In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...) can be interpreted as modal formulas over a flow of time, where the logic of each instant is Łukasiewicz, with a finite or infinite number of truth values. As a main result, we obtain validity with respect to all flows of times that are non-branching to the future, and completeness with respect to all finite linear flows of time, or to an appropriate single infinite linear flow of time. It may be argued that this reduces the problem of establishing a meaningful interpretation of the truth values in BL logic to the analogous problem for Łukasiewicz logic. (shrink)

In Hájek et al. (J Symb Logic 65(2):669–682, 2000) the authors introduce the concept of supersound logic, proving that first-order Gödel logic enjoys this property, whilst first-order Łukasiewicz and product logics do not; in Hájek and Shepherdson (Ann Pure Appl Logic 109(1–2):65–69, 2001) this result is improved showing that, among the logics given by continuous t-norms, Gödel logic is the only one that is supersound. In this paper we will generalize the previous results. Two conditions will be presented: the first (...) one implies the supersoundness and the second one non-supersoundness. To develop these results we will use, between the other machineries, the techniques of completions of MTL-chains developed in Labuschagne and van Alten (Proceedings of the ninth international conference on intelligent technologies, 2008) and van Alten (2009). We list some of the main results. The first-order versions of MTL, SMTL, IMTL, WNM, NM, RDP are supersound; the first-order version of an axiomatic extension of BL is supersound if and only it is n-potent (i.e. it proves the formula ${\varphi^{n}\,\to\,\varphi^{n\,{+}\,1}}$ for some ${n\,\in\,\mathbb{N}^+}$ ). Concerning the negative results, we have that the first-order versions of ΠMTL, WCMTL and of each non-n-potent axiomatic extension of BL are not supersound. (shrink)

Inspired by the work done by Baaz et al. (Ann Pure Appl Log 147(1–2): 23–47, 2007; Lecture Notes in Computer Science, vol 4790/2007, pp 77–91, 2007) for first-order Gödel logics, we investigate Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order tautologies of some subalgebras of the standard Nilpotent Minimum algebra, establishing also a connection between the validity in an NM-chain of certain first-order formulas and its order type. Furthermore, we analyze axiomatizability, undecidability and (...) the monadic fragments. (shrink)

In the field of many-valued logics, Hájek’s Basic Logic BL was introduced in Hájek (Metamathematics of fuzzy logic, trends in logic. Kluwer Academic Publishers, Berlin, 1998). In this paper we will study four families of n-contractive (i.e. that satisfy the axiom \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\phi^n\rightarrow\phi^{n+1}}$$\end{document}, for some \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n\in\mathbb{N}^+}$$\end{document}) axiomatic extensions of BL and their corresponding varieties: BLn, SBLn, BLn and SBLn. Concerning BLn we have that (...) every BLn-chain is isomorphic to an ordinal sum of MV-chains of at most n + 1 elements, whilst every BLn-chain is isomorphic to an ordinal sum of MVn-chains (for SBLn and SBLn a similar property holds, with the difference that the first component must be the two elements boolean algebra); all these varieties are locally finite. Moving to the content of the paper, after a preliminary section, we will study generic and k-generic algebras, completeness and computational complexity results, amalgamation and interpolation properties. Finally, we will analyze the first-order versions of these logics, from the point of view of completeness and arithmetical complexity. (shrink)

In 1950, B.A. Trakhtenbrot showed that the set of first-order tautologies associated to finite models is not recursively enumerable. In 1999, P. Hájek generalized this result to the first-order versions of Łukasiewicz, Gödel and Product logics, w.r.t. their standard algebras. In this paper we extend the analysis to the first-order versions of axiomatic extensions of MTL. Our main result is the following. Let \ be a class of MTL-chains. Then the set of all first-order tautologies associated to the finite models (...) over chains in \, fTAUT\, is \ -hard. Let TAUT\ be the set of propositional tautologies of \. If TAUT\ is decidable, we have that fTAUT\ is in \. We have similar results also if we expand the language with the Δ operator. (shrink)

We present the logic BLChang, an axiomatic extension of BL (see [23]) whose corresponding algebras form the smallest variety containing all the ordinal sums of perfect MV-chains. We will analyze this logic and the corresponding algebraic semantics in the propositional and in the first-order case. As we will see, moreover, the variety of BLChang-algebras will be strictly connected to the one generated by Chang’s MV-algebra (that is, the variety generated by all the perfect MV-algebras): we will also give some new (...) results concerning these last structures and their logic. (shrink)

The notion of subject matter is a key concern of contemporary philosophy of language and logic. A central task for a theory of subject matter is to characterise the notion of sentential subject matter, that is, to assign to each sentence of a given language a subject matter that may count as its subject matter. In this paper, we elaborate upon David Lewis’ account of subject matter. Lewis’ proposal is simple and elegant but lacks a satisfactory characterisation of sentential subject (...) matter. Drawing on linguistic literature on focus and on the question under discussion, we offer a neo-Lewisian account of subject matter, which retains all the virtues of Lewis’ but also includes an attractive characterisation of sentential subject matter. (shrink)

This paper defends a relational view of time based on recent work on quantum gravity. Julian barbour's relational approach to physical theory, in particular, is developed as a basis for a relational, rather than anti-realist, metaphysics of time.

The question of whether transgender athletes should be permitted to compete in accordance with their gender identity is an evolving debate. Most competitive sports have male and female categories. One of the primary challenges with this categorization system, however, is that some transgender athletes (and especially transgender women) may be prevented from competing in accordance with their gender identity. The reason for this restriction is because of the idea that transgender women have an unfair advantage over their cisgender counterparts; this (...) is seen as a problem since sports are typically guided a principle called ‘the skill thesis’, which suggests that sports are supposed to determine who is most skillful by maintaining a fair starting point. In this paper, I argue that if the skill thesis ought to be maintained and there continues to exist no conclusive evidence in support of unfair advantages possessed by trans women, then we may want to re-consider the gender binary in sport. Rather than having male/female categories, it may make more sense to categorize athletes based other sport-specific factors (e.g., height, weight, etc.). This may help to maintain the skill thesis while at the same time removing potentially unfair and discriminatory barriers against transgender athletes. (shrink)

This open access book assesses the prospects of (re)adopting organization as a pivotal concept in biology. It shows how organization can nourish biological thinking and practice, by reconnecting with the idea of biology as the science of organized systems. The book provides a comprehensive state-of-the-art picture of the characterizations and uses of the concept of organization in both biological science and philosophy of biology. It also deals with a variety of themes – including evolution, organogenesis, heredity, cognition and ecology – (...) with respect to which the concept of organization can guide the elaboration of original models and new experimental protocols. It will be of interest to biologists and scholars working in philosophy of science alike. (shrink)

The present paper discusses different approaches to metaphysics and defends a specific, non-deflationary approach that nevertheless qualifies as scientifically-grounded and, consequently, as acceptable from the naturalistic viewpoint. By critically assessing some recent work on science and metaphysics, we argue that such a sophisticated form of naturalism, which preserves the autonomy of metaphysics as an a priori enterprise yet pays due attention to the indications coming from our best science, is not only workable but recommended.

We study the EPR-type correlations from the perspective of the relational interpretation of quantum mechanics. We argue that these correlations do not entail any form of “non-locality”, when viewed in the context of this interpretation. The abandonment of strict Einstein realism implied by the relational stance permits to reconcile quantum mechanics, completeness, (operationally defined) separability, and locality.

This book examines the paradox of digital enhancement: we simultaneously desire to be governed by the logic of perfection and to be self-governed. Through genealogical and aesthetic critique, Sarah Bianchi questions the costs of our digital present and conceptualizes how to critically construct an enlightened agency.

This paper investigates the reception and discussion of Jakob von Uexküll’s biological theory by two German thinkers of his time, Helmuth Plessner and Kurt Goldstein. It demonstrates how their bio-philosophical perspectives are on the one hand indebted to Uexküll’s theory and, on the other, critical of its tendency to excessively harmonize the relationship between living beings and their environment. This original critical reading of the _Umweltlehre_ is rooted in ambiguities within Uexküll’s own thought - between a dynamic conception of the (...) organism-environment relationship and the idea of "conformity to a plan" -,, which is here examined in the second section. In the third and fourth sections we will then focus on Plessner and Goldstein respectively, demonstrating how for these two authors the harmony between organism and environment is not an original state, but only reveals itself against the background of a tension; as such, it can only be partial, unstable and always changing. The two thinkers avoid the rigid alternative between Darwin’s concept of adaptation (_Anpassung_) and Uexküll’s “fitting into” (_Einpassung_) by theorizing the ideal state of the relationship between organism and environment in terms of “adequacy” (_Adäquatheit_) and “adaptability” (_Adaptiertheit_). Between organism and environment there is neither absolute separation nor perfect harmony, but rather a gap which can never be definitively fixed. (shrink)

Anerkennung ist ein schillernder Begriff, der erst seit wenigen Jahrzehnten Aufmerksamkeit findet, aber in Ethik, politischer Philosophie und Kritischer Theorie mit großen Erwartungen verbunden wird. Sein Ursprung in den Intersubjektivitätstheorien Fichtes und Hegels lässt hoffen, dass er von sich aus Impulse für Freiheit und Gerechtigkeit in sich trägt. Vor diesem Hintergrund ist es eine Entdeckung ersten Ranges, dass ein Denker wie Nietzsche den Begriff der Anerkennung in durchaus grundlegender Weise verwendet, ohne den erst Ende des 20. Jahrhunderts mit ihm verknüpften (...) Hoffnungen zu widersprechen. Nietzsches Verständnis von Anerkennung zeigt sich in seiner Lebensphilosophie. Wie die Individuen konkret "einander nöthig" sind, arbeitet Sarah Bianchi anerkennungstheoretisch für das ganze menschliche Leben in seinen verschiedenen Dimensionen heraus. Qua Anerkennung sind die Individuen vom Selbstverhältnis, über zwischenmenschliche Beziehungen bis hin zum Recht und Staat existentiell verwoben. (shrink)

Widely recognized as one of the main characteristics of Latin Aristotelianism, the 'Christianisation' of Aristotle from the thirteenth to the seventeenth century has received as yet little attention. Aiming to answer the need for a more systematic investigation, the articles here collected approach Christian readings of the Stagirite|s works from different perspectives. Setting aside abstract discussions about |degrees of orthodoxy|, they address a few specific questions: which |images| of Aristotle were offered by Medieval and Renaissance interpreters, and in particular how (...) did some of them argue that - far from being a pagan or even an impious thinker - he did not contradict the truths revealed by Holy Scripture? (shrink)

volume I. Philosophical inquiries and general theoretical concerns -- volume II. The kaleidoscope of different international law theories.

Boffa non-well-founded set theory allows for several distinct sets equal to their respective singletons, the so-called ‘Quine atoms’. Rieger contends that this theory cannot be a faithful description of set-theoretic reality. He argues that, even after granting that there are non-well-founded sets, ‘the extensional nature of sets’ precludes numerically distinct Quine atoms. In this paper we uncover important similarities between Rieger’s argument and how non-rigid structures are conceived within mathematical structuralism. This opens the way for an objection against Rieger, whilst (...) affording the theoretical resources for a defence of Boffa set theory as a faithful description of set-theoretic reality. (shrink)

Who gets to decide what it means to live a healthy lifestyle, and how important a healthy lifestyle is to a good life? As more governments make preventing obesity and diet-related illness a priority, it's become more important to consider the ethics and acceptability of their efforts. When it comes to laws and policies that promote healthy eating--such as special taxes on sugary drinks and the banning of food deemed unhealthy--critics argue that these policies are paternalistic, and that they limit (...) individual autonomy over food choices. In Healthy Eating Policy and Political Philosophy: A Public Reason Approach, Anne Barnhill and Matteo Bonotti show that both paternalistic justifications for healthy eating efforts and anti-paternalistic arguments against them can be grounded in perfectionist views that overly prioritize some values over others. The authors therefore propose a more inclusive, public reason approach to healthy eating policy that will be appealing to those who take pluralism and cultural diversity seriously, by providing a framework through which different kinds of values, including but not limited to autonomy and health, can be factored into the public justification for healthy eating efforts. Additionally, the book adopts a 'farm to fork' approach to the ethics of healthy eating efforts: it engages with theories and debates in political philosophy, considers the implications of different theoretical positions for healthy eating efforts, and then develops a concrete tool for assessing policies that will be of interest to both scholars and policymakers. As well as offering a novel normative analysis of healthy eating policy, the authors offer a new theoretical framework that will be applicable to a wide range of public policy scenarios. (shrink)

The aim of this paper is twofold: first, I provide a cluster of theories of truth in classical logic that is (internally) consistent with global reflection principles: the theories of positive truth (and falsity). After that, I analyse the _epistemic value_ of such theories. I do so employing the framework of cognitive projects introduced by Wright (Proc Aristot Soc 78:167–245, 2004), and employed—in the context of theories of truth—by Fischer et al. (Noûs 2019. https://doi.org/10.1111/nous.12292 ). In particular, I will argue (...) that theories of positive truth are _trustworthy_, analogously to the theories of full disquotational truth. Moreover, I argue that, for a given cognitive project, _if_ the acceptance of trustworthy theories is taken to be an _epistemic norm_ of cognitive project, then one has good reasons to accept theories of positive truth over other rival theories of truth in classical logic. On the other hand, the latter theories are deemed epistemically unacceptable. (shrink)