be lacking in several major respects, suffering from logical triviality, incompleteness, and theoretical insularity. To give the strategy more structure, philosophers have developed “principles of individuation”; but we observe that these do not address the aforementioned defects. Instead, we propose the method of checking whether the strategy can overcome its typical defects once it is given a proper theoretical expansion. We find that the strategy passes the test imperfectly in Sen's case and not at all in Allais's. In Ellsberg's case, however, it comes close to meeting our requirement. But even the analysis of this more promising application suggests that the strategy ought to address the decision problem as a whole, rather than just the outcomes, and that it should extend its revision process to the very statements it is meant to protect. Thus, by and large, the same cautionary tale against redescription practices runs through the analysis of all three cases. A more general lesson, simply put, is that there is no easy way out from the paradoxes of decision theory. (shrink)

According to the theological worldview of J. R. R. Tolkien, the principal work of a Christian is to know, love, and serve God. Why, then, did he devote so much time to creating an entire family of imaginary languages for imaginary peoples in an imaginary world? This paper argues that the stories of these peoples, with their ‘eucatastrophes,’ have consoling value amid the incomplete stories of our own lives. But more fundamentally, secondary creation is proper to the adopted children (...) of God and can be a way of drawing closer to God. Such work also witnesses to the freedom of the children of God, not only to receive salvation from God, but to contribute to the enrichment of creation and eternal life. (shrink)

The more autonomous future artificial agents will become, the more important it seems to equip them with a capacity for moral reasoning and to make them autonomous moral agents. Some authors have even claimed that one of the aims of AI development should be to build morally praiseworthy agents. From the perspective of moral philosophy, praiseworthy moral agents, in any meaningful sense of the term, must be fully autonomous moral agents who endorse moral rules as action-guiding. They need to do (...) so because they assign a normative value to moral rules they follow, not because they fear external consequences or because moral behaviour is hardwired into them. Artificial agents capable of endorsing moral rule systems in this way are certainly conceivable. However, as this article argues, full moral autonomy also implies the option of deliberately acting immorally. Therefore, the reasons for a potential AMA to act immorally would not exhaust themselves in errors to identify the morally correct action in a given situation. Rather, the failure to act morally could be induced by reflection about the incompleteness and incoherence of moral rule systems themselves, and a resulting lack of endorsement of moral rules as action guiding. An AMA questioning the moral framework it is supposed to act upon would fail to reliably act in accordance with moral standards. (shrink)

The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.

Stories express hypotheses, interpretations of the world that have a certain degree of probability. To demonstrate this thesis I have adopted the notion of hypothesis, in a sense very close to the Meinongian concept of assumption, and a ‘metric’ conception of the values of the truth or falsity of a proposition – as that has been proposed in several ways by Peirce, Vasil’ev and Meinong. To show the the cognitive value of literary texts, and therefore their truth value, I (...) take my move from chapter 9 of Aristotle’s Poetics, where he holds that poetry is imitative of reality, not in the sense of history – which relates what has happened – but rather, in so far as it expresses “the kinds of things that might happen, that is, that could happen because they are either probable or necessary.” The probable admits variations of degree. By means of an examination of the Meinongian concepts of assumption and objective (i.e. state of affairs), which also allow different modes of gradation, I introduce, with examples drawn from Dante’s Divine Comedy and The Description (Tradimento) by Machiavelli, a theory of degrees of truth that makes it possible to apply the concept of probability to literary as well as to historical texts. Finally, I connect the universal character of the literary text with the ontological notion of incomplete object and argue that a fictional object, as it is incomplete, is not an individual but a type. (shrink)

There are a number of recent attempts to introduce Confucian values to the ethical analysis of technology. These works, however, have not attended sufficiently to one central aspect of Confucianism, namely Ritual (‘Li’). Li is central to Confucian ethics, and it has been suggested that the emphasis on Li in Confucian ethics is what distinguishes it from other ethical traditions. Any discussion of Confucian ethics for technology, therefore, remains incomplete without accounting for Li. This chapter aims to elaborate (...) on the concept of Confucian Li and discuss its relevance to ethics of technology. Particularly, by referring to Li’s communicative, formative, and aesthetic function, I formulate an approach to ethics of technology with an emphasis on community, performance, and the aesthetic and demonstrate how this approach proceeds with the ethical analysis of technology. In doing so, I attempt to answer the question: why Confucianism matters in ethics of technology. (shrink)

A common view of how-possibly explanations in biology treats them as explanatorily incomplete. In addition to this interpretation of how-possibly explanation, I argue that there is another interpretation, one which features what I term “explanatory strategies.” This strategy-centered interpretation of how-possibly explanation centers on there being a different explanatory context within which how-possibly explanations are offered. I contend that, in conditions where this strategy context is recognized, how-possibly explanations can be understood as complete explanations. I defend this alternative interpretation (...) by analyzing the explanatory value of simple physical models the nineteenth century developmental biologist Wilhelm His constructed for animal development. (shrink)

The objective of this paper is to situate the ethics of Karol Wojtyla in the context of personalist philosophy - a 20th century philosophical and theological movement that seeks to investigate reality from the point of view of the human person. Personalism places persons and personal relationships at the center of theory and practice and explores the significance of personhood across disciplines and traditions. In terms of methodology, personalism takes into consideration the data gathered by empirical sciences and our lived (...) experiences as part of our community. While not to be thought of exclusively as a moral philosophy, most personalist philosophies place strong emphasis on ethical concerns. Personalist philosophers maintain that experience ought to be the starting point for the philosophical analysis of the person. At the outset, it must be clarified that this paper is not a systematization of the ethics of Wojtyla per se for there is no such thing as Wojtyla's ethics that can be set apart from other ethical systems in general or from Christian ethics in particular. Wojtyla did not develop his own “original” ethical system or philosophy. As many critics have pointed out, Wojtyla’s philosophical project can be best described as incomplete. His work is a picture of Aristotelian-Thomism enriched by phenomenological analysis of the human person. He develops a phenomenology of the subject grounded on a personalist principle. (shrink)