In this paper, we show by a proof-theoretical argument that in a logic without structural rules, that is in noncommutative linear logic with exponentials, every formula A for which exchange rules (and weakening and contraction as well) are admissible is provably equivalent to ?A. This property shows that the expressive power of "noncommutative exponentials" is much more important than that of "commutative exponentials".

In this paper, we show by a proof-theoretical argument that in a logic without structural rules, that is in noncommutative linear logic with exponentials, every formula A for which exchange rules are admissible is provably equivalent to?A. This property shows that the expressive power of "noncommutative exponentials" is much more important than that of "commutative exponentials".

This paper is dedicated to extending and adapting to modal logic the approach of fractional semantics to classical logic. This is a multi-valued semantics governed by pure proof-theoretic considerations, whose truth-values are the rational numbers in the closed interval $[0,1]$. Focusing on the modal logic K, the proposed methodology relies on three key components: bilateral sequent calculus, invertibility of the logical rules, and stability (proof-invariance). We show that our semantic analysis of K affords an informational refinement with respect to the (...) standard Kripkean semantics (a new proof of Dugundji’s theorem is a case in point) and it raises the prospect of a proof-theoretic semantics for modal logic. (shrink)

This article presents a new semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of (...) traditional Boolean semantics, obtained by breaking the symmetry between tautologies and contradictions. (shrink)

Abductive reasoning involves finding the missing premise of an “unsaturated” deductive inference, thereby selecting a possible _explanans_ for a conclusion based on a set of previously accepted premises. In this paper, we explore abductive reasoning from a structural proof-theory perspective. We present a hybrid sequent calculus for classical propositional logic that uses sequents and antisequents to define a procedure for identifying the set of analytic hypotheses that a rational agent would be expected to select as _explanans_ when presented with an (...) abductive problem. Specifically, we show that this set may not include the deductively minimal hypothesis due to the presence of redundant information. We also establish that the set of all analytic hypotheses exhausts all possible solutions to the given problem. Finally, we propose a deductive criterion for differentiating between the best _explanans_ candidates and other hypotheses. (shrink)

In a recent paper, under the auspices of an unorthodox variety of bilateralism, we introduced a new kind of proof-theoretic semantics for the base modal logic \(\mathbf{K}\), whose values lie in the closed interval \([0,1]\) of rational numbers [14]. In this paper, after clarifying our conception of bilateralism – dubbed “soft bilateralism” – we generalize the fractional method to encompass extensions and weakenings of \(\mathbf{K}\). Specifically, we introduce well-behaved hypersequent calculi for the deontic logic \(\mathbf{D}\) and the non-normal modal logics (...) \(\mathbf{E}\) and \(\mathbf{M}\) and thoroughly investigate their structural properties. (shrink)

According to the implicit commitment thesis, once accepting a mathematical formal system S, one is implicitly committed to additional resources not immediately available in S. Traditionally, this thesis has been understood as entailing that, in accepting S, we are bound to accept reflection principles for S and therefore claims in the language of S that are not derivable in S itself. It has recently become clear, however, that such reading of the implicit commitment thesis cannot be compatible with well-established positions (...) in the foundations of mathematics which consider a specific theory S as self-justifying and doubt the legitimacy of any principle that is not derivable in S: examples are Tait’s finitism and the role played in it by Primitive Recursive Arithmetic, Isaacson’s thesis and Peano Arithmetic, Nelson’s ultrafinitism and sub-exponential arithmetical systems. This casts doubts on the very adequacy of the implicit commitment thesis for arithmetical theories. In the paper we show that such foundational standpoints are nonetheless compatible with the implicit commitment thesis. We also show that they can even be compatible with genuine soundness extensions of S with suitable form of reflection. The analysis we propose is as follows: when accepting a system S, we are bound to accept a fixed set of principles extending S and expressing minimal soundness requirements for S, such as the fact that the non-logical axioms of S are true. We call this invariant component the semantic core of implicit commitment. But there is also a variable component of implicit commitment that crucially depends on the justification given for our acceptance of S in which, for instance, may or may not appear reflection principles for S. We claim that the proposed framework regulates in a natural and uniform way our acceptance of different arithmetical theories. (shrink)

According to David Lewis, the predicate ‘knows’ is context-sensitive in the sense that its truth conditions vary across conversational contexts, which stretch or compress the domain of error possibilities to be eliminated by the subject’s evidence. Our concern in this paper is to thematize, assess, and overcome within a neo-Lewisian contextualist project two important mismatches between our use of ‘know’ in ordinary life and the use of ‘know’ by ‘Lewisian’ ordinary speakers. The first mismatch is that Lewisian contextualism still overgenerates (...) the error possibilities which cannot be ignored in a given context, since it is oblivious to the distinction between ‘invented’ and ‘discovered’ possibilities. The second mismatch is a full-scale one: an adequate account of knowledge attribution is not exhausted by the subject’s negative capacity of pruning branches off the tree of counterpossibilities. We therefore introduce a new vector of value, which explains how ‘know’ comes in degrees: the satisfaction of ‘know better’ is made to depend on the capacity of imagining possibilities connected in a relevant way with the subject’s beliefs. (shrink)

In this paper we will discuss the first order multiplicative intuitionistic fragment of linear logic, MILL1, and its applications to linguistics. We give an embedding translation from formulas in the Lambek Calculus to formulas in MILL1 and show this translation is sound and complete. We then exploit the extra power of the first order fragment to give an account of a number of linguistic phenomena which have no satisfactory treatment in the Lambek Calculus.

Arrow’s information paradox features the most radical kind of information asymmetry by diagnosing an inherent conflict between two parties inclined to exchange information. In this paper, we argue that this paradox is more richly textured than generally supposed by current economic discussion on it and that its meaning encroaches on philosophy. In particular, we uncovers the ‘epistemic’ and more genuine version of the paradox, which looms on our cognitive lives like a sort of tax on curiosity. Finally, we sketch the (...) relation between Arrow’s information paradox and the notion of zero-knowledge proofs in cryptography: roughly speaking, zero-knowledge proofs are protocols that enable a prover to convince a verifier that a statement is true, without conveying any additional information. (shrink)

This book contains more than 15 essays that explore issues in truth, existence, and explanation. It features cutting-edge research in the philosophy of mathematics and logic. Renowned philosophers, mathematicians, and younger scholars provide an insightful contribution to the lively debate in this interdisciplinary field of inquiry. The essays look at realism vs. anti-realism as well as inflationary vs. deflationary theories of truth. The contributors also consider mathematical fictionalism, structuralism, the nature and role of axioms, constructive existence, and generality. In addition, (...) coverage also looks at the explanatory role of mathematics and the philosophical relevance of mathematical explanation. The book will appeal to a broad mathematical and philosophical audience. It contains work from FilMat, the Italian Network for the Philosophy of Mathematics. These papers collected here were also presented at their second international conference, held at the University of Chieti-Pescara, May 2016. (shrink)

The very fact that the Gödel sentence $$\mathcal {G}$$ is independent of Peano Arithmetic fuels controversy over our access to the truth of $$\mathcal {G}$$. In particular, does the truth of $$\mathcal {G}$$ $$ ) precede the truth of its numerical instances $$\varphi $$, $$\varphi $$, $$\varphi, \ldots $$, as the so-called standard argument induces one to believe? This paper offers a shift in perspective on this old problem. We start by reassessing Michael Dummett’s 1963 argument which seems to speak (...) in favour of the priority of the truth of the numerical instances of $$\mathcal {G}$$ over the truth of $$\mathcal {G}$$ itself. In opposition to some recent criticisms of Dummett’s argument, we argue that the latter is not reducible to the standard one. We then point out its prototypical nature in the sense individuated by Jacques Herbrand. This shift in perspective brings us to the claim that the controversy over the priority between $$\mathcal {G}$$ and its numerical instances endures only because the problem is ultimately ill-posed. An encompassing moral about the epistemological mechanism of prototype proofs is also drawn. (shrink)

The aim of this paper is to argue that logic can play an important role in the “toolbox” of molecular biology. We show how biochemical pathways, i.e., transitions from a molecular aggregate to another molecular aggregate, can be viewed as deductive processes. In particular, our logical approach to molecular biology — developed in the form of a natural deduction system — is centered on the notion of Curry-Howard isomorphism, a cornerstone in nineteenth-century proof-theory.

Some real life processes, including molecular ones, are context-sensitive, in the sense that their outcome depends on side conditions that are most of the times difficult, or impossible, to express fully in advance. In this paper, we survey and discuss a logical account of context-sensitiveness in molecular processes, based on a kind of non-classical logic. This account also allows us to revisit the relationship between logic and philosophy of science (and philosophy of biology, in particular).

An important part of the Unified Medical Language System (UMLS) is its Semantic Network, consisting of 134 Semantic Types connected to each other by edges formed by one or more of 54 distinct Relation Types. This Network is however for many purposes overcomplex, and various groups have thus made attempts at simplification. Here we take this work further by simplifying the relations which involve the three Semantic Types – Diagnostic Procedure, Laboratory Procedure and Therapeutic or Preventive Procedure. We define operators (...) which can be used to generate terms instantiating types from this selected set when applied to terms designating certain other Semantic Types, including almost all the terms specifying clinical tasks. Usage of such operators thus provides a useful and economical way of specifying clinical tasks. The operators allow us to define a mapping between those types within the UMLS which do not represent clinical tasks and those which do. This mapping then provides a basis for an ontology of clinical tasks that can be used in the formulation of computer-interpretable clinical guideline models. (shrink)

Outcomes research in healthcare has been a topic much addressed in recent years. Efforts in this direction have been supplemented by work in the areas of guidelines for clinical practice and computer-interpretable workflow and careflow models.In what follows we present the outlines of a framework for understanding the relations between organizations, guidelines, individual patients and patient-related functions. The derived framework provides a means to extract the knowledge contained in the guideline text at different granularities, in ways that can help us (...) to assign tasks within the healthcare organization and to assess clinical performance in realizing the guideline. It does this in a way that preserves the flexibility of the organization in the adoption of the guidelines. (shrink)

Predictivists use the no miracle argument to argue that “novel” predictions are decisive evidence for theories, while mere accommodation of “old” data cannot confirm to a significant degree. But deductivists claim that since confirmation is a logical theory-data relationship, predicted data cannot confirm more than merely deduced data, and cite historical cases in which known data confirmed theories quite strongly. On the other hand, the advantage of prediction over accommodation is needed by scientific realists to resist Laudan’s criticisms of the (...) no miracle argument. So, if the deductivists are right, the most powerful argument for realism collapses. There seems to be an inescapable contradiction between these prima facie plausible arguments of predictivists and deductivists; but this puzzle can be solved by understanding what exactly counts as novelty, if novel predictions must support the no miracle argument, i.e., if they must be explainable only by the truth of theories. Taking my cues from the use-novelty tradition, I argue that (1) the predicted data must not be used essentially in building the theory or choosing the auxiliary assumptions. This is possible if the theory and its auxiliary assumptions are plausible independently of the predicted data, and I analyze the consequences of this requirement in terms of best explanation of diverse bodies of data. Moreover, the predicted data must be (2) a priori improbable, and (3) heterogeneous to the essentially used data. My proposed notion of novelty, therefore, is not historical, but functional. Hence, deductivists are right that confirmation is independent of time and of historical contingencies such as if the theorist knew a datum, used it, or intended to accommodate it. Predictivists, however, are right that not all consequences confirm equally, and confirmation is not purely a logical theory-data relation, as it crucially involves background epistemic conditions and the notion of best explanation. Conditions (1)–(3) make the difference between prediction and accommodation, and account for the confirming power of theoretical virtues such as non ad-hocness, non-fudging, non-overfitting, independence and consilience. I thus show that functional novelty (a) avoids the deductivist objections to predictivism, (b) is a gradual notion, in accordance with the common intuition that confirmation comes in degrees, and (c) supports the no miracle argument, so vindicating scientific realism. (shrink)

There are two possible realist defense strategies against the pessimistic meta-induction and Laudan’s meta-modus tollens: the selective strategy, claiming that discarded theories are partially true, and the discontinuity strategy, denying that pessimism about past theories can be extended to current ones. A radical version of discontinuity realism is proposed by Gerald Doppelt: rather than discriminating between true and false components within theories, he holds that superseded theories cannot be shown to be even partially true, while present best theories are demonstrably (...) completely true. I argue that this position, running counter both the cumulativity of science and fallibilism, is untenable; it cannot account for the success of past theories, nor for the failures of current theories, and rather than shutting the door to the pessimistic historical objections it opens it wide. The best strategy, instead, joins the selective idea there was both some truth and some falsity in discarded theories, like in current ones, with the moderate discontinuity idea that the truth rate in present best theories is much greater than in past ones. (shrink)

Entrevista concedida por Antonio Negri a Homero Santiago e Mario Marino por ocasião do lançamento da segunda edição da tradução brasileira de A anomalia selvagem: poder e potência em Espinosa.

Criticisms à la Laudan can block the “no miracles” argument for the (approximate) truth of whole theories. Realists have thus retrenched, arguing that at least the individual claims deployed in the derivation of novel predictions should be considered (approximately) true. But for Lyons (2002) there are historical counterexamples even to this weaker “deployment” realism: he lists a number of novel predictions supposedly derived from (radically) false claims. But if so, those successes would seem unexplainable, even by Lyons’ “modest surrealism” or (...) other surrogates to realism. In fact, I argue, some of those predictions were an easy guess, or independently probable in the light of available evidence; hence, they are no counterexamples to deployment realism, for the no miracles argument wouldn’t apply to them. In other instances, pace Lyon, the prediction was actually false, and could be reinterpreted as true only by interpreting as true also the claim from which it was derived; or again, a false claim was employed in the derivation of a true prediction, but inessentially, the essential role being played by a weaker true claim. But as soon as the paradoxical air of such historical cases is explained away in any of these manners, they cease to represent counterexamples to deployment realism. If, as I suggest, all of them can be dealt with by these strategies, a theoretical claim can still be assumed to be true if it is crucial in deriving an improbable novel prediction. (shrink)

El propósito de este artículo consiste en mostrar el carácter social del contractualismo de Fichte. Para realizar ese propósito se comienza examinando la conexión entre trabajo y ciudadanía como una condición de la legitimidad política. Luego se presenta esa conexión en el marco del siempre posible desarrollo histórico de la naturaleza humana. Por último, se indican las razones de la recepción de Fichte como un precursor del socialismo germánico.

Gerald Doppelt claims that Deployment Realism cannot withstand the antirealist objections based on the “pessimistic meta-induction” and Laudan’s historical counterexamples. Moreover it is incomplete, as it purports to explain the predictive success of theories, but overlooks the necessity to explain also their explanatory success. Accordingly, he proposes a new version of realism, presented as the best explanation of both predictive and explanatory success, and committed only to the truth of best current theories, not of the discarded ones. Elsewhere I criticized (...) his new brand of realism. Here instead I argue that Doppelt has not shown that Deployment Realism cannot solve the problems raised by the history of science, explaining explanatory success does not add much to explaining novel predictive success, and Doppelt is right that truth is not a sufficient explanans, but for different reasons, and this does not refute Deployment Realism, but helps to detail it better. In a more explicit formulation, the realist IBE concludes not only to the truth of theories, but also to the reliability of scientists and scientific method, the order and simplicity of nature, and the approximate truth of background theories. (shrink)

Many formulations of scientific realism (SR) include some commitment to metaphysical realism (MR). On the other hand, authors like Schlick, Carnap and Putnam held forms of scientific realism coupled with metaphysical antirealism (and this has analogies in Kant). So we might ask: do scientific realists really need MR? or is MR already implied by SR, so that SR is actually incompatible with metaphysical antirealism? And if MR must really be added to SR, why is that so? And which additional arguments (...) scientific realists need to support it? After reviewing and classifying a number of different kinds of realisms, metaphysical and not, I answer that SR and MR are logically independent of each other, so that there is no logical inconsistency in holding SR while rejecting MR. However, I argue that the “no miracle” argument (NMA) not only is the “ultimate” argument for SR, but by the same token it also supports MR. Therefore one cannot effectively defend SR without also subscribing to MR, but this can be done at no additional argumentative cost. I show this by discussing not only the standard version of the NMA, but also three more versions which are not usually considered as such in the literature. (shrink)

Originally published as Scientific Research, this pair of volumes constitutes a fundamental treatise on the strategy of science. Mario Bunge, one of the major figures of the century in the development of a scientific epistemology, describes and analyzes scientific philosophy, as well as discloses its philosophical presuppositions. This work may be used as a map to identify the various stages in the road to scientific knowledge. Philosophy of Science is divided into two volumes, each with two parts. Part 1 (...) offers a preview of the scheme of science and the logical and semantical took that will be used throughout the work. The account of scientific research begins with part 2, where Bunge discusses formulating the problem to be solved, hypothesis, scientific law, and theory. The second volume opens with part 3, which deals with the application of theories to explanation, prediction, and action. This section is graced by an outstanding discussion of the philosophy of technology. Part 4 begins with measurement and experiment. It then examines risks in jumping to conclusions from data to hypotheses as well as the converse procedure. Bunge begins this mammoth work with a section entitled "How to Use This Book." He writes that it is intended for both independent reading and reference as well as for use in courses on scientific method and the philosophy of science. It suits a variety of purposes from introductory to advanced levels. Philosophy of Science is a versatile, informative, and useful text that will benefit professors, researchers, and students in a variety of disciplines, ranging from the behavioral and biological sciences to the physical sciences. (shrink)

With special relativity, we seem to be facing a conundrum. It is a very well-tested theory; in this way, the Minkowski spacetime must be “capturing” essential features of space and time. However, its geometry seems to be incompatible with any sort of global notion of time. We might only have local notions of now (present moment) and time flow, at best. In this note, we will explore the possibility that a pretty much global notion of now (and time flow) might (...) be hiding in plain sight in the geometry of the Minkowski spacetime. (shrink)

This paper assesses the novelty of NSMs - or better, of any social and political movement in contemporary Western societies - in the light of their capacity to develop systems of relationships which cut across established social and political cleavages. It illustrates first the relational bases of Rokkan's concept of cleavage, and its contribution to the understanding of social movements; it then shows how Simmel's concept of the intersection of social circles and his distinction between concentric and crosscutting circles may (...) be fruitfully applied to the analysis of political cleavages and their changing forms. In the conclusions, the elements of an approach to the study of the newness of social movements, based on the integration of Rokkan's and Simmel's principles, are introduced. (shrink)

Different methods are available in clinical ethics consultation. In our experience as ethics consultants, certain individual methods have proven insufficient, and so we use a combination of methods. Based on these considerations, we first critically analyze the pros and cons of two well-known methods in the working field of clinical ethics, namely Beauchamp and Childress’s four-principle approach and Jonsen, Siegler, and Winslade’s four-box method. We then present the circle method, which we have used and refined during several clinical ethics consultations (...) in the hospital setting. (shrink)

The question of the animal is one of the most intensely debated in the contemporary philosophical arena. The present article makes the case that Husserl’s phenomenological approach offers a stimulating and open-ended perspective on this discussion. The animal, indeed, is an instance of extreme otherness, which pushes phenomenology to its limits. The paper opens with an outline of the methodological issues raised by the question of the animal. It then examines what the animal—at this point, taken as a whole—and the (...) human being have in common and what Husserl sees as the main differences between them. A critical aspect here is the question of personhood. Finally, Sect. 3 traces Husserl’s progression from a general concept of animality to detailed and nuanced phenomenological descriptions of different animals and their intra- and inter-specific relationships. Husserl understands that the threshold that joins and divides human beings and animals is difficult to pin down, because there is more than one threshold: it is plural. (shrink)

El presente artículo es una breve aproximación al contexto legal y político de las comunidades judías catalanas entre 1240 y 1391. A través del uso combinado de fuentes hebreas y cristianas, se ofrecerá una síntesis de la compleja red de factores, reglas y teorías que moldearon el ecosistema social de las comunidades hebreas en Cataluña. En este sentido, el autogobierno comunal era el resultado de la convergencia entre la legislación real y la producción normativa y teórica de las comunidades. Nuestro (...) objetivo es presentar el carácter poliédrico de esta realidad a través de los privilegios concedidos por los monarcas aragoneses a sus súbditos judíos, los modelos políticos desarrollados por los intelectuales hebreos, la legislación interna de las comunidades y el conjunto de factores sociales e históricos que impulsaron la evolución del sistema comunal. (shrink)

In this paper, it is presented a historical account of the formulation of the quantum relativistic wave equation of an electron – the Dirac equation, issues regarding its interpretation that arose from the very beginning, and the later formulation of this equation in relation to a quantized electron-positron field, which implies a new interpretation. The way in which solutions obtained under each interpretation of the equation relate to one another is also considered for the simple case of hydrogen-like problems.

On the basis of Levin’s claim that truth is not a scientific explanatory factor, Michel Ghins argues that the “no miracle” argument (NMA) is not scientific, therefore scientific realism is not a scientific hypothesis, and naturalism is wrong. I argue that there are genuine senses of ‘scientific’ and ‘explanation’ in which truth can yield scientific explanations. Hence, the NMA can be considered scientific in the sense that it hinges on a scientific explanation, it follows a typically scientific inferential pattern (IBE), (...) and it is based on an empirical fact (the success of science). Scientific realism, in turn, is scientific in the sense that it is supported both by a meta-level scientific argument (the NMA), and by first level scientific arguments through semantic ascent and generalization. However, both the NMA and scientific realism are not purely scientific, since they go beyond properly scientific concerns, and require additional philosophical reasoning. In turn, naturalism is correct in the sense that philosophy is continuous with science, partly based on it, and potentially equally well warranted. Beside denying the scientific nature of the NMA, Ghins raises some objections to its cogency , to which I reply in the final section. (shrink)

Review of: Communauté (Gemeinschaft), Martin Buber (2018) Paris: Éditions de l’éclat, 157 pp., ISBN 978-2-84162-432-4, p/bk, €10.