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)

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)

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)

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)

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.

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 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.

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)

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).

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)

Transmission of justification across inference is a valuable and indeed ubiquitous epistemic phenomenon in everyday life and science. It is thanks to the phenomenon of epistemic transmission that inferential reasoning is a means for substantiating predictions of future events and, more generally, for expanding the sphere of our justified beliefs or reinforcing the justification of beliefs that we already entertain. However, transmission of justification is not without exceptions. As a few epistemologists have come to realise, more or less trivial forms (...) of circularity can prevent justification from transmitting from p to q even if one has justification for p and one is aware of the inferential link from p to q. In interesting cases this happens because one can acquire justification for p only if one has independent justification for q. In this case the justification for q cannot depend on the justification for p and the inferential link from p to q, as genuine transmission would require. The phenomenon of transmission failure seems to shed light on philosophical puzzles, such as Moore's proof of a material world and McKinsey's paradox, and it plays a central role in various philosophical debates. For this reason it is being granted continued and increasing attention. (shrink)

In this paper we focus on transmission and failure of transmission of warrant. We identify three individually necessary and jointly sufficient conditions for transmission of warrant, and we show that their satisfaction grounds a number of interesting epistemic phenomena that have not been sufficiently appreciated in the literature. We then scrutinise Wright’s analysis of transmission failure and improve on extant readings of it. Nonetheless, we present a Bayesian counterexample that shows that Wright’s analysis is partially incoherent with our analysis of (...) warrant transmission and prima facie defective. We conclude exploring three alternative lines of reply: developing a more satisfactory account of transmission failure, which we outline; dismissing the Bayesian counterexample by rejecting some of its assumptions; reinterpreting Wright’s analysis to make it immune to the counterexample. (shrink)

Should decision-making algorithms be held to higher standards of transparency than human beings? The way we answer this question directly impacts what we demand from explainable algorithms, how we govern them via regulatory proposals, and how explainable algorithms may help resolve the social problems associated with decision making supported by artificial intelligence. Some argue that algorithms and humans should be held to the same standards of transparency and that a double standard of transparency is hardly justified. We give two arguments (...) to the contrary and specify two kinds of situations for which higher standards of transparency are required from algorithmic decisions as compared to humans. Our arguments have direct implications on the demands from explainable algorithms in decision-making contexts such as automated transportation. (shrink)

L’epistemologia (detta anche filosofia della conoscenza o gnoseologia) è la disciplina filosofica che studia come gli esseri umani si rapportano da un punto di vista cognitivo alla realtà che li circonda. Le questioni fondamentali che la interessano sono principalmente di natura normativa. Riguardano il modo in cui dovremmo regolare le nostre credenze alla luce dell’informazione in nostro possesso, e la natura della conoscenza umana ed i suoi limiti. Questo capitolo è organizzato in modo corrispondente. La prima sezione tratta della nozione (...) di giustificazione epistemica, la seconda quella di conoscenza, e la terza introduce il problema filosofico dello scetticismo. (shrink)

This paper focuses on extant approaches to counteract the consumption of fake news online. Proponents of structural approaches suggest that our proneness to consuming fake news could only be reduced by reshaping the architecture of online environments. Proponents of educational approaches suggest that fake news consumers should be empowered to improve their epistemic agency. In this paper, we address a question that is relevant to this debate: namely, whether fake news consumers commit mistakes for which they can be criticized and (...) that they could easily avoid by reforming their doxastic conduct. Proponents of structural approaches, like R. Rini and B. Millar, have defended in different ways a negative answer to this question. In this paper, we criticize their views and suggest that individual users could improve on their epistemic practice by widening their information diet. (shrink)

This chapter introduces a novel account of fake news and explains how it differs from other definitions on the market. The account locates the fakeness of an alleged news report in two main aspects related to its production, namely that its creators do not think to have sufficient evidence in favor of what they divulge and they fail to display the appropriate attitude towards the truth of the information they share. A key feature of our analysis is that it does (...) not require that fake news must be circulated with the intention to deceive one’s audience. In this way, our account overcomes a potential limitation of the current philosophical discussion about fake news, which appears to individuate the main problem with this phenomenon in the fact that fake news consumers are misled and misinformed. In contrast, the proposed analysis shows that an additional (and perhaps equally fundamental) problem uncovered by the spread of fake news is a widespread pathological relationship with information, one on which we consume information not to satisfy our interest in the truth but to strengthen our social identities and quench our hunger for social recognition. (shrink)

It is generally argued that if the wave-function in the de Broglie–Bohm theory is a physical field, it must be a field in configuration space. Nevertheless, it is possible to interpret the wave-function as a multi-field in three-dimensional space. This approach hasn’t received the attention yet it really deserves. The aim of this paper is threefold: first, we show that the wave-function is naturally and straightforwardly construed as a multi-field; second, we show why this interpretation is superior to other interpretations (...) discussed in the literature; third, we clarify common misconceptions. (shrink)

Most social scientists and philosophers claim that sociology and philosophy are disjoint fields of inquiry. Some have wondered how to trace the precise boundary between them. Mario Bunge argues that the two fields are so entangled with one another that no demarcation is possible or, indeed, desirable. In fact, sociological research has demonstrably philosophical pre-suppositions. In turn, some findings of sociology are bound to correct or enrich the philosophical theories that deal with the world, our knowledge of it, or (...) the ways of acting upon it. While Bunge's thesis would hardly have shocked Mill, Marx, Durkheim, or Weber, it is alien to the current sociological mainstream and dominant philosophical schools. Bunge demonstrates that philosophical problematics arise in social science research. A fertile philosophy of social science unearths critical presuppositions, analyzes key concepts, refines effective research strategies, crafts coherent and realistic syntheses, and identifies important new problems. Bunge examines Marx's and Durkheim's thesis that social facts are as objective as physical facts; the so-called Thomas theorem that refutes the behaviorist thesis that social agents react to social stimuli rather than to the way we perceive them; and Merton's thesis on the ethos of basic science which shows that science and morality are intertwined. He considers selected philosophical problems raised by contemporary social studies and argues forcefully against tolerance of shabby work in academic social science and philosophy alike. (shrink)

Slightly revised version of the author's habilitation--Universitèat Gèottingen, 2014.

This paper investigates the historical origin and ancestors of typicality, which is now a central concept in Boltzmannian Statistical Mechanics and Bohmian Mechanics. Although Ludwig Boltzmann did not use the word typicality, its main idea, namely, that something happens almost always or is valid for almost all cases, plays a crucial role for his explanation of how thermodynamic systems approach equilibrium. At the beginning of the 20th century, the focus on almost always or almost everywhere was fruitful for developing measure (...) theory and probability theory. It was apparently Hugh Everett III who first mentioned typicality in physics in 1957 while searching for a justification of the Born rule in his interpretation of quantum mechanics. The historically closest concept before these developments is moral certainty, which was invented by the medieval French theologian Jean Gerson, and it became a standard concept at least until the Age of Enlightenment, when Jakob Bernoulli proved the Law of Large numbers. (shrink)

Lots of Websites offer the possibility to donate human beings. Another problem of ethics of communications.