This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every has the explicit fixed point property. Our main result states that every complete modal logic L having the Craig's interpolation property and such that , where and are suitable modal formulas, has the explicit fixed point property.

Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property.

We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).

This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important many-valued logics (...) like BL, Ł and Π, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics. (shrink)

This note contains a correct proof of the fact that the set of all first-order formulas which are valid in all predicate Kripke frames for Hájek's many-valued logic BL is not arithmetical. The result was claimed in [5], but the proof given there was incorrect.

This paper wishes to problematize the foundations of production governance and offer an analytical perspective on the interrelation between agents’ preferences, strategic choice, and the public sphere . The value is in the idea of preferences being social in nature and in the application both to the internal stakeholders of the organisation and its impacts on people outside. Using the concept of ‘strategic failure’ we suggest that social preferences reflected in deliberative social praxis can reduce false beliefs and increase individual (...) wellbeing. From this approach, the paper offers a taxonomy of production organisations, based on social preferences about two variables: the governance form other strategic decisions that characterize the management of a company at a more operational level, once its fundamental legal form has been chosen. Each dimension is then categorised alongside two basic preferences: towards inclusion or exclusion of ‘publics’ that have no substantial access to decision power about these variables. Our framework explains governance heterogeneity by contrasting exclusive and inclusive social preferences in cooperatives, social enterprises, as well as traditional corporations. A discussion of the evolution of social preferences and organizational forms is addressed through examples and regional experiences. (shrink)

Theoretical and manipulative abduction conjectures and manipulations : the extra-theoretical dimension of scientific discovery. -- Non-explanatory and instrumental abduction : plausibility, implausibility, ignorance preservation. -- Semiotic brains and artificial minds : how brains make up material cognitive systems. -- Neuromultimodal abduction : pre-wired brains, embidiment, neurospaces. -- Animal abduction : from mindless organisms to srtifactual mediators. -- Abduction, affordances, and cognitive niches : sharing representations and creating chances through cognitive niche construction. -- Abduction in human and logical agents : hasty (...) generalizers, hybrid abducers, fallacies. -- Morphodynamical abduction : causation of hypotheses by attractors dynamics. (shrink)

This is the first dedicated commentary to Sextus Empiricus’ treatise _Against the Arithmeticians_, dealing with crucial issues in the history of the sceptical, Platonic and Pythagorean traditions and in the ancient philosophy of mathematics.

Lorenzo Valla (1407–1457) ranks among the greatest scholars and thinkers of the Renaissance. He secured lasting fame for his brilliant critical skills, most famously in his exposure of the “Donation of Constantine,” the forged document upon which the papacy based claims to political power. Lesser known in the English-speaking world is Valla's work in the philosophy of language—the basis of his reputation as the greatest philosopher of the humanist movement. Dialectical Disputations, translated here for the first time into any (...) modern language, is his principal contribution to the philosophy of language and logic. With this savage attack on the scholastic tradition of Aristotelian logic, Valla aimed to supersede it with a new logic based on the actual historical usage of classical Latin and on a commonsense approach to semantics and argument. Valla provides a logic that could be used by lawyers, preachers, statesmen, and others who needed to succeed in public debate—one that was stylistically correct and rhetorically elegant, and thus could dispense with the technical language of the scholastics, a “tribe of Peripatetics, perverters of natural meanings.” Valla's reformed dialectic became a milestone in the development of humanist logic and contains startling anticipations of modern theories of semantics and language. Volume 1 contains Book I, in which Valla refutes Aristotle's logical works on the categories, transcendentals, and predicables, with excursions into natural and moral philosophy and theology. (shrink)

In recent years, a new dispute has risen to prominence: the dispute between realists and anti-realists about causal powers. Albeit sometimes overlooked, the meta-ontological features of this “question of realism for powers” are quite peculiar. For friends and foes of causal powers have characterized their contrasting views in a variety of different ways; as existence claims, as semantic or truth-making claims, as fundamentality claims, as claims about the nature of certain properties. Not only does this multiplicity of interpretations make it (...) unclear what the genuine bone of contention is, if there is one; some of them appear to be mutually exclusive. Some light can be shed on this apparent yet widespread confusion by distinguishing three degrees of ontological involvement in dispositional truths; viz., three ways, of increasing robustness, to read ontological commitments from dispositional truths. Relatedly, by exploring the literature, and focusing on some selected examples of power realism and anti-realism, we can observe that power realists vastly disagree over the intrinsic nature ad make-up of dispositional properties. Such examples furthermore invite the thought that the question of realism for powers is best understood not as the debate around the existence of properties with a distinctive identity, but rather as a debate about metaphysical hierarchy. Finally, some anti-realists positions are indistinguishable from realist ones, using merely intensional resources: power realism is best appreciated by going hyperintensional. (shrink)

This paper attempts a reconstruction of reason’s contribution to empirical truth in connection with Kant’s definition of truth as the agreement of cognition with its object. I argue that Kant’s treatment of truth in the Transcendental Analytic gets completed in the Appendix to the Transcendental Dialectic with an often neglected but compelling argument (what I shall call the Variety Argument). This argument postulates such a variety in the appearances as to undermine any attempt at formulating empirical truths. Crucially, I argue (...) that this variety does not depict an extreme-case scenario, but our own epistemic situation without reason. Reason completes Kant’s theory of truth by allowing the understanding (i.) to form empirical concepts and (ii.) approximate to empirical truth. (shrink)

In this paper, we embark on the complicated discussion about the nature of vice in Virtue Ethics through a twofold approach: first, by taking seriously the claim that virtues (and certain flavours of vices) are genuinely dispositional features possessed by agents, and secondly, by employing a pluralistic attitude borrowed from Battaly’s pluralism (2008). Through these lenses, we identify three varieties of viciousness: incontinence, indifference, and malevolence. The upshot is that the notion of vice is not as categorically homogeneous as that (...) of virtue: some states of viciousness consist in interference of present virtuous dispositions, or mimicking of absent vicious ones, whereas others can be considered genuine dispositions themselves. Furthermore, this set-up can provide an interesting, albeit highly idealized story as to how, through the interference in one’s environment, one gets acquainted with vice in various degrees. Finally, this approach can be illuminating vis-à-vis Virtue Ethics in general; e.g. we can employ it to discuss more productively Johnston’s (2003) objection to Hursthouse’s (1999) account of moral conduct. Finally, this approach can be illuminating vis-a-vis Virtue Ethics in general; e.g. we can employ it to discuss more productively Johnston’s (2003) objection to Hursthouse’s (1999) account of moral conduct. (shrink)

Philosophers have debated at length the epistemological status of scientific thought experiments. I contend that the literature on this topic still lacks a common conceptual framework, a lacuna that produces radical disagreement among the participants in this debate. To remedy this problem, I suggest focusing on the distinction between the internal and the external validity of an experiment, which is also crucial for thought experiments. I then develop an account of both kinds of validity in the context of thought experiments. (...) I show that we can naturally conceptualise internal validity in terms of games of make-believe. Then, I argue that external validity is best defined as accurate representation of a target system. Finally, I turn back to the current debate on thought experiments and show that my diarchic account provides a general framework that can be shared by the competing philosophical views, as well as a fruitful guide for their reconciliation. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in [Maudlin 2012] and [Malament, unpublished]. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of [Tarski 1959]: a predicate of betwenness and a (...) four place predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane - which obeys the Euclidean axioms in [Tarski and Givant, 1999] - and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagora’s theorem. We conclude with a Representation Theorem relating models of our system that satisfy second order continuity to the mathematical structure called ‘Minkowski spacetime’ in physics textbooks. (shrink)

This article aims to justify the positive role in the empirical investigation of nature that Kant attributes to the idea of God in the Critique of Pure Reason. In particular, I propose to read the Transcendental Ideal section and the Appendix to the Transcendental Dialectic together to see whether they can reciprocally illuminate each other. I argue that it is only by looking at the transcendental deduction of the ideas of reason and the resulting analogical conception of God that a (...) fully legitimate positive use of the idea of God can be vindicated. (shrink)

Discussions about dispositional and categorical properties have become commonplace in metaphysics. Unfortunately, dispositionality and categoricity are disputed notions: usual characterizations are piecemeal and not widely applicable, thus threatening to make agreements and disagreements on the matter merely verbal—and also making it arduous to map a logical space of positions about dispositional and categorical properties in which all parties can comfortably fit. This paper offers a prescription for this important difficulty, or at least an inkling thereof. This will be achieved by (...) comparing pairs of positions and exploring their background metaphysics to discover where alleged agreements and disagreements concerning dispositionality and categoricity really lie; more specifically, the Pure Powers view and the Powerful Qualities view will be under scrutiny. Over this background, the prescription functions by isolating a successful identity-based characterization of categoricity, while abandoning the correspondent identity-based characterization of dispositionality. On the contrary, according to this prescription a property is dispositional if and only if it is solely in virtue of possessing that property that its bearer is assigned a certain dispositional profile. A crucial consequence of this prescription is that, while supporters of the Pure Powers view often characterize their position as an essentialist one, the dispositionality of properties needn’t always be a matter of essence. (shrink)

We present an elementary system of axioms for the geometry of Minkowski spacetime. It strikes a balance between a simple and streamlined set of axioms and the attempt to give a direct formalization in first-order logic of the standard account of Minkowski spacetime in Maudlin and Malament. It is intended for future use in the formalization of physical theories in Minkowski spacetime. The choice of primitives is in the spirit of Tarski : a predicate of betwenness and a four place (...) predicate to compare the square of the relativistic intervals. Minkowski spacetime is described as a four dimensional ‘vector space’ that can be decomposed everywhere into a spacelike hyperplane—which obeys the Euclidean axioms in Tarski and Givant, 175–214 1999)—and an orthogonal timelike line. The length of other ‘vectors’ are calculated according to Pythagoras’ theorem. We conclude with a Representation Theorem relating models \ of our system \ that satisfy second order continuity to the mathematical structure \, called ‘Minkowski spacetime’ in physics textbooks. (shrink)

The Recursive Bayesian Net formalism was originally developed for modelling nested causal relationships. In this paper we argue that the formalism can also be applied to modelling the hierarchical structure of mechanisms. The resulting network contains quantitative information about probabilities, as well as qualitative information about mechanistic structure and causal relations. Since information about probabilities, mechanisms and causal relations is vital for prediction, explanation and control respectively, an RBN can be applied to all these tasks. We show in particular how (...) a simple two-level RBN can be used to model a mechanism in cancer science. The higher level of our model contains variables at the clinical level, while the lower level maps the structure of the cell's mechanism for apoptosis. (shrink)

This book aims to develop the tradition of philosophical hermeneutics, the theoretical account of interpretive (as opposed to explanatory) understanding--the account of meanings and contexts rather than causes and predictions--usually restricted to the domain of literary and textual analysis, in new directions by exploiting its potential as an instrument of critique. It refutes commonly held claims that hermeneutic analyses are necessarily relativistic, Eurocentric, or critically impotent and demonstrates how hermeneutic procedures can inform analyses of urgent current and cross-cultural issues such (...) as the biology of race, female genital excision, and the so-called "culture of poverty" thesis. Lorenzo Simpson demonstrates that a robust methodology of philosophical hermeneutics is well positioned to intervene in critical political and social issues in global ethics and justice in concert with critical theory's emancipatory aims. (shrink)

The standard representation of the Central Dogma (CD) of Molecular Biology conspicuously ignores metabolism. However, both the metabolites and the biochemical fluxes behind any biological phenomenon are encrypted in the DNA sequence. Metabolism constrains and even changes the information flow when the DNA‐encoded instructions conflict with the homeostasis of the biochemical network. Inspection of adaptive virulence programs and emergence of xenobiotic‐biodegradation pathways in environmental bacteria suggest that their main evolutionary drive is the expansion of their metabolic networks towards new chemical (...) landscapes rather than perpetuation and spreading of their DNA sequences. Faulty enzymatic reactions on suboptimal substrates often produce reactive oxygen species (ROS), a process that fosters DNA diversification and ultimately couples catabolism of the new chemicals to growth. All this calls for a revision of the CD in which metabolism (rather than DNA) has the leading role. (shrink)

The evolution of the concept of subjectivity in the works of Jacques Lacan.

A popular stance amongst philosophers is one according to which, in Lewis’ words, “identity is utterly simple and unproblematic”. Building from Lewis’ famous passage on the matter, we reconstruct, and then criticize, an argument to the conclusion that identities cannot be grounded. With the help of relatively uncontroversial assumption concerning identity facts, we show that not all identities are equi-fundamental, and, on the contrary, some appear to be provided potential grounding bases using two-level identity criteria. Further potential grounding bases for (...) identities are presented. Identity might be utterly simple and unproblematic, but this is not sufficient to conclude that identities are ungrounded, or fundamental. (shrink)

Cultural evolutionary theory has been alternatively compared to a theory of forces, such as Newtonian mechanics, or the kinetic theory of gases. In this article, I clarify the scope and significance of these metatheoretical characterisations. First, I discuss the kinetic analogy, which has been recently put forward by Tim Lewens. According to it, cultural evolutionary theory is grounded on a bottom-up methodology, which highlights the additive effects of social learning biases on the emergence of large-scale cultural phenomena. Lewens supports this (...) claim by arguing that it is a consequence of cultural evolutionists’ widespread commitment to population thinking. While I concur with Lewens that cultural evolutionists often actually conceive cultural change in aggregative terms, I think that the kinetic framework does not properly account for the explanatory import of population-level descriptions in cultural evolutionary theory. Starting from a criticism of Lewens’ interpretation of population thinking, I argue that the explanatory role of such descriptions is best understood within a dynamical framework—that is, a framework according to which cultural evolutionary theory is a theory of forces. After having spelled out the main features of this alternative interpretation, I elucidate in which respects it helps to outline a more accurate characterisation of the overarching structure of cultural evolutionary theory. (shrink)

In this paper, I offer a systematic account of Kant’s view on ‘phenomenal substance’. Several studies have recently analyzed Kant’s notion of substance. However, I submit that more needs to be said about how this notion is reconceptualized within the critical framework to vindicate a genuine and legitimate sense of substance in the phenomenal realm. More specifically, I show that Kant’s transcendental idealism does not commit him to a rejection of substantiality in phenomena. Rather, Kant isolates a general notion of (...) substance (as ultimate subject) and argues that (i) the relationality of phenomena is compatible with this notion; and that (ii) matter and all its parts are the ultimate subjects of everything existing in space (as what is independently movable in space). I suggest that vindicating a genuine and legitimate notion of phenomenal substance has far-ranging consequences for the interpretation of Kant’s empirical realism. (shrink)

This article analyses a sceptical challenge resulting from metaphysical approaches to the problem of the necessity of empirical laws of nature in Kant’s critical philosophy (what I shall call ‘essentialist’ readings). I argue that this challenge may jeopardize the purpose of empirical enquiry (and therefore the plausibility of essentialist readings), but that Kant has internal resources to address it in the Dialectic of the Critique of Pure Reason. I show that reading this problem through the lens of the Dialectic allows (...) us to reconcile the metaphysical question of necessitation of laws with a robust sense of empirical cognition. (shrink)

In this paper I would like to reconstruct Patočka’s effort to give a faithful account of the phenomena, without betraying these phenomena with an objectivistic theory of perception. Only by remaining close to the things themselves will we be able to understand them as an appeal, as a call, while understanding ourselves as a response to this call. On the basis of this “ontological rehabilitation of the sensible”, which reveals Patočka’s affinity with Merleau-Ponty as much as his departure from Husserl, (...) I will criticize the idealism of Husserlian phenomenology and reconsider the a priori of correlation in a different fashion. World and subject will then find a different articulation, grounded in the ontological couple of movement and feeling. The analysis will consist of three parts: in the first part I will introduce the problematic of the opposition between phenomenological and physical space; the second part will deal with the notion of movement; the third part will concentrate on Patočka’s new account of subjectivity, the a-subjective cogito, arising precisely from the fundamental coupling of κίνησις and πάθος. Embodiment, qua original phenomenon, will be constantly present in the background of this analysis. (shrink)

The aim of this paper is to propose a novel reading of the critical legitimacy of the regulative use of reason in the Transcendental Dialectic of Kant's Critique of Pure Reason. After introducing some key terminology of the Dialectic, I analyse the shortcomings of two influential accounts of the regulative use of reason and identify their common problem in their commitment to the descriptivity of the ideas of reason. I then offer my rule‐based account of the regulative use of reason (...) by clarifying how Kant transforms reason's metaphysical inclinations into prescriptive rules of bottom‐up empirical research. Finally, I explain why such interpretation of reason is metaphysically innocent and thereby a promising approach to understand its role in Kant's scientific project. (shrink)

Scientific models typically contain idealizations, or assumptions that are known not to be true. Philosophers have long questioned the nature of idealizations: Are they heuristic tools that will be abandoned? Or rather fictional representations of reality? And how can we reconcile them with realism about knowledge of nature? Immanuel Kant developed an account of scientific investigation that can inspire a new approach to the contemporary debate. Kant argued that scientific investigation is possible only if guided by ideal assumptions—what he calls (...) “regulative ideas”. These ideas are not true of objects of nature, and yet they are not heuristic tools or fictional represen- tations. They are necessary rules governing the construction and assessment of scientific explanations. In this paper, I suggest that some idealizations can be interpreted as having necessary regulative value and as being compatible with scientific realism. I first analyze the puzzle of the nature of idealization and present the main approaches to this topic in the literature. Second, I reconsider the puzzle vis-a-vis a restricted, Kantian definition of idealization and a novel characterization of the relation between idealization and truth. Finally, I discuss in detail an example of idealization (the Hardy-Weinberg equilibrium) along the suggested Kantian lines. (shrink)

Organ trafficking is officially banned in several countries and by the main Nephrology Societies. However, this practice is widespread and is allowed or tolerated in many countries, hence, in the absence of a universal law, the caregiver may be asked for advice, placing him/her in a difficult balance between legal aspects, moral principles and ethical judgments.In spite of the Istanbul declaration, which is a widely shared position statement against organ trafficking, the controversy on mercenary organ donation is still open and (...) some experts argue against taking a negative stance. In the absence of clear evidence showing the clinical disadvantages of mercenary transplantation compared to chronic dialysis, self-determination of the patient may conflict with other ethical principles, first of all non-maleficence. The present paper was drawn up with the participation of the students, as part of the ethics course at our medical school. It discusses the situation in which the physician acts as a counselor for the patient in the way of a sort of “reverse” informed consent, in which the patient asks advice regarding a complex personal decision, and includes a peculiar application of the four principles to the donor and recipient parties. (shrink)

There are various forms of teleological thinking central to debates in the early modern and modern periods, debates in which David Hume (1711–1776) is a key figure. In the first section, we shall introduce three levels at which teleological considerations have been incorporated into philosophical accounts of man and nature, and sketch Hume’s criticisms of these approaches. In the second section, we turn to Hume’s non-teleological ‘science of man’. In the third section, we show how Hume has an account of (...) human flourishing that is not dependent on teleology. In the fourth section, we shall speculate as to the relation between Hume’s account of human nature and contemporary evolutionary accounts of morality and reasoning. (shrink)