Global properties of canonical derivability predicates in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, (...) interpolation and the fixed point theorem. (shrink)

Bossi, A. and S. Valentini, An intuitionistic theory of types with assumptions of high-arity variables, Annals of Pure and Applied Logic 57 93–149. After an introductory discussion on Martin-Löf's Intuitionistic Theory of Types , the paper introduces the notion of assumption of high-arity variable. Then the original theory is extended in a very uniform way by means of the new assumptions. Some improvements allowed by high-arity variables are shown. The main result of the paper is a normal form theorem (...) for HITT. The detailed proof follows a computability method ‘a la Tait’. The main consequences of the normal form theorem are: the consistency of HITT, which also implies the consistency of ITT, and the computability of any judgement derived within HITT. Besides that, a canonical form theorem is shown: to any derivable judgement we can associate a canonical one whose derivation ends with an introductory rule. The standard disjunction and existential properties follow. Moreover, by using the computational interpretation of types it immediately follows that the execution of any proved correct program terminates. (shrink)

The Queen's College, Oxford, UK In his article `Facts and Principles', G.A. Cohen attempts to refute constructivist approaches to justification by showing that, contrary to what their proponents claim, fundamental normative principles are fact- in sensitive. We argue that Cohen's `fact-insensitivity thesis' does not provide a successful refutation of constructivism because it pertains to an area of meta-ethics which differs from the one tackled by constructivists. While Cohen's thesis concerns the logical structure of normative principles, constructivists ask how normative principles (...) should be justified . In particular, their claim that justified fundamental normative principles are fact-sensitive follows from a commitment to agnosticism about the existence of objective moral facts. We therefore conclude that, in order to refute constructivism, Cohen would have to address questions of justification, and take a stand on those long-standing meta-ethical debates about the ontological status of moral notions (for example, realism versus anti-realism) with respect to which he himself wants to remain agnostic. Key Words: John Rawls • normative justification • realism versus anti-realism • methodological versus substantive principles. (shrink)

Understanding terrestrial carbon metabolism is critical because terrestrial ecosystems play a major role in the global carbon cycle. Furthermore, humans have severely disrupted the carbon cycle in ways that will alter the climate system and directly affect terrestrial metabolism. Changes in terrestrial metabolism may well be as important an indicator of global change as the changing temperature signal. Improving our understanding of the carbon cycle at various spatial and temporal scales will require the integration of multiple, complementary and independent methods (...) that are used by different research communities. Tools such as air sampling networks, inverse numerical methods, and satellite data allow us to study the strength and location of the global- and continental-scale carbon sources and sinks. Bottom-up studies provide estimates of carbon fluxes at finer spatial scales and examine the mechanisms that control fluxes at the ecosystem, landscape, and regional scales. Bottom-up approaches include comparative and process studies that provide the necessary mechanistic information to develop and validate terrestrial biospheric models. An iteration and reiteration of top-down and bottom-up approaches will be necessary to help constrain measurements at various scales. We propose a major international effort to coordinate and lead research programs of global scope of the carbon cycle. (shrink)

In this paper we analyze an extension of Martin-Löf s intensional set theory by means of a set contructor P such that the elements of P are the subsets of the set S. Since it seems natural to require some kind of extensionality on the equality among subsets, it turns out that such an extension cannot be constructive. In fact we will prove that this extension is classic, that is “ true holds for any proposition A.

When and why do socially constructed norms—including the laws of the land, norms of etiquette, and informal customs—generate moral obligations? I argue that the answer lies in the duty to respect others, specifically to give them what I call “agency respect.” This is the kind of respect that people are owed in light of how they exercise their agency. My central thesis is this: To the extent that (i) existing norms are underpinned by people’s commitments as agents and (ii) they (...) do not conflict with morality, they place moral demands on us on agency-respect grounds. This view of the moral force of socially constructed norms, I suggest, is superior to views that deny the moral force of such norms, and it elegantly explains certain instances of wrongdoing that would otherwise remain unaccounted for. (shrink)

In his recent bookThe Idea of Justice, Amartya Sen suggests that political philosophy should move beyond the dominant, Rawls-inspired, methodological paradigm – what Sen calls ‘transcendental institutionalism’ – towards a more practically oriented approach to justice: ‘realization-focused comparison’. In this article, I argue that Sen's call for a paradigm shift in thinking about justice is unwarranted. I show that his criticisms of the Rawlsian approach are either based on misunderstandings, or correct but of little consequence, and conclude that the Rawlsian (...) approach already delivers much of what Sen himself wants from a theory of justice. (shrink)

An intuitionistic version of Cantor's theorem, which shows that there is no surjective function from the type of the natural numbers N into the type N → N of the functions from N into N, is proved within Martin-Löf's Intuitionistic Type Theory with the universe of the small types.

In this paper we propose an approach to vagueness characterised by two features. The first one is philosophical: we move along a Kantian path emphasizing the knowing subject’s conceptual apparatus. The second one is formal: to face vagueness, and our philosophical view on it, we propose to use topology and formal topology. We show that the Kantian and the topological features joined together allow us an atypical, but promising, way of considering vagueness.

A life without liberty and material resources is not a good life. Equally, a life devoid of meaningful social relationships—such as friendships, family attachments, and romances—is not a good life. From this it is tempting to conclude that just as individuals have rights to liberty and material resources, they also have rights to access meaningful social relationships. I argue that this conclusion can be defended only in a narrow set of cases. ‘Pure’ social relationship deprivation—that is, deprivation that is not (...) caused, or accompanied, by deficits in liberties and material resources— mostly generates demands of private beneficence. I suggest that social relationship deprivation is unjust, hence a rights violation, only when it is due to factors—such as one’s race—that are irrelevant to one’s being a good participant in social relationships. I thus conclude that access to meaningful social relationships is not a fundamental concern for theories of justice. (shrink)

In 1996, Krivine applied Friedman's A-translation in order to get an intuitionistic version of Gödel completeness result for first-order classical logic and countable languages and models. Such a result is known to be intuitionistically underivable 559), but Krivine was able to derive intuitionistically a weak form of it, namely, he proved that every consistent classical theory has a model. In this paper, we want to analyze the ideas Krivine's remarkable result relies on, ideas which where somehow hidden by the heavy (...) formal machinery used in the original proof. We show that the ideas in Krivine's proof can be used to intuitionistically derive some crucial mathematical results, which were supposed to be purely classical up to now: the Ultrafilter Theorem for countable Boolean algebras, and the maximal ideal theorem for countable rings. (shrink)

One of the distinctive features of the obligation to obey the law is its content-independence. We ought to do what the law commands because the law commands it, and not because of the law's content—i.e., the independent merits of the actions it prescribes. Despite its popularity, the notion of content-independence is marked by ambiguity. In this paper, I first clarify what content-independence is. I then develop a simple test—the “content-independence test”—which allows us to establish whether any candidate justification of the (...) obligation to obey the law delivers genuine content-independence. I apply this test to prominent such justifications and conclude that several of them, surprisingly, fail it. (shrink)

Much contemporary political philosophy claims to be Kant-inspired, but its aims and method differ from Kant's own. In his recent book, Force and Freedom, Arthur Ripstein advocates a more orthodox Kantian outlook, presenting it as superior to dominant (Kant-inspired) views. The most striking feature of this outlook is its attempt to ground the whole of political morality in one right: the right to freedom, understood as the right to be independent of others’ choices. Is Ripstein's Kantian project successful? In this (...) research note I argue that it is not. First, I suggest that Ripstein's notion of freedom is viciously circular. It is meant to ground all rights, but in fact it presupposes an account of those rights. Second, I show that—independently of its inability to ground a whole political morality—such a moralized understanding of freedom is normatively unappealing. (shrink)

In late 2012, Hurricane Sandy hit the East Coast of the U.S., causing much suffering and devastation. Those who could have easily helped Sandy’s victims had a duty to do so. But was this a rightfully enforceable duty of justice, or a non-enforceable duty of beneficence? The answer to this question is often thought to depend on the kind of help offered: the provision of immediate bodily services is not enforceable; the transfer of material resources is. I argue that this (...) double standard is unjustified, and defend a version of what I call “Social Samaritanism.” On this view, within political communities, the duty to help the needy—whether via bodily services or resource transfers—is always an enforceable demand of justice, except when the needy are reckless; across independent political communities, it is always a matter of beneficence. I defend this alternative double standard, and consider its implications for the case of Sandy. (shrink)

Just as different sciences deal with different facts—say, physics versus biology—so we may ask a similar question about normative theories. Is normative political theory concerned with the same normative facts as moral theory or different ones? By developing an analogy with the sciences, we argue that the normative facts of political theory belong to a higher— more coarse-grained—level than those of moral theory. The latter are multiply realizable by the former: competing facts at the moral level can underpin the same (...) facts at the political one. Consequently, some questions that moral theories answer are indeterminate at the political level. This proposal offers a novel interpretation of John Rawls’s idea that, in public reasoning, we should abstract away from comprehensive moral doctrines. We contrast our distinction between facts at different levels with the distinction between admissible and inadmissible evidence and discuss some implications for the practice of political theory. (shrink)

Millions of people in our world are in need of assistance: from the global poor, to refugees, from the victims of natural disasters, to those of violent crimes. What are our responsibilities towards them? Christian Barry and Gerhard Øverland’s answer is plausible and straightforward: we have enforceable duties to assist others in need whenever we can do so ‘at relatively moderate cost to ourselves, and others’. Barry and Øverland defend this answer on the ground that it best fits our intuitions (...) in a variety of hypothetical rescue scenarios. I argue that, although Barry and Øverland’s view is intuitively appealing, appeal to intuitive cases is insufficient to vindicate it satisfactorily. Intuitive cases alone do not allow us to establish: (i) what costs count as moderate and (ii) whether assistance-based responsibilities are, in fact, enforceable. These considerations suggest that Barry and Øverland’s defence of their preferred answer to the assistance question may be incomplete. (shrink)

We propose a formal representation of objects , those being mathematical or empirical objects. The powerful framework inside which we represent them in a unique and coherent way is grounded, on the formal side, in a logical approach with a direct mathematical semantics in the well-established field of constructive topology, and, on the philosophical side, in a neo-Kantian perspective emphasizing the knowing subject’s role, which is constructive for the mathematical objects and constitutive for the empirical ones.

This work deals with the exponential fragment of Girard's linear logic without the contraction rule, a logical system which has a natural relation with the direct logic . A new sequent calculus for this logic is presented in order to remove the weakening rule and recover its behavior via a special treatment of the propositional constants, so that the process of cut-elimination can be performed using only “local” reductions. Hence a typed calculus, which admits only local rewriting rules, can be (...) introduced in a natural manner. Its main properties — normalizability and confluence — has been investigated; moreover this calculus has been proved to satisfy a Curry-Howard isomorphism with respect to the logical system in question. MSC: 03B40, 03F05. (shrink)

Whenever fellow humans suffer due to natural catastrophes, we have a duty to help them. This duty is not only acknowledged in moral theory, but also expressed in ordinary people’s reactions to phenomena such as tsunamis, hurricanes, and earthquakes. Despite being widely acknowledged, this duty is also widely disputed: some believe it is a matter of justice, others a matter of charity. Although central to debates in international political theory, the distinction between justice and charity is hardly ever systematically drawn. (...) To fill this gap in the literature, I consider three accounts of this distinction, the ‘Agent-based’, the ‘Recipient-based’, and the ‘Mixed’ View, and argue that they are all unsatisfactory. I then offer a fourth alternative, the ‘Autonomy’ View, which successfully overcomes the difficulties affecting its rivals. I conclude by considering the implications of this view for the moral grounds of disaster relief in earthquake-stricken Haiti, New Zealand, and Japan. (shrink)

In his thought-provoking book, Why Law Matters, Alon Harel defends two key claims: one ontological, the other axiological. First, he argues that constitutions and judicial review are necessary constituents of a just society. Second, he suggests that these institutions are not only means to the realization of worthy ends, but also non-instrumentally valuable. I agree with Harel that constitutions and judicial review have more than instrumental value, but I am not persuaded by his arguments in support of this conclusion. I (...) argue that Harel’s ontological claim is unsustainable, and that his axiological claim needs revision. Regarding the former, I show that constitutions and judicial review are only contingent constituents of a just society. Regarding the latter, I contest Harel’s specific account of the value of constitutions and judicial review. Harel grounds the non-instrumental value of constitutions in freedom as non-domination but, upon scrutiny, it emerges that their non-instrumental value lies elsewhere. Further, Harel holds that the non-instrumental value of judicial review stems from its embodying a right to a fair hearing. I argue that this right has non-instrumental value only under a particular set of circumstances. I thus conclude, contrary to Harel, that the non-instrumental value of judicial review is contingent on those circumstances obtaining. (shrink)

In this paper a proof of the normal form theorem for the closed terms of Girard's system F is given by using a computability method à la Tait. It is worth noting that most of the standard consequences of the normal form theorem can be obtained using this version of the theorem as well. From the proof-theoretical point of view the interest of the proof is that the definition of computable derivation here used does not seem to be well founded. (...) MSC: 03F05, 03B15. (shrink)

The purpose of the paper is to show how the reading of Kafka’s Prometheus offered by Hans Blumenberg in Arbeit am Mythos authorizes a re-understanding of this short story as a device within which the meta-representative moment and the questioning moment are configured as two indissolubly linked aspects. In this perspective, starting from the recognition of the key role played by the mechanism of irony in the construction of the Kafkaesque short story, the article aims to highlight the three different (...) levels of articulation of such a mechanism, with particular reference to its ability to exhibit – at the same time – the transcendibility of the datum and the need to think the sense as «infinite deferral». (shrink)

In this paper we show that the usual intuitionistic characterization of the decidability of the propositional function B prop [x : A], i. e. to require that the predicate ∨ ¬ B) is provable, is equivalent, when working within the framework of Martin-Löf's Intuitionistic Type Theory, to require that there exists a decision function ψ: A → Boole such that = Booletrue) ↔ B). Since we will also show that the proposition x = Booletrue [x: Boole] is decidable, we can (...) alternatively say that the main result of this paper is a proof that the decidability of the predicate Bprop [x : A] can be effectively reduced by a function ψ A → Boole to the decidability of the predicate ψ = Booletrue [x : A]. All the proofs are carried out within the Intuitionistic Type Theory and hence the decision function ψ, together with a proof of its correctness, is effectively constructed as a function of the proof of ∨ ¬ B). (shrink)

We analyze some extensions of Martin-Löf 's constructive type theory by means of extensional set constructors and we show that often the most natural requirements over them lead to classical logic or even to inconsistency.

This paper deals with Kant’s view of a “philosophical chiliasmus”, by which it is to be understood the political hope of a perpetual peace between the world’s states. In his philosophical and political writings, Kant shows how this peace can be achieved through diplomatic means, trying to define the original concept of a “cosmopolitical right” (Weltbürgerrecht). This paper aims at highlighting the modernity of Kant’s political perspective, which has been renewed and developed in the twentieth century by many philosophers and (...) jurists as Hans Kelsen and John Rawls. (shrink)

The changes and general alarm of the current COVID-19 pandemic have amplified the sense of precariousness and vulnerability for family members who, in addition to the emotional trauma of the cancer diagnosis, add the distress and fear of the risks associated with infection. The primary objectives of the present study were to investigate the psychological impact of the COVID-19 pandemic on the parents of pediatric cancer patients, and the level of stress, anxiety, and the child’s quality of life perceived by (...) the parents during the COVID-19 epidemic. The parents of 45 consecutive children with solid and hematological tumors were enrolled. Four questionnaires were administered to the parents at the beginning of the pandemic lockdown. A 75% of parents exhibited remarkable levels of anxiety, with 60 subjects in state scale and 45 subjects in trait scale having scores that reached and exceeded the STAI-Y cut off. The bivariate matrix of correlation found a significant positive correlation between the IES-R and PSS scores. There was a positive correlation between the PSS and PedsQL scale and a negative correlation between IES-R and STAI-Y. The results confirm that parents of pediatric cancer patients have a high psychological risk for post-traumatic symptoms, high stress levels, and the presence of clinically significant levels of anxiety. (shrink)

This handbook offers a deep analysis of the main forms of legal reasoning and argumentation from both a logical-philosophical and legal perspective. These forms are covered in an exhaustive and critical fashion, and the handbook accordingly divides in three parts: the first one introduces and discusses the basic concepts of practical reasoning. The second one discusses the main general forms of reasoning and argumentation relevant for legal discourse. The third one looks at their application in law as well as at (...) the different areas of legal reasoning. The handbook’s division in three parts reflects its conceptual architecture, since legal reasoning and argumentation are considered in relation to the more general types of reasoning. (shrink)

This handbook offers a deep analysis of the main forms of legal reasoning and argumentation from both a logical-philosophical and legal perspective. These forms are covered in an exhaustive and critical fashion, and the handbook accordingly divides in three parts: the first one introduces and discusses the basic concepts of practical reasoning. The second one discusses the main general forms of reasoning and argumentation relevant for legal discourse. The third one looks at their application in law as well as at (...) the different areas of legal reasoning. The handbook’s division in three parts reflects its conceptual architecture, since legal reasoning and argumentation are considered in relation to the more general types of reasoning. (shrink)

This handbook offers a deep analysis of the main forms of legal reasoning and argumentation from both a logical-philosophical and legal perspective. These forms are covered in an exhaustive and critical fashion, and the handbook accordingly divides in three parts: the first one introduces and discusses the basic concepts of practical reasoning. The second one discusses the main general forms of reasoning and argumentation relevant for legal discourse. The third one looks at their application in law as well as at (...) the different areas of legal reasoning. The handbook’s division in three parts reflects its conceptual architecture, since legal reasoning and argumentation are considered in relation to the more general types of reasoning. (shrink)

The dialogue focuses on the major issues of the contemporary theoretical debate on judicial review and the Supreme Court's role in American constitutional democracy. The discussion begins with the US Supreme Court's case Hamdan v. Rumsfeld, successfully argued by Prof. Katyal last year, and covers important issues such as the separation and balance of powers after 9/11, the legitimacy of the laws of terror, the relation between US constitutional law and foreign law, the counter‐majoritarian difficulties posed by the exercise of (...) judicial review, and the legal academy's influence on legal practice. (shrink)

Deficits in social cognition and more specifically in communication have an important impact on the real-life functioning of people with schizophrenia. In particular, patients have severe problems in communicative-pragmatics, for example, in correctly inferring the speaker’s communicative intention in everyday conversational interactions. This limit is associated with morphological and functional alteration of the left middle temporal gyrus, a cerebral area involved in various communicative processes, in particular in the distinction of ironic communicative intention from sincere and deceitful ones. We performed (...) an fMRI study on 20 patients with SZ and 20 matched healthy controls while performing a pragmatic task testing the comprehension of sincere, deceitful, and ironic communicative intentions. We considered the L-MTG as the region of interest. SZ patients showed difficulties in the correct comprehension of all types of communicative intentions and, when correctly answering to the task, they exhibited a higher activation of the L-MTG, as compared to HC, under all experimental conditions. This greater involvement of the L-MTG in the group of patients could depend on different factors, such as the increasing inferential effort required in correctly understanding the speaker’s communicative intentions, and the higher integrative semantic processes involved in sentence processing. Future studies with a larger sample size and functional connectivity analysis are needed to study deeper the specific role of the L-MTG in pragmatic processes in SZ, also in relation to other brain areas. (shrink)

In 1983, Valentini presented a syntactic proof of cut elimination for a sequent calculus GLSV for the provability logic GL where we have added the subscript V for “Valentini”. The sequents in GLSV were built from sets, as opposed to multisets, thus avoiding an explicit contraction rule. From a syntactic point of view, it is more satisfying and formal to explicitly identify the applications of the contraction rule that are ‘hidden’ in these set based proofs of cut elimination. (...) There is often an underly ing assumption that the move to a proof of cut elimination for sequents built from multisets is easy. Recently, however, it has been claimed that Valentini’s arguments to eliminate cut do not terminate when applied to a multiset formulation of GLSV with an explicit rule of contraction. The claim has led to much confusion and various authors have sought new proofs of cut elimination for GL in a multiset setting. Here we refute this claim by placing Valentini’s arguments in a formal setting and proving cut elimination for sequents built from multisets. The formal setting is particularly important for sequents built from multisets, in order to accurately account for the interplay between the weakening and contraction rules. Furthermore, Valentini’s original proof relies on a novel induction parameter called “width” which is computed ‘globally’. It is diffi cult to verify the correctness of his induction argument based on “width”. In our formulation however, verification of the induction argument is straight forward. Finally, the multiset setting also introduces a new complication in the the case of contractions above cut when the cut formula is boxed. We deal with this using a new transformation based on Valentini’s original arguments. Finally, we show that the algorithm purporting to show the non termi nation of Valentini’s arguments is not a faithful representation of the original arguments, but is instead a transformation already known to be insufficient. (shrink)

The dilemma I present for Laura Valentini’s paradox of ideal theory concerns a theory which includes idealizations but also an account of how you apply the theory to less ideal reality. If this does not count as an ideal theory, then theories of justice need not be ideal. If it does, then ideal theories can be action guiding.

Laura Valentini’s Justice in a Globalized World presents, with admirable clarity, a new, hybrid conception of global justice that builds on insights from both cosmopolitans and statists, especially their relational variants. Relational cosmopolitans generally argue that substantial economic cooperation and interdependence (i.e., the relevant economic relations) trigger robust obligations of distributive justice. They then argue that, as a matter of fact, these relations obtain globally in virtue of intensifying global trade, capital flows, and labor migration. Thus, relational cosmopolitans conclude (...) that obligations of distributive justice directly apply to the global economic order. Relational statists, by contrast, argue that obligations of distributive justice are trigged by coercive, political relations. Furthermore, these coercive relations only obtain—and can only be justified—within a state. As a consequence, the global order is a ‘secondary site’ of justice that ought to be con. (shrink)