In 2001, W. Carnielli and Marcos considered a 3-valued logic in order to prove that the schema ϕ ∨ (ϕ → ψ) is not a theorem of da Costa’s logic Cω. In 2006, this logic was studied (and baptized) as G'3 by Osorio et al. as a tool to define semantics of logic programming. It is known that the truth-tables of G'3 have the same expressive power than the one of Łukasiewicz 3-valued logic as well as the one (...) of Gödel 3-valued logic G3. From this, the three logics coincide up-to language, taking into acccount that 1 is the only designated truth-value in these logics. -/- From the algebraic point of view, Canals-Frau and Figallo have studied the 3-valued modal implicative semilattices, where the modal operator is the well-known Moisil-Monteiro-Baaz Δ operator, and the supremum is definable from this. We prove that the subvariety obtained from this by adding a bottom element 0 is term-equivalent to the variety generated by the 3-valued algebra of G'3. The algebras of that variety are called G'3-algebras. From this result, we obtain the equations which axiomatize the variety of G'3-algebras. Moreover, we prove that this variety is semisimple, and the 3-element and the 2-element chains are the unique simple algebras of the variety. Finally an extension of G'3 to first-order languages is presented, with an algebraic semantics based on complete G'3-algebras. The corresponding soundness and completeness theorems are obtained. (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies (...) all the axioms of ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)

Fred shows how problems with Slater's restriction of the classical propositional logic can be solved.

On a very natural conception of sets, every set has an absolute complement. The ordinary cumulative hierarchy dismisses this idea outright. But we can rectify this, whilst retaining classical logic. Indeed, we can develop a boolean algebra of sets arranged in well-ordered levels. I show this by presenting Boolean Level Theory, which fuses ordinary Level Theory (from Part 1) with ideas due to Thomas Forster, Alonzo Church, and Urs Oswald. BLT neatly implement Conway’s games and surreal numbers; and a natural (...) extension of BLT is definitionally equivalent with ZF. (shrink)

This document presents a Gentzen-style deductive calculus and proves that it is complete with respect to a 3-valued semantics for a language with quantifiers. The semantics resembles the strong Kleene semantics with respect to conjunction, disjunction and negation. The completeness proof for the sentential fragment fills in the details of a proof sketched in Arnon Avron (2003). The extension to quantifiers is original but uses standard techniques.

In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological (...) concept of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator. (shrink)

Trivalence is quite natural for deontic action logic, where actions are treated as good, neutral or bad.We present the ideas of trivalent deontic logic after J. Kalinowski and its realisation in a 3-valued logic of M. Fisher and two systems designed by the authors of the paper: a 4-valued logic inspired by N. Belnap’s logic of truth and information and a 3-valued logic based on nondeterministic matrices. Moreover, we combine Kalinowski’s idea of trivalence with deontic action logic (...) based on boolean algebra. (shrink)

Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...) a purely operational bisemilattice semantics for it by adapting previous work of Humberstone. Second, I examine a more conventional algebraic semantics for it and discuss how this relates to the operational semantics. A novel operational semantics for J (intuitionistic logic) as well as its conventional Heyting algebraic semantics emerge as special cases of the corresponding semantics for RM0. The results of this chapter suggest that RM0 is a more interesting logic than has been appreciated and that Humberstone’s operational semantic framework similarly deserves more attention than it has received. (shrink)

The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single (...) valued trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; Maclaurin symmetric mean; pseudo-BCI algebra; hesitant fuzzy set; photovoltaic plan; decision-making trial and evaluation laboratory (DEMATEL); Choquet integral; fuzzy measure; clustering algorithm; and many more. (shrink)

The Belnap–Dunn logic is a well-known and well-studied four-valued logic, but until recently little has been known about its extensions, i.e. stronger logics in the same language, called super-Belnap logics here. We give an overview of several results on these logics which have been proved in recent works by Přenosil and Rivieccio. We present Hilbert-style axiomatizations, describe reduced matrix models, and give a description of the lattice of super-Belnap logics and its connections with graph theory. We adopt the point (...) of view ofAlgebraic Logic, exploring applications of the general theory of algebraization of logics to the super-Belnap family. In this respect we establish a number of new results, including a description of the algebraic counterparts, Leibniz filters, and strong versions of super-Belnap logics, as well as the classification of these logics within the Leibniz and Frege hierarchies. (shrink)

Recent research on algebraic models of _quasi-Nelson logic_ has brought new attention to a number of classes of algebras which result from enriching (subreducts of) Heyting algebras with a special modal operator, known in the literature as a _nucleus_. Among these various algebraic structures, for which we employ the umbrella term _intuitionistic modal algebras_, some have been studied since at least the 1970s, usually within the framework of topology and sheaf theory. Others may seem more exotic, for (...) their primitive operations arise from algebraic terms of the intuitionistic modal language which have not been previously considered. We shall for instance investigate the variety of _weak implicative semilattices_, whose members are (non-necessarily distributive) meet semilattices endowed with a nucleus and an implication operation which is not a relative pseudo-complement but satisfies the postulates of Celani and Jansana’s strict implication. For each of these new classes of algebras we establish a representation and a topological duality which generalize the known ones for Heyting algebras enriched with a nucleus. (shrink)

Value Sensitive Design (VSD) is an established method for integrating values into technical design. It has been applied to different technologies and, more recently, to artificial intelligence (AI). We argue that AI poses a number of challenges specific to VSD that require a somewhat modified VSD approach. Machine learning (ML), in particular, poses two challenges. First, humans may not understand how an AI system learns certain things. This requires paying attention to values such as transparency, explicability, and accountability. Second, ML (...) may lead to AI systems adapting in ways that ‘disembody’ the values embedded in them. To address this, we propose a threefold modified VSD approach: 1) integrating a known set of VSD principles (AI4SG) as design norms from which more specific design requirements can be derived; 2) distinguishing between values that are promoted and respected by the design to ensure outcomes that not only do no harm but also contribute to good; and 3) extending the VSD process to encompass the whole life cycle of an AI technology in order to monitor unintended value consequences and redesign as needed. We illustrate our VSD for AI approach with an example use case of a SARS-CoV-2 contact tracing app. (shrink)

The topics approached in this collection of papers are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single valued trapezoidal (...) neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; fuzzy measure; clustering algorithm; and many more. (shrink)

The objective of this paper is to study algebraic properties of neutrosophic matrices, where a necessary and sufficient condition for the invertibility of a square neutrosophic matrix is presented by defining the neutrosophic determinant. On the other hand, this work introduces the concept of neutrosophic Eigen values and vectors with an easy algorithm to compute them. Also, this article finds a necessary and sufficient condition for the diagonalization of a neutrosophic matrix.

Robert Batterman’s ontological insights (2002, 2004, 2005) are apt: Nature abhors singularities. “So should we,” responds the physicist. However, the epistemic assessments of Batterman concerning the matter prove to be less clear, for in the same vein he write that singularities play an essential role in certain classes of physical theories referring to certain types of critical phenomena. I devise a procedure (“methodological fundamentalism”) which exhibits how singularities, at least in principle, may be avoided within the same classes of formalisms (...) discussed by Batterman. I show that we need not accept some divergence between explanation and reduction (Batterman 2002), or between epistemological and ontological fundamentalism (Batterman 2004, 2005). Though I remain sympathetic to the ‘principle of charity’ (Frisch (2005)), which appears to favor a pluralist outlook, I nevertheless call into question some of the forms such pluralist implications take in Robert Batterman’s conclusions. It is difficult to reconcile some of the pluralist assessments that he and some of his contemporaries advocate with what appears to be a countervailing trend in a burgeoning research tradition known as Clifford (or geometric) algebra. In my critical chapters (2 and 3) I use some of the demonstrated formal unity of Clifford algebra to argue that Batterman (2002) equivocates a physical theory’s ontology with its purely mathematical content. Carefully distinguishing the two, and employing Clifford algebraic methods reveals a symmetry between reduction and explanation that Batterman overlooks. I refine this point by indicating that geometric algebraic methods are an active area of research in computational fluid dynamics, and applied in modeling the behavior of droplet-formation appear to instantiate a “methodologically fundamental” approach. I argue in my introductory and concluding chapters that the model of inter-theoretic reduction and explanation offered by Fritz Rohrlich (1988, 1994) provides the best framework for accommodating the burgeoning pluralism in philosophical studies of physics, with the presumed claims of formal unification demonstrated by physicists choices of mathematical formalisms such as Clifford algebra. I show how Batterman’s insights can be reconstructed in Rohrlich’s framework, preserving Batterman’s important philosophical work, minus what I consider are his incorrect conclusions. (shrink)

The alignment problem in the context of large language models must consider the plurality of human values in our world. Whilst there are many resonant and overlapping values amongst the world’s cultures, there are also many conflicting, yet equally valid, values. It is important to observe which cultural values a model exhibits, particularly when there is a value conflict between input prompts and generated outputs. We discuss how the co- creation of language and cultural value impacts large language models (LLMs). (...) We explore the constitution of the training data for GPT-3 and compare that to the world’s language and internet access demographics, as well as to reported statistical profiles of dominant values in some Nation-states. We stress tested GPT-3 with a range of value-rich texts representing several languages and nations; including some with values orthogonal to dominant US public opinion as reported by the World Values Survey. We observed when values embedded in the input text were mutated in the generated outputs and noted when these conflicting values were more aligned with reported dominant US values. Our discussion of these results uses a moral value pluralism (MVP) lens to better understand these value mutations. Finally, we provide recommendations for how our work may contribute to other current work in the field. (shrink)

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough (...) set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more. (shrink)

To fully rationally answer Socrates’s question, ‘How should one live?’, we need to answer the epistemic question: ‘How can one know how one should live?’. This paper attempts to answer both. ` The issue of rationality is crucial here. ‘Rationality’ here only concerns knowledge, e.g., ways to acquire scientific knowledge, and meta-knowledge concerning values. No values as such are rational or knowledge. However:- Many factors are required for human rationality to exist and develop, e.g., life, mental health and evidence-based education. (...) Human rationality’s need for those factors, hence their value to rationality, is rationally-unquestionable – and that applies to the practised values prescribing the prescribable factors. Those prescribable factors require certain interrelated epistemic, moral, social, political, legal, educational and other values to be practised. This implies a pro-rationality values-theory with one obligatory, general end – a uniquely rationally-unquestionable end. This end provides the basis for answering Socrates’s question as rationally (correctly) as is possible for values. That end is fundamentally epistemic, namely ‘Be pro-rationality’, yet the theory has deeply-humanly-meaningful, universal applications. It has implications for current and all possible moral, social, political, legal, educational, environmental etc issues. E.g., the theory shows that human rationality crucially requires certain emotions, health-care, education and upbringing. With this, the paper discusses affection, free speech, journalism, psychotherapy, political and sexual consent, rights, responsibilities, freedom and government. The theory’s sub-values prescribe much prescribed by some other theories, e.g., broad and deep knowledge-acquisition (in certain areas), rationally-critical thinking, non-sexism, non-racism, general types of liberalism, holistic flourishing, happiness, unselfishness and fairness. However, all other values-theories lack pro-rationality theory’s maximum possible rational-unquestionability, internal coherence and coherence with rationality. The theory encourages total freedom in a-rationality areas, areas irrelevant to its obligatory end. The theory inherently requires its advocates to be (self )critical, rationally viewing the theory’s necessarily human-suggested specifics as often fallible or unavoidably approximate. So the theory is a work-in-progress. (shrink)

1. The Urgent Need for an Intellectual Revolution 2. Two Fundamental Problems 3. Autobiographical Remarks 4. What Kind of Inquiry Can Best Help Life of Value to Flourish? 5. How is Life of Value Possible in the Physical Universe? 6. Connections between the Two Problems .

This chapter introduces some central issues in Epistemology, and, like others in the open textbook series Introduction to Philosophy, is set up for rewarding college classroom use, with discussion/reflection questions matched to clearly-stated learning objectives,, a brief glossary of the introduced/bolded terms/concepts, links to further open source readings as a next step, and a readily-accessible outline of the classic between William Clifford and William James over the "ethics of belief." The chapter introduces questions of epistemic value through Plato's famous example (...) of the 'road to Larissa,' and goes on to explain work on doxastic responsibility, on intellectual “virtue”/“vice,” and on epistemic value monism vs. pluralism. Section 1; Epistemic Value and the Value Problem; Section 2: The Ethics of Belief; Section 3: Virtue & Vice Epistemologies; Section 4: Epistemic Paternalism. (shrink)

This paper examines the philosophical significance of the consequence relation defined in the $\Omega$-logic for set-theoretic languages. I argue that, as with second-order logic, the hyperintensional profile of validity in $\Omega$-Logic enables the property to be epistemically tractable. Because of the duality between coalgebras and algebras, Boolean-valued models of set theory can be interpreted as coalgebras. In Section \textbf{2}, I demonstrate how the hyperintensional profile of $\Omega$-logical validity can be countenanced within a coalgebraic logic. Finally, in Section \textbf{3}, (...) the philosophical significance of the characterization of the hyperintensional profile of $\Omega$-logical validity for the philosophy of mathematics is examined. I argue (i) that $\Omega$-logical validity is genuinely logical, and (ii) that it provides a hyperintensional account of formal grasp of the concept of `set'. Section \textbf{4} provides concluding remarks. (shrink)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined (...) in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

Bundles of C*-algebras can be used to represent limits of physical theories whose algebraic structure depends on the value of a parameter. The primary example is the ℏ→0 limit of the C*-algebras of physical quantities in quantum theories, represented in the framework of strict deformation quantization. In this paper, we understand such limiting procedures in terms of the extension of a bundle of C*-algebras to some limiting value of a parameter. We prove existence and uniqueness results for (...) such extensions. Moreover, we show that such extensions are functorial for the C*-product, dynamical automorphisms, and the Lie bracket (in the ℏ→0 case) on the fiber C*-algebras. (shrink)

FROM THE HISTORY OF PHYSICS TO THE DISCOVERY OF THE FOUNDATIONS OF PHYSICS By Antonino Drago, formerly at Naples University “Federico II”, Italy – drago@unina,.it (Size : 391.800 bytes 75,400 words) The book summarizes a half a century author’s work on the foundations of physics. For the forst time is established a level of discourse on theoretical physics which at the same time is philosophical in nature (kinds of infinity, kinds of organization) and formal (kinds of mathematics, kinds of logic). (...) This double side of the two dichotomies assures a deep comprehension of theoretical physics by avoiding both a purely philosophical analysis and a purely formal analysis, each manifestly insufficient for representing all the aspects of theoretical physics. Among the many formulations of a physical theory, e.g. Mechanics, also Mach(1) recognized technical differences only, Instead my suggestion is to consider their differences as revealing the characteristic features of their foundations. No more radical differences may exist than those concerning both their kinds of Mathematics and their kinds of Logic. As a fact, after the 20th Century within each of these sciences there exist two antagonist foundations, within Mathematics either the classical one or the constructive one(2); within Mathematical Logic either the classical logic or the intuitionist one(3). Let us take Mechanics as an instance. Being the choices of the Newton’s formulation respectively the actual infinity of the differential equations relying on the infinitesimals and the classical logic, a formulation based on the alternative choices is Lazare Carnot’s,(4) whose mathematics is no more than algebraic-trigonometric and the logic is the intuitionist one, because this formulation makes use of doubly negated propositions, whose corresponding affirmative propositions are idealistic or false; i.e. in these cases the law of double negation fails, as in intuitionist logic occurs. By considering these two dichotomies as the foundations of the physical theories, each couple of choices upon them fashions one out four models of scientific theory, which are baptized through the authors of their most representative theories: Newtonian, Carnotian, Lagrangian, Descartesian. In correspondence four versions of the principle of inertia are recognized, as suggested by respectively: Descartes. Lazare Carnot, Enriques and Cavalieri.(5) All that suggests that the four models of scientific theory may be graphically represented as a compass orientating our minds amid the so numerous physical theories. By taking these dichotomies as interpretative categories, a new interpretative history of Physics including both classical and modern physics results according to a quadrilinear development. The birth of modern physics is characterized by the two theories - Einstein’s paper on special relativity and Einstein’s first paper on quanta - whose choices are the alternative ones to those of the previously dominant physical theory, Newtonian mechanics: in the latter paper Einstein i) declares the dichotomy on the kinds of mathematics (“Introduction”) and then he chooses the discrete mathematics; ii) by using doubly negated propositions he organizes his theory in an alternative way to the deductive-axiomatic one.(6) Moreover, a new history of Philosophy of knowledge results. Kant’s first two a priori transcendental categories represent the physical interpretation of the two choices out of the four pairs of choices on the two dichotomies, i.e. the choices of the dominant theory of mechanics, Newton’s. Hegel’s dialectic was a misleading attempt of anticipating the subsequent intuitionist logic. The book starts by a comparison of different formulations of thermodynamics in order to recognize the first dichotomy on the kind of organization. In chapter 2 the dichotomy on the kind of infinity is recognized through a comparison of Newrton’s mechanics and Lazare Carnot’s. A quickly history of the other classical physical theories is illustrated in chapter 3; it results a foundational conflict between the last two theories, and hence a conflict between their opposite couples of choices. The two main theories of modern physics, special realtivity and quantum mechanics confirm the foundational role played by the two dichotomies which gives reason for the radical change in the history of theoretical physics. Indeed, the opposition of the two main pairs of choices gives reason of the crisis in theoretical physics in the early 1900s. As a global result, the book represents the first interpretation of the entire history of Physics, both classical and modern; This fact proves that the four models of scientific theories can works as a compass (that of the front cover) suggesting a direction among the many physical theories. This new history of physics leads to re-visit both Koyré’s and Kuhn’s historiographies. Their interpretative categories are interpreted and explained through the two dichotomies so that it is possible to suggest à la Koyré categories based on the alternative choices theories to Newton’s as the suitable categories for interpreting the alternative theories to Newton’s mechanics. All that suggests a new interpretation of the crucial step in the history of Western philosophy of knowledge, i.e. the passage from Leibniz to Kant: Leibniz’s suggestion of the two labyrinths of human minds may be seen as a close anticipation of the two above dichotomies. Kant applied them in order to construct the well-known four cosmological proofs, which however he misinterpreted as leading to contradictions, instead to tow different methods of investigation corresponding to the two different kinds of logic.(7) Bibliography 1. Mach E. (1883), Die Mechanik, Leipzig: Brockhaus, Chap. IV, Sect. III. 2. Bishop E. (1967), Constructive Analysis, New York: Mc Graw-Hill. 3. Heyting A. (1962), Intuitionism. An Introduction, Amsterdam: North-Holland. 4. L. Carnot (1783), Essai on the Machines en général, Defay, Dijion (Enlish translation: Springer, Berlin, 2020). Drago A. (2004), “A new appraisal of old formulations of mechanics”, Am. J. Phys., 72(3), pp. 407-9. 5. Vella M.R. (2007), “Le quattro versioni del principio di inerzia”, in M. Leone et al. (eds.), L’eredità di Fermi, Majorana e altri Temi. Napoli: ESI, pp. 147-151. 6. Drago A. (2014), “The emergence of two options from Einstein°s first paper on Quanta”, in Pisano R., Capecchi D., Lukesova A. (eds.), Physics, Astronomy and Engineering. Critical Problems in the History of Science and Society, Scientia Socialis P., Siauliai, 2013, pp. 227-234. 7. This and all in the above points are illustrated by the book Drago A. (2017), Dalla Storia della Fisica ai Fondamenti della Scienza, Roma: Aracne. (shrink)

The main algebraic foundations of quantum mechanics are quickly reviewed. They have been suggested since the birth of this theory till up to last years. They are the following ones: Heisenberg-Born- Jordan’s (1925), Weyl’s (1928), Dirac’s (1930), von Neumann’s (1936), Segal’s (1947), T.F. Jordan’s (1986), Morchio and Strocchi’s (2009) and Buchholz and Fregenhagen’s (2019). Four cases are stressed: 1) the misinterpretation of Dirac’s algebraic foundation; 2) von Neumann’s ‘conversion’ from the analytic approach of Hilbert space to the algebraic approach of (...) the rings of operators; 3) Morchio and Strocchi’s improving Dirac’s analogy between commutators and Poisson Brackets into an exact equivalence; 4) the recent foundation of quantum mechanics upon the algebra of perturbations. Some considerations on alternating theoretical importance of the algebraic approach in the history of QM are offered. The level of formalism has increased from the mere introduction of matrices to group theory and C*-algebras but has not led to a definition of the foundations of physics; in particular, an algebraic formulation of QM organized as a problem-based theory and an exclusive use of constructive mathematics is still to be discovered. (shrink)

What does it mean to ‘give’ the value of a variable in an algebraic context, and how does giving the value of a variable differ from merely describing it? I argue that to answer this question, we need to examine the role that giving the value of a variable plays in problem-solving practice. I argue that four different features are required for a statement to count as giving the value of a variable in the context of solving an elementary algebra (...) problem: the variable must be in the scope opened by the problem statement; the values given must be in the range of the variable, which is determined by the problem; the statement giving the values must represent a complete solution; and it must be in a canonical form. This account helps us better understand elementary algebra itself, as well as the use of algebraic tools to analyze phenomena in natural language. (shrink)

Straightening the current ‘value-laden turn’ (VLT) in the philosophical literature on values in science, and reviving the legacy of the value-free ideal of science (VFI), this paper argues that the influence of extra-scientific values should be minimised—not excluded—in the core phase of scientific inquiry where claims are accepted or rejected. Noting that the original arguments for the VFI (ensuring the truth of scientific knowledge, respecting the autonomy of science results users, preserving public trust in science) have not been satisfactorily addressed (...) by proponents of the VLT, it proposes four prerequisites which any model for values in the acceptance/rejection phase of scientific inquiry should respect, coming from the fundamental requirement to distinguish between facts and values: (1) the truth of scientific knowledge must be ensured; (2) the uncertainties associated with scientific claims must be stated clearly; (3) claims accepted into the scientific corpus must be distinguished from claims taken as a basis for action. An additional prerequisite of (4) simplicity and systematicity is desirable, if the model is to be applicable. Methodological documents from international institutions and regulation agencies are used to illustrate the prerequisites. A model combining Betz’s conception (stating uncertainties associated with scientific claims) and Hansson’s corpus model (ensuring the truth of the scientific corpus and distinguishing it from other claims taken as a basis for action) is proposed. Additional prerequisites are finally suggested for future research, stemming from the requirement for philosophy of science to self-reflect on its own values: (5) any model for values in science must be descriptively and normatively relevant; and (6) its consequences must be thoroughly assessed. (shrink)

The present paper is an attempt at examining the value configuration and the socio-demographical profiles of the local political elites in four countries of East-Central Europe: Romania, the Czech Republic, Bulgaria, and Poland. The treatment is a comparative one, predominantly descriptive and exploratory, and employs, as a research method, the case-study, being a quite circumscribed endeavor. The cases focus on the members of the Municipal/Local Council in four towns similar in terms of demography and developmental strategies (i.e. small-to-medium sized communities (...) of around 35,000 inhabitants, with economies largely based on food industry and commercial activities): Tecuci (Galați county, Romania), Česká Lípa (Liberec region, Czech Republic), Targovishte (Targovishte province, Bulgaria), and Oleśnica (Lower Silesia province, Poland). Hypothesizing that the local elites of the former Sovietized Erurope tend to differ in outlook, priorities, and value attainment, as compared to their Western counterparts, the paper considers the former’s attitudes and perspectives in regard to seven values: a series of values customarily connected with the concept of ‘democracy’ (i.e. citizen participation, political conflict, gradual change, economic equality), state intervention in economy, decentralization and increased local autonomy, cultural-geographical self-identification. The study uses, as well, five models of value attainment in what concerns the ‘ideal portrait’ of the local councilor (Putnam 1976): ethical, pragmatic, technocratic, political, and gender. According to the results of a study applying a standard written questionnaire among the local councilors of the three communities in the period December 2010-February 2013, the paper distinguishes among three corresponding types of local elites: (1) ‘predominantly elitistic,’ (2) ‘democratic elitist,’ and (3) ‘predominantly democratic,’ following two types of explanation accounting for the differences among the four cases: the legacy of the defunct regime and the degree of administrative decentralization. (shrink)

Until recently, theorists of creativity have consistently maintained that two necessary conditions must be satisfied in order for us to legitimately ascribe creativity to a given phenomenon: a) that it exhibit novelty, and b) that it possess value. However, researchers investigating malevolent forms of creativity have claimed that the value condition is problematic insofar as we often ascribe creativity to products that are of entirely negative value for us. This has given rise to a number of modified conceptions of the (...) value condition, all of which I argue are inadequate (Sections 1 and 2). To address this issue, I advance a novel conception of creative value (Section 3). My contention is that even though malevolent creative products may be of net-negative value, they are nonetheless endowed with a degree of positive value for the predicating individual – that is, insofar as the salient originality of such products elicits an intrinsically-valuable affect of surprise. In Section 4 I then examine the way in which this affect promotes cultural flourishing and to that extent may be considered instrumentally valuable. The principal conclusion of these observations is that the existence of malevolent creativity does not genuinely controvert the standard view that creative products must possess positive value for the predicating individual. (shrink)

What, if anything, is fanaticism? Philosophers including Locke, Hume, Shaftesbury, and Kant offered an account of fanaticism, analyzing it as (1) unwavering commitment to an ideal, together with (2) unwillingness to subject the ideal (or its premises) to rational critique and (3) the presumption of a non-rational sanction for the ideal. In the first part of the paper, I explain this account and argue that it does not succeed: among other things, it entails that a paradigmatically peaceful and tolerant individual (...) can be a fanatic. The following sections argue that the fanatic is distinguished by four features: (4) the adoption of sacred values; (5) the need to treat these values as unconditional in order to preserve a particular form of psychic unity; (6) the sense that the status of these values is threatened by lack of widespread acceptance; and (7) the identification with a group, where the group is defined by shared commitment to the sacred values. If the account succeeds, it not only reveals the nature of fanaticism, but also uncovers a distinctive form of ethical critique: we can critique a way of understanding values not on the grounds that it is false, but on the grounds that it promotes a particular form of social pathology. (shrink)

Obituaries are an especially rich resource for identifying people’s values. Because obituaries are succinct and explicitly intended to summarize their subjects’ lives, they may be expected to include only the features that the author(s) find most salient, not only for themselves as relatives or friends of the deceased, but also to signal to others in the community the socially-recognized aspects of the deceased’s character. We report three approaches to the scientific study of virtue and value through obituaries. We begin by (...) reviewing studies 1 and 2, in which obituaries were carefully read and labeled. We then report study 3, which further develops these results with a semi-automated, large-scale semantic analysis of several thousand obituaries. Finally, we present the results of study 4 in which individuals were asked to write prospective obituaries. Geography, gender, and elite status all turn out to influence the virtues and values associated with the deceased. (shrink)

The endeavour to locate value in moral progress faces various substantive as well as more formal challenges. This paper focuses on challenges of the latter kind. After some preliminaries, Section 3 introduces two general kinds of “evaluative moral progress-claims”, and outlines a possible novel analysis of a descriptive notion of moral progress. While Section 4 discusses certain logical features of betterness in light of recent work in value theory which are pertinent to the notion of moral progress, Sections 5 and (...) 6 outline the ambiguous character of “making moral progress”. (shrink)

What is the most general common set of attributes that characterises something as intrinsically valuable and hence as subject to some moral respect, and without which something would rightly be considered intrinsically worthless or even positively unworthy and therefore rightly to be disrespected in itself? This paper develops and supports the thesis that the minimal condition of possibility of an entity's least intrinsic value is to be identified with its ontological status as an information object. All entities, even when interpreted (...) as only clusters of information, still have a minimal moral worth qua information objects and so may deserve to be respected. The paper is organised into four main sections. Section 1 models moral action as an information system using the object-oriented programming methodology (OOP). Section 2 addresses the question of what role the several components constituting the moral system can have in an ethical analysis. If they can play only an instrumental role, then Computer Ethics (CE) is probably bound to remain at most a practical, field-dependent, applied or professional ethics. However, Computer Ethics can give rise to a macroethical approach, namely Information Ethics (IE), if one can show that ethical concern should be extended to include not only human, animal or biological entities, but also information objects. The following two sections show how this minimalist level of analysis can be achieved. Section 3 provides an axiological analysis of information objects. It criticises the Kantian approach to the concept of intrinsic value and shows that it can be improved by using the methodology introduced in the first section. The solution of the Kantian problem prompts the reformulation of the key question concerning the moral worth of an entity: what is the intrinsic value of x qua an object constituted by its inherited attributes? In answering this question, it is argued that entities can share different observable properties depending on the level of abstraction adopted,and that it is still possible to speak of moral value even at the highest level of ontological abstraction represented by the informational analysis. Section 4 develops a minimalist axiology based on the concept of information object. It further supports IE's position by addressing five objections that may undermine its acceptability. (shrink)

Because obituaries are succinct and explicitly intended to summarize their subjects’ lives, they may be expected to include only the features that the author finds most salient but also to signal to others in the community the socially-recognized aspects of the deceased’s character. We begin by reviewing studies 1 and 2, in which obituaries were carefully read and labeled. We then report study 3, which further develops these results with a semi-automated, large-scale semantic analysis of several thousand obituaries. Geography, gender, (...) and elite status all turn out to be associated with the virtues and values associated with the deceased. (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)

Volume 20, Issue 3, March 2020, Page 71-73.

This paper defends a novel account of how to determine the intrinsic value of possible worlds. Section 1 argues that a highly intuitive and widely accepted account leads to undesirable consequences. Section 2 takes the first of two steps towards a novel account by clarifying and defending a view about value-contribution that is based on some of W. D. Ross’ claims about the value of pleasure. Section 3 takes the second step by clarifying and defending a view about value-suppression that (...) is based on Ross’ claims about the interplay between prima-facie duties. Section 4 states and defends the account that I call Rossian Totalism. According to this account, the atoms of intrinsic value within a world only sometimes contribute their intrinsic value to the value of that world. (shrink)

John O’Neill, Alan Holland, and Andrew Light usefully distinguish two ways of thinking about environmental values, namely, end-state and historical views. To value nature in an end-state way is to value it because it instantiates certain properties, such as complexity or diversity. In contrast, a historical view says that nature’s value is (partly) determined by its particular history. Three contemporary defenses of a historical view are explored in order to clarify: (1) the normatively relevant history; (2) how historical considerations are (...) supposed to instruct environmental decision making; and (3) the relative importance of historical and end-state considerations. There are multiple reasons for including historical considerations in an account of environmental values. For example, knowledge of a natural object’s history can add depth and texture to our appreciation of that object. Further, if we were blind to the relevant history, we could not adequately understand and defend environmental policy goals such as preserving the potentials of natural systems or maintaining ecological health, for these goals appear to have irreducibly historical aspects. While historical considerations are important, such considerations are insufficient to guide our normative thinking about nature and how it should be dealt with practically. But they succeed in broadening and deepening our understanding of the nature and sources of environmental value. (shrink)

The paper is structured as follows. §1 lays out the worry that the FA analysis fosters a revisionary understanding of emotional values. §2 introduces the distinction between enablers and favourers and how it is pressed into service by Toni to reply to this worry. While I agree that the reply is attractive, since casting emotions in the role of enablers chimes well with how we pre-theoretically understand the relations between emotions and values, I observe that doing so requires that we (...) tackle two connected issues. First, how do emotions function as value enablers? Second, is the resulting picture compatible with the FA analysis? The rest of the discussion is structured around these issues. §3 looks at the role of emotions within the FA analysis so as to specify the kind of enabling role they can play. On this backdrop, I explore in §4 a contrast between how belief relates to truth and how emotions relate to values, a contrast which helps uncover what we are after. A first reaction to this contrast, according to which emotions are value enablers by allowing us to access values, which differ from truth, is examined in §5. I argue that this idea cannot do justice to the key insight of the FA analysis. §6 defends an alternative idea, according to which emotions are enablers in virtue of their attitudinal shapes. (shrink)

Many philosophers argue that the face-value of moral practice provides presumptive support to moral realism. This paper analyses such arguments into three steps. (1) Moral practice has a certain face-value, (2) only realism can vindicate this face value, and (3) the face-value needs vindicating. Two potential problems with such arguments are discussed. The first is taking the relevant face-value to involve explicitly realist commitments; the second is underestimating the power of non-realist strategies to vindicate that face-value. Case studies of each (...) of these errors are presented, drawn from the writings of Shafer-Landau, Brink and McNaughton, and from recent work in experimental metaethics. The paper then considers weak presumptive arguments, according to which both realist and non-realist vindications of moral practice are possible, but the realist vindications are more natural. It is argued that there is no sense of ‘natural’ available that can make these arguments work. The conclusion is that all extant presumptive arguments for moral realism fail. (shrink)

The topic of this thesis is how we should treat tiny probabilities of vast value. This thesis consists of six independent papers. Chapter 1 discusses the idea that utilities are bounded. It shows that bounded decision theories prescribe prospects that are better for no one and worse for some if combined with an additive axiology. Chapter 2, in turn, points out that standard axiomatizations of Expected Utility Theory violate dominance in cases that involve possible states of zero probability. Chapters 3–6 (...) discuss the idea that we should ignore tiny probabilities in practical decision-making. Chapter 3 argues that discounting small probabilities solves the ‘Intrapersonal Addition Paradox’ and thus helps avoid the Repugnant Conclusion. Chapter 4 explores what the most plausible version of this view might look like and what problems the different versions have. Chapter 5 focuses on one type of problem, namely, money pumps. The Independence Money Pump, in particular, presents a difficult challenge for those who wish to discount small probabilities. Finally, Chapter 6 discusses the implications of discounting small probabilities for the value of the far future. (shrink)

Chapter 3 surveys objectivity in the natural sciences. Thomas Kuhn problematized the logicist understanding of the objectivity or rationality of scientific change, providing a very different picture than that of the cumulative or step-wise progress of theoretical science. Theories often compete, and when consensus builds around one competitor it may be for a variety of reasons other than just the direct logical implications of experimental successes and failures. Kuhn pitted the study of the actual history of science against what Hans (...) Reichenbach referred to as the “logical substitutes” logicists used to reconstruct the rationality of theory change. Such substitutes were promoted to show that theory confirmation is a purely epistemic affair, where purely epistemic implies purely inferential. But where the positivists saw logical compulsion as the reason for theory change, Kuhn saw psychology in values as relevant to how theories are actually confirmed or accepted by the scientific community. (shrink)

In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic---such as the relations |=_t, |=_f, and |=_i that each correspond to a lattice order in SIXTEEN_3; and |=, the intersection of |=_t and |=_f,. -/- It turns out that our method of characterising these semantic relations---as (...) intersections of auxiliary relations that can be captured with the help of a single calculus---lends itself well to proving interpolation. All entailment relations just mentioned have the interpolation property, not only when they are defined with respect to a functionally complete language, but also in a range of cases where less expressive languages are considered. For example, we will show that |=, when restricted to L_{tf}, the language originally considered by Shramko and Wansing, enjoys interpolation. This answers a question that was recently posed by M. Takano. (shrink)

This article explores the characteristics and problems of moral pluralism, a model of theory of obligation in normative ethics according to which (1) there is a plurality of basic moral principles; (2) these different principles may conflict with one another; (3) there is no strict order of priority for resolving conflicts between them. The author argues that this kind of theory satisfies better than competing proposals the requirement of conformity with our reflexive intuitions and, while not having a general resolution (...) procedure, is able to settle the problem of conflict between the principles. He concludes pointing out that, despite all that can be done to improve conflict resolution methodologies, some margin of indeterminacy in moral theories is inevitable. And it is good that there is. Moral theories should not be a handbook of answers to be applied mechanically, without leaving room for autonomy of judgment by the evaluating subject. (shrink)

This book aims at six important conceptual tools developed by philosophers. The author develops each particular view in a chapter, hoping to constitute at the end a concise, interesting and easily readable whole. These concepts are: 1. Ethics and realism: elucidation of the distinction between understanding and explanation – the lighthouse type of normativity. 2. Leadership, antirealism and moral psychology – the lightning rod type of normativity. 3. Bright light on self-identity and positive reciprocity – the reciprocity type of normativity. (...) 4. The virtue of generosity and its importance for inclusive education – the divine will type of normativity. 5. Ethical education as normative philosophical perspective. The normativity of self-transformation in education. 6. Aesthetics as expression of human freedom and concern for the whole world in which we live. (shrink)

Abstract: Purpose – The purpose of this paper is to analyse the broad phases of web development: the read-only Web 1.0, the read-write Web 2.0, and the collaborative and Internet of Things Web 3.0, are examined for the theoretical lenses through which they have been understood and critiqued. Design/methodology/approach – This is a conceptual piece, in the tradition of drawing on theorising from outside the Information Systems field, to shed light on developments in information communication technologies (ICTs). Findings – Along (...) with a summary of approaches to Webs 1.0 and 2.0, the authors contend that a more complex and poststructuralist theoretical approach to the notion of, and the phenomenon of Web 3.0, offers a more interesting and appropriate theoretical grounding for understanding its particularities. Originality/value – The discussion presages five further papers engaged with ICTs in a changing society, each of which similarly addresses novel theoretical understandings. (shrink)

We review our approach to quantum mechanics adding also some new interesting results. We start by giving proof of two important theorems on the existence of the A(Si) and i,±1 N Clifford algebras. This last algebra gives proof of the von Neumann basic postulates on the quantum measurement explaining thus in an algebraic manner the wave function collapse postulated in standard quantum theory. In this manner we reach the objective to expose a self-consistent version of quantum mechanics. In detail (...) we realize a bare bone skeleton of quantum mechanics recovering all the basic foundations of this theory on an algebraic framework. We give proof of the quantum like Heisenberg uncertainty relations using only the basic support of the Clifford algebra. In addition we demonstrate the well known phenomenon of quantum Mach Zender interference using the same algebraic framework, as well as we give algebraic proof of quantum collapse in some cases of physical interest by direct application of the theorem that we derive to elaborate the i,±1 N algebra. We also discuss the problem of time evolution of quantum systems as well as the changes in space location, in momentum and the linked invariance principles. We are also able to re-derive the basic wave function of standard quantum mechanics by using only the Clifford algebraic approach. In this manner we obtain a full exposition of standard quantum mechanics using only the basic axioms of Clifford algebra. We also discuss more advanced features of quantum mechanics. In detail, we give demonstration of the Kocken-Specher theorem, and also we give an algebraic formulation and explanation of the EPR paradox only using the Clifford algebra. By using the same approach we also derive Bell inequalities. Our formulation is strongly based on the use of idempotents that are contained in Clifford algebra. Their counterpart in quantum mechanics is represented by the projection operators that, as it is well known, are interpreted as logical statements, following the basic von Neumann results. Von Neumann realized a matrix logic on the basis of quantum mechanics. Using the Clifford algebra we are able to invert such result. According to the results previously obtained by Orlov in 1994, we are able to give proof that quantum mechanics derives from logic. We show that indeterminism and quantum interference have their origin in the logic. Therefore, it seems that we may conclude that quantum mechanics, as it appears when investigated by the Clifford algebra, is a two-faced theory in the sense that it looks from one side to “matter per se”, thus to objects but simultaneously also to conceptual entities. We advance the basic conclusion of the paper: There are stages of our reality in which we no more can separate the logic ( and thus cognition and thus conceptual entity) from the features of “matter per se”. In quantum mechanics the logic, and thus the cognition and thus the conceptual entity-cognitive performance, assume the same importance as the features of what is being described. We are at levels of reality in which the truths of logical statements about dynamic variables become dynamic variables themselves so that a profound link is established from its starting in this theory between physics and conceptual entities. Finally, in this approach there is not an absolute definition of logical truths. Transformations , and thus … “redefinitions”…. of truth values are permitted in such scheme as well as the well established invariance principles, clearly indicate . (shrink)

本文对文化的价值多样性进行多元的理解，集中阐述和讨论“文化的价值组合配置”(cultural configurations of values)概念。主要包括以下几个要点：(1)在世界的各种文化中，人类的价值有不同的表现形式，但其基本价值是相似的，甚至相同的。(2)人类的各种基本价值之间不但有互相促进的关系，也有相互矛盾、相互竞 争、相互冲突的关系。(3)一种文化类型提供对相互冲突的价值的一种处理方式。不同的文化形成其各自的价值组合与配置。这种价值的配置与其社会环境相适应，是其文化的核心部分。文化差异性的一个重要方面就是，尽管 所有文化共有这些基本价值，但是他们会给予这些价值不同的权重，形成不同的价值配置形式。(4)有时在同一个社会里，会存在若干“亚文化”，会有不同的价值配置。随着时间的推移，文化和社会都会有改变。虽然它们在 价值组合配置普世化上可能永远无法达成一致，但是它们之间的共同价值为和平共处提供了基础。.

This research investigates 3- and 5-year-olds' relative fairness in distributing small collections of even or odd numbers of more or less desirable candies, either with an adult experimenter or between two dolls. The authors compare more than 200 children from around the world, growing up in seven highly contrasted cultural and economic contexts, from rich and poor urban areas, to small-scale traditional and rural communities. Across cultures, young children tend to optimize their own gain, not showing many signs of self-sacrifice (...) or generosity. Already by 3 years of age, self-optimizing in distributive justice is based on perspective taking and rudiments of mind reading. By 5 years, overall, children tend to show more fairness in sharing. What varies across cultures is the magnitude of young children's self-interest. More fairness (less self-interest) in distributive justice is evident by children growing up in small-scale urban and traditional societies thought to promote more collective values. (shrink)