We investigate a speci c model of knowledge and beliefs and their dynamics. The model is inspired by public announcement logic and the approach to puzzles concerning knowledge using that logic. In the model epistemic considerations are based on ontology. The main notion that constitutes a bridge between these two disciplines is the notion of epistemic capacities. Within the model we study scenarios in which agents can receive false announcements and can have incomplete or improper views about other agent's (...) epistemic capacities. Moreover, we try to express the description of problem speci cation using the tools from applied ontology { RDF format for information and the Protege editor. (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)

The notion of comparative probability defined in Bayesian subjectivist theory stems from an intuitive idea that, for a given pair of events, one event may be considered “more probable” than the other. Yet it is conceivable that there are cases where it is indeterminate as to which event is more probable, due to, e.g., lack of robust statistical information. We take that these cases involve indeterminate comparative probabilities. This paper provides a Savage-style decision-theoretic foundation for indeterminate comparative probabilities.

Those incompleteness theorems mean the relation of (Peano) arithmetic and (ZFC) set theory, or philosophically, the relation of arithmetical finiteness and actual infinity. The same is managed in the framework of set theory by the axiom of choice (respectively, by the equivalent well-ordering "theorem'). One may discuss that incompleteness form the viewpoint of set theory by the axiom of choice rather than the usual viewpoint meant in the proof of theorems. The logical corollaries from that "nonstandard" viewpoint the relation of (...) set theory and arithmetic are demonstrated. (shrink)

Two strategies to infinity are equally relevant for it is as universal and thus complete as open and thus incomplete. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, thеse phenomena can be elucidated as both complete and incomplete, after which choice is the border (...) between them. A special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or “observer”, or “user” to infinity implied by Henkin’s proposition as the only consistent ones as to infinity. (shrink)

The idea that citizens have a right to receive information that is relevant for their suitable exercise of political rights and liberties is well established in democratic societies. However, this right has never been systematically analyzed, thus remaining a blurry concept. This article tackles this conceptual gap by conceptualizing citizens’ right to information. After reviewing previous approaches to this idea, I locate citizens’ right to information on the map of communication rights, and put forward a systematic framework (...) for both justifying and analyzing it. This framework focuses on this right’s grounds, its function, its holders, its content, and its correlative duties. Although the conceptualization offered here will be incomplete, it will be enough to distinguish the general concept of citizens’ right to information from both its specific conceptions and from the other two best-known rights of the public: freedom of information and the public’s right to know. (shrink)

Chaitin’s incompleteness result related to random reals and the halting probability has been advertised as the ultimate and the strongest possible version of the incompleteness and undecidability theorems. It is argued that such claims are exaggerations.

Traditional outcome-orientated egalitarian principles require access to information about the size of individual holdings. Recent egalitarian political theory has sought to accommodate considerations of responsibility. Such a move may seem problematic, in that a new informational burden is thereby introduced, with no apparent decrease in the existing burden. This article uses a simple model with simulated data to examine the extent to which outcome egalitarianism and responsibility-sensitive egalitarianism (‘luck egalitarianism’) can be accurately applied where information is incomplete (...) or erroneous. It is found that, while outcome egalitarianism tends to be more accurately applied, its advantage is not overwhelming, and in many prima facie plausible circumstances luck egalitarianism would be more accurately applied. This suggests that luck egalitarianism cannot be rejected as utopian. Furthermore, while some argue that, in practice, luck egalitarianism is best realized indirectly, by securing equality of outcome, our evidence suggests that a luck egalitarian rule of regulation offers a far more accurate implementation of the luck egalitarian ideal than does an outcome egalitarian rule of regulation. (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)

This is a completely informal presentation of the ideas behind the diagonal lemma. One really can't see this important result from too many different angles. This one aims at getting the main idea across. (For the cognoscenti, it is in the spirit of Quine's treatment in terms of "appended to its own quotation".).

When matter is falling into a black hole, the associated information becomes unavailable to the black hole's exterior. If the black hole disappears by Hawking evaporation, the information seems to be lost in the singularity, leading to Hawking's information paradox: the unitary evolution seems to be broken, because a pure separate quantum state can evolve into a mixed one.



This article proposes a new interpretation of the black hole singularities, which restores the information conservation. For the Schwarzschild (...) black hole, it presents new coordinates, which move the singularity at the future infinity (although it can still be reached in finite proper time). For the evaporating black holes, this article shows that we can still cure the apparently destructive effects of the singularity on the information conservation. For this, we propose to allow the metric to be degenerate at some points, and use the singular semiriemannian geometry. This view, which results naturally from the Cauchy problem, repairs the incomplete geodesics.



The reinterpretation of singularities suggested here allows (in the context of standard General Relativity) the information conservation and unitary evolution to be restored, both for eternal and for evaporating black holes.

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Peano arithmetic cannot serve as the ground of mathematics for it is inconsistent to infinity, and infinity is necessary for its foundation. Though Peano arithmetic cannot be complemented by any axiom of infinity, there exists at least one (logical) axiomatics consistent to infinity. That is nothing else than a new reading at issue and comparative interpretation of Gödel’s papers (1930; 1931) meant here. Peano arithmetic admits anyway generalizations consistent to infinity and thus to some addable axiom(s) of infinity. The most (...) utilized example of those generalizations is the complex Hilbert space. Any generalization of Peano arithmetic consistent to infinity, e.g. the complex Hilbert space, can serve as a foundation for mathematics to found itself and by itself. (shrink)

"Complexity" is a catchword of certain extremely popular and rapidly developing interdisciplinary new sciences, often called accordingly the sciences of complexity. It is often closely associated with another notably popular but ambiguous word, "information"; information, in turn, may be justly called the central new concept in the whole 20th century science. Moreover, the notion of information is regularly coupled with a key concept of thermodynamics, viz. entropy. And like this was not enough it is quite usual to (...) add one more at present extraordinarily popular notion, namely chaos, and wed it with the abovementioned concepts. It is my aim in this paper to critically analyse this conceptual mess from a logical and philosophical point of view concentrating on the concepts of complexity and information and the question concerning the true relation between them. (shrink)

A new layer of complexity, constituted of networks of information token recurrence, has been identified in socio-technical systems such as the Wikipedia online community and the Zooniverse citizen science platform. The identification of this complexity reveals that our current understanding of the actual structure of those systems, and consequently the structure of the entire World Wide Web, is incomplete, which raises novel questions for data science research but also from the perspective of social epistemology. Here we establish the (...) principled foundations and practical advantages of analyzing information diffusion within and across Web systems with Transcendental Information Cascades, and outline resulting directions for future study in the area of socio-technical systems. We also suggest that Transcendental Information Cascades may be applicable to any kind of time-evolving system that can be observed using digital technologies, and that the structures found in such systems comprise properties common to all naturally occurring complex systems. (shrink)

The previous two parts of the paper demonstrate that the interpretation of Fermat’s last theorem (FLT) in Hilbert arithmetic meant both in a narrow sense and in a wide sense can suggest a proof by induction in Part I and by means of the Kochen - Specker theorem in Part II. The same interpretation can serve also for a proof FLT based on Gleason’s theorem and partly similar to that in Part II. The concept of (probabilistic) measure of a subspace (...) of Hilbert space and especially its uniqueness can be unambiguously linked to that of partial algebra or incommensurability, or interpreted as a relation of the two dual branches of Hilbert arithmetic in a wide sense. The investigation of the last relation allows for FLT and Gleason’s theorem to be equated in a sense, as two dual counterparts, and the former to be inferred from the latter, as well as vice versa under an additional condition relevant to the Gödel incompleteness of arithmetic to set theory. The qubit Hilbert space itself in turn can be interpreted by the unity of FLT and Gleason’s theorem. The proof of such a fundamental result in number theory as FLT by means of Hilbert arithmetic in a wide sense can be generalized to an idea about “quantum number theory”. It is able to research mathematically the origin of Peano arithmetic from Hilbert arithmetic by mediation of the “nonstandard bijection” and its two dual branches inherently linking it to information theory. Then, infinitesimal analysis and its revolutionary application to physics can be also re-realized in that wider context, for example, as an exploration of the way for physical quantity of time (respectively, for time derivative in any temporal process considered in physics) to appear at all. Finally, the result admits a philosophical reflection of how any hierarchy arises or changes itself only thanks to its dual and idempotent counterpart. (shrink)

Modern cosmology has two competing theories of the origin of the universe: the "Singularity theory" and the "Superstring theory". Four Dilemmas of the "Super-string theory" are presented: the incompleteness of the eleven space–time dimensions,the inextricable dependence on the “Space–Time Background”, the "Zero-Brane the-ory" admitting stuff smaller than the Planck scale, and the pure mathematical theory that cannot be falsified by experiments. Although the "Singularity theory" is faced with many critiques from the "Superstring theory", from the perspective of Informa-tion Ontology, treating (...) the "Singularity" as "Origin Information" can dissolve these troubles well. For the "Singularity theory", the new philosophical thinking frame-work effectively explains the parameter problems of the universe, and gives satisfied response to the challenges from the "Superstring theory". As a result, the "Singularity theory" has a more competitive advantage on the origin of the universe. (shrink)

On the heels of Franzén's fine technical exposition of Gödel's incompleteness theorems and related topics (Franzén 2004) comes this survey of the incompleteness theorems aimed at a general audience. Gödel's Theorem: An Incomplete Guide to its Use and Abuse is an extended and self-contained exposition of the incompleteness theorems and a discussion of what informal consequences can, and in particular cannot, be drawn from them.

The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum (...) information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

Cultural evolution is normally framed in informational terms. However, it is not clear whether this is an adequate way to model cultural evolutionary phenomena and what, precisely, “information” is supposed to mean in this context. Would cultural evolutionary theory benefit from a well-developed theory of cultural information? The prevailing sentiment is that, in contradistinction to biology, informational language should be used nontechnically in this context for descriptive, but not explanatory, purposes. Against this view, this article makes the case (...) for the need to take a proper biology-based “informational turn” in the cultural evolutionary sciences. I argue that the current vague use of informational language misses out on the potential benefits for advancing understanding of phenomena that information-theoretic reasoning has provided in other sciences, especially genetics. In particular, by emphasizing the informational aspects of cultural evolutionary processes, this approach can clarify some conceptual and methodological problems that have plagued cultural evolutionary theory since its inception, including (1) how to determine the channel conditions of cultural information flow, (2) the nature and scope of cultural information, and (3) how to quantify trends of cultural cumulation. More generally, theories of cultural evolution will be incomplete until the mechanisms underlying cultural processes are better understood and integrated into the explanations. This article explores the adequacy of an information-theoretic framework to accomplish these purposes. (shrink)

A thought experiment demonstrates that physicalism about consciousness entails a para- doxical duplication of physical information. Moreover, objective existence acquires the status of a physical property. To avoid this paradox, one requires a concept of objectivity in which individuation is finite and incomplete. Finite individuation requires objective uncertainty and is thus corroborated by the contemporary sciences. Finite individuation and objective uncer- tainty prevent existence from becoming a physical property, thus defeating physicalism about consciousness and resolving the paradox.

Attacks on migrant and refugee entrepreneurs and their properties by South African rivals and ordinary citizens have become a common phenomenon throughout the country, including the city of Cape Town. Business robberies often result in deaths or serious injuries. The Somali Community Board has noted that over 400 Somali refugees, many of them informal traders, were murdered in South Africa between early 2002 and mid-2010. The police are frequently accused by migrants of fomenting or turning a blind eye to xenophobic (...) attacks on their businesses. Meanwhile, the government refuses to acknowledge the existence of xenophobia or the xenophobic rhetoric in many of these attacks, claiming instead that they are simply the actions of criminal elements. Photographs published in the media of the looting of migrant stores do not tend to feature hardened criminals, but ordinary citizens including children in school uniform. -/- Migrant businesses are portrayed by officials, citizens and the media as having a negative impact on the South African economy and undermining the livelihoods of South Africans. The prevalence of such perceptions helps to explain growing xenophobic sentiment against migrants and refugees. Contrary to these popular perceptions, an emerging literature on migrant entrepreneurship is beginning to demonstrate the positive economic contributions of migrants and refugees to the country. This report examines the nature of informal migrant and refugee entrepreneurship in Cape Town and whether or not the negative stereotypes have any validity. It also seeks to examine what economic contributions migrants and refugees make to the local economy. -/- The report is based on the research conducted by the Growing Informal Cities project, a partnership between SAMP/IMRC, the African Centre for Cities at the University of Cape Town, the Gauteng City-Region Observatory (GCRO) and Eduardo Mondlane University in Maputo. A questionnaire was administered to a sample of 518 migrant owners of microenterprises, which had to meet three basic criteria for inclusion: (a) owned by a non-South African; (b) in operation for at least two years; and (c) unregistered with the South African Revenue Services (SARS). Although migrant entrepreneurs are located in most areas of the city, certain areas have particular concentrations of migrant-owned businesses. "e questionnaires were administered in four such areas: Imizamo Yethu, Philippi, Bellville, and Cape Town CBD. Thirty in-depth interviews were also conducted with selected owners of informal micro-enterprises. Two focus group discussions were held in the Cape Town CBD and Philippi respectively. Fifteen key informant interviews were held with various stakeholders in Cape Town to understand the operation and constraints faced by migrants operating in the city’s informal economy. -/- The major findings of the personal profile of the migrant and refugee entrepreneurs were as follows: -/- • The entrepreneurs came from over 20 different countries of which Zimbabwe, Somalia, the Democratic Republic of the Congo (DRC), Nigeria, Malawi, Ethiopia and Cameroon were the most prominent. Just over a third were from other countries in the SADC. The prominence of Zimbabwean entrepreneurs in the Cape Town informal economy is not surprising, given the events in that country over the past decade and a half and resultant mass migration to South Africa. A total of 57% of the entrepreneurs were from other African countries, especially the DRC, Somalia, Nigeria and Ethiopia. "e majority of migrants from these countries (except Nigeria) came to South Africa as refugees. -/- • A third of the entrepreneurs had refugee permits. Of these, nearly 60% came from only three countries: the DRC, Ethiopia and Somalia. A further 31% held asylum-seeker permits. Of these, 32% were Zimbabwean while another 30% came from DRC, Ethiopia and Somalia. Nearly 12% had permanent residence permits while 8% were holders of work permits. Only 7% of the respondents indicated that they did not have official documentation to stay in South Africa. Thus, the majority of migrant entrepreneurs have forced migrants who are entitled to human rights protection under international and South African refugee law. • Very few of the entrepreneurs entered South Africa before 1994. Only 8% arrived in the immediate post-apartheid years. While another 20% came in the period 2000to 2004, the vast majority (70%) came during the last decade. As many as 44% arrived between 2005 and 2009 and a further 27% thereafter. Migration from Zimbabwe, in particular, escalated between 2005 and 2009 as the country plunged deeper into crisis. • Despite the perception that unemployment at home is a driver of migration to South Africa, only 14% of the entrepreneurs were unemployed immediately before leaving for South Africa. Another 19% were students. Twenty-six percent were working in the informal economy in their home countries. -/- .......INCOMPLETE..... (shrink)

In previous work, we studied four well known systems of qualitative probabilistic inference, and presented data from computer simulations in an attempt to illustrate the performance of the systems. These simulations evaluated the four systems in terms of their tendency to license inference to accurate and informative conclusions, given incomplete information about a randomly selected probability distribution. In our earlier work, the procedure used in generating the unknown probability distribution (representing the true stochastic state of the world) tended (...) to yield probability distributions with moderately high entropy levels. In the present article, we present data charting the performance of the four systems when reasoning in environments of various entropy levels. The results illustrate variations in the performance of the respective reasoning systems that derive from the entropy of the environment, and allow for a more inclusive assessment of the reliability and robustness of the four systems. (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)

In recent years, interest in desert-based theories of justice has increased, and this seems to represent a challenge to equality-based theories of justice.[i] The best distribution of outcomeadvantage with respect to desert, after all, need not be the most equal distribution of outcomeadvantage. Some individuals may deserve more than others. Outcome egalitarianism is, however, implausible, and so the conflict of outcome desert with outcome equality is of little significance.[ii] Most contemporary versions of egalitarianism are concerned with neutralizing the differential effects (...) of brute luck and not with equality of outcome. I shall argue that, in order to be plausible, a desert-based theory of justice can and must be compatible with this form of egalitarianism. There is, however, a stronger form of brute luck egalitarianism, which, as I shall explain, is concerned with equalizing the advantages from brute luck—and not merely with neutralizing the differential effects thereof. Under idealized conditions in which agents have perfect information about the outcomes that their choices generate, even this stronger form of egalitarianism, I shall show, is compatible with pure desert theory. Under conditions of incomplete information, however, strong brute luck egalitarianism is incompatible with a pure desert theory that appeals, as I shall explain, to moral, rather than prudential, desert. (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)

How children seek knowledge and evaluate claims may depend on their understanding of the source of knowledge. What shifts in their understandings about why scientists might disagree and how claims about the state of the world are justified? Until about the age of 41/2, knowledge is seen as self-evident. Children believe that knowledge of reality comes directly through our senses and what others tell us. They appeal to these external sources in order to know. The attainment of Theory of Mind (...) (ToM) at this age is commonly seen as the significant shift in development in understanding disagreements in knowledge claims. Children attaining ToM understand that someone exposed to incorrect or incomplete information might have false beliefs. Disagreement, then, is still attributed to objective sources of knowledge. The current study examines the later developing Interpretive Theory of Mind (iToM) as the basis for children’s understanding of how people with access to the same information might disagree and what this means for how to provide justification for a knowledge claim. Fourteen 2nd graders with the most iToM responses to four tasks and 14 with the fewest iToM responses were selected from a larger sample of 91. In analyses of interviews about a story in which two experts make different claims about a scientific phenomenon, those in the high iToM group noted subjective perspective and processes as the source of disagreement and suggested the need for investigation as the means to knowing. In contrast, those in the low iToM group mostly could not explain the source of disagreement and held that knowledge is acquired from external sources. A comparison of the interviews regarding the science story 2 years later allows for a qualitative description of the development. Those in the low iToM group showed more general recognition of subjective and constructive processes in knowing whereas those in the high iToM group identified interpretive processes and the relativity of perspectives with implications for how observations were conducted and interpreted. Only those in the high iToM group referred to the importance of evidence as a basis for knowledge claims at either point in the study. (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)

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)

The previous Part I of the paper discusses the option of the Gödel incompleteness statement (1931: whether “Satz VI” or “Satz X”) to be an axiom due to the pair of the axiom of induction in arithmetic and the axiom of infinity in set theory after interpreting them as logical negations to each other. The present Part II considers the previous Gödel’s paper (1930) (and more precisely, the negation of “Satz VII”, or “the completeness theorem”) as a necessary condition for (...) granting the Gödel incompleteness statement to be a theorem just as the statement itself, to be an axiom. Then, the “completeness paper” can be interpreted as relevant to Hilbert mathematics, according to which mathematics and reality as well as arithmetic and set theory are rather entangled or complementary rather than mathematics to obey reality able only to create models of the latter. According to that, both papers (1930; 1931) can be seen as advocating Russell’s logicism or the intensional propositional logic versus both extensional arithmetic and set theory. Reconstructing history of philosophy, Aristotle’s logic and doctrine can be opposed to those of Plato or the pre-Socratic schools as establishing ontology or intensionality versus extensionality. Husserl’s phenomenology can be analogically realized including and particularly as philosophy of mathematics. One can identify propositional logic and set theory by virtue of Gödel’s completeness theorem (1930: “Satz VII”) and even both and arithmetic in the sense of the “compactness theorem” (1930: “Satz X”) therefore opposing the latter to the “incompleteness paper” (1931). An approach identifying homomorphically propositional logic and set theory as the same structure of Boolean algebra, and arithmetic as the “half” of it in a rigorous construction involving information and its unit of a bit. Propositional logic and set theory are correspondingly identified as the shared zero-order logic of the class of all first-order logics and the class at issue correspondingly. Then, quantum mechanics does not need any quantum logics, but only the relation of propositional logic, set theory, arithmetic, and information: rather a change of the attitude into more mathematical, philosophical, and speculative than physical, empirical and experimental. Hilbert’s epsilon calculus can be situated in the same framework of the relation of propositional logic and the class of all mathematical theories. The horizon of Part III investigating Hilbert mathematics (i.e. according to the Pythagorean viewpoint about the world as mathematical) versus Gödel mathematics (i.e. the usual understanding of mathematics as all mathematical models of the world external to it) is outlined. (shrink)

In the 1951 Gibbs lecture, Gödel asserted his famous dichotomy, where the notion of informal proof is at work. G. Priest developed an argument, grounded on the notion of naïve proof, to the effect that Gödel’s first incompleteness theorem suggests the presence of dialetheias. In this paper, we adopt a plausible ideal notion of naïve proof, in agreement with Gödel’s conception, superseding the criticisms against the usual notion of naïve proof used by real working mathematicians. We explore the connection between (...) Gödel’s theorem and naïve proof so understood, both from a classical and a dialetheic perspective. (shrink)

Gentzen’s approach by transfinite induction and that of intuitionist Heyting arithmetic to completeness and the self-foundation of mathematics are compared and opposed to the Gödel incompleteness results as to Peano arithmetic. Quantum mechanics involves infinity by Hilbert space, but it is finitist as any experimental science. The absence of hidden variables in it interpretable as its completeness should resurrect Hilbert’s finitism at the cost of relevant modification of the latter already hinted by intuitionism and Gentzen’s approaches for completeness. This paper (...) investigates both conditions and philosophical background necessary for that modification. The main conclusion is that the concept of infinity as underlying contemporary mathematics cannot be reduced to a single Peano arithmetic, but to at least two ones independent of each other. Intuitionism, quantum mechanics, and Gentzen’s approaches to completeness an even Hilbert’s finitism can be unified from that viewpoint. Mathematics may found itself by a way of finitism complemented by choice. The concept of information as the quantity of choices underlies that viewpoint. Quantum mechanics interpretable in terms of information and quantum information is inseparable from mathematics and its foundation. (shrink)

The paper continues the consideration of Hilbert mathematics to mathematics itself as an additional “dimension” allowing for the most difficult and fundamental problems to be attacked in a new general and universal way shareable between all of them. That dimension consists in the parameter of the “distance between finiteness and infinity”, particularly able to interpret standard mathematics as a particular case, the basis of which are arithmetic, set theory and propositional logic: that is as a special “flat” case of Hilbert (...) mathematics. The following four essential problems are considered for the idea to be elucidated: Fermat’s last theorem proved by Andrew Wiles; Poincaré’s conjecture proved by Grigori Perelman and the only resolved from the seven Millennium problems offered by the Clay Mathematics Institute (CMI); the four-color theorem proved “machine-likely” by enumerating all cases and the crucial software assistance; the Yang-Mills existence and mass gap problem also suggested by CMI and yet unresolved. They are intentionally chosen to belong to quite different mathematical areas (number theory, topology, mathematical physics) just to demonstrate the power of the approach able to unite and even unify them from the viewpoint of Hilbert mathematics. Also, specific ideas relevant to each of them are considered. Fermat’s last theorem is shown as a Gödel insoluble statement by means of Yablo’s paradox. Thus, Wiles’s proof as a corollary from the modularity theorem and thus needing both arithmetic and set theory involves necessarily an inverse Grothendieck universe. On the contrary, its proof in “Fermat arithmetic” introduced by “epoché to infinity” (following the pattern of Husserl’s original “epoché to reality”) can be suggested by Hilbert arithmetic relevant to Hilbert mathematics, the mediation of which can be removed in the final analysis as a “Wittgenstein ladder”. Poincaré’s conjecture can be reinterpreted physically by Minkowski space and thus reduced to the “nonstandard homeomorphism” of a bit of information mathematically. Perelman’s proof can be accordingly reinterpreted. However, it is valid in Gödel (or Gödelian) mathematics, but not in Hilbert mathematics in general, where the question of whether it holds remains open. The four-color theorem can be also deduced from the nonstandard homeomorphism at issue, but the available proof by enumerating a finite set of all possible cases is more general and relevant to Hilbert mathematics as well, therefore being an indirect argument in favor of the validity of Poincaré’s conjecture in Hilbert mathematics. The Yang-Mills existence and mass gap problem furthermore suggests the most general viewpoint to the relation of Hilbert and Gödel mathematics justifying the qubit Hilbert space as the dual counterpart of Hilbert arithmetic in a narrow sense, in turn being inferable from Hilbert arithmetic in a wide sense. The conjecture that many if not almost all great problems in contemporary mathematics rely on (or at least relate to) the Gödel incompleteness is suggested. It implies that Hilbert mathematics is the natural medium for their discussion or eventual solutions. (shrink)

A practical viewpoint links reality, representation, and language to calculation by the concept of Turing (1936) machine being the mathematical model of our computers. After the Gödel incompleteness theorems (1931) or the insolvability of the so-called halting problem (Turing 1936; Church 1936) as to a classical machine of Turing, one of the simplest hypotheses is completeness to be suggested for two ones. That is consistent with the provability of completeness by means of two independent Peano arithmetics discussed in Section I. (...) Many modifications of Turing machines cum quantum ones are researched in Section II for the Halting problem and completeness, and the model of two independent Turing machines seems to generalize them. Then, that pair can be postulated as the formal definition of reality therefore being complete unlike any of them standalone, remaining incomplete without its complementary counterpart. Representation is formal defined as a one-to-one mapping between the two Turing machines, and the set of all those mappings can be considered as “language” therefore including metaphors as mappings different than representation. Section III investigates that formal relation of “reality”, “representation”, and “language” modeled by (at least two) Turing machines. The independence of (two) Turing machines is interpreted by means of game theory and especially of the Nash equilibrium in Section IV. Choice and information as the quantity of choices are involved. That approach seems to be equivalent to that based on set theory and the concept of actual infinity in mathematics and allowing of practical implementations. (shrink)

The paper addresses Leon Hen.kin's proposition as a " lighthouse", which can elucidate a vast territory of knowledge uniformly: logic, set theory, information theory, and quantum mechanics: Two strategies to infinity are equally relevant for it is as universal and t hus complete as open and thus incomplete. Henkin's, Godel's, Robert Jeroslow's, and Hartley Rogers' proposition are reformulated so that both completeness and incompleteness to be unified and thus reduced as a joint property of infinity and of all (...) infinite sets. However, only Henkin's proposition equivalent to an internal position to infinity is consistent . This can be retraced back to set theory and its axioms, where that of choice is a key. Quantum mechanics is forced to introduce infinity implicitly by Hilbert space, on which is founded its formalism. One can demonstrate that some essential properties of quantum information, entanglement, and quantum computer originate directly from infinity once it is involved in quantum mechanics. Thus, these phenomena can be elucidated as both complete and incomplete, after which choice is the border between them. A special kind of invariance to the axiom of choice shared by quantum mechanics is discussed to be involved that border between the completeness and incompleteness of infinity in a consistent way. The so-called paradox of Albert Einstein, Boris Podolsky, and Nathan Rosen is interpreted entirely in the same terms only of set theory. Quantum computer can demonstrate especially clearly the privilege of the internal position, or " observer'' , or "user" to infinity implied by Henkin's proposition as the only consistent ones as to infinity. An essential area of contemporary knowledge may be synthesized from a single viewpoint. (shrink)

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.

In this paper, we aim to provide an in-depth discussion of nickel's crucial position in the manufacturing sector in the context of the United Nations' Sustainable Development Goals (SDGs), which represent growing environmental imperatives. These SDGs have gained unprecedented urgency due to looming concerns of incompletion. It should be emphasized that the information compiled herein is derived from authoritative sources and is limited in its ability to give comprehensive coverage within the scope of this article. The raised issues are (...) of broad interest in terms of environmental dynamics in the global nickel mining, extraction, and refining arenas. As a result, the content given below may not precisely comply with the local situations dictated by geographical, geological, and socio-economic characteristics. The fundamental goal of this discussion is to clarify the economic-environmental interaction and the pragmatic meanings of the term "sustainable" in the context of the nickel industry. (shrink)

Many philosophers favour the simple knowledge account of assertion, which says you may assert something only if you know it. The simple account is true but importantly incomplete. I defend a more informative thesis, namely, that you may assert something only if your assertion expresses knowledge. I call this 'the express knowledge account of assertion', which I argue better handles a wider range of cases while at the same time explaining the simple knowledge account's appeal. §1 introduces some new (...) data that a knowledge account of assertion well explains. §2 explains the simple knowledge account's advantage over two of its main competitors. §3 presents a problem for the simple account and offers a solution, which is to adopt the express knowledge account. §4 encapsulates the case for the express knowledge account, and offers a unifying vision for the epistemology of belief and assertion. §5 answers an objection. §6 briefly sums up. Even those who ultimately reject my conclusion can still benefit from the new data presented in §1, and learn an important lesson from the problem discussed in §3, which demonstrates a general constraint on an acceptable account of the norm of assertion. (shrink)

More philosophical effort is spent articulating evolutionary rationales for the development of belief-like capacities than for precursors of desires or preferences. Nobody, though, seriously expects naturally evolved minds to be disinterested epistemologists. We agree that world-representing states won’t pay their way without supporting capacities that prioritise from an organism’s available repertoire of activities in light of stored (and occurrent) information. Some concede that desire-like states would be one way of solving this problem. Taking preferences as my starting point instead (...) of belief-like states, I defend two conclusions. First, psychologically real preference states, which approximately token expected utilities, have a quite general evolutionary rationale. They are a solution to the problem of efficiently allocating capacities with incompatible uses. This argument is a version of the Environmental Complexity Thesis. Second, preferences can plausibly function and naturally evolve without belief-like states, even though the converse claim is incredible. Preferences, that is, can mediate between discriminations of occurrent states (‘internal’ or ‘external’) and the processes selecting activity without mediation by stored indicative representations. By tokening expected utilities of actions conditional on discriminated state, they can increase the rate at which the ‘right thing’ is done at appropriate times, and they can do this without the support of belief-like, world-representing states. Preferences, even incomplete and noisy sets of them, are a fuel for success that will tend to be favoured when environments are complex in ways that matter to an organism, and when the organisms have complex behavioural repertoires with heterogenous returns and costs. (shrink)

In a previous article on cosmological arguments, I have put forward a few examples of complete infinite and circular explanations, and argued that complete non-wellfounded explanations such as these might explain the present state of the world better than their well-founded theistic counterparts (Billon, 2021). Although my aim was broader, the examples I gave there implied merely causal explanations. In this article, I would like to do three things: • Specify some general informative conditions for complete and incomplete non-wellfounded (...) causal explanations that can be used to assess candidate explanations and to generate new examples of complete non-wellfounded explanations. • Show that these conditions, which concern chains of causal explanations, easily generalize to chains of metaphysical, grounding explanations and even to chains involving other “determination relations” such as supervenience. • Apply these general conditions to the recent debates against the existence of nonwellfounded chains of grounds and show, with a couple of precise examples, that the latter can be complete, and that just like in the case of causal explanations, non-wellfoundedness can in fact be an aset rather than a liability. (shrink)

In this chapter we argue that emotions are mediated in an incomplete way in online social media because of the heavy reliance on textual messages which fosters a rationalistic bias and an inclination towards less nuanced emotional expressions. This incompleteness can happen either by obscuring emotions, showing less than the original intensity, misinterpreting emotions, or eliciting emotions without feedback and context. Online interactions and deliberations tend to contribute rather than overcome stalemates and informational bubbles, partially due to prevalence of (...) anti-social emotions. It is tempting to see emotions as being the cause of the problem of online verbal aggression and bullying. However, we argue that social media are actually designed in a predominantly rationalistic way, because of the reliance on text-based communication, thereby filtering out social emotions and leaving space for easily expressed antisocial emotions. Based on research on emotions that sees these as key ingredients to moral interaction and deliberation, as well as on research on text-based versus non-verbal communication, we propose a richer understanding of emotions, requiring different designs of online deliberation platforms. We propose that such designs should move from text-centred designs and should find ways to incorporate the complete expression of the full range of human emotions so that these can play a constructive role in online deliberations. (shrink)

People increasingly form beliefs based on information gained from automatically filtered Internet ‎sources such as search engines. However, the workings of such sources are often opaque, preventing ‎subjects from knowing whether the information provided is biased or incomplete. Users’ reliance on ‎Internet technologies whose modes of operation are concealed from them raises serious concerns about ‎the justificatory status of the beliefs they end up forming. Yet it is unclear how to address these concerns ‎within standard theories of (...) knowledge and justification. To shed light on the problem, we introduce a ‎novel conceptual framework that clarifies the relations between justified belief, epistemic responsibility, ‎action, and the technological resources available to a subject. We argue that justified belief is subject to ‎certain epistemic responsibilities that accompany the subject’s particular decision-taking circumstances, ‎and that one typical responsibility is to ascertain, so far as one can, whether the information upon which ‎the judgment will rest is biased or incomplete. What this responsibility comprises is partly determined by ‎the inquiry-enabling technologies available to the subject. We argue that a subject’s beliefs that are ‎formed based on Internet-filtered information are less justified than they would be if she either knew how ‎filtering worked or relied on additional sources, and that the subject may have the epistemic ‎responsibility to take measures to enhance the justificatory status of such beliefs.‎. (shrink)

Einstein wrote his famous sentence "God does not play dice with the universe" in a letter to Max Born in 1920. All experiments have confirmed that quantum mechanics is neither wrong nor “incomplete”. One can says that God does play dice with the universe. Let quantum mechanics be granted as the rules generalizing all results of playing some imaginary God’s dice. If that is the case, one can ask how God’s dice should look like. God’s dice turns out to (...) be a qubit and thus having the shape of a unit ball. Any item in the universe as well the universe itself is both infinitely many rolls and a single roll of that dice for it has infinitely many “sides”. Thus both the smooth motion of classical physics and the discrete motion introduced in addition by quantum mechanics can be described uniformly correspondingly as an infinite series converges to some limit and as a quantum jump directly into that limit. The second, imaginary dimension of God’s dice corresponds to energy, i.e. to the velocity of information change between two probabilities in both series and jump. (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)

Many existing biomedical vocabulary standards rest on incomplete, inconsistent or confused accounts of basic terms pertaining to diseases, diagnoses, and clinical phenotypes. Here we outline what we believe to be a logically and biologically coherent framework for the representation of such entities and of the relations between them. We defend a view of disease as involving in every case some physical basis within the organism that bears a disposition toward the execution of pathological processes. We present our view in (...) the form of a list of terms and definitions designed to provide a consistent starting point for the representation of both disease and diagnosis in information systems in the future. (shrink)

The foundations of research ethics are riven with fault lines emanating from a fear that if research is too closely connected to weighty social purposes an imperative to advance the common good through research will justify abrogating the rights and welfare of study participants. The result is an impoverished conception of the nature of research, an incomplete focus on actors who bear important moral responsibilities, and a system of ethics and oversight highly attuned to the dangers of research but (...) largely silent about threats of ineffective, inefficient, and inequitable medical practices and health systems. -/- In For the Common Good: Philosophical Foundations of Research Ethics, Alex John London defends a conception of the common good that grounds a moral imperative with two requirements. The first is to promote research that generates the information necessary to enable key social institutions to effectively, efficiently, and equitably safeguard the basic interests of individuals. The second is to ensure that research is organized as a voluntary scheme of social cooperation that respects its various contributors' moral claims to be treated as free and equal. Connecting research to the goals of a just social order grounds a framework for assessing and managing research risk that reconciles these requirements and justifies key oversight practices in non-paternalistic terms. Reconceiving research ethics as resolving coordination problems and providing credible assurance that these requirements are being met expands the issues and actors that fall within the purview of the field and provides the foundation for a more unified and coherent approach to domestic and international research. -/- This is an open access title available under the terms of a CC BY-NC-ND 4.0 license. It is free to read at Oxford Scholarship Online and offered as a free PDF download from OUP and selected open access locations. (shrink)

Review of "Exploring Randomness" (200) and "The Unknowable" (1999) by Gregory Chaitin.

The potential benefits of cognitive skills in enhancing mathematics ability have been claimed by numerous researchers. Since mathematics requires a complete understanding and grasp of abstract concepts, it is essential to explore how learning with metacognitive skills affects mathematics learning. Thus, the study investigates the students' metacognitive awareness and conceptual understanding of integers. A descriptive-correlational method approach was utilized, and it was carried out on 303 seventh-grade students. The data were obtained using a metacognitive awareness inventory and achievement test on (...) integers. It was further revealed that the students have average metacognitive awareness and performed well in the fundamental operation of integers. Follow-up qualitative analysis revealed that students who were high achievers had the best understanding, average achievers had corrected or incomplete understanding, and low achievers had a functional misconception of integers. Moreover, the student's metacognitive awareness was significantly related to their conceptual understanding of integers. This indicates that student's higher-order thinking skills, such as metacognition, are essential since they are associated with building conceptual skills. Thus, teachers should encourage students' metacognitive awareness to improve students' conceptual understanding of integers. The study provides relevant information for educational managers on the potential factors to be considered in improving mathematics education practices, particularly in promoting metacognition among high school students. (shrink)

Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information .In this paper we develop an hybrid structure called “ rough neutrosophic sets” and studied their properties.

A sorites argument is a symptom of the vagueness of the predicate with which it is constructed. A vague predicate admits of at least one dimension of variation (and typically more than one) in its intended range along which we are at a loss when to say the predicate ceases to apply, though we start out confident that it does. It is this feature of them that the sorites arguments exploit. Exactly how is part of the subject of this paper. (...) The majority of philosophers writing on vagueness take it to be a kind of semantic phenomenon. If we are right, they are correct in this assumption, which is surely the default position, but they have not so far provided a satisfactory account of the implications of this or a satisfactory diagnosis of the sorites arguments. Other philosophers have urged more exotic responses, which range from the view that the fault lies not in our language, but in the world, which they propose to be populated with vague objects which our semantics precisely reflects, to the view that the world and language are both perfectly in order, but that the fault lies with our knowledge of the properties of the words we use (epistemicism). In contrast to the exotica to which some philosophers have found themselves driven in an attempt to respond to the sorites puzzles, we undertake a defense of the commonsense view that vague terms are semantically vague. Our strategy is to take fresh look at the phenomenon of vagueness. Rather than attempting to adjudicate between different extant theories, we begin with certain pre-theoretic intuitions about vague terms, and a default position on classical logic. The aim is to see whether (i) a natural story can be told which will explain the vagueness phenomenon and the puzzling nature of soritical arguments, and, in the course of this, to see whether (ii) there arises any compelling pressure to give up the natural stance. We conclude that there is a simple and natural story to be told, and we tell it, and that there is no good reason to abandon our intuitively compelling starting point. The importance of the strategy lies in its dialectical structure. Not all positions on vagueness are on a par. Some are so incredible that even their defenders think of them as positions of last resort, positions to which we must be driven by the power of philosophical argument. We aim to show that there is no pressure to adopt these incredible positions, obviating the need to respond to them directly. If we are right, semantic vagueness is neither surprising, nor threatening. It provides no reason to suppose that the logic of natural languages is not classical or to give up any independently plausible principle of bivalence. Properly understood, it provides us with a satisfying diagnosis of the sorites argumentation. It would be rash to claim to have any completely novel view about a topic so well worked as vagueness. But we believe that the subject, though ancient, still retains its power to inform and challenge us. In particular, we will argue that taking seriously the central phenomenon of predicate vagueness—the “boundarylessness” of vague predicates—on the commonsense assumption that vagueness is semantic, leads ineluctably to the view that no sentences containing vague expressions (henceforth ‘vague sentences’) are truth-evaluable. This runs counter to much of the literature on vagueness, which commonly assumes that, though some applications of vague predicates to objects fail to be truth-evaluable, in clear positive and negative cases vague sentences are unproblematically true or false. It is clarity on this, and related points, that removes the puzzles associated with vagueness, and helps us to a satisfying diagnosis of why the sorites arguments both seem compelling and yet so obviously a bit of trickery. We give a proof that semantically vague predicates neither apply nor fail-to-apply to anything, and that consequently it is a mistake to diagnose sorites arguments, as is commonly done, by attempting to locate in them a false premise. Sorites arguments are not sound, but not unsound either. We offer an explanation of their appeal, and defend our position against a variety of worries that might arise about it. The plan of the paper is as follows. We first introduce an important distinction in terms of which we characterize what has gone wrong with vague predicates. We characterize what we believe to be our natural starting point in thinking about the phenomenon of vagueness, from which only a powerful argument should move us, and then trace out the consequences of accepting this starting point. We consider the charge that among the consequences of semantic vagueness are that we must give up classical logic and the principle of bivalence, which has figured prominently in arguments for epistemicism. We argue there are no such consequences of our view: neither the view that the logic of natural languages is classical, nor any plausible principle of bivalence, need be given up. Next, we offer a diagnosis of what has gone wrong in sorites arguments on the basis of our account. We then present an argument to show that our account must be accepted on pain of embracing (in one way or another) the epistemic view of “vagueness”, i.e., of denying that there are any semantically vague terms at all. Next, we discuss some worries that may arise about the intelligibility of our linguistic practices if our account is correct. We argue none of these worries should force us from our intuitive starting point. Finally, we cast a quick glance at other forms of semantic incompleteness. (shrink)

Many researchers determine the question “Why anything rather than nothing?” as the most ancient and fundamental philosophical problem. Furthermore, it is very close to the idea of Creation shared by religion, science, and philosophy, e.g. as the “Big Bang”, the doctrine of “first cause” or “causa sui”, the Creation in six days in the Bible, etc. Thus, the solution of quantum mechanics, being scientific in fact, can be interpreted also philosophically, and even religiously. However, only the philosophical interpretation is the (...) topic of the text. The essence of the answer of quantum mechanics is: 1. The creation is necessary in a rigorous mathematical sense. Thus, it does not need any choice, free will, subject, God, etc. to appear. The world exists in virtue of mathematical necessity, e.g. as any mathematical truth such as 2+2=4. 2. The being is less than nothing rather than more than nothing. So, the creation is not an increase of nothing, but the decrease of nothing: it is a deficiency in relation of nothing. Time and its “arrow” are the way of that diminishing or incompleteness to nothing. (shrink)