Following a proposal of Humberstone, this paper studies a semantics for modal logic based on partial “possibilities” rather than total “worlds.” There are a number of reasons, philosophical and mathematical, to find this alternative semantics attractive. Here we focus on the construction of possibility models with a finitary flavor. Our main completeness result shows that for a number of standard modal logics, we can build a canonical possibility model, wherein every logically consistent formula is satisfied, by simply taking each (...) individual finite formula (modulo equivalence) to be a possibility, rather than each infinite maximally consistent set of formulas as in the usual canonical world models. Constructing these locally finite canonical models involves solving a problem in general modal logic of independent interest, related to the study of adjoint pairs of modal operators: for a given modal logic L, can we find for every formula phi a formula f(phi) such that for every formula psi, phi -> BOX psi is provable in L if and only if f(phi) -> psi is provable in L? We answer this question for a number of standard modal logics, using model-theoretic arguments with world semantics. This second main result allows us to build for each logic a canonical possibility model out of the lattice of formulas related by provable implication in the logic. (shrink)

The final portion of the thesis surveys proposals for the introduction of hidden variables into quantum mechanics, proofs of the impossibility of such hidden-variable proposals, and criticisms of these impossibility proofs. And arguments in favour of the partial-Boolean algebra, rather than the orthomodular lattice, formalization of the quantum propositional structures are reviewed. ;As for , each quantum state-induced expectation-function on a P truth-functionally assigns 1 and 0 values to the elements in a ultrafilter and dual ultraideal of P, where (...) in general the union of an ultrafilter and its dual ultraideal is smaller than the entire structure. Thus it is argued that each expectation-function is the quantum analog of a classical semantic mapping, even though the domain where each expectation-function is bivalent and truth-functional is usually a non-Boolean substructure of P. ;In classical propositional logic, propositions form a Boolean algebra, and each semantic mapping assigns the value 1 to the members of a certain subset of the algebra, namely, an ultrafilter, and assigns 0 to the members of the dual ultraideal, where the union of these two subsets is the entire algebra. The propositional structures of classical mechanics are likewise Boolean algebras, so one can straightforwardly provide a classical semantics, which also satisfies . However, quantum propositional structures are non-Boolean, so it is an open question whether a semantics satisfying , and can be provided. ;Von Neumann first proposed that the algebraic structures of the subspaces of Hilbert space be regarded as the propositional structures P of quantum mechanics. These structures have been formalized in two ways: as orthomodular lattices which have the binary operations "and", "or", defined among all elements, compatible and incompatible ; and as partial-Boolean algebras which have the binary operations defined among only compatible elements. In the thesis, two basic senses in which these structures are non-Boolean are discriminated. And two notions of truth-functionality are distinguished: truth-functionality ,) applicable to the Plattices; and truth-functionality ) applicable to both the Plattices and partial-Boolean algebras. Then it is shown how the lattice definitions of "and", "or", among incompatibles rule out a bivalent, truth-functional ,) semantics for any PQM lattice containing incompatible elements. In contrast, the Gleason and Kochen-Specker proofs of the impossibility of hidden-variables for quantum mechanics show the impossibility of a bivalent, truth-functional ) semantics for three-or-higher dimensional Hilbert space PQM structures; and the presence of incompatible elements is necessary but is not sufficient to rule out such a semantics. ;The thesis investigates the possibility of a classical semantics for quantum propositional structures. A classical semantics is defined as a set of mappings each of which is bivalent, i.e., the value 1 or 0 is assigned to each proposition, and truth-functional, i.e., the logical operations are preserved. In addition, this set must be "full", i.e., any pair of distinct propositions is assigned different values by some mapping in the set. When the propositions make assertions about the properties of classical or of quantum systems, the mappings should also be "state-induced", i.e., values assigned by the semantics should accord with values assigned by classical or by quantum mechanics. (shrink)

Any attempt to construct a realist interpretation of quantum theory founders on the Kochen-Specker theorem, which asserts the impossibility of assigning values to quantum quantities in a way that preserves functional relations between them. We construct a new type of valuation which is defined on all operators, and which respects an appropriate version of the functional composition principle. The truth-values assigned to propositions are (i) contextual; and (ii) multi-valued, where the space of contexts and the multi-valued logic for each context (...) come naturally from the topos theory of presheaves. The first step in our theory is to demonstrate that the Kochen-Specker theorem is equivalent to the statement that a certain presheaf defined on the category of self-adjoint operators has no global elements. We then show how the use of ideas drawn from the theory of presheaves leads to the definition of a generalised valuation in quantum theory whose values are sieves of operators. In particular, we show how each quantum state leads to such a generalised valuation. A key ingredient throughout is the idea that, in a situation where no normal truth-value can be given to a proposition asserting that the value of a physical quantity A lies in a set D of real numbers , it is nevertheless possible to ascribe a partial truth-value which is determined by the set of all coarse-grained propositions that assert that some function f(A) lies in f(D), and that are true in a normal sense. The set of all such coarse-grainings forms a sieve on the category of self-adjoint operators, and is hence fundamentally related to the theory of presheave. (shrink)

We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). (...) There are two main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4). (shrink)

This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; in part mathematical---the valuations arise naturally in the theory of presheaves; and in (...) part conceptual---the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2 and 3) the notion of a topos (of which presheaves give just one kind of example); and explain how this notion gives a satisfactory general framework for making sense of the idea of partial truth. Then I review (in Section 4) how our proposal applies this framework to the case of physical theories. (shrink)

Based on existence equations, quasivarieties of heterogeneous partial algebras have the same algebraic description as those of total algebras. Because of the restriction of the valuations to the free variables of a formula — the usual reference to the needed variables e.g. for identities (in order to get useful and manageable results) is essentially replaced here by the use of the logical Craig projections — already varieties of heterogeneous partial algebras behave to some extent rather like quasivarieties (...) than having the properties known from varieties of total homogeneous algebras. It is one of the main aims of this note to make this more explicit. On the other hand we want to list several results known for quasivarieties of heterogeneous partial algebras — and adopt them to the extended signature — after having recalled the language and the main concepts necessary for the understanding of the results. (shrink)

Based on existence equations, quasivarieties of heterogeneous partial algebras have the same algebraic description as those of total algebras. Because of the restriction of the valuations to the free variables of a formula — the usual reference to the needed variables e.g. for identities (in order to get useful and manageable results) is essentially replaced here by the use of the “logical Craig projections” — already varieties of heterogeneous partial algebras behave to some extent rather like quasivarieties (...) than having the properties known from varieties of total homogeneous algebras. It is one of the main aims of this note to make this more explicit. On the other hand we want to list several results known for quasivarieties of heterogeneous partial algebras — and adopt them to the extended signature — after having recalled the language and the main concepts necessary for the understanding of the results. (shrink)

This paper is dedicated to the memory of Mike Dunn. His untimely death is a loss not only to logic, computer science, and philosophy, but to all of us who knew and loved him. The paper gives an argument for closure under γ in standard systems of relevance logic (first proved by Meyer and Dunn 1969). For definiteness, I chose the example of R. The proof also applies to E and to the quantified systems RQ and EQ. The argument uses (...) semantic tableaux (with one exceptional rule not satisfying the subformula property). It avoids the previous arguments’ use of cutting down inconsistent sets of formulas to consistent sets. Like all tableau arguments, it extends partial valuations to total valuations. (shrink)

This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed solutions (“the revenge of the Liar”). This solution complements the classical procedure of determining the truth values of sentences by its own failure and, when the procedure fails, through an appropriate semantic shift allows us to express the failure in a classical two-valued language. (...) Formally speaking, the solution is a language with one meaning of symbols and two valuations of the truth values of sentences. The primary valuation is a classical valuation that is partial in the presence of the truth predicate. It enables us to determine the classical truth value of a sentence or leads to the failure of that determination. The language with the primary valuation is precisely the largest intrinsic fixed point of the strong Kleene three-valued semantics (LIFPSK3). The semantic shift that allows us to express the failure of the primary valuation is precisely the classical closure of LIFPSK3: it extends LIFPSK3 to a classical language in parts where LIFPSK3 is undetermined. Thus, this article provides an argumentation, which has not been present in contemporary debates so far, for the choice of LIFPSK3 and its classical closure as the right model for the truth predicate. In the end, an erroneous critique of Kripke-Feferman axiomatic theory of truth, which is present in contemporary literature, is pointed out. (shrink)

In a previous paper, we have proposed assigning as the value of a physical quantity in quantum theory, a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; and in part mathematical---the valuation arises naturally in the topos theory of presheaves. This paper discusses the conceptual aspects of this proposal. We also undertake two other tasks. First, we explain how the proposed (...) class='Hi'>valuations could arise much more generally than just in quantum physics; in particular, they arise as naturally in classical physics. Second, we give another motivation for such valuations (that applies equally to classical and quantum physics). This arises from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. (shrink)

A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth--functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a "weak" interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure "statability" operators are also examined.

This article engages the French pragmatism of Laurent Thévenot, Luc Boltanski and Bruno Latour in debates on how to forge a moral-political sociology of ecological valuation, justification and critique. Picking up the debate initiated by Thévenot on the possible emergence of a novel ‘green’ order of worth, the article juxtaposes the sociology of critical capacity of Boltanski and Thévenot with the actor-network theory of Bruno Latour. In doing so, the article suggests that each of these three pragmatic sociologists succeeds, in (...) characteristically different ways, in theoretically articulating an important but partial socio-political grammar of ecological worth. This claim is substantiated by invoking three case studies into environmental critique and compromise, on transnational carbon markets, urban sustainability projects, and Japanese whaling, respectively. Against this backdrop, the article concludes that – when read together as grammarians of the ecological bond – pragmatic sociology provides important insights into the bounded multiplicity of nature’s worth in political modernity. (shrink)

A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth–functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a “weak” interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure “statability” operators are also examined.

This book presents an up-to-date, unified treatment of research in bounded arithmetic and complexity of propositional logic, with emphasis on independence proofs and lower bound proofs. The author discusses the deep connections between logic and complexity theory and lists a number of intriguing open problems. An introduction to the basics of logic and complexity theory is followed by discussion of important results in propositional proof systems and systems of bounded arithmetic. More advanced topics are then treated, including polynomial simulations and (...) conservativity results, various witnessing theorems, the translation of bounded formulas (and their proofs) into propositional ones, the method of random partial restrictions and its applications, direct independence proofs, complete systems of partial relations, lower bounds to the size of constant-depth propositional proofs, the method of Boolean valuations, the issue of hard tautologies and optimal proof systems, combinatorics and complexity theory within bounded arithmetic, and relations to complexity issues of predicate calculus. Students and researchers in mathematical logic and complexity theory will find this comprehensive treatment an excellent guide to this expanding interdisciplinary area. (shrink)

One of the main problems of the orthoframe approach to quantum logic was that orthomodularity could not be captured by any first-order condition. This paper studies an elementary and natural class of orthomodular frames that can work around this limitation. Set-theoretically, the frames we propose form a natural subclass of the orthoframes, where is an irreflexive and symmetric relation on X. More specifically, they are partially-ordered orthoframes with a designated subset. Our frame class contains the canonical orthomodular frame of the (...) logic and therefore characterises orthomodular quantum logic. To prove soundness, a further restriction is placed on admissible valuations which requires that they be point-generated in addition to the requirement that they return stable sets. (shrink)

The article explores the interaction of verbal and nonverbal semantic levels in the performance of Christian ritual. The article maps the distinction between theoretical and performative knowledge onto Barnard and Teasdale's Interacting Cognitive Systems model to give a (partial) account of how meaning emerges in ritual participation. With Christian ritual, both know-how and know-that are needed. Above all, it is their interaction that generate the richness of meaning in ritual performance. Three core claims are made. First, many contemporary concepts (...) of ritual have at least one flaw in that they do not grasp the relationality between verbal and nonverbal, wherein both dimensions have a semantic integrity of their own. Second, there is an ideological valuation of the semantic levels. The experiential level is not only meaningful in its own right, but the fundamental ground of spiritual knowing. Third, combining learning styles and kinds of attention can be valuable for eliciting the full semantic richness of ritual participation. (shrink)

The primary objective of this research is to examine the potential influence of environmental, social, and governance (ESG) disclosure on cash holdings. Additionally, the study explores the role of earnings management (EM) practices as a mediating factor in this relationship. The sample comprises 797 companies listed on financial markets across 19 European countries, and the data spans from 2013 to 2019. The outcomes indicate a significant negative correlation between ESG disclosure and cash holdings, implying that ESG performance can be used (...) by management to resolve disputes with stakeholders. The outcomes further indicate that the existence of EM practices partially mediates the link between ESG disclosure and cash holdings. Moreover, they are robust by substitute cash holdings specification, three distinct initiatives of ESG disclosure (i.e., environment, social, and governance), and a two-stage least squares assessment. Therefore, the findings document that nonfinancial reporting in the form of ESG disclosure can assist in controlling agency conflict, leading to better valuations of company performance by stakeholders. (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hubert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set C(A) of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that C(A) consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Hey ting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n x n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski-Mulvey) of the "Bohrification" A̱ of A, which is a commutative Rickart C*-algebra in the topos of functors from C(A) to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns-Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hubert space H and probability valuations on the internal Gelfand spectrum of A̱ for A = B(H). (shrink)

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these difficulties, suggested by the ideas of Bohr, emerges if instead of single projections one considers elementary propositions to be families (...) of projections indexed by a partially ordered set \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} of appropriate commutative subalgebras of A. In fact, to achieve both maximal generality and ease of use within topos theory, we assume that A is a so-called Rickart C*-algebra and that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}(A)}$$\end{document} consists of all unital commutative Rickart C*-subalgebras of A. Such families of projections form a Heyting algebra in a natural way, so that the associated propositional logic is intuitionistic: distributivity is recovered at the expense of the law of the excluded middle. Subsequently, generalizing an earlier computation for n × n matrices, we prove that the Heyting algebra thus associated to A arises as a basis for the internal Gelfand spectrum (in the sense of Banaschewski–Mulvey) of the “Bohrification” \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} of A, which is a commutative Rickart C*-algebra in the topos of functors from \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{C}A}$$\end{document} to the category of sets. We explain the relationship of this construction to partial Boolean algebras and Bruns–Lakser completions. Finally, we establish a connection between probability measures on the lattice of projections on a Hilbert space H and probability valuations on the internal Gelfand spectrum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\underline A}$$\end{document} for A = B(H). (shrink)

The paper examines some doctrines of the Davidsonian Programme of truth conditional Semantics that relates truth to meaning using Tarski’s T-Convention, in relation to its efficacy in a semantic valuation of the EkeGusii proverb: Nda ’indongi ereta morogi ereta moibi which exemplifies a kind of complex sentence that a given system of Semantics is meant to account for. The coverage of Davidsonian truth-conditional notion of T-convention and that of compositionality are considered to have only a partial reach in accounting (...) for the meaning of the proverb by not incorporating pragmatic aspects. The failure of T-convention is not alleviated by the adoption of radical interpretation as posited by Davidson but is extended to consider aspects of pragmatic enrichment and dynamic Semantics. (shrink)

In traditional analytic philosophy, critical thinking is defined along Cartesian lines as rational and linear reasoning preclusive of intuitions, emotions and lived experience. According to Michael Gilbert, this view – which he calls the Natural Light Theory (NLT) – fails because it arbitrarily excludes standard feminist forms of argumentation and neglects the essentially social nature of argumentation. In this paper, I argue that while Gilbert’s criticism is correct for argumentation in general, NLT fails in a distinctive and particularly problematic manner (...) in moral argumentation contexts. This is because NLT calls for disputants to adopt an impartial attitude, which overlooks the fact that moral disputants qua moral agents are necessarily partial to their own values and interests. Adopting the impartial perspective would therefore alienate them from their values and interests, causing a kind of “moral schizophrenia.” Finally, I urge a re-valuation of epistemic virtue in argumentation. (shrink)

Special groups [M. Dickmann, F. Miraglia, Special Groups : Boolean-Theoretic Methods in the Theory of Quadratic Forms, Memoirs Amer. Math. Soc., vol. 689, Amer. Math. Soc., Providence, RI, 2000] are a first-order axiomatization of the theory of quadratic forms. In Section 2 we investigate reduced special groups which are a lattice under their natural representation partial order ; we show that this lattice property is preserved under most of the standard constructions on RSGs; in particular finite RSGs and RSGs (...) of finite chain length are lattice ordered. We prove that the lattice property fails for the RSGs of function fields of real algebraic varieties over a uniquely ordered field dense in its real closure, unless their stability index is 1 . We show that Open Problem 1 has a positive answer for the RSG of the field Q . In the final section we explore the meaning of Open Problem 1 for formally real fields, in terms of their orders and real valuations; we introduce the notion of “parameter-rank” of a positive-primitive first-order formula of the language for special groups. (shrink)

Macpherson and Steinhorn 165–209) introduce some variants of the notion of o-minimality. One of the most interesting is C-minimality, which provides a natural setting to study algebraically closed-valued fields and some valued groups. In this paper we go further in the study of the structure of C-minimal valued groups, giving a partial characterization in the abelian case. We obtain the following principle: for abelian valued groups G for which the valuation satisfies some kind of compatibility with the multiplication by (...) any prime number p, being C-minimal is equivalent to the o-minimality of the expansion of the chain of valuations by the maps induced by the multiplication by each prime number in G, and by some unary predicates controlling the cardinality of the residual structures. This result is quite nice, because the class considered contains all the natural examples of abelian C-minimal valued groups of 165–209), and allows us to find many more examples. (shrink)

The actual introduction of a non-reflexive and non-idempotent q -consequence gave birth to the concept of logical three-valuedness based on the idea of noncomplementary categories of rejection and acceptance. A q -consequence may not have bivalent description, the property claimed by Suszko’s Thesis on logical two-valuedness, ( ST ), of structural logics, i.e. structural consequence operations. Recall that ( ST ) shifts logical values over the set of matrix values and it refers to the division of matrix universe into two (...) subsets of designated and undesignated elements using their characteristic functions as logical valuations, cf. [4] The extension of the idea operates with three-valued function, with the third value ascribed to those elements of the matrix which are neither rejected nor accepted. Accordingly, the logical three-valuedness departs naturally from the division of the matrix universe into three subsets and the ( ST ) counterpart says that any inference based on a structural q -consequence may have a bivalent or a three-valued description. After a short presentation of the three-valued inferential framework, we discuss a solution for further exploration of the idea leading to logical n -valuedness for n > 3. Apparently, the first step in that direction is easy and it consists of a division of the matrix universe into more than three subsets. The next move, i.e. a definition of a matrix consequence-like relation being neither a consequence nor a q -consequence, seems extremely difficult. Therefore, here we consider only finite linear matrices with one-argument functions “labelling” respective matrix subsets. By means of these functions it is possible to represent a q-consequence as a “partial” Tarski’s consequence and, ultimately, to define a logically more-valued consequence-like relation. We believe, that the present partial proposal deserves an attention by itself but also that it may lead to a general approach to logically many-valued inference. (shrink)

The article introduces extended models for the propositional dynamic logic PDL. In extended models, valuation assigns to every state a set of atomic formulas and a PDL program. The program is informally construed as an action preferred by a contextually fixed agent. PDL is then extended by introducing a conditional connective expressing partial correctness claims. The main contribution of the article is the observation that the partial correctness conditional is in fact a substructural implication. It is shown that (...) a variant of the minimal distributive substructural logic DB is a fragment of PDLS, an extension of PDL that contains the partial correctness conditional and fusion. It is also shown that the main results can be extended to a specific class of positive substructural logics. (shrink)

The study of social, ethical, and political issues from a naturalistic perspective has been pervasive in social sciences and the humanities in the last decades. This articulation of empirical research with philosophical and normative reflection is increasingly getting attention in academic circles and the public spheres, given the prevalence of urgent needs and challenges that society is facing on a global scale. The contemporary world is full of challenges or what some philosophers have called ‘existential risks’ to humanity. Nuclear wars, (...) natural and/or engineered pandemics, climate change, global totalitarianism, and emergent technologies, are some of the challenges mentioned by many authors devoted to the study of long-term potential risks for the survival of the human species. However, while there are many reasons to be a pessimist about the future of humanity, there is also a lot of ink wasted in showing that the world today is far better than we had in the past and also that there have been many instances of social and moral progress in the last centuries. Some authors have even claimed that “we have made more progress over the last 100 years than in the first 100,000”. According to ‘our world in data’, some of the most relevant advances of humanity in the last centuries have to do with the reduction of poverty and/or inequality, better health and security, the decline of violence and war, and the development of democracy and institutional mechanisms to guarantee individual freedom and rights. Yet, there is a more concrete concern that our world faces nowadays, and requires a particularly detailed analysis. In a few words, the advance in information and communication technologies, the huge volume of people migration because of prevalent instances of global inequality, and the reality of an interconnected world that just mirrors an extensive history of massive human intergroup relations open the question about the feasibility of social and moral progress in the contexts of diverse, multicultural, and unequal societies. This makes it crucial to reflect not only on whether human societies may keep advancing on a path of social progress, but how this can be achieved by addressing the challenges of inequality and potential intergroup conflict. This concern closely relates to the further consolidation of democratic values and the achievement of a more generalized consideration of the equal moral value of human individuals far from group, ethnic, or collective distinctions. This vision of progress follows the moral convictions that have been considered right and worthy to be pursued by most ethical theories explored by philosophers and social scientists so far. This work aims to contribute to the study of the mechanisms and feasibility of social and moral progress grounded on the precept of human equality and is guided by the idea that social and moral progress in a plural world requires the accomplishment of a more democratic and tolerant society. These forms of progress have already been defined by philosophers Allen Buchanan and Russel Powell as inclusivist forms of moral progress. According to these authors, inclusivist moral progress is featured by the transformation of moral judgments, motivations, and norms guided by the rejection of “group-based restrictions on moral standing and moral status” (2018). The work of Buchanan and Powell is fundamental for the argumentation developed in this work since they have pioneered a more complex debate in the field of evolutionary social sciences and philosophical anthropology. In brief, these authors have inquired how human nature, conceptualized by the advances in evolutionary thinking and the empirical sciences, is related to our moral convictions and the possibilities that we have to establish certain forms of social and moral progress. The work of Buchanan and Powell contributes to the debate on moral progress by incorporating empirically-informed concepts and arguments. With this objective in mind, they develop their discussion around a generalized tension between exclusivist and inclusivist forms of moral progress. This tension revolves around the question of whether and to what extent human moral concerns, motivations, and norms, are limited or bounded by social identities, group thinking, or collective values. This question is at the center of this work. In other words, I aim to answer whether and to what extent the nature of our social and moral cognition hinders or enables the development of inclusivist forms of morality and moral progress. As I mentioned so far, the distinction between exclusivist and inclusivist forms of morality has a practical implication and facilitates the reflection on the mechanisms and feasibility of concrete forms of progress based on the precept of human equality, which is the road to progress that we should follow according to most ethical theories. The distinction between exclusivist and inclusivist morality is not used here as a form of summarizing highly divergent descriptive approaches to morality, but as a way to address the practical implications of morality research, particularly around the question of the feasibility of social forms of progress based on the precept of equality and tolerance. My objective then has less to do with offering a conceptualization of human morality or with the proposition of a new ethical perspective. Instead, I aim to identify, from an empirically informed perspective, what enables the achievement of egalitarian forms of social progress, to subsequently offer a normative reflection about what we should do if we want to accomplish such inclusivist forms of progress. This task is of great relevance, having in mind that some theoretical proposals on the matter have claimed that human prosocial behavior and morality are constrained by exclusivist fixed tendencies as a product of our evolutionary history. According to these views, human morality is a group-centered cognitive and behavioral expression that has severe limits in its scope and extent, which hinders in the end the emergence of inclusivist forms of moral concerns and behaviors. These claims align with the philosophical intuition about the ‘dissociation of empathy’, or the fact that human individuals tend to express empathy and sympathy preferably for members of their group whereas their empathic and moral concern and recognition for outgroup individuals tend to be reduced or eliminated in real-life social interactions. Multiple theorists have expressed, however, that these assumptions are wrong for empirical and philosophical reasons, which results in a serious challenge to the conception of human morality as exclusivist by nature. Furthermore, simple intuition and practical experience constantly show us that human individuals can develop and endorse a broad spectrum of moral considerations and adopt an arguably inclusivist stance concerning the kind of persons or agents that deserve moral concern. Moreover, and adopting a historical perspective, the expansion of cultural and commercial exchanges, the consolidation of democracy, the development of welfare states, or the emergence of institutions based on the concept of universal human rights, have partially driven human progress based on the impartial concern for the well-being of persons. These historical instances of cultural evolution and institutional design have shown that it is feasible to promote behaviors and attitudes grounded in impersonal prosocial and inclusivist principles. This optimistic perspective, however, still begs the question of the exact relationship between social, cultural, and historical contexts, and the emergence of certain behavioral expressions of inclusivist morality. This is crucial since a great number of human individuals around the world still do not make part of these instances of social progress, and some authors have suggested that such instances of social and moral progress are particularly favored by the contexts of the WEIRD world, that is the world of Western, Educated, Industrialized, Rich, and Democratic societies. Some of these approaches consider moral inclusivity a ‘luxury good’ and follow the ‘dependency thesis’ according to which the expression of moral inclusivity depends on the presence of very concrete material conditions that trigger inclusivist and impersonal prosocial tendencies that human beings are not able to express in threatening contexts without physical security. This thesis is problematic for various reasons and has led to incomplete explanations about the enabling and causal factors of inclusivist moral progress, as well as unsatisfactory suggestions about what we should do to foster the accomplishment of more generalized instances of progress based on inclusivist concerns. In an attempt to contribute to this debate, the main objective of this thesis is to offer an alternative proposal about the nature of human morality and a more detailed reflection on what we should do if we want to further accomplish such instances of progress. More precisely, this work adopts a particular developmental and constructivist vision of human morality to answer the question of how feasible it is to reach generalized forms of social progress based on the precepts of moral inclusivity. Furthermore, it offers some ideas about what are the most adequate and favorable conditions to foster such progress both at the individual and the collective level. At this point, a preliminary clarification of some starting points is necessary. In the first place, and contrary to what other authors have proposed when debating moral progress from an empirically-based approach, my perspective adopts a radical developmental and constructivist perspective, following particularly the conceptual and empirical ideas of the social-domain theory in moral psychology. From this perspective, morality is a domain of normative and social knowledge that develops and emerges in human interactions. Moral concerns, judgments, and norms are not only the result of the expression of innate adaptive intuitions, nor the product of social conformity and a simple process of mirroring the normativity that communities have established to organize their social life. Human individuals, instead, construct moral concerns and judgments during their situated interactions. More specifically, the constructivist tradition claims that we need to research how moral concerns, judgments, and reasons emerge in social interactions and how human beings construct the content of their moral knowledge in the first place. Based on these ideas, morality is defined here as the result of a constructive process through which human individuals, by the means of constant interactions on a background of mutual respect and recognition, develop evaluative concerns about how we ought to treat others, and how to ‘care’ and ‘respect’ others’ well-being, needs, and vulnerabilities. This developmental-constructivist theory of human psychology contributes to an alternative understanding of the origins of moral variability and informs a very particular normative stance about the most desirable contexts needed for the urgent accomplishment of inclusivist forms of morality in contemporary societies. This is so given that the very same definition of morality adopted presupposes the feature of inclusivity. The main objective of this work is then to argue, based on a developmental perspective, what are the most favorable conditions to foster the development of moral inclusivity and what we should do to accomplish concrete instances of moral progress that truly help us to overcome our most urgent moral challenges. The whole thesis is organized as follows. In part I, I show how received visions about human social evolution have informed conceptions of morality as an adaptive function evolved to solve the challenges of cooperative life. Based on these assumptions, some theories argue that human morality is limited by the boundaries of group thinking, and always obeys the mandates of collective interests and the will of the majority. However, this conception has problematic implications from a normative and ethical perspective. The aim of Chapter 1 is to present this introductory debate in detail. In chapter 2, I consider a relevant amount of scientific evidence that helps to consolidate a more optimistic and inclusivist perspective about the starting conditions of human prosocial behavior. Later, I will summarize some ideas offered to explain the possible evolutionary mechanisms that led to the consolidation of these inclusivist capacities. However, I will also show how evolutionary theories that share the same adaptationist foundations but initially seem relevant to explain the feasibility of moral inclusivity, result incomplete when considering the complexity of moral behavior and its ethical implications. Part II is devoted to presenting a developmental alternative to the adaptationist versions around the starting conditions of morality. In this section, I first summarize the epistemological, conceptual, and empirical basis of a constructivist perspective already proposed by several authors in the last decades. This is the goal of chapter 3. More precisely, I adopt the conceptualization of morality established by the social-domain theory school and clarify its conception of the situated development of moral concerns, motivations, and norms. All these ideas are essential for my argumentation on the feasibility of inclusivist moral progress offered later. Chapter 4 provides a more detailed idea of constructivist thinking about moral development, by analyzing one particular dimension: the development of moral concerns for fairness and the sense of justice in distributive dilemmas. In Part III, I assume a constructivist perspective on morality to contribute to the philosophy of moral progress. In particular, I discuss the implications of such a perspective for the conceptualization of human moral nature and discuss what are the most favorable conditions for moral inclusivity to emerge. Answering that question is of enormous relevance since favoring the transition of human societies towards more inclusivist forms of moral concern and behavior supposes a more generalized accomplishment of our most urgent moral convictions. Previous developmental or culturally-sensible attempts to explore this issue are already on the market. As mentioned before, most authors have approached the topic by situating the cultural evolution and development of (inclusivist) moral progress in the WEIRD world. For instance, some of these authors claim that very concrete material conditions (mostly present in the Western World) have been necessary for triggering inclusivist and impersonal prosocial tendencies that human beings are not able to express in threatening contexts without physical security. Despite their interest in explaining inclusivist morality and the feasibility of inclusivist forms of progress following a naturalistic and culturally situated approach, these theories are problematic for two main reasons. In the first place, most of the authors that explain moral progress tend to focus exclusively on the consolidation of liberal values in the Western world and the underlying adoption of laws, social-epistemic practices, and public narratives about tolerance and inclusivity, as unequivocal signs of inclusivist morality. Nevertheless, there is an enormous distance between the institutional and public support of inclusivist moral values or the construction of public images of tolerance and inclusivity, and the real materialization of impersonal moralities in situated social interactions. Secondly, the variability of human moral behavior is far bigger than most of the theories in moral psychology and moral progress tend to assume. Accordingly, inclusivist and exclusivist forms of morality may develop simultaneously in similar or divergent geographical and socio-ecological environments, including those with harsh conditions such as competition for scarce resources, potential intergroup conflict, and risks of disease transmission. In addition, harsh environmental conditions are usually present in almost all societies around the globe, and the presence of socio-ecological conditions such as physical security and prosperity, predominant in highly resourced populations, do not prevent the existence of exclusivist moral tendencies. My model explores a different perspective on the relationships between cultural, institutional, and historical factors, and the situated development of human morality. This supposes a clear distinction from previous approaches to the matter since it offers a different view on what we should do to pursue further instances of inclusivist social progress. In the fifth chapter, I first analyze the proposals of some defenders of the ‘dependency’ theory. The attention is focused on the ‘Evolutionary Developmental Model’ proposed by Buchanan and Powell (2018). Based on a critique of this approach, I will argue that to explain the evolution and development of human morality in its multiple manifestations, it is essential to put focus on social interactions. This also involves a different perspective on human-environment relations that in line with a constructivist worldview makes an innovative contribution to the philosophy of moral behavior and moral progress. Later, in the sixth chapter, I will define my alternative relational view of inclusivist morality and I will offer my view on how to establish favorable conditions that make inclusivist morality possible. Complementing the constructivist approach, my conception is based on the essential role of equality and individuality and on how moral inclusivity is favored if moral concerns do not develop driven by the accomplishment of group-centered, binding, and communitarian concerns and values. In brief, my relational model suggests that the accomplishment of moral inclusivity not only depends on the overall achievement of certain levels of physical security or economic prosperity. Instead, its development is favored by transforming the interactional contexts in which moral concerns towards autonomy and individuality emerge. In arguing so, I will need to start with a critique of contemporary situated and embodied approaches in ethics. Then, I will show how societies guided by the accomplishment of group-centered values of power, dominance, and relational inequality tend to express exclusivist moral behaviors, while individualistic societies tend to be more inclusivist. Starting from this diagnosis, my final attempt is then to reflect on which are the best conditions for the moral valuation of individuality to emerge and what we should do to promote the accomplishment of moral inclusivity at the societal level. (shrink)

Why do relationships of friendship and love support partiality, but not relationships of hatred or commitments of racism? Where does partiality end and why? I take the intuitive starting point that important cases of partiality are meaningful. I develop a view whereby meaning is understood in terms of transcending self-limitations in order to connect with things of external value. I then show how this view can be used to distinguish central cases of legitimate partiality from cases of illegitimate partiality and (...) how it puts pressure on the traditional way of thinking about partiality. (shrink)

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

This paper introduces the logic _Q__L__E__T_ _F_, a quantified extension of the logic of evidence and truth _L__E__T_ _F_, together with a corresponding sound and complete first-order non-deterministic valuation semantics. _L__E__T_ _F_ is a paraconsistent and paracomplete sentential logic that extends the logic of first-degree entailment (_FDE_) with a classicality operator ∘ and a non-classicality operator ∙, dual to each other: while ∘_A_ entails that _A_ behaves classically, ∙_A_ follows from _A_’s violating some classically valid inferences. The semantics of _Q__L__E__T_ (...) _F_ combines structures that interpret negated predicates in terms of anti-extensions with first-order non-deterministic valuations, and completeness is obtained through a generalization of Henkin’s method. By providing sound and complete semantics for first-order extensions of _FDE_, _K3_, and _LP_, we show how these tools, which we call here the method of _anti-extensions + valuations_, can be naturally applied to a number of non-classical logics. (shrink)

This paper considers some issues to do with valuational presentations of consequence relations, and the Galois connections between spaces of valuations and spaces of consequence relations. Some of what we present is known, and some even well-known; but much is new. The aim is a systematic overview of a range of results applicable to nonreflexive and nontransitive logics, as well as more familiar logics. We conclude by considering some connectives suggested by this approach.

We give a valuation theoretic characterization for a real closed field to be recursively saturated. This builds on work in [9], where the authors gave such a characterization forκ-saturation, for a cardinal$\kappa \ge \aleph _0 $. Our result extends the characterization of Harnik and Ressayre [7] for a divisible ordered abelian group to be recursively saturated.

A central question for psychologists, economists, and philosophers is how human lives should be valued. Whereas egalitarian considerations give rise to models emphasizing that every life should be valued equally, empirical research has demonstrated that valuations of lives depend on a variety of factors that often do not conform to specific normative expectations. Such factors include emotional reactions to the victims and cognitive considerations leading to biased perceptions of lives at risk (e.g., attention, mental imagery, pseudo-inefficacy, and scope neglect). (...) They can lead to a valuation function with decreasing marginal value and sometimes even decreasing absolute value as the number of victims increases. As a result, people spend more money to save an individual while at the same time being insensitive and apathetic to large losses of life, despite endorsing egalitarian norms. In this conceptual paper, we propose a descriptive model highlighting the role of different motivations and the conditions under which cognitions and emotions result in deviations from egalitarian normative valuations of human lives. (shrink)

In this paper it is shown how a partial semantics for presuppositions can be given which is empirically more satisfactory than its predecessors, and how this semantics can be integrated with a technically sound, compositional grammar in the Montagovian fashion. Additionally, it is argued that the classical objection to partial accounts of presupposition projection, namely that they lack “flexibility,” is based on a misconception. Partial logics can give rise to flexible predictions without postulating any ad hoc ambiguities. (...) Finally, it is shown how the partial foundation can be combined with a dynamic system of common-ground maintenance to account for accommodation. (shrink)

Valuation consists in a positive or negative response by a subject S to an entity X. Any positive or negative response has a structure that involves a cognitive and a non-cognitive component, as well as a reason relationship between these. This structure is shown to be present in the explicit value judgement 'Hans is a kraut', and then also pointed out in the reflex-like feeding behaviour of a frog, where S treats X as providing an affordance. The conclusion is that (...) valuation need not involve mental states. The article ends with a discussion of the elusive question: what makes a response positive or negative? (shrink)

Is there anything irrational, or self-undermining, about having "inconsistent" attitudes of caring or valuing? In this paper, I argue that, contra suggestions of Harry Frankfurt and Charles Taylor, the answer is "No." Here I focus on "valuations," which are endorsed desires or attitudes. The proper characterization of what I call "valuational inconsistency" I claim, involves not logical form (valuing A and not-A), but rather the co-possibility of what is valued; valuations are inconsistent when there is no possible world (...) in which what is valued can co-exist. Essentially conflicting valuations, I show, are no worse for an agent than contingently conflicting ones, which are common and no threat to rationality or well-being. Partly based on reflections about a conflicted mother, who values staying at home and also having a career, I argue that valuational inconsistency does not render a person unable to act, does not make a person's actions ineffective because of vacillation, does not undermine a person's autonomy, and need not make a person dissatisfied with himself. I defend my characterization of inconsistency as an apt one; I offer some reasons to value inconsistency itself; and I draw out some implications for coherence thinking in moral philosophy. (shrink)

Theories of moral desert focus only on the personal culpability of the agent to determine the amount of blame and punishment the agent deserves. I defend an alternative account of desert, one that does not focus only facts about offenders and their offenses. In this revised framework, personal culpability can do no more than set upper and lower limits for deserved blame and punishment. For more precise judgments within that spectrum, additional factors must be considered, factors that are independent of (...) the agent and the offense. I refer to this as the ‘partial conception’ of desert because takes facts about victims—their behavior, desires, and attitudes—into account for desert judgments. On my view, then, agents who are equally culpable may deserve different amounts of blame or punishment, depending on these victim-related factors. (shrink)

Valuation is portrayed here as a dynamic and interactive process, not a static notion linked to willingness to pay. Valuation through economic measures can be built upon by creating trusting and legitimising procedures of stakeholder negotiation and mediation. This is a familiar practice in the US, but it is only beginning to be recognised as an environmental management tool in the UK. The introduction of strategic environmental and landuse appraisal plans for shorelines, estuaries, river catchments and rural landscapes, combined with (...) the mobilisation of protest around landuse proposals that are not seemingly justified on the basis of 'need' suggest that a more legitimate participatory form of democracy is required to reveal valuation through consensual negotiation. (shrink)

In this paper, we present valuation semantics for the Propositional Intuitionistic Calculus (also called Heyting Calculus) and three important subcalculi: the Implicative, the Positive and the Minimal Calculus (also known as Kolmogoroff or Johansson Calculus). Algorithms based in our definitions yields decision methods for these calculi. DOI:10.5007/1808-1711.2010v14n1p125.

This paper investigates how people conceive and evaluate nature through language, in a climate change context. With material consisting of 1,200 answers to open-ended questions in nationally representative surveys in Norway, we explore what semantic roles and values the respondents attribute to nature as well as to how they interact with the public debate about climate change. We observe that different conceptions and valuations of nature are tied to different perspectives on the climate change issue: some address the responsibilities (...) of causing climate change, others its consequences, and others yet its potential solutions. The study provides knowledge about the variety of conceptions of nature that can be mobilised by individuals and suggests that policy measures and public communication could benefit by taking this diversity into account. (shrink)

The moral issues about nationalism arise from the character of nationalism as a form of partiality. Nationalists care more about their own nation and its members than about other nations and their members; in that way nationalists are partial to their own national group. The question, then, is whether this national partiality is morally justified or, on the contrary, whether everyone ought to care impartially about all members of all nations. As Jeff McMahan emphasizes in [another chapter of the (...) book in which this essay appears], a philosophical examination of this question must consider the specific features of nationalism as one form of partiality among others. Some partiality--for example, toward one's spouse and children--seems morally acceptable and even a duty. According to commonsense moral thinking, one not only may but also should care more about one's family members than about strangers. But other instances of partiality, most notably racial partiality, are in most circumstances widely condemned. Is national partiality more like familial partiality or more like racial partiality? To answer this question, we must know what in general justifies attitudes of partiality. Caring more about certain people is appropriate when one stands in certain special relations to those people. But what are these relations, and to what degree do they hold among members of the same nation? Assuming they are present within families and not within races, to what degree are they present within nations? (shrink)

In this article, I question the plausibility of Metz’s African moral theory from an oft-neglected moral topic of partiality. Metz defends an Afro-communitarian moral theory that posits that the rightness of actions is entirely definable by relationships of identity and solidarity (or, friendship). I offer two objections to this relational moral theory. First, I argue that justifying partiality strictly by invoking relationships (of friendship) ultimately fails to properly value the individual for her own sake – this is called the ‘focus (...) problem’ in the literature. Second, I argue that a relationship-based theory cannot accommodate the agent-related partiality since it posits some relationship to be morally fundamental. My critique ultimately reveals the inadequacy of a relationship-based moral theory insofar as it overlooks some crucial moral considerations grounded on the individual herself in her own right. (shrink)

Economics takes an individualistic approach to human behaviour. This is reflected in the use of 'contingent valuation' surveys to conduct cost benefit analysis for economic policy evaluation. An individual's valuation of a policy is assumed to be unaffected by the burdens it places on others. We report a survey experiment to test this supposition in the context of climate change policy. Willingness to pay for climate change mitigation was higher when richer individuals were to bear higher costs than when, as (...) is usual, no explicit information was provided about cost distribution. This result is inconsistent with the usual interpretation of contingent valuation data. It also suggests that the data may be biased indicators of policy acceptance. Additional survey questions suggest that a collective mode of reasoning is common. (shrink)

Discussion of partial grounds that aren't parts of full grounds; definition of full grounding in terms of partial grounding.

Values, Valuations, and Axiological Norms in Richard Rorty's Neopragmatism sympathetically discusses Richard Rorty's neopragmatist philosophy. This book brings together a range of interpretations and possibilities on a variety of humanistic topics, including philosophy, literature, culture, film, economics, social issues, politics, and more. Skowroński involves the work of philosophers such as Kant, Dewey, Santayana, and Kołakowski as he delves into various philosophical problems using the lens of Rorty’s neopragmatist thought.

It’s an undeniable fact about our moral lives that we are partial towards certain people and projects. Despite this, it has traditionally been very hard to justify partiality. In this paper I defend a novel partialist theory. The context of the paper is the debate between three different views of how partiality is justified. According to the first view, partiality is justified by facts about our ground projects. According to the second view, partiality is justified by facts about our (...) relationships with the things that we are partial towards. And according to the third view, partiality is justified by facts about the things that we are partial towards. I argue that all three views contain part of the truth. We can see this by adopting a more sophisticated view of the weight of reasons. Once we do this, it will be clear that both facts about individuals and facts about relationships play a role in explaining why we often have stronger reason to act well towards those things we are partial towards. Further, I argue, facts about projects help explain why facts about relationships play the role that they do in determining the strength of our reasons. (shrink)

We study the algebraic implications of the non-independence property and variants thereof on infinite fields, motivated by the conjecture that all such fields which are neither real closed nor separably closed admit a henselian valuation. Our results mainly focus on Hahn fields and build up on Will Johnson’s “The canonical topology on dp-minimal fields” :1850007, 2018).